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Modélisation de Cycle de Rakine Organique

Auteur : Fontaine, François

Promoteur(s) : Lemort, Vincent

Faculté : Faculté des Sciences appliquées

Diplôme : Master en ingénieur civil électromécanicien, à finalité spécialisée en énergétique

Année académique : 2017-2018

URI/URL : http://hdl.handle.net/2268.2/5391

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Master thesis submitted in fulfilment of therequirements for the degree of Master in

Electromecanic EngineeringUniversity of Liège

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Faculty of Applied SciencesThermodynamic Laboratory Department

Discipline : Energy Engineering

Design and Simulation Model ofMedium Scale Organic Rankine

Cycles - Validation on Waste HeatRecovery Plant and Case Studies

As part of an intership at Enertime SA

Author : François Fontaine

Under the supervision of Lemort Vincent, Vergé Léa

Board of examiners:Academic supervisor : Vincent Lemort, Prof. at University of Liege

Industrial supervisor : Léa Vergé, Head of engineer department at Enertime

Academic examiner : Pierre Dewallef, Prof. at University of Liege

Academic examiner : Remi Dickes, FRS/FNRS research fellow at Universityof Liege

Date of defence : 7th of September 2018

Contents

Abstract 8

1 Introduction 91 The Organic Rankine Cycle technology . . . . . . . . . . . . . . . . . . . . . 9

1.1 Definition and purpose of ORC . . . . . . . . . . . . . . . . . . . . . 91.2 Organic fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3 Market actual state . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 The modelling of ORC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Different purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 State of art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Thesis content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

I Model Description and Implementation 18

2 Model General Description 191 Objectives of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Choice of programming language . . . . . . . . . . . . . . . . . . . . . . . . 203 The relevance of object oriented programming . . . . . . . . . . . . . . . . . 21

3 Design Model 231 Inputs, options, parameters and outputs . . . . . . . . . . . . . . . . . . . . 232 The five supported types of cycles . . . . . . . . . . . . . . . . . . . . . . . . 25

2.1 C1 configuration: basic . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 C2 configuration: recuperator . . . . . . . . . . . . . . . . . . . . . . 282.3 C3 configuration: preheater . . . . . . . . . . . . . . . . . . . . . . . 292.4 C4 configuration: recuperator and preheater in parallel . . . . . . . . 322.5 C5 configuration: recuperator and preheater in series . . . . . . . . . 35

3 Components library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1 Evaporator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.3 Condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4 Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

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3.5 Recuperator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.6 Preheater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.7 Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.8 General variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Simulation Model 481 Inputs and outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 Simulation model structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.1 Algorithm description . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Part load operation modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1 Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2 Heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4 Solver consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

II Case Studies 59

5 Model validation on a waste heat recovery ORC 601 ORC description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

1.1 Overall overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601.2 Design operational point . . . . . . . . . . . . . . . . . . . . . . . . . 61

2 Database considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642.1 Choice of the comparison points . . . . . . . . . . . . . . . . . . . . . 642.2 Sensor accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3 Simulation hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1 First comparison point: November 21, 15:30 to 16:00 . . . . . . . . . 714.2 Second comparison point: December 7, 17:19 . . . . . . . . . . . . . . 734.3 Third comparison point: October 31, 00:00 . . . . . . . . . . . . . . . 74

5 Part load laws discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.1 Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.2 Heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.1 Model forces and weaknesses . . . . . . . . . . . . . . . . . . . . . . . 816.2 Possible improvements . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6 Model application on a geothermal ORC with air-condenser 861 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862 Adopted approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

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7 Conclusion 971 Overall retrospective of the model . . . . . . . . . . . . . . . . . . . . . . . . 972 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Appendices 1001 Interface user Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

1.1 Objective of the interface . . . . . . . . . . . . . . . . . . . . . . . . . 1001.2 Design window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001.3 Simulation window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1061.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

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List of Figures

1.1 Rankine Cycle working principle . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The advantage of dry fluids. [5] . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Diverse fields of application of ORC. [5] . . . . . . . . . . . . . . . . . . . . . 111.4 Number of installed ORC projects per year and per application in July 2016.

[8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.5 Share of the installed capacity per application in July 2016. [8] . . . . . . . . 15

3.1 Left side: C1 cycle configuration. Right side: Example of classic T-s diagramwith R1233zd as organic fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Detailed algorithm structure of C1 cycle. . . . . . . . . . . . . . . . . . . . . 263.3 Global resolution pattern for a C1 or a C5 configuration. . . . . . . . . . . . 283.4 Left side: C2 cycle configuration. Right side: Example of classic T-s diagram

with SES36 as organic fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.5 Detailed algorithm structure of C2 cycle. . . . . . . . . . . . . . . . . . . . . 303.6 Global resolution pattern for a C2 or a C3 cycle. . . . . . . . . . . . . . . . . 303.7 Left side: C3 cycle configuration. Right side: Example of classic T-s diagram

with SES36 as organic fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.8 Detailed algorithm structure of C3 configuration. . . . . . . . . . . . . . . . 313.9 Left side: C4 cycle configuration. Right side: Example of classic T-s diagram

with MM as organic fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.10 Detailed algorithm structure of C4 configuration. . . . . . . . . . . . . . . . 333.11 Global resolution pattern for a C4 cycle. . . . . . . . . . . . . . . . . . . . . 343.12 Left side: C5 cycle configuration. Right side: Example of classic T-s diagram

with R245fa as organic fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.13 Detailed algorithm structure of C5 cycle. . . . . . . . . . . . . . . . . . . . . 363.14 Moving Boundary Model of the heat exchanger applied to the evaporator. . . 383.15 Global exchange coefficient matrix structure. . . . . . . . . . . . . . . . . . . 41

4.1 Detailed algorithm structure of SimC1. . . . . . . . . . . . . . . . . . . . . . 514.2 Detailed algorithm structure of SimC2. . . . . . . . . . . . . . . . . . . . . . 524.3 Detailed algorithm structure of SimC3. . . . . . . . . . . . . . . . . . . . . . 534.4 Detailed algorithm structure of SimC4. . . . . . . . . . . . . . . . . . . . . . 544.5 Detailed algorithm structure of SimC5. . . . . . . . . . . . . . . . . . . . . . 54

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5.1 Evaporator and preheater layout. . . . . . . . . . . . . . . . . . . . . . . . . 615.2 Organic Rankine Cycle global overview. . . . . . . . . . . . . . . . . . . . . . 625.3 Nominal operating point of the ORC. Principal variables, T-s diagram and

mass distribution. Figures taken from the developed interface (see appendices). 635.4 Nominal exchange coefficient considered for area calculation. . . . . . . . . . 645.5 First comparison point: November 21 - Representative sample of cold, hot

and medium sources behaviours. . . . . . . . . . . . . . . . . . . . . . . . . . 655.6 Representation of the time needed to adapt the mass flow to the hot source

thermal power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.7 Second comparison point: December 7 - Representative sample of cold, hot

and medium sources behaviours. . . . . . . . . . . . . . . . . . . . . . . . . . 675.8 Third comparison point: October 31 - Representative sample of cold, hot and

medium sources behaviours. . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.9 Sensors location and type. T stand for temperature, P for pressure and F for

volumetric flow rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.10 Comparison of different values of mass flow - Representation of the uncertainty. 705.11 Evaporator simulated temperature profile on November 1 at 16:00. . . . . . . 735.12 Evaporator inlet quality versus time in the night between October 31 and

November 1. The red point represents the considered operational point. . . . 755.13 Turbine law check on the three different comparison points. . . . . . . . . . . 775.14 Turbine law fitting on the measured values of the three samples. . . . . . . . 785.15 Exchange coefficient part load law check with the three samples. . . . . . . . 805.16 Exchange coefficient part load law fitted on the measurements. . . . . . . . . 805.17 Robustness test of the model. Representation of the number of iterations

necessary to solve the model with a given guess value. Each graph representsthe test with only one of the guess value that changes. . . . . . . . . . . . . 82

6.1 Nominal operational point of the geothermal cycle and T-s diagram represen-tation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2 Mass flow rate variation using the two different strategies. . . . . . . . . . . 906.3 Temperature regimes during the whole year using two different strategies. . . 916.4 Consumption and production of electricity: comparison of the results obtained

with the two strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.5 Electrical power consumption of the fans for a design ambient temperature at

10 and 15◦C in the constant Pcd strategy. . . . . . . . . . . . . . . . . . . . . 946.6 Electrical power production for both design design temperatures and both

strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.7 Electrical power production for both design temperatures and both strategies. 95

7.1 Global Design window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.2 Cycle configuration choice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.3 Design input options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.4 Design input options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

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7.5 Design buttons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.6 Global results display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.7 HEX results display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.8 Simulation window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.9 Simulation status messages. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

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Abstract

The energy transition is becoming in the whole world an important topic. As the re-sources are getting scarcer, the search for new energy sources and the rush for energeticefficiency grow sharply. In this context, the Organic Rankine Cycle (ORC) could be one ofthe solutions to the challenges the energy sector is facing.

This technology is now sufficiently mature to have its own market. Still, the ORC needsto be improved in performance and cost in order to become a real competitive option onthe energy market. For this purpose, performing and accurate thermodynamic models arein development in concerned industries as well as in universities.

After a general introduction, the document is divided in two parts. The first one proposesan ORC model developed at (and for) Enertime SA [1], a French company that sells mediumscale ORC machines and engineering services. This model is able to cover a wide range ofmedium to large scale machines, and to answer to simulation and design problems. It isdesigned to be as general as possible, but with sufficient accuracy and the opportunity foreasy further development. The first part of the report is thus dedicated to the descriptionof the model and its implementation.

In a second part, the model is confronted to two case studies. The first one is a wasteheat recovery ORC of 3 MW based in China. Measurements were retrieved from effectiveoperating points to analyze and validate the accuracy of the model. The second one focuseson a specific application of the model in order to illustrate the potential of it. The model isthere used to answer to a specific industrial problem related to the design and the control ofan air-condenser in a geothermal ORC application.

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Chapter 1

Introduction

This first chapter presents an overview of the ORC technology. First, the general workingprinciple and the purposes of the Organic Rankine Cycle are described. A summary of theactual state of the ORC market is also depicted. In a second part, the state of art of theORC modelling is proposed. The third part describes the objective of this work and presentsthe detailed content of the document.

1 The Organic Rankine Cycle technology

1.1 Definition and purpose of ORCThe Organic Rankine Cycle is a derivative of the basic Rankine Cycle used in a wide range

of power production plants. The Rankine Cycle is basically an idealized thermodynamic cyclethat converts heat into electricity by mean of a fluid phase change. The working principleof such a cycle is depicted in Fig.1.1.

Figure 1.1: Rankine Cycle working principle

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The fluid commonly used in Rankine cycle is water. Indeed, it is a very well known fluid,with good thermal properties, great availability and low price. The principle is to feed aturbine (TU) with steam to convert the fluid energy into electricity (Wtu). The RankineCycle takes advantage of a phase change from vapour to liquid to bring back the fluid athigh pressure (HP) thanks to a pump (PU) at a low energetic cost (Wpu). During thecondensation, heat must be rejected to a cold source (Qcd). The vaporization of the water iscarried in the evaporator where the heat from the hot source is absorbed (Qev). In Fig.1.1,the cycle is idealized. In reality, the fluid must be further heated before entering the turbine.This operation is called superheating and it is used to avoid the presence of a too largeamount of condensate in the steam turbine. Indeed, the droplets can damage the turbineand thus reduce its lifetime.

For most of the heat sources, this cycle works perfectly and can achieve rather good ef-ficiency. However, this is not an economically viable solution for low temperature (≤400◦C)or low power hot sources. Firstly, the electric efficiency is very degraded at low temperaturebecause of the constraints it implies on evaporation pressure and superheating. Then, theusage of a steam turbine at low inlet temperature leads to expensive multistage technologyand to liquid formation during expansion. The high cost combined to the low electric outputmakes the steam cycle not adapted to this kind of sources.

The Organic Rankine Cycle provides solutions to this problem by replacing water withan organic fluid with special properties. These fluids have more appropriate evaporatingpressure and temperature and require less energy to evaporate. Moreover, the special shapeof their saturation curve allows the use of simpler (thus less expansive) turbines. As can beseen in Fig.1.2, the expansion with organic ”dry” fluids stays in the superheated area. Theabsence of liquid phase induce high reliability and long-lasting turbines. Furthermore, thehigh molecular mass of the fluid implies lower rotation speed and less turbine stages, andthus a simpler design.

Figure 1.2: The advantage of dry fluids. [5]

The properties of ORC makes it completely suitable for low to medium temperature/power

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hot source. The cost reduction, combined with a correct efficiency, allows the technologyto be competitive in special applications, summarized in Fig.1.3. As can be seen, the mainhot sources types are waste heat, geothermal, biomass and solar. They are all considered asgreen energies. It is therefore clear that the ORC will play an important role in the energytransition.

Figure 1.3: Diverse fields of application of ORC. [5]

1.2 Organic fluidsThe choice of the fluid is of course of prime importance. It is driven by some key

requirements that the fluid must meet:

• High thermal stability: Contrarily to refrigeration application, the fluid in an ORCmust sustain repeated high temperature without degrading its properties.

• Adapted saturation curve: The fluid must have a suitable critical temperature andpressure, a low freezing point and an inclined saturation curve like in Fig.1.2.

• High molecular mass: As mentioned before, this will reduce the turbine complexity,and thus its cost.

• Good thermal conductivity: This is of course a fundamental property for any fluidused in thermodynamic cycles as it facilitates the heat transfer. This requirement cansometimes be in conflict with the desired high molecular mass.

• Low viscosity: A less viscous fluid will decrease the friction losses along the pipesand the other components. It implies lower pressure drops and thus a lower pumpconsumption.

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• High latent heat and density: This allows the fluid to absorb more heat with areduced mass flow rate. It thus decreases the electric consumption of the pump.

• Acceptable price and commercial availability: As the fluid is much more specificthan simple water, it is important to have a sufficient reserve at a correct price. Thisis even more critical for medium to large scale ORC (≥1MW) where several tons offluid are used.

• Sufficient safety: One should always avoid using flammable or toxic fluids. Fur-thermore, the fluid must be material compatible to prevent equipment corrosion andleakages. Some fluids used in ORC do not meet those requirements (pentane for in-stance) as the risk is considered as manageable.

• Low environmental toxicity: This requirement gained importance since the stan-dards on Ozone Depletion Potential (ODP) and Global Warming Potential (GWP)have entered into force. Chemical industries have been putting much effort into creat-ing fluids that decompose quickly into the atmosphere. The ODP and GWP of thosefluids are thus much reduced. However, it does not mean that the gas resulting fromthe decomposition are good for the environment. One should thus be careful with thechoice of fluid regarding the environment.

Nowadays, the most widely used fluids for ORC applications are:

• Siloxanes: These fluids originate from the organosilicon chemistry and present a”≡ Si−O−Si ≡” group in their molecular composition. They have very suitable phys-ical properties: low flammability and toxicity, high molecular mass, and good thermalstability at high temperature. They are often available as mixture. Indeed, mixturesare used to obtain a varying boiling temperature at a constant pressure. This is par-ticularly convenient in waste heat recovery where the hot source power can be erratic.The irreversibilities are thus decreased because the binary mixture can boil over a widerrange of temperatures. The most famous examples of siloxanes for ORC applicationare the Hexamethyldisiloxane (MM) and the Octamethyltrisiloxane (MDM).

• Hydrofluorocarbons: In this group, commonly called HFCs, one can find some ofthe most famous refrigerants. For instance the R245fa (1,1,1,3,3-Pentafluoropropane)which is commonly used in a lot of ORC applications. This fluid present a zero ODP(which was the purpose of its creation) and is nearly non toxic. However, because oftheir high GWP, they are getting phased out in several countries. They are thus slowlyreplaced by a fourth generation of refrigerants: Hydrofluoroolefins (HFOs).

• Hydrocarbons: These fluids usually present good thermodynamic properties butcan have some flammability issues. A widely used candidate from this group is theN-Pentane.

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Whether a fluid is suitable or not depends mainly on the applications. For example, thehot and cold source temperatures determine which boiling and condensing temperature therefrigerant must have. The size of the machine is also determinant. For big machines, thequantity of fluid in the cycle can reach several tons. The price of the latter (usually around20 e/kg) is thus an important factor and will greatly influence the choice of refrigerant.

1.3 Market actual stateThe Rankine Cycle has been used extensively for a long time and is now a mature tech-

nology. Until these past years, little attention has been granted to its organic alternative.However, the first commercial ORC was developed in 1853 for ship propulsion and usedether as a secondary fluid vaporized by steam. In the late 19th, an engine developed byOfeldt working with Naphta (a derivative of petrol) had experienced a great success. Butthe technology has been forgotten for long because of the increasing reliability of internalcombustion engines and the progress of steam turbines. Nowadays, thanks to the growinginterest into energy transition and to the technological and chemical progresses, the ORCshave gained popularity.

According to ORC World Map [8], the total installed power based on ORC technologyreached at least 2749 MWel in 2016, distributed by 563 power plants. The planned projectsat this time were reaching some extra 523 MWel, meaning that the market was rapidly grow-ing. As can be seen in Fig.1.4, the ORC market is experiencing a great expansion since 2005.However, the ORC is very far from being a major power producing technology. Indeed, abig nuclear plant can produce more than all the ORC plants around the world. The OrganicRankine Cycle is thus not yet a big player in power production. This makes sense as thefirst purpose of the ORC is to value the low quality heat source. By nature, this technologycan only be a complement to big power production. It is until now mostly used in littleto medium scale projects, usually coupled with renewable (and remote) energy source or inwaste heat recovery.

One can also observe that the most popular ORC applications are biomass and wasteheat recovery. Yet, in terms of capacity installed, a very large part of the whole capacity(more than 75%) comes from the geothermal power plants, as can be observed in Fig.1.5.The projects with geothermal energy are thus much bigger than the ones with other heatsources.

From a geographical point of view, the United States have the largest capacity installed.This can be explained by their geothermal potential. They are followed by Turkey, NewZealand and the Philippines for the same reason. Germany and Italy are the most signifi-cant regarding the biomass application. This can be due to favourable energy policy [8]. Itshould also be noted that the world leader manufacturer (Ormat [2]) is a US company, andthat its two closest competitors (Exergy [4] and Turboden [3]) are Italians.

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Figure 1.4: Number of installed ORC projects per year and per application in July 2016. [8]

As a conclusion, the ORC market has been growing fast since the last few years and isreally promising. Yet, despite that the technology already proved itself, it is still an outsiderin the energy world. It needs to be more competitive for real market penetration. This canbe achieved by improving its performance or lowering its cost.

2 The modelling of ORC

2.1 Different purposesIn the design process of an ORC plant, the manufacturer has to answer many questions.

What is the power output that the plant could reach? What kind of heat exchangers (HEX)are needed? Which temperature will the refrigerant experience? Which fluid should be used?What should be the size of the pipes? How much fluid should be bought? These are someof the many interrogations that the manufacturer is facing. To respond properly, he mustconsider two main objectives:

• Provide a machine that is efficiently working and that satisfies the client demand.

• Assess the right cost to the machine in order to make an accurate commercial offer.

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Figure 1.5: Share of the installed capacity per application in July 2016. [8]

Indeed, if the cycle does not match the expected (and contractual) performances, themanufacturer is exposed to financial penalties. On the other hand, a wrong price approxi-mation can lead either to a rejected offer or to lower profit margin.

Furthermore, the contract between the client and the manufacturer usually includes aperformance term for partial load. It is in fact very important because in some application(WHR mainly) the ORC will mainly work in off-design conditions. Therefore, the manufac-turer has to know the behaviour of the cycle components when the input conditions vary, inorder to be able to choose a reasonable security margin on the contractual performances toprotect himself from penalties.

The behaviour of the cycle in off-design conditions is also very important to forecast inorder to set adapted operation rules. The way of controlling the cycle depends on how it willreact to external changes. Predicting the state of the ORC also allows to detect potentialrisks of failure. Protective measures can thus be applied in advance.

To answer effectively to all these issues (and many more), the manufacturer needs a tool.This is the purpose of ORC modelling.

2.2 State of artMany types of ORC models have been designed, each having special features to respond

to the objectives for which they have been developed. But among the numerous models, onecan identify some specific characteristics that help to classify them.

15

First of all, a distinction must be made between steady-state and dynamic models. Inthe first category, an assumption of static equilibrium (or steady-state) is made. This is astrong hypothesis for ORC because the hot source can fluctuate strongly (e.g. waste heatrecovery at vehicles exhaust). But these models present the advantage of being simpler andless numerical intensive. In general, good results can be reached and static models providea good idea of the state of the machine. They are mostly used for off-design simulation orin design processes. On the other hand, the dynamic models are used to simulate a systemin transient conditions. They provide a fine knowledge of what is happening in the systemat any time and thus allow the user to define the best control strategies. They are preferredfor systems with variable inputs and important inertia.

Static models can be divided in two sub-categories. The first one focus on the sizing ofthe machine. Starting from hot and cold source nominal specifications, the goal is to sizethe components of the cycle and to obtain the electric power output in nominal conditions.Second category models try to predict the state of a defined cycle if the conditions at the hotand cold sources inlets are changing. This is often more complicated because the behaviourof some variables at partial load are difficult to forecast.

In this last category (off-design simulation models), one can classify the models accordingto the inputs choices. Of course, the hot source (HS) and cold source (CS) inlet states andmass flow rates are common inputs to all simulation models. But some other variables needto be imposed in order to compute the whole cycle. An usual and logical choice is to considerthe geometry of the HEX. Most models then use the expander or pump rotation speed tocompute the mass flow rate. Some models add to these inputs the superheating and/or thesubcooling of the fluid at the evaporator and the condenser, like the model of Gurgenci H.[16]. Another possible choice is to use the total mass of refrigerant, that is conserved in thecycle if there is no charge control system. These models are referred as ”charge sensitive”.One example is the model proposed by Dickes R. [7].

It should also be noted that all the ORCs are not using the same components. Forinstance, the size of the machine influences the type of exchangers. For instance, brazedplates HEX are usually preferred for small to medium applications while shell and tubesexchangers are better suited for large plants. The type and the size of the expander and thepump also vary from a machine to another due to the large range of technologies available.It is thus impossible to develop a model that could match every ORC. Furthermore, differentconfigurations of cycle exist. It is sometimes economically interesting to add a preheater or arecuperator to the cycle to improve its performance. This will be further discussed in section2.

Lastly, models can use different libraries for computing the thermodynamic state of thefluid in the cycle. Although they usually give quite similar results, they are not especially

16

used in the same way and they sometimes have slight different features. As examples, onecould cite Refprop and Coolprop [12] [13].

In conclusion, the range of ORC models is really wide. Some commercial modellingplatforms already exist, for instance Aspen Plus, Chemcad or SimSci Pro/II [11] [10] [9].But these softwares, although they can help manufacturers in many ways, remain veryexpensive, especially for little businesses. In a lot of cases, personalised and specific modelsare developed within companies using programming languages such as Matlab, EES, Excelor Python. The latter are hardly ever released for public. Academics are also developingvery interesting models. However, these are often hard to use for manufacturer because ofthe specificity of their projects.

3 Thesis contentThe previous sections were only an introduction to the ORC technology and gave the

reader a succinct overview of the state of art. As could be seen, many models of steady stateORC already exist in the literature. But most of them actually have a restricted range ofapplication.

A first objective of the thesis was to create a tool that is as general as possible that couldbe reused in a wide range of projects. Of course, creating a universal ORC model in fewmonths is not possible. But the work presented here could be used as a basis of such a model.

The following Chapters (2,3 and 4) of Part I thus propose a model of ORC that hasbeen developed during an internship at Enertime SA [1], a French ORC provider companybased in Paris. It is thus adapted to their specific use and their projects. However, a specialattention has been paid to allow other developers to easily add new features to the basicmodel, so that it apply to a wider range of machines.

A second objective was to confront this model to real operating machine measures and touse it in a specific application. This is the purpose of the Part II of this report (Chapters 5and 6). It will be dedicated to two case studies. The first one, presented in Chapter 5, is anexisting waste heat recovery plant of 3MW based in China. In this chapter, the model willbe confronted to collected measures and a critical discussion will be conducted to proposefurther improvements. In Chapter 6, the model will be used to answer to a specific questionrelated to air-condenser design and control in a geothermal ORC application. Two differ-ent fans control strategies will be implemented and compared, in order to choose the best one.

Chapter 7 finally concludes the work and summarize the results. Please note that thenomenclature can be found at the end of the document as well as the bibliography. A userguide of the interface that was developed is also proposed in appendices.

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Part I

Model Description andImplementation

18

Chapter 2

Model General Description

In this chapter, the model is described in a very sketchy way. First, the objectives of themodel are described. Then, the choice of programming language is discussed. Finally, theuse of object oriented structure is justified in a brief discussion about the advantages that itbrings.

1 Objectives of the modelThe initial requirements that the model has to fulfill are:

• Possibility of design and simulation: The first objective is to allow the user tochoose between sizing or off-design simulation. The purpose of these two modes wereexplained in section 2.1.

• User friendliness: The model must be easy to use. It must be accessible to anyone,even for someone who does not know the programming language.

• Robustness: The model should run without failure if reasonable guesses and inputsare provided. If possible, automatic guesses must be set. It should also detect inap-propriate inputs.

• Accuracy: The precision of the model is of course a key parameter, especially forsimulation mode where the part load evolution is difficult to predict. This criteria willbe checked in Chapter 5 thanks to database from an existing Enertime machine.

• Versatility: The tool must be applicable to a wide range of projects to be reallyuseful. The user should have the choice between different cycle configurations andbetween several input options.

• Easiness of improvement: A complete and efficient tool cannot be developed byan individual in few months. It is therefore important that other users can easilyparticipate to further development. The code must be written in a way that allowsnew features to be added as new needs are appearing.

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As said earlier, dynamic models are not adapted to design and partial load simulation.They focus on transient behaviour, which is not the goal of this study. The model presentedhere is thus a steady-state model and does not take into account the inertia of the system.

2 Choice of programming languageIn thermodynamic modelling, one can find different programming possibilities. As exam-

ples offrequently used languages, one can cite Matlab, Modelica, EES or Python. Modelicais a powerful tool to build object oriented dynamic models, but it is not very suited forsteady state calculations. Matlab is a better choice, because it is a robust and widely usedsoftware. Unfortunately, the license is quite expensive. The price is not worth to pay if theuser takes advantage of only a small part of the program possibilities. This restricts thechoice to the two remaining options: EES or Python.

EES (Engineer Equation Solver) is, as its name suggests, an equation solver. But it isespecially focused on thermodynamic systems. EES has several advantages, like the includedthermodynamic and its quite low price. But the main force of the solver is the use of anacausal language.

Acausal modelling could be preferred for several reasons. First, the order of the equationsdoes not matter. An equal sign is thus not an assignment but a declaration. The solver ofEES rearranges the equations into ”blocks”, representing smaller systems of equations. Thecausality is determined at the aggregate system level. Secondly, the problem can be writtenindependently of its boundaries. This means that any variable can be used as an input oran output as well. This improves greatly the re-usability of the model.

However, acausal modelling can have drawbacks when the system becomes very large andsophisticated. Indeed, it is sometimes very complicated to debug a code written randomly,especially when the model is lengthy. Acausal modelling thus requires careful programming,with step by step checks. Moreover, the larger the system the less robust the solver. Thelatter always needs initial guesses to find a first solution and iterates on it. These guesseshave to be meticulously chosen to make the computation converge toward the exact solution.Adding equations means adding guesses and increasing the difficulty of solving the system.The system becomes thus less robust as it gets larger.

On the contrary, Python is a causal language. The inputs and the outputs of the modelshave to be previously fixed, which makes it less flexible. On the other hand, the computingis reputed for its robustness and speed. Besides, Python has many other interesting fea-tures. The most important is maybe its open access and its transparency. This results in avery large and remarkably active community. Consequently, the language is endlessly grow-ing as the users continuously add and share new features. For instance, libraries allow tohandle excel files, create figures, make personalized interfaces, solve optimization problems,

20

etc. Furthermore, the language is user-friendly in its structure and is easy to use and learnthanks to numerous tutorials and support forums. Lastly, Python allows object orientedcoding, which is a powerful tool for building large and well organised models.

In the end, the choice fell on Python. The main reason was that Enertime already had aEES model and was looking for a different tool to challenge the existing one. As the modelis expected to extensively grow along its development, the robustness of Python was also akey argument. Furthermore, the user-friendliness coupled with the object oriented structuremakes the model likely to be easily further developed by other members of Enertime after-wards. Finally, the various features of Python should propose a very different tool for thecompany with a wide range of new possibilities.

However, because of the causal construction brought on by Python language, it is muchmore challenging to reach an acceptable versatility. As said before, the main goal was tocreate a tool that could be adapted to the widest range of applications possible. Therefore,the real challenge of the work was to create a code structure that allows the model to beused in different ways while keeping valid the robustness and user friendliness criteria. Thisspecific model construction is the key innovation of the work, and it will be described allalong Chapters 3 and 4.

3 The relevance of object oriented programmingAs explained in Section 2, Python offers the opportunity for object oriented program-

ming. This is a powerful tool to build organized and hierarchical models. It also facilitatesthe code comprehension, maintenance and enhancement. The principle is to define entitiesthat can interact with each other. The global model (the parent) is thus composed of severalsub-models (the children) that are linked together. In Python, an object is identified by itsclass. The class contains the different variables and methods that define the object. Themethods are the functions that are related to the class. This is basically what the object cando. For instance, one could define a class ”Heat Exchanger” and create a ”Condenser” objectfrom it. The Condenser could then call its ”Power” method that computes the thermal heatexchanged.

As one can guess, this code structure is particularly well suited to thermodynamic cycles.The most logical way to build an ORC model is to create an object for each component ofthe cycle. To connect these objects together, a ”state” dictionary1 is used. It represents thethermodynamic state of the fluid at the boundaries of the component. The state dictionarycontains the density, the temperature, the pressure, the enthalpy and the entropy of thefluid. Each component will be extensively described in Section 3 of Chapter 3, but the basicprinciple is to define at least a ”Design” and a ”Simulation” method for each object. All the

1A dictionary is a Python entity that contains several elements, each of them identified by its key.

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objects are then assembled together to create different ORC configurations.

The object oriented method also presents another great advantage. It is very easy foranyone to add new features to the model without affecting the integrity of the general code.One can simply add a new method to an object, or create a new object and connect it tothe others. Facilitating further developments is also critical to go towards a complete andperforming model.

Finally, as the model is likely to have a lot of parameters, inputs and outputs, it ispreferable to create a tool that helps the user to handle it easily. This is the purpose of theuser interface, that covers the whole model. A description of the latter is proposed in theappendices.

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Chapter 3

Design Model

In the design stage, one has to define the nominal operating conditions of every compo-nent in order to size them properly. The design stage should give an idea of the maximalperformance of the cycle. The model also helps taking the best decisions during the designprocess. Which fluid to use, which technology to choose and at what price, are some of thequestions that need to be answered. The model should allow the user to easily compare thedifferent options he has.

This chapter focuses on the implementation of the design model. The purpose of thedesign is explained in section 1. A review of the different options offered to the user isproposed in section 2. The different configurations of ORC covered by the model are thendescribed, as well as their general implementation. Further details about the components aregiven in section 3. All along this chapter, the model hypotheses and constituting equationsare presented.

1 Inputs, options, parameters and outputsThe design of an ORC machine is originally based on the hot source energy that has to

be transformed in electricity. One thus knows the temperature and the pressure at the hotsource inlet. The minimal temperature and pressure at which the hot source fluid is rejectedis also specified. For instance, some fumes cannot be cooled under a given temperature toavoid formation of corrosive chemical compounds. When the fluid is later used for anotherprocess after giving its heat, it should also keep a sufficient temperature or pressure. Whennot specified, the outlet temperature should be the result of technico-economic balance be-tween the price and the performance of the evaporator. The nominal mass flow rate of thehot source is also considered as known. The same reasoning is applied to the second hotsource (that will be hereafter called ”medium source”) that is used if a preheater is required.For the cold source, the mass flow rate is not needed because it will be computed as a result.

However, this is not sufficient to fully determine the design of an ORC machine. The

23

manufacturer has to gather additional information. In this model, the following additionalinputs are considered:

• Evaporating and condensing temperatures (or pressures),

• the subcooling and the superheating,

• the isentropic efficiency of the turbine and the efficiency of the pump,

• The pressure drops across the pipes and the HEXs,

• the refrigerant type.

If a recuperator is used, its pinch point must also be provided.

As explained in Chapter 2, one of the challenges of this work was to compete with theflexibility of the acausal model in EES. In Python, inputs must be fixed in advance andcannot be changed. However, thanks to conditional programming, it is still possible to givethe opportunity to choose between several previously determined input options, that arelisted hereafter:

• Instead of giving the hot or medium source mass flow rate (or volumetric flow rate),one can chose to impose directly the heat exchanged at the evaporator.

• Instead of giving the evaporating and condensing temperature (or pressure), one canimpose the evaporator and/or condenser pinch points. This might be more relevantand easier to use, because the pinch points are directly related to the size (and thus tothe cost) of the HEX. Imposing a smaller pinch point means accepting a higher costfor higher performances.

• The Net Positive Suction Head (NPSH) of the pump can be imposed instead of thesubcooling at the condenser outlet. The user can thus compute how far the fluid shouldbe subcooled to avoid cavitation in the pump.

These options have been carefully selected to be the most useful ones in Enertime designprocesses. Furthermore, the thermodynamic library can also be chosen between CoolProp orRefProp. Other available options relate to specific cycle configurations or specific methods(fluid mass calculation for example) and will be described in sections 2 or 3.

The basic information that the model should provide are the electrical power output,the cycle efficiency, the heat exchanged and the thermodynamic state of the working fluidat every stage of the cycle as well as its mass flow rate. It should also compute the stateof the cold and hot sources fluids. Of course, this can be extended by adding features tothe model. For instance, the presented model can additionally give a raw estimation of theexchange area of the HEXs, an approximation of the mass of fluid in the cycle and thenominal diameters of the pipes.

24

Figure 3.1: Left side: C1 cycle configuration. Right side: Example of classic T-s diagramwith R1233zd as organic fluid.

2 The five supported types of cyclesThe basic ORC cycle, explained in section 1.1, is the simplest configuration that can

be found on the market. But in some cases, it can be profitable to add an additional heatexchanger that will use the residual heat at the turbine outlet to warm up the fluid at thepump outlet before its vaporization. Such a heat exchanger, called a recuperator, is com-monly seen in ORC using very dry fluids. It is sometimes also possible to take advantageof a secondary heat source to preheat the fluid before vaporization. This heat transfer iscarried in the preheater. One can thus add a recuperator, a preheater, or both to a basiccycle. When both heat exchangers are used, they are usually placed in series, the recuperatorbeing placed before the preheater. Nevertheless, in biomass projects, it can be preferable toplace them in parallel.

It is important for a manufacturer to have the possibility to compare several cycle con-figurations before choosing the best one. The model should therefore support the differentcycle options that exist on the market. With the possibilities listed above, it makes thus 5cycle options, that will be explained in details in this section.

2.1 C1 configuration: basicThe cycle denoted C1 refers to the basic configuration, represented in Fig.3.1 of Chapter

1. The principle of this cycle has been extensively explained in section 1.1. In this sectionwill be described the implementation of this cycle, as it is the foundation of all the otherconfigurations.

The algorithm structure of the C1 configuration is represented in Fig3.2. In this diagram,the relations between the components is highlighted. Every component is represented by a

25

Figure 3.2: Detailed algorithm structure of C1 cycle.

box. The inputs are always coming from the left side, the parameters from above and theoutputs are flowing to the right. The input of the global C1 model are coloured in red.

The two blocks (in green and blue) represent entities that need guesses to be solved ina causal way. Let’s first focus on Block 1. It contains the 4 main C1 objects: evaporator(EV), condenser (CD), turbine (TU) and pump (PU). As can be observed, the mass flowrate of refrigerant is determined at EV and is reused by all the other objects. Nevertheless,this mass flow rate is determined by a power balance in EV. This means that the inlet ofthe evaporator must be known in order to compute it. Therefore, a first run of Block 1 iscarried with a guess for EV inlet temperature (represented in green) that must be providedas inputs. The same applies to the condenser where the inlet temperature must be knownto determine the cold source (CS) mass flow rate. This way, the outlets of CD and EV aredetermined as well as the refrigerant mass flow rate. One can therefore compute the TU andPU objects and find their outlet temperatures. The outlet of the TU (or PU) being the inletof CD (or EV), the Block 1 can be computed again with the correct values of inlet HEXtemperatures. This is what is represented in the centre of Fig.3.3, that represents the globalresolution pattern of C1 configuration. The Block 1 is looped only once because the firstiteration provides the exact inlet states of EV and CD. Therefore, the next iteration will forsure find the right mass flow rate.

As can be seen in Fig.3.2, Block 1 is included in Block 2. This entity is also a causalmethod that needs 2 guesses to run. As stated in Section 1, the design model offers thepossibility to choose between giving the HEX pinch points or directly giving the vaporizing

26

and condensing pressures (or temperatures). If the second alternative is selected, Block 2will run only once. But if the a pinch point is provided, it is not possible anymore to solvethe cycle straightforwardly.

In this case, the numerical solver fsolve from the Python library scipy.optimize is used.The goal of this solver is to find the root of non linear multivariate functions. More detailsabout the solver will be given in Chapter 4. The function provided to the solver is thereforeBlock 2. With initial guesses on Tvap (vaporizing temperature) and Tcd (condensing temper-ature), a first approximation of the pinch points can be computed. With the real values ofpinch points as inputs, one can compute the following residuals:

Res1b2 = 1− PPcd,calc/PPcd,input (3.1)Res2b2 = 1− PPev,calc/PPev,input (3.2)

Those residuals are returned to the solver that will make them converge toward zero byiterating on Tvap and Tcd. Solving the cycle based on pinch points is thus more computationalintensive. For a more rapid calculation, one should impose either Tcd or Tvap (or both).Concerning the initial guesses, automatic values are computed like below:

Tvap = THS,out − PPev (3.3)Tcd = TCS,out + PPcd (3.4)

This way, the user does not have to provide further guesses. The system being not toocomplicated, the resolution is quite robust and if the inputs are correct and not too exotic,the solver hardly ever fails.

Fig.3.3 represents the algorithm structure from a global point of view. The model firstcomputes the hot and cold sources with the given inputs (plus the components parameters).These sources will be used to compute a first time the Block 1. This block then runs a sec-ond time to determine the right mass flow rate. Then, if the pinch points are provided, themodel loops again on Block 2 with new Tcd/Tvap and Block 1 is launched again twice. Thisprocess continues until residual are close enough to zero. If the residuals have converged,or if the phase change temperatures are directly given, the model can compute the globalperformance of the ORC and finally displays the results.

One should note that Fig.3.2 and 3.3 are simplified version of the model for the sakeof clarity and comprehension. In reality, the objects outputs shown are not the only onesreturned by the components. But for simplicity reason, only the basic outputs and the onesthat are needed by other components are shown. Furthermore, the piping does not appearin the figures. In the code, the components are connected through pipe objects, that will

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Figure 3.3: Global resolution pattern for a C1 or a C5 configuration.

be described in a dedicated section (3.7). Finally, input options are not represented. Forexample, the input MHS can be replaced by Qev, or the subcooling can be replaced by thepump NPSH.

2.2 C2 configuration: recuperatorThe previous cycle was the most basic version that can be found on the market. In

some cases, it can be interesting to add a recuperator (RE) to the cycle. Such a cycle isrepresented in Fig.3.4. The principle is to add a HEX that will transfer the residual heat ofthe turbine outlet vapour to preheat the evaporator liquid inlet. It will increase the cycleefficiency as part of the evaporator power is now provided ”freely” by the recuperator. Ofcourse, the recuperator has a certain cost, and a technico-economic analysis must be carriedin order to determine if it is worth to add it or not. With very dry fluids (i.e fluids withvery inclined saturation curves like MM or SES36), it is recommended to use it. Indeed, abig part of the heat exchanged in the condenser is used to cool down the organic vapour. Itis therefore wiser to take advantage of this heat in a recuperator.

The structure of the C2 algorithm is represented in Fig.3.5 and is very similar to C1. Ascan be observed, an additional input is needed to design the recuperator, which is its pinchpoint. Like in last section, the pinch point value only is not sufficient to solve the cycle in acausal way. Therefore, an internal block containing RE only is added. Block 0 requires theoutlet temperature at liquid side (Tliq,out) as guess to compute the pinch point. A residualis then computed the same way as in last section and is brought to zero by mean of fsolve:

Resb0 = 1− PPre,calc/PPre,input (3.5)The initial guess is once again automatically set:

Tliq,out,init = Tvap,in − PPre (3.6)The outputs of the Block 1 are this time the outlet temperatures at both side of RE,

because they are also the inlet temperatures of EV and CD.

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Figure 3.4: Left side: C2 cycle configuration. Right side: Example of classic T-s diagramwith SES36 as organic fluid.

The general solving pattern is represented in Fig.3.6. The only difference with the Fig.3.3is the additional Block 0 inside Block 1. This means that every time Block 1 is called, aloop is launched to solve the recuperator only. Of course, Block 0 is a SISO system and istherefore quite easy to solve. Still, there is a price to pay in terms of computational time.

2.3 C3 configuration: preheater

Cycle C3 introduces an additional degree of complexity to the cycle. In some projects,it is recommended to add a preheater (PR) before the evaporator. The resulting cycle isrepresented in Fig.3.7. A preheater can be used when a secondary heat source is availableor when the principal heat source can be further cooled. Once again, a technico-economicanalysis must be carried to estimate the relevance of this additional HEX.

The algorithm of C3 cycle looks like the one of C2, but with some additional objects. Thefirst one is the Medium Source (MS). The inlet of this heat source can be either imposed, orequal to the outlet of HS. The medium source is then connected to PR. Aside from the PRparameters, no further inputs must be provided for the computation of the energy balancein the preheater, because everything is imposed by MS specifications. The last differenceis that, in the case of a C3 configuration, the evaporator inlet is now the preheater outlet.Except for those differences, the solving pattern is exactly the same as for a C2 configurationrepresented in Fig.3.6.

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Figure 3.5: Detailed algorithm structure of C2 cycle.

Figure 3.6: Global resolution pattern for a C2 or a C3 cycle.

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Figure 3.7: Left side: C3 cycle configuration. Right side: Example of classic T-s diagramwith SES36 as organic fluid.

Figure 3.8: Detailed algorithm structure of C3 configuration.

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Figure 3.9: Left side: C4 cycle configuration. Right side: Example of classic T-s diagramwith MM as organic fluid.

2.4 C4 configuration: recuperator and preheater in parallel

The cycle C4 is the most complicated of all and also the most exotic. Contrarily to C3,the recuperator and the preheater are combined in a parallel configuration, as depicted inFig.3.9. This special configuration is used in biomass plants. The heat source in this caseis usually thermal oil that gets heated by the hot fumes in a HEX placed above the boilers.The fumes at the inlet of the heat exchanger are typically at 1000◦C and allow the oil tobe heated with a temperature difference that is around 60◦C. The oil loop then goes to theORC evaporator. For the good functioning of an evaporator working with MM (usual fluidin biomass ORCs), the temperature at HS inlet must be of at least 310◦C. With a delta Tof 60◦C, this gives an oil temperature at the EV outlet of 250◦C. The order of magnitudeof the pinch point of the HEX in the boiler being of 60◦C, the fumes exhaust temperatureis around 320◦C, which is still very hot. Yet, in biomass application, the heat source is notfree, contrarily to WHR or solar ORC. As the fuel must be paid, it is very important from aneconomical point of view to get the most out of it. Therefore, a second HEX will be placedjust after the one in the boiler to further cool the fumes. This second HEX is of courseconnected to the preheater of the ORC by a secondary oil loop. In order to get as much heatas possible from the fumes, the oil must be cooled in the preheater at its maximum. Thebest way to achieve this is to place the preheater right after the pump so that its inlet onrefrigerant side is not yet heated by the recuperator (unlike in C3 configuration). Therefore,the preheater should be placed in parallel from the recuperator.

For this configuration, no new objects are created. However, new equations must beadded to account for the distribution of the mass flow rate at PU outlet. The purple boxesthat appear in Fig.3.10 (SPLIT and 3W) represent the equations related to the 3 ways valvesthat partition the mass flow rate and then bring it back together.

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Figure 3.10: Detailed algorithm structure of C4 configuration.

Because of the mass flow rate split at the pump outlet, the cycle is more complicatedand an additional block has to be solved. Indeed, in the 3 first configuration, the evapora-tor inlet temperature could be computed without requiring the refrigerant mass flow rate.Therefore, at the first iteration of Block 1, it is expected that the inlet temperatures of CDand EV are correct and that running Block 1 once again would lead to the right Mwf . Butin the C4 configuration, both sides of the recuperator do not have the same mass flow rate.Therefore, Tliq,out depends on the mass flow rate at liquid side of RE, the latter dependingon the total mass flow rate (Mwf ) and its distribution between PR and RE (Mfrac). And ifTliq,out depends on total mass flow rate, then EV inlet temperature as well.

This is the reason why the Block 3 appears on Fig.3.10. The goal of this block is to findthe right Mwf and Mfrac by forcing two residues to converge to zero. Because of the mass flowrate split, an additional input is needed in the system, which is the PR outlet temperature. Itcan be directly given as input or computed. Indeed, the temperature difference between REand PR outlet (∆Tpr−re) or between PR outlet and Tvap (∆Tpr−ev) can be provided instead.The first residue will thus depend on this input and is calculated in one of the three followingways:

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Figure 3.11: Global resolution pattern for a C4 cycle.

Res1b3 = 1− Tpr,out − Tre,out,liq∆Tpr−re

(3.7)

or Res1b3 = 1− Tvap − Tpr,out∆Tpr−ev

(3.8)

or Res1b3 = 1− Tpr,out,calc/Tpr,out,input (3.9)

The second residue has to be related with a variable that does not depend on Mwf . Asthe outlet of EV is entirely defined by Tvap and the superheating (both inputs of the model),the EV outlet enthalpy is chosen to compute the second residue as follows:

Res2b3 = 1− hev,out,b1/hev,out,b3 (3.10)

where hev,out,b1 is the enthalpy computed at the outlet of EV in Block 1 and hev,out,b3is the enthalpy computed at the outlet of Block 3, based on the enthalpy at the outlet ofthe 3 ways valve and the power provided by HS. For the initial guesses on Mwf , the valuecomputed at the evaporator in Block 1 is taken. For the distribution of the mass flow ratebetween PR and RE, the following initial value is chosen:

Mfrac = |QHS| − |QMS||QHS|

(3.11)

The resulting global resolution pattern is represented in Fig.3.11. Even if this cycleis more complicated to solve, the solver is very robust and the resolution is carried outquite easily. Nevertheless, the nested solver structure can lead to a relatively long time ofcomputation. It is therefore advised to use Tvap and Tcd as inputs for the C4 configurationwhen possible.

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Figure 3.12: Left side: C5 cycle configuration. Right side: Example of classic T-s diagramwith R245fa as organic fluid.

2.5 C5 configuration: recuperator and preheater in seriesOf course, it is also possible to find ORC with preheater but without recuperator. This

refers to the C5 configuration, that is represented in Fig.3.12. The purpose of the preheaterhas been explained in Section 2.3. The detailed algorithm structure is represented in Fig.3.13and speak for itself. Because of the absence of recuperator, the global pattern is the sameas for a C1 cycle and can thus be found back in Fig.3.3.

3 Components libraryThe model structure being detailed above, the section focuses on the description of the

different components appearing in the previous section. The constituting equations of everyobject are given, as well as the underlying hypotheses. Let’s remind that every class ofobject contains several methods. In this section, the design methods are explained as well aspossible additional methods that were added. Some features and outputs of those methodsare not described, in order to focus on the most important results. The methods referringto the simulation part of the model is described in Chapter 4.

3.1 EvaporatorFirst of all, it is important to define the scope of the developed model:

• The model is fitted for Shell and Tubes heat exchangers (STHEX). Therefore, thecorrelations that are used do not particularly apply to other types of HEX.

• Only sub-critical pressures are supported.

35

Figure 3.13: Detailed algorithm structure of C5 cycle.

This being said, inputs, outputs and parameters of the EV model are determined by thepurpose of the model. This section focuses on the design of the ORC. The goal is thus toobtain as much information as possible based on:

• the working fluid and the hot source fluid,• the hot source fluid inlet and outlet states as well as its mass/volumetric flow (or its

available thermal power),• the vaporising temperature/pressure (or the pinch point),• the superheating,• the working fluid inlet temperature.

The hot source in/outlet states must be provided in terms of pressure and temperatureif the fluid is liquid or vapour and in terms of quality if it is two-phase. Please also notethat the fluids must be supported by Refprop or Coolprop libraries. If a fluid consideredas incompressible by Coolprop is provided (like Therminol 66 or glycoled water for the coldsource), quality cannot be computed. Two-phase state is therefore not supported in thiscase and the fluid is supposed to be liquid. This is not a strong hypothesis as the purposeof those fluids is exactly to avoid phase changes. One can also choose to use a brine. In thiscase, the specific heat capacity is asked and the enthalpy is computed based on this heatcapacity and temperature. The remaining properties are computed as if the fluid was water.

36

Moreover, another simplifying hypothesis has been made: the pressure drops across bothHEX sides are not computed and must be assumed. This hypothesis is inherent to the Mov-ing Boundary Model methodology adopted.

In the EV class, several methods gives different information about the HEX. The workingprinciple of the 3 methods related to the design model. These methods applies in any HEXof the model (condenser, preheater and recuperator) are investigated in this section, withslight modifications from one to another.

1) Design Moving Boundary Model

In the literature, two modelling strategies for the HEX are co-existing: Finite ElementModels (FEM) or Moving Boundary Models (MBM). In FEM, the HEX is divided in finitevolumes of the same fixed size. In MBM, the division is made between zones of differentphases. As the operating conditions are varying, the boundaries of the cells are moving. TheFEM approach can return extremely accurate results if the mesh is sufficiently refined. Butit leads to high computational cost and it is thus not recommended for ”daily” simulations.In this work, the MBM approach has been chosen for its computational speed.

In a lot of ORC models presented in the literature, HEX are programmed for supportingparticular exchanges. In general, only single phase hot/cold source fluids are supported witha refrigerant entering in single phase and leaving in the other phase. It was the case ofthe EES model used by Enertime. Nevertheless, it reduces a lot the range of applicationsof the model, because different temperature profiles relatively common cannot be modelled.Given the versatility objective of the presented model, it is very important to allow the mostcomplex cases of heat exchanges to be solved.

To this purpose, the developed MBM uses a methodology that is inspired from thework of Ian H.Bell [17]. In his work, Bell proposed a model that could support any phaseconfiguration for a counter-flow heat exchanger. Such a model has also been used for instanceby Ziviani [18] in his charge sensitive simulation model. For medium to large scale ORC(which is the scope of this work), mainly shell and tubes HEX (STHEX) are used. This typeof configuration can be, in first approximation, considered as cross-flow HEX because of thevertical flow path of the fluid. Although Ian H.Bell’s model does not completely fit this kindof applications, the model developed in this work uses the same kind of strategy to supportany temperature profile.

The goal of the MBM models is to return the state of the fluid inside the STHEX, thetemperature profile as well as the heat transfer rate. The methodology is based on a ”StateMatrix” determination and is schemed in Fig.3.14.

It aims to create a State Matrix that contains the fluids states at all cell boundaries.

37

Figure 3.14: Moving Boundary Model of the heat exchanger applied to the evaporator.

It is perfectly possible to determine the phase configuration of both fluids based only onthe knowledge of the inlet and outlet states at both sides. However, it is here additionallysupposed that the working fluid enters in liquid or two-phase state, and leaves in vapourstate. This hypothesis saves a bit of computational time, and is hardly ever contradicted, asthe purpose of the EV is basically to vaporize the fluid.

As explained in the previous section, the inlet state, the vaporizing temperature and thesuperheating are inputs of the EV model as well as the hot source specifications. Therefore,the working fluid temperature profile is completely known, as well as the in/outlet statesof the hot source. The State Matrix (SM) can be initialized as shown in the first step ofFig.3.14. Note that this figure represents only an example and that the fluid could for ex-ample enter two-phase. Initially, the matrix contains only the very few properties neededfor the computing process, i.e the temperature, pressure and quality of both fluids, as wellas the entropy of the working fluid, which is used as reference x-axis in the T-s diagramrepresentation. At this step, some parts of the SM are left empty (red crosses).

Based on those information, it is possible to determine the working fluid mass flow ratethanks to a simple energy balance. It should be noted that a given dissipation coefficient istaken into account. The proportion of heat (in %) that is lost to the ambience is asked asinput. Thus, the power absorbed by the working fluid is slightly lower than the power lost by

38

the hot fluid. The same things applies for the preheater. The thermal power of each cell canthen be computed and therefore the hot fluid enthalpy(ies) corresponding to the dew or/andbubble points of the working fluid are determined. The pressures being given as inputs,the missing cells of the matrix can thus be filled. Please note that the pressure drop is im-posed at the outlet of the working fluid phase change cell, or at the middle cell if not relevant.

In a third step, the SM will be browsed cell by cell to detect the possible phase changesthat could occur. The principle is to compare the qualities at the cell boundaries and to adda bubble or/and a dew point if needed. New columns are then added to the SM to representthese new boundaries.

In the last step, energy balances are carried to fill the missing boundaries. Additionalfluid properties are also added to the SM (density, enthalpy and entropy). The whole processthus results in a matrix that contains all the properties of both fluids at all boundaries.

Another method based on the pinch point has also been included, even if it is not usedin the cycle models. It simply reuses the design method explained above and iterates on aninitial Tvap guess to find the right pinch point. The residue is calculated like in equation 3.1,and is brought to zero by the solver fsolve.

2) Cells property calculation

Taking the State Matrix as input, this method will compute interesting properties of eachcell and will store them in a matrix called ”Zone Matrix” (ZM). The outputs of each cell arethe following:

• Pinch point: Very easy to compute with boundaries temperatures.

• Thermal power exchanged: Already computed in the MBM.

• Logarithmic Mean Temperature Difference (LMTD): This variable is used to computethe required exchange area for a certain power Q in a counter-flow ideal HEX usingthe following formula:

Q = A ∗ U ∗ LMTD (3.12)

with A the total exchange area and U the global exchange coefficient of the cell. TheLMTD is defined as:

LMTD = ∆T1 −∆T2

ln(∆T1/∆T2) (3.13)

with ∆T1 the difference between the hot fluid inlet and the cold fluid outlet temper-atures and ∆T2 the difference between the cold fluid inlet and the hot fluid outlettemperatures. During the computation, if the initial guesses are not relevant, theLMTD might not be computable. In a robustness perspective, if ∆T1 = ∆T2, thenLMTD is set to ∆T1. Furthermore, if ∆T1 ≤ 0 than LMTD = ∆T2 (and conversely).

39

• Efficiency (ε): The efficiency gives an idea of the cell performance and is given by

ε = Q/Qmax (3.14)with Qmax = Cmin(Tin,h − Tin,c) (3.15)

Cmin = min(Mccp,c, Mhcp,h) (3.16)

The closer the efficiency to 1, the closer the pinch point to 0.

• Number of Transfer Unit (NTU): Depending on the characteristics and the geometryof the HEX, a given efficiency goes along with a certain NTU, that can be used tocompute the transfer area according to:

NTU = A ∗ UCmin

(3.17)

In this model, STHEX are considered as they are the most used type of HEX for largeheat transfers. For a geometry with 1 shell pass and 2 tubes passes (the basic case),the following correlation for the ε−NTU method can be used:

R = Cmin/Cmax (3.18)

E =( 2ε− 1−R1 +R2

)0.5

(3.19)

NTU = −(1 +R2)−0.5 ∗ log(E − 1E + 1

)(3.20)

As can be observed, if E ≤ 1 the NTU is not computable. In this case, in order toavoid solver failing, the correlation is replaced by the one of an ideal counter-flow HEX:

ε = 1− e(R−1)∗NTU

1−R ∗ e(R−1)∗NTU (3.21)

Finally, in the case of a cell with one of the fluids experiencing a phase change, thecorrelation is independent of the flow arrangement and one has to use:

ε = 1− e−NTU (3.22)

• Transfer Area (A): As stated here above, there are two ways to compute A. In thismodel, one can choose between Eq. 3.12 or 3.17. In the case of a cell where bothfluids change phases, the LMTD method is automatically used because of the lack ofcorrelation for ε−NTU . To apply the LMTD method to a STHEX, the LMTD valuehas to be corrected by a factor F . In this model, a STHEX with n shell passes and 2ntubes passes is considered. Therefore, F can be determined thanks to 2 coefficients Rand P:

R = (T1 − T2)/(t2 − t1) (3.23)P = (t2 − t1)/(T1 − t1) (3.24)

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if R = 1

S = P/(n− (n− 1) ∗ P )F = S∗

√2

(1−S)∗log(

2−S∗(2−√

2)2−S∗(2+

√2)

) (3.25)

if R 6= 1

α =

(1−R∗P

1−P

)1/n

S = (α− 1)/(α−R)F =

√R2+1∗log( 1−S

1−RS )(R−1)∗log

(2−S(R+1−

√R2+1

2−S(R+1+√

R2+1

) (3.26)

where T refers to shell side temperatures, t refers to tubes side temperatures, 1 standsfor inlet and 2 for outlet. If F is not computable because of a negative logarithm orsquare root, then F is set to 1.

In equations 3.12 or 3.17 appears the cell overall exchange coefficient U. This coefficientdepends on flow characteristics, HEX geometry, fluids and material in presence. The precisecomputation of this coefficient can be tricky, as lots of HE specifications are needed. Whenthe manufacturer is in the design phase, he does not know these specifications. Therefore, itis not possible at this stage to compute correctly U without making a lot of strong assump-tions. For this reason, a simplified approach has been chosen where U must be provided asinput directly. Indeed, it is much simpler for the user to assume U than to assume a lot oftechnical specificities during the early design stage. Orders of magnitude of U can be foundin the literature, otherwise the value should rely on the technical datasheets of previous HEXpurchases.

One can argue that assuming the same U for every cell is a strong assumption, as thiscoefficient is known to change significantly depending on the fluids phases. To take thiseffect into account, the possibility is offered to specify a given U value for each combinationof phases in the cell. Therefore, a matrix of U must be given in the following shape:

Figure 3.15: Global exchange coefficient matrix structure.

This matrix allows to take into account the fact that the transfer coefficient is higher ina phase change than in liquid or vapour phase for example.

In the end, when all the cells properties are computed, the total required exchange areaAtot is computed by summing all the cells areas.

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3) Refrigerant mass calculation

To mass of refrigerant present in the evaporator is computed based on:

• the type of fluid,

• the refrigerant allocation (shell or tube),

• the State Matrix (SM) and the Zone Matrix (ZM) of the HEX,

• the tubes inner volume,

• a volume ratio such as r = Vtubes/Vshell.

As previously stated, the geometry is not always known at the design stage. Therefore,it can be tricky to guess the tubes volume. It is more convenient to replace this input bythe ratio Vtubes/Atot, so that the volume in the tubes is calculated based on the transfer area,which is an image of the HEX size. This ratio can be computed for a known HEX and bereused as first approximation afterwards. In this model, the choice of the input is left to theuser.

With the fluid allocation, and the ratio r, one can compute the total volume Vtot that isfilled by the refrigerant in the HEX. Then, a volume is assessed to each cell based on theexchange area of the cells contained in ZM: Vcell = Acell

Atot∗ Vtot. This is a very strong assump-

tion because the STHEX can exhibit very complicated internal geometries and the volumeoccupied by each cell can be extremely complicated to compute. But it can be accepted asfirst approximation, in case of lack of information.

If, in a considered cell, the refrigerant is in liquid or vapour phase, then the mass com-putation is very straightforward:

Mcell = Vcell ∗ρin + ρout

2 (3.27)

However, in case of phase change, the determination of an equivalent density is more com-plicated. In this case, one must compute at any point the ratio of the cross sectional areasoccupied by the vapour Acs,v over the total cross sectional area Acs, called the void fraction.This void fraction (α) depends on the fluid flow pattern , and can be computed via the localquality x following:

α(x) = Acs,vAcs

= 11 + 1−x

x

(ρv

ρl

)S

(3.28)

with ρv/l the dew and bubble densities, and S the slip ratio. The latter represents the ratiobetween vapour and the liquid phase velocities (uv/ul).

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Given the void fraction (α), one can compute the fluid mass at any point of the HEXwith M = Acs∗(ρv∗α+ρl∗(1−α)). Integrating this equation over the whole cell length givesthe total mass trapped in this cell. For sake of simplification, it is assumed that the qualityvaries linearly in the cell. For the numerical integration the cell is divided in n divisions,with n = round(|xout − xin|). In each division, the quality xdiv and the cross sectional areaare considered constant. Each division has therefore the same volume Vdiv = Vcell

nand thus

Mdiv = Vdiv ∗ (ρv ∗ α(xdiv) + ρl ∗ (1− α(xdiv))) (3.29)

To obtain the cell mass, the division’s masses are simply summed as for a rectangle integra-tion method. And the total HEX mass is the sum of the cell’s masses.

To compute the void fraction, one also has to determine the Slip ratio. This is not adirectly accessible variable, and correlations must thus be used to approximate its value.According to Esbrı paper [19], a good slip ratio correlation for STHEX can be the Chishlomequation:

S =(

1− x ∗ (1− ρlρv

))0.5

(3.30)

In Esbrı paper [19], the correlation performance is based on a dynamic analysis but itis assumed that the results can be extended for static models. Moreover, the paper onlyfocused on evaporator. In the present model, this correlation will be extended to the otherHEX of the cycle.

3.2 TurbineIn design mode, the inputs of the turbine are:

• The working fluid,• The mass flow rate,• The inlet state,• The outlet pressure,• The isentropic efficiency,• The generator and transformer efficiencies,• The additional losses.

The outlet state of the turbine is computed via the outlet pressure and the isentropicefficiency. The gross mechanical power output can be computed thanks to the mass flow rate.However, the isentropic efficiency only takes into account the losses that are internal to thefluid. There exists other losses that will heat the mechanical components of the turbine (thefriction between the bearing for example). This power is to be dissipated by the lubricating

43

oil. This is why constant additional losses have been taken into account. Then, to obtainthe net electrical power output, the gross mechanical power is multiplied by the generatorand the transformer efficiency.

The fluid mass in the turbine is almost impossible to compute. However, in large ORCs,it is actually negligible compared to the fluid mass in the HEX and the pipes. Indeed, theturbine is not a large component and moreover the fluid is in vapour phase. Therefore, ithas been chosen to assess the same constant fluid mass of 100 kg inside the turbine whateverthe cycle. The total mass is not much impacted by the turbine contribution in any case.

3.3 CondenserThe condenser (CD) design model is mostly the same as the EV one. The methods for

computing the cells properties and the refrigerant mass are exactly identical. The hypothesisis made that the working fluid enters in vapour or two-phase state and leaves in liquid state,for the same reason as in the evaporator. The MBM follows the same principle as in EV,except for two differences.

First, in the EV, the refrigerant mass flow rate is computed by means of the hot fluidmass flow rate. In the CD, the refrigerant mass flow rate is known and thus the cold sourcemass flow rate is computed.

Secondly, an option is added for defining the refrigerant output temperature. The choiceis left between giving the NPSH of the pump or directly the subcooling. If the subcooling isprovided, the outlet temperature is straightforwardly computed. However, the NPSH optioncan sometimes be more convenient when the subcooling is imposed by the security of thedownstream pump. In this case, the CD outlet temperature is computed by solving thefollowing system of equations:

Pvap = Psat(Tpu,in) (3.31)ρpu,in = ρ(Tpu,in, Ppu,in) (3.32)

NPSH = Ppu,in − Pvapρpu,in ∗ 9.81 (3.33)

The pump inlet pressure Ppu,in is simply the CD outlet pressure less the pressure drop inpipes between CD and PU. Therefore, the outlet CD piping pressure drop must be providedas additional input compared to the EV.

3.4 PumpIn design mode, the inputs of the pump are:

• The working fluid,

44

• The mass flow rate,

• The inlet state,

• The outlet pressure,

• The pump efficiency,

• The motor efficiency.

As the pump is not designed by Enertime itself, the isentropic efficiency is not available.Nevertheless, the pump manufacturer usually provides a general efficiency, which includesall the losses of the pump. In order to find the isentropic efficiency, a pump mechanicalefficiency (ηmec) must be imposed such as εglobal = εis ∗ εmec. In the present model, a constantmechanical efficiency of 0.95 has been assumed. Even if it is only a rough guess value, thepump outlet temperature is not much impacted, because the fluid is in liquid state.

Thanks to the isentropic efficiency, the outlet state can be computed. The mechanicalpower consumption is determined by:

Wmec = V ∗ (Pout − Pin)εglobal

(3.34)

where V is the volumetric flow rate. The electrical power consumption is then deducedfrom the motor efficiency.

As for the turbine, a constant mass of refrigerant equal to 20 kg is supposed to be trappedin the pump.

3.5 RecuperatorMass flow rates on both sides of the recuperator are known, but the outlet temperatures

have to be determined. As explained in Section 2.2, the outlet temperatures are not directlyprovided, but the pinch point PPre,input is given. A system of equation must therefore besolved with an initial guess. This guess is chosen to correspond to the liquid side outlettemperature. The initial value is automatically set at Tliq,out = Tvap,in − PPre,input.

Thanks to this guess, the temperature profile can be fully determined in a causal way bya MBM that uses the same working principle as in the other HEXs. The only difference isthat no mass flow rate has to be provided in the initialization step. The vapour side outlettemperature is needed. In the recuperator, the assumption is made of a liquid state on highpressure side. This is relevant as a certain subcooling is always maintained in the condenserand as the heat from the vapour side is hardly ever sufficient to start vaporizing the liquidstate. Therefore, the phase change detection stage of the MBM is only conducted at vapourside. Once the temperature profile is fully determined, a residual on PPre,input is computed.

45

This residual is forced to converge to zero by the fsolve method.

The cells properties and the mass computation methods are the same as for the otherHEXs.

3.6 PreheaterThe preheater takes the medium source specifications as well as the working fluid inlet

state and mass flow rate as inputs. Therefore, in the initialization stage of the MBM, thegoal is to determine the working fluid outlet state. The rest of the model follows the sameprinciple as in the other HEXs (using again the same cells properties and mass computationmethods). The only difference is that no assumption on in/outlet phases are made for thepreheater, contrarily to the other heat exchangers.

3.7 PipesIn design mode, the inputs of the pipe model are:

• The working fluid,

• The mass flow rate,

• The inlet state,

• The pressure drop,

• The length,

• The maximal fluid velocity.

In regular pipes, the outlet state of the fluid is computed via the pressure drop and ahypothesis of isenthalpic transformation. Another method has been added in order to takeinto account the dissipation in some pipes (from EV to TU, from TU to RE or from TU toCD). In those pipes, a temperature loss must be given as input. The fluid transformation inthe pipe is computed in two steps: an isenthalpic phase (like in regular pipes) followed byan isobaric phase with a given temperature drop.

In the pipe’s class is also included a nominal diameter (DN) calculation method. Thenominal diameter should be designed so that the pressure drop does not go upon a givenlimit. In the present model, the pressure drop limit is set via a maximal fluid velocity vmaxin the pipe:

v = min

(√2 ∗∆Pρmean

, vmax

)(3.35)

The suitable diameter is then computed:

46

D =

√√√√ 4 ∗ Mv ∗ π ∗ ρmean

(3.36)

This diameter D is then rounded to the upper existing standard DN. The maximal veloc-ity depends on the pipe location. For vibration considerations, the maximal velocity is setat 2 m/s in liquid pipes and 15 m/s in vapour pipes (except for MM and MDM, where 40m/s can be accepted). For the TU-CD pipe, the pressure drop is critical because it impactsthe TU outlet pressure and thus the power produced. For this pipe, the value is set at 8m/s, even if the fluid is in vapour state.

Thanks to the DN and the length of the pipe, one can compute the pipe volume andtherefore the trapped mass of fluid. It should be noted that an additional pipe is taken intoaccount, which is the TU bypass. This pipe is not used but is still filled with fluid and musttherefore be taken into account in the mass computation.

3.8 General variablesIn this last class, the global performances are computed. The net electrical power output

is Wnet = Wtu − Waux, with Waux being the sum of the PU and the TU lubrication systemconsumption. The latter is an input of the model. The efficiency of the cycle is:

η = Wnet

Qin

C1,C2= Wnet

Qev

C3,C4,C5= Wnet

Qev + Qpr

(3.37)

In this class, the components masses are summed to get the total fluid mass in the cycle.It also contains methods that draw cycle T-s diagrams and mass distribution pie charts.

This class is the last one called in the resolution process. After this, the results aredisplayed in a visual layout that is described in the appendices where the interface is detailed.

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Chapter 4

Simulation Model

A design model is not sufficient in a lot of cases. In practice, the cycle will hardly everrun within nominal conditions. A simulation model can therefore help the manufacturer tosolve numerous problems that do not relate to the design stage.

First, it is important to predict the performances of the cycle when the hot source isnot at its optimal conditions. The part load performances can only be determined a priorithanks to simulations.

Furthermore, when a machine is constructed and when the cycle is in operation, problemscan always arise. To detect the cause of the issues, it can be convenient to have a modelthat can predict the cycle behaviour in any conditions. Simulations can also predict faultsand problems that are not obvious at first sight.

Then, a precise enough simulation model can give access to variables that are not measur-able on site, allowing to reduce the number of required measures and thus the instrumentationcosts.

Finally, simulation models can be used to solve optimization problems and to determineefficient control methods. Different ways of controlling the cycle can be tested to determinewhat the best option.

This chapter is dedicated to the description of the simulation part of the ORC model.The first section describes the considered inputs and the required outputs. The second onedetails the model structure for each cycle configuration. The constituting equations of thepart load models are explained component by component in the third section. Lastly, adiscussion will be carried about the solver that has been used in the fourth section.

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1 Inputs and outputs

The purpose of the simulation is fairly different from the design model, and so are the in-puts. In the simulation model, the goal is to find the performances of a designed ORC whenthe cold/hot sources inlet conditions are changing. The HS and CS outlets are therefore notknown in advance. This means that the inputs at the sources are only the inlet states andthe mass flow rates.

However, this is of course not sufficient to compute the cycle. Since the ORC has beenpreviously designed, the HEX exchange areas can also be used as inputs, because they shouldnot change from an operating point to another.

A usual choice is generally to add to the inputs the superheating at evaporator outlet orthe pump speed. Indeed, this is a usual control value when operating the cycle: the operatorcan adjust the pump rotation speed to keep the superheating at it optimal value. Indeed,the goal is to stay at the superheating value providing the best cycle performances, withoutrisking to generate droplets in the turbine. In the present model, the superheating has beenchosen as input.

A final input must still be included for a charge sensitive model: the mass of refrigerant.Otherwise, the subcooling is generally imposed. Physically, keeping the mass constant is thebest option to choose. Indeed, in reality, the subcooling is totally determined by the pumpspeed (or the superheating) and the mass of refrigerant. The more organic fluid in the cycle,the higher the liquid level in the condenser. However, using charge sensitive models leads tothree problems. First, the mass of refrigerant is not easy to compute. As could be seen inSection 3.1, the mass computation requires a lot of strong hypotheses and some empiricalcorrelations. Using a mass model that is not accurate can lead to substantial result errors.Secondly, this kind of models are difficult to solve because of the difficulty of mass determi-nation. A solver that takes the subcooling as input will be more robust and rapid. Lastly,the initial mass used in the cycle in design condition must of course be known for runningthe simulation. However, the exact mass of refrigerant present in the cycle was not knownprecisely. Using an approximation of the mass as input of the model could lead to evenlarger errors. Even with a precise knowledge of the total mass in the cycle, the subcoolingis difficult to deduce. It requires heavy and complicated HEX models. On the contrary, thesubcooling itself is a value that is easily measurable with sensors at any time. Therefore,having a model that takes as input the subcooling is relevant in this case, and is sufficientto perform a model validation.

The outputs of the model are roughly the same as in design mode. But instead of givingthe HEX exchange areas, the model will compute the hot/cold sources outlet states.

49

2 Simulation model structureBecause the inputs have changed, it is not possible to use the same implementation

for design and for simulation mode. In this section, the algorithm of the different cycleconfigurations are described, like in Section 2 of Chapter 3.

2.1 Algorithm descriptionIn design mode, as a condensing and evaporating temperatures were given, it was possi-

ble to compute the cycle in a causal way, without requiring any solver. In simulation mode,with the set of inputs that were considered above, a solver is needed anyway.

Like in design mode when the pinch points were provided, the solver uses guess values tosolve the problem and compute a residual. The residual will be brought to zero by iteratingon the cycle function. In this case, the residual is based on the design HEX exchange areas.

The exchange area calculation being more complex than the pinch point one, the solveris less robust than in design mode. Therefore, it is important to give the opportunity to theuser to choose the guess values. The solving method is also an option, as well as its tolerance.These considerations will be developed in Section 4. Moreover, because of solving difficulties,nested solvers like in design mode have to be avoided. This is made possible by the fact thatthe pinch points cannot be inputs anymore and by a wise choice of guess variables. Thischoice depends on the cycle configurations, as will be explained in the following sections.

Simulation of C1 cycle

The detailed simulation algorithm of configuration C1, called SimC1, is represented inFig.4.1. As can be observed, it is completely different from C1 design algorithm.

First of all, only one block appears in the figure. As previously stated, nested loops areavoided to save computing time. To allow the whole cycle to be solved in a single causalblock, the guess variables must be carefully chosen. The most logical choice is to use Tvapand Tcd because this option allows to compute the rest of the cycle in a causal way, just likein C1 cycle.

The second difference is that the hot and cold sources are now part of the block, becausethey cannot be completely defined without solving Block 1. Indeed, the outlets are one ofthe outputs of EV and CD boxes.

Then, the order of the components in the resolution has changed. The evaporator is notthe mass flow rate defining component anymore. Instead, the turbine is used. Usually, thepump law is used to link the pressure levels to the mass flow rate. However, Enertime isdeveloping its own turbines for every machine. The modelling of the turbine, notably with

50

Figure 4.1: Detailed algorithm structure of SimC1.

CFD, is thus very mature and has lead to a turbine law that will be described in Section 3.Turbine law is thus considered instead of pump law, and the turbine becomes the mass flowrate determining component for the rest of the cycle. Solving PU and TU at first allows tocompute easily the HEX inlets.

It should be noticed that pressure drops along the pipes and the HEX are supposed tobe the same as in design mode and are kept constant. This is a strong hypothesis, especiallyfor the condenser. In reality, the pressure drops vary with the mass flow rate and thereforeinfluence the turbine outlet pressure. The relative error made at low pressure part of thecycle being more important than at high pressure part, it can lead to quite large errors.Nevertheless, computing the pressure drops in STHEX coupled with a MBM model is a verydifficult task and requires deep HEX geometry knowledge. For the sake of simplicity (forthe user and for the algorithm speed), this strong hypothesis has been accepted. Therefore,the whole cycle is, like in design mode, completely defined in pressure thanks to Tvap andTcd (thus Pvap and Pcd).

Another difference is that the outputs used to derive the residuals come from the exchangeareas and not from the pinch points:

Res1 = 1− Acd,calc/Acd,input (4.1)Res2 = 1− Aev,calc/Aev,input (4.2)

Finally, some components require new parameters, related to the considered part load

51

Figure 4.2: Detailed algorithm structure of SimC2.

laws, as explained in Section3.

Simulation of C2 cycle

To solve the second configuration in simulation mode, one more guess is needed, as canbe seen in Fig.4.2. Indeed, the inlets of RE are known but a new variable is needed to getthe outlets. The variable that seems the easiest to guess is the RE outlet temperature onliquid side. Once the recuperator is solved, the rest of the cycle is just like SimC1.

Of course, a new guess variable means a new residual. Obviously, the residual is linkedto the RE exchange area:

Res3 = 1− Are,calc/Are,input (4.3)

Simulation of C3 cycle

The SimC3 algorithm is a bit different from the preceding one because of the inclusionof the medium source. It is represented in Fig.4.3. Indeed, if the same inputs options thanfor MS design are considered, the medium source inlet is in some cases dependant of thehot source outlet. Therefore, the evaporator must be computed before the preheater. Thiscannot be done without a new guess on the evaporator inlet temperature. This implies anew residual:

52

Figure 4.3: Detailed algorithm structure of SimC3.

Res4 = 1− Apr,calc/Apr,input (4.4)

It should be noticed that in the case of a two-phase EV inlet, the quality must be providedas guess instead of the temperature.

Simulation of C4 cycle

The SimC4 algorithm is depicted in Fig.4.4. The number of HEXs being the same inSimC3 and SimC4, it should not be necessary to add a new iteration variable. Neverthe-less,guessing EV inlet temperature is not relevant anymore because it does not allow to solvethe whole cycle causally. Instead, the mass flow rate distribution Mfrac is considered, so thatthe difficulty linked to the 3 ways valves can be easily avoided. One should also rememberthat the preheater outlet temperature must be provided in the configuration 4 (directly orindirectly, see equation 3.7). This way, the evaporator inlet can be easily computed. Theresiduals remain the same as in SimC3.

Simulation of C5 cycle

Finally, the last configuration is quite easy to understand and is presented in Fig.4.5. Itis just the same as the SimC3 one, but without the recuperator. In this case, only 3 iterationvariables are needed and therefore three residuals.

53

Figure 4.4: Detailed algorithm structure of SimC4.

Figure 4.5: Detailed algorithm structure of SimC5.

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3 Part load operation modellingThis section describes the simulation methods included in the components classes. The

part load equations are detailed, as well as the hypotheses. These laws are not validatedwith real data in this section, as they are part of the next chapter.

3.1 TurbineAs previously said, the turbines of Enertime are developed internally. The law used in this

model has been developed for their own turbine and might not fit other turbo-machinery. Itis based mainly on CFD analysis. The same can be said for the part load isentropic efficiencylaw.

The CFD results reveal that the turbine inlet pressure Pin is varying almost linearly withthe mass flow rate M . Therefore, the turbine law used by Enertime’s models is quite simple:

M = (Pin − a0)a1

(4.5)

The coefficients a0 and a1 are specific to the considered turbine and must be used asinputs. However, if these coefficients were not known, the model computes them automat-ically. In this case, one point of the linear curve is given by the optimal design conditions.As it is clear that if no fluid is flowing no pressure is provided by the pump, a reasonableapproximation is to make the line pass through the origin, even if a point of zero pressuredoes not exist. Therefore, in automatic mode, one has:

a0 = 0 (4.6)a1 = Ptu,in,d/Md (4.7)

For the isentropic efficiency, the problem is more complicated. Indeed, this parameterdepends on the inlet and the outlet pressure. A simple linear law cannot be used in thiscase. Therefore, the model developed internally by Enertime (based again on CFD results)is the following:

rout = Pout/Pout,d (4.8)rin = Pin/Pin,d (4.9)

rin,opt = b0 + b1 ∗ rout (4.10)

rout,opt = rin − b0

b1(4.11)

ηis = ηis,d ∗(

1−∣∣∣∣rin − rin,optv0

∣∣∣∣v1)∗(

1−∣∣∣∣rout − rout,opth0

∣∣∣∣h1)

(4.12)

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where b0, b1, v0, v1, h0, h1 are coefficients that relate to a specific turbine, like a0 and a1.They are gathered in a coefficient array, called Ctu in the preceding figures. To obtain thesecoefficients, CFD computations is required. Like in design mode, the losses that are notcomputed with CFD are taken into account via constant losses.

Finally, the last change compared to the design mode is the generator efficiency. To takeinto account of the efficiency fall at part load, a quadratic law based on the mechanical poweroutput is used:

ηgen = ηgen,d ∗

1− Cgen ∗(

1− Wgross,mec

Wgross,mec,d

)2 (4.13)

where Cgen is a coefficient provided as input. The latter depends on the generator and isusually quite small, as the efficiency at part load is still very high for electrical generators.

3.2 Heat exchangersThe MBM developed in design mode is still in application in simulation, except for some

slight changes. In design mode, the initialization part of the MBM was to find Mwf based onthe in/outlets and on the hot source mass flow rate (see Fig.3.14). In simulation, the samemethod is used but this time both mass flow rates are known and one has to determine theoutlet at refrigerant side.

However, the performances of the heat exchangers change at part load. The coefficientof transfer is impacted by the flow pattern, the fluid speed and the fluid properties onboth sides. Here, a simplified approach considering that the global exchange coefficient Udecreases with the refrigerant mass flow rate is used:

U = Ud ∗(Mwf

Mwf,d

)CHEX

(4.14)

This is a really strong simplification. First, the exchange coefficient also depends onother factor, such as the mass flow rate. Furthermore, this law supposes that the restrictingside in terms of U is the refrigerant side, because Mwf is used. Computing U is in factfar from being easy, but a simplified approach has been chosen because it does not requiremuch information about HEXs. Of course, it is important to check whether this simplifiedequation gives accurate enough results or not. This is the subject of the Chapter 5.

The coefficient CHEX ,present in the figures, is provided as input. A value must be givenfor each phase combination, like in the matrix of exchange coefficients appearing in Fig.3.15,so that the value of U can change less in two-phase cells than in the others, which is generallythe case. Enertime is using this law with coefficients found in the literature. Those will bevalidated in the next chapter.

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The cell property calculation and the mass calculation methods are the same as in designmode and are simply reused.

3.3 PumpAs said before, the isentropic efficiency does not impact much the cycle. Therefore, it is

not very relevant to elaborate complex part load law. A simplified approach has once againbeen preferred. The pump efficiency is supposed to vary with the mass flow rate accordingto:

η = ηd ∗

1− Cpu ∗(

1− Mwf

Mwf,d

)2 (4.15)

with Cpu being a coefficient that must be provided as input. The motor efficiency followsthe same kind of law as the generator one:

ηmot = ηmot,d ∗

1− Cmot ∗(

1− Wgross,mec

Wgross,mec,d

)2 (4.16)

with Cmot being also quite small.

3.4 PipesThe pipe component does not change between the design and the simulation. The only

exception is that the DN is fixed in simulation, and therefore the volume of refrigerant aswell. The mass of fluid in the pipe thus only depends on the boundaries densities.

4 Solver considerationMany tools in python libraries exist for solving optimization problems. The library that

has been chosen for this model is scipy.optimize [20] because it contains a lot of methodsand it is the most widely used. Many solvers are proposed in scipy.optimize, but few ofthem apply for multi-dimensional non-linear problems. The most complete solver is root[21], which finds the root of the function thanks to a chosen algorithm. Different algorithmsare available: Levenberg-Marquardt, Broyden, Anderson, Krylov, etc. All of them can beused in the model.

After testing different options, the algorithm that is the most robust to solve ORC modelproblem revealed as being the hybr method. This algorithm uses a modification of the Powellhybrid method that has been implemented in MINPACK [22], an old minimization library.Note that the solver fsolve is actually a particular case of root, used with the method hybr.

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Three convergence criteria are implemented in MINPACK. However, only one of them isused by the hybr method. This convergence criterion should theoretically guarantee that

‖D(x− x∗)‖ ≤ Xtol(Dx∗) (4.17)with D the scaling matrix, Xtol the user-provided tolerance, x the current approximation

and x∗ the actual solution. In the case of this model, x is the vector of HEXs approximatedexchange areas and x∗ the vector of design areas.

Nevertheless, Eq.4.17 cannot be used as it is presented because x∗ is not known a priori.The criterion in use is thus:

∆ ≤ Xtol(Dx∗) (4.18)where ∆ i the step bound. The convergence criterion can sometimes cause issues. In-

deed, it can happen that the criterion is satisfied even if residues are not brought to zero.Therefore, one should be careful and check the end-residuals once the solver has worked,especially if the solution found is close to the initial guesses. If they are non-null, one shouldconsider adjusting the guess values. It is also possible to force the solver to further iterate byreducing the tolerance. In general Xtol should always be smaller than 10−5. The higher thetolerance, the longer the computation. The default tolerance used in this model is therefore10−6. This can be reduced to the machine precision.

It should be noted that root is not a bounded solver. It is thus not possible to imposeminimum and maximum values to the iteration variables like in EES. Such solvers of courseexist, but they are less adapted to the present model and are less easy to use.

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Part II

Case Studies

59

Chapter 5

Model validation on a waste heatrecovery ORC

This second part of the document is dedicated to the validation and the application of themodel. This chapter particularly focuses on the confrontation of the model with a databaseof measurements coming from an instrumented ORC cycle constructed by Enertime. Thegoal here is to estimate the accuracy of the model, to discuss the results, to check the partload laws considered and to suggest possible improvements the model.

Firstly, the reference ORC will be described in details and the design operational pointwill be given. Then, the database that is used will be presented and a discussion about thesensors accuracy will be carried out. After explaining the simulation hypotheses, the resultson three different operational points will be discussed. Next, the part load hypotheses willbe tested and criticized. Finally, a model retrospective will be presented, with its forces,weaknesses and further improvements.

1 ORC descriptionThe machine that is used as reference is a WHR ORC that has been constructed by

Enertime in China. It has been running for many months, and enough measurements arenow available for a relevant model analysis. In this section, the machine will be describedin details. Since it is the basis of the simulations, the nominal operational point will also bepresented.

1.1 Overall overviewThe reference ORC is a C5 cycle working with R245fa. It does not have any recuperator

but it has a preheater. The hot source is superheated vapour that is condensed into theevaporator. For the good functioning of the industrial process, the hot source outlet statemust remain liquid. The medium source is liquid hot water and comes from another indus-

60

Figure 5.1: Evaporator and preheater layout.

trial process. The cold source is also a water loop.

The evaporator and preheater configuration is a bit particular. Indeed, in most cases,the preheater is smaller than the evaporator and provides a relatively small part of the totalheat. Here, the preheater is much bigger than the evaporator. The fluid vaporization alreadystarts in the preheater and is finished in the evaporator. In reality, both HEX are combinedin series to form one large HEX, as can be seen in Fig.5.1.

In the evaporator, the R245fa is passing through the shell side. The heat exchange areareferred in the datasheets is 76 m2 for a shell volume of 988 litres. In the preheater, therefrigerant is also on shell side. It is much bigger, with a area of 1425 m2 and a shell volumeof 2688 litres. As for the condenser, the refrigerant is once again in the shell. It is the largestof the HEX. It has a 3801 m2 area and a shell volume of 9166 litres.

The whole cycle is depicted in Fig.5.2. The turbine cannot be seen on this layout becauseit is behind the condenser. As can be observed, there are not only one but two pumps inparallel after the condenser for maintenance purpose.

1.2 Design operational pointThe nominal operation point of this ORC is represented in Fig.5.3. It is the result of

the design process of Enertime. It has been computed using the Coolprop library. In thisfigure appears the principal characteristics and orders of magnitude of the cycle. Some per-formances variables could not be disclosed for confidentiality reasons. These variables have

61

Figure 5.2: Organic Rankine Cycle global overview.

the mention CF. Particularly, the turbine performances are kept confidential, as the turbo-machinery is designed by Enertime.

As can be observed, the hot source is at 180 ◦C and 6 bar with a mass flow rate of4.15 kg/s. This mass flow rate is very small, but 9 MW are still exchanged in the HEXbecause of the use of the latent heat. At the medium source, the fluid is entering at 150◦C and 12 bar with a mass flow rate of 61.1 kg/s. More than 15 MW are exchanged inthe preheater. At the cold source, the cooling fluid enters the condenser at 23 ◦C with amass flow rate of 507 kg/s and gains 10◦C. The nominal refrigerant mass flow rate is 100 kg/s.

The T-s diagram clearly shows the convenience of using a MBM for the HEX. The temper-ature profile in the EV-PR is quite exotic. As can be seen, the superheating and subcoolingare quite small (2 and 4 K). In real operation, these are much larger for the safety of theturbine and the pump. The R245fa having a saturation curve that is not very inclined, it isnot economically interesting to use a recuperator.

As one can observe, the computed exchange areas are not the same as the one announcedin the datasheets. Indeed, the exchange areas values rely on the exchange coefficient consid-ered. This exchange coefficient is very difficult to guess because the geometry of the HEXis not simple and thus the flow pattern is complicated to predict. Therefore, some standardexchange coefficients have been considered, presented in Fig.5.4. These values are the onesthat are usually taken by Enertime in first approximation. They are known to give a goodorder of magnitude for the exchange areas. Without good guesses on exchange coefficient,and considered that the STHEX are not counter-flow HEX, the areas calculation is not com-pletely reliable. Still, it can give a good idea of the size of the HEX relatively to each other.

One should also note that the areas from the datasheets are overrated. Safety margins

62

Figure 5.3: Nominal operating point of the ORC. Principal variables, T-s diagram and massdistribution. Figures taken from the developed interface (see appendices).63

Figure 5.4: Nominal exchange coefficient considered for area calculation.

have been considered to be sure that the HEX could at least reach the announced nominalperformances even with fouling. The ORC being quite recent, there should be almost nofouling yet. This means that, in simulation mode, one should take in account that the HEXare more efficient than it could be predicted with the design areas from Fig5.3.

The estimated mass of fluid is around 7 tons. The largest part of it is contained intothe condenser, because of its large shell volume. There is also 1300 kg in the pipes. Almostall the rest is contained into the preheater, due to its large liquid phase. The mass of fluidin the evaporator is negligible because of its small size and liquid phase part. According toEnertime engineers, the order of magnitude is close to what was really injected in the ORC.

2 Database considerationsThe database that is used provides from measurements taken with cycle sensors since the

start of the machine. Unfortunately, only a fraction of the whole database is accessible forEnertime. Moreover, it is impossible to find in these data some perfectly stable operationalpoints. Indeed, the hot source mass flow and temperature are quite chaotic, forcing thepump to constantly adapt the mass flow.

In this section will be presented the three operational points that could be retrieved fromthe data. They have been chosen as basis of comparison for the model simulation results.The sensors accuracy will also be discussed.

2.1 Choice of the comparison pointsThe first measurement point that has been chosen was taken the 21st of November around

16:00 and is represented in Fig.5.5. Although the sample does not look stable, the time scaleis very large in the figures. Indeed, a period of 7 hours is represented to have a global view ofthe hot/cold sources behaviours. In reality, the inertia of the ORC is very low, and a stableperiod of a dozen minutes is sufficient to have the ORC back at a steady-state point. Thisis what is shown in Fig.5.6. As can be observed, the refrigerant mass flow rate follows verywell the shape of the thermal power curve. There is almost no shift between the curves. If a

64

Figure 5.5: First comparison point: November 21 - Representative sample of cold, hot andmedium sources behaviours.

big inertia was present in the system, the refrigerant mass flow curve would be time shiftedand smoothed.

The 21st of November at 16:00 is thus a relevant operational point in which the cold/hotsources have been stable enough for a while, as can be observed in Fig.5.5. Yet, the hotsource mass flow rate measurement is erratic. In order to diminish the incertitude on themeasurement, mean values over a certain period will be considered in the analysis insteadof instantaneous measurements. The considered period is the one between the two blackvertical bars. Therefore, the operational point that has been chosen is the mean operationalpoint between 15:30 and 16:00 of November 21.

As can be seen in Fig.5.5, this operational point is not that far from the design point,except for the hot and cold sources source mass flow rates. The inlet temperatures remainquite high.

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Figure 5.6: Representation of the time needed to adapt the mass flow to the hot sourcethermal power.

The second operational point has been chosen between 16:59 and 17:19 on the 7th ofDecember and is represented in Fig.5.7. In this figure, the time scale is much smaller andthe curves look smoother. In this case, the medium source will provide less power becauseits mass flow and temperature are very degraded. The hot and cold sources mass flow arealso very low. It must be noticed that the cold source inlet temperature is not stable at thispoint. One must keep this in mind when analyzing the results.

Finally, the third and last point is between 23:30 and 00:00 on the 31st of October, andis represented in Fig.5.8. It has been chosen because it is very far from the nominal point.As can be observed, the measurement of the hot source mass flow rate is very inaccurate andit oscillates a lot. The sensor might not be adapted to such low values, and it is thereforevery important to consider a mean value over the chosen period.

2.2 Sensor accuracyThe considered cycle is instrumented with temperature, pressure and volumetric flow rate

sensors. The location of the sensors in the cycle is depicted in Fig.5.9. Only the instrumen-tation that is used in this analysis is shown in this figure. The sensors that are installed tothe refrigerant loop itself have been positioned by Enertime. The rest of the sensors (at thecold/hot sources) were installed by another company. Therefore, even if the access to thesemeasurements has been granted, the datasheets of the sensors were not accessible. We willtherefore consider that they use the same technology and are at the same order of magnitude

66

Figure 5.7: Second comparison point: December 7 - Representative sample of cold, hot andmedium sources behaviours.

of accuracy than the ones on the refrigerant loop. The volumetric flow rate sensor is a vortexflow meter Proline Prowirl F200 [23]. Its accuracy depends on the flow pattern and thus theReynolds number. The pressure sensors are Cerabar PMP131 or PMP55 [24]. They workwith a ceramic membrane that transmit the pressure to a piezoelectric cell. Finally, thetemperatures are measured thanks to modular thermoresistances Omnigrad TR88 [25].

The incertitude on the raw measurements is quite small in general. It depends on thesensor quality, the operating conditions and the value of the measurement. Except for therefrigerant volumetric flow rate measurement, the sensors used are quite reliable. However,in this analysis will be used variables that are not directly measured. For example, the ther-mal power is calculated based on temperature, pressure and mass flow rate measurements.All of these measurements have individual uncertainties that will propagate. It is sometimesvery tricky to determine what is the uncertainty of each of those variables. Furthermore, thesensors have not been re-calibrated since the start of the machine, and this can also causesome errors.

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Figure 5.8: Third comparison point: October 31 - Representative sample of cold, hot andmedium sources behaviours.

In general, it has been computed that the variables that are not calculated thanks tothe refrigerant mass flow rate have uncertainty of around 1% or less, except for the turbineoutlet pressure, where the maximal error is 2.21%. This comes from the fact that the samesensors are used for the turbine outlet and inlet pressures. The relative error being the same,the uncertainty is much bigger at the low pressure side.

For the variables involving Mwf , it is very difficult to know the precision of the measure-ment. Even if the sensor is supposed to provide a reliable measurement, the values have beenquestioned by Enertime numerous times. Moreover, the measurement does not coincide withthe mass flow that can be computed thanks to power balance at the HEX or thanks to theCFD turbine law. This is represented in Fig.5.10, where the mass flow rates coming from thesensor (in red) is compared to computed mass flows. It can be observed that the uncertaintyis sometimes quite large. Therefore, what should be trusted? Indeed, no orders of magnitudeof the hot/cold sources mass flow rates are known, making the mass flow rates computed

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Figure 5.9: Sensors location and type. T stand for temperature, P for pressure and F forvolumetric flow rate.

with power balances not reliable. Concerning the CFD law, one should remember that itremains a theoretical computation, and might not represent correctly the reality. For themass flow rate based on a turbine power balance, it uses efficiencies that are approximatedand temperatures that are measured with limited precision. The mass flow rate uncertaintymust thus be taken into account when the precision of the model will be discussed.

3 Simulation hypothesesThe objective is to use the model to simulate these three points and compare the results

with the measurements. The design cycle on which the simulation will be based is the onepresented in section 1.2. The inputs of the models are the mass flow rates and inlet tempera-tures of the hot/cold sources from the database. The superheating is computed thanks to themeasurements of the outlet pressure and temperature on the working fluid side of the evapo-rator. The outlet pressure is used to approximate the saturation temperature and thereforeto calculate the superheating. For the subcooling, the CD inlet pressure is used to approx-imate the saturation temperature and the CD outlet temperature is taken at the pump inlet.

The part load laws coefficients for the pump, the motor and the generator are the fol-lowing:

Cgen = 0.07 , Cmot = 0.1 , Cpu = 0.4 (5.1)

These values have been used for long by Enertime and are known to give good approxi-mation. For the HEX global exchange coefficient part load law, the value of CHEX dependson the phase conditions. For liquid or vapour phases it will be supposed that CHEX equal0.645. For two-phase fluid on one side only CHEX equal 0.785. And for two-phase on both

69

Figure 5.10: Comparison of different values of mass flow - Representation of the uncertainty.

side one has CHEX equal 0.9.

For the turbine, the coefficients a1 and a0 will be set automatically in first approximation.The rest of the coefficients come from the CFD analysis of the ORC turbine and are thefollowing:

b0 = 0.261 , b1 = 0.726 , v0 = 1.089 , v1 = 2.468 , h0 = 2.902 , h1 = 4.923 (5.2)

As said in section 1.2, one should not consider the HEX exchange areas predicted in thecycle design because the HEX have been overrated. To take this into account, the designvalue of the exchange areas (that are used for the residuals computations) must be increased.In the datasheets, a global exchange coefficient is provided with and without fouling. It hasbeen decided to increase the area proportionally to the increase of U from its dirty to itsclean value. In practice, Aev,d was increased by 27.9%, Acd,d by 50.7% and Apr,d by 15.4%.

One could wonder why the nominal exchange coefficient and areas were not directlypicked from the datasheets. In reality, it was important to keep the AU product relevantfrom the design phase to the simulation phase. Indeed, even if the design exchange areaswere false due to wrong exchange coefficients considered, the product AU computed in designmode is still correct and must be used (aside from the overrating) as basis of the simulationmode to be consistent. If the A and U from the datasheets were chosen, the consistencywith the calculated design will be lost. Moreover, the exchange coefficient that is found inthe datasheet is a global one and is difficult to adapt to this cell model.

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The exchanged areas will be computed thanks to the ε − NTU method. In practice, ithas been observed than LMTD and ε−NTU methods provide rather similar results. Usingone or the other is thus not determinant. The solver method used is the hybrid method,because it is usually the most performing of all. The guesses on Tvap,Tcd and xev,in that mustbe provided come from the measured values at the considered operational point.

4 ResultsIn this section will be compared the results returned by the simulation model given the

inputs stated in last section. All variables can obviously not be compared. Only the mostrelevant are summarized in this analysis:

• refrigerant mass flow rate,

• power exchanged (heat and electricity),

• cycle efficiency and turbine isentropic efficiency,

• in/outlet turbine pressures,

• hot/cold source outlet temperature,

• the iterative variables (vaporizing/condensing temperatures and evaporator inlet qual-ity).

The goal is to evaluate the model accuracy, to check the hypotheses validity and todetermine how it could be improved.

4.1 First comparison point: November 21, 15:30 to 16:00The results are summarized in Tab.5.2. Once again, some variables are kept confidential.

In this case, only the error between the measures and the model results will be considered.In this first comparison point, the cycle works at 62% of its nominal load (meaning that62% of the nominal electrical output is produced). The error on the PR and CD powers arearound 4%. Having no further information about the precision of the measurement (thatare taken on hot and cold fluid sides), it is difficult to know if this is a acceptable value ornot. Still, the simulation provides a good order of magnitude.

Regarding the EV power, the error is larger. As was stated in last section, the measure-ment of the hot source mass flow rate is erratic, and could lead to large errors in the measuredEV power calculation. Therefore, it is very difficult to know if the simulated power is wrongor not. Nevertheless, all the computed powers are above the measurements. This couldmean that the factors of exchange area overrating are not relevant. However, without thesefactors, simulations results exhibit much larger errors and are completely underestimating

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Variables Model Results Measurements Relative errors [%]Mwf [kg/s] CF CF +7Qcd [kW] 16164 15537 +4Qev [kW] 3498 3269 +7Qpr [kW] 14825 14330 +3.45Tcs,out [◦C] 32.69 32.2 +1.5Wtu,el [kW] CF CF +6.2η [%] CF CF +2Ptu,in [bar] 15.9 16 -0.9Ptu,out [bar] 2.19 2.36 -7ηis [%] CF CF +3.9THS,out 111.19 147.33 -24.1xpr,out [%] 65.55 66.07 -0.8

Absolute errors [K]Tcd 35.85 38.07 -2.22Tvap 111.79 111.76 +0.03

Table 5.1: Comparison of the results of the simulation with the mean value of the measure-ments between 15:30 and 16:00 of November 21. CFstands for ”Confidential”.

the exchanged powers. Therefore, a factor should be used, but the one that was proposedfor this simulation might be exaggerated.

The produced electrical power value also exhibits a quite large error. This can come fromthe large error on Ptu,out, that is linked to the CD power error. The computed power beingtoo large, the condensing pressure is too low (indeed Tcd is almost 6% to low) and so is theturbine outlet pressure. The overestimation of the refrigerant mass flow rate, that is linkedto the overestimation of PR and EV power, also plays an important role. The simulated TU,PR and EV powers being too large, the individual effects cancel each other and it gives acycle efficiency that is very close to the measurement. Of course, this cannot be consideredas a sign of quality.

One can also observe a huge error on the hot source outlet temperature. To have abetter view of what is happening in the evaporator, the temperature profile is representedin Fig.5.11. As can be observed, the cell 1 seems to have a problem of pinch point. Thiscan also come from the fact that the EV design exchange area is too big and the outlettemperature is forced to be as small as possible. Indeed, the inlet temperature is an inputand the condensing temperature is fixed by the inlet pressure. Fortunately, the extremeerror on the outlet temperature does not impact the rest of the temperature profile nor theexchanged power because this cell represents a very small part of the HEX. However, even ifthe global quality of the results remains unchanged, the fact that the solver is searching fora THS,out that is almost equal to Tev,in is problematic. Indeed, the solver must iterate to finda solution that satisfies Aev = Aev,d without crossing the temperature profile. This leads to

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Figure 5.11: Evaporator simulated temperature profile on November 1 at 16:00.

an increase in the number of iterations and also decreases the robustness of the model.

The rest of the values exhibits acceptable accuracy compared to the measurements. Thecomputed vaporizing temperature and the EV inlet quality are very precise. One can alsoobserve that the TU inlet pressure is coherent with the measurement, contrarily to therefrigerant mass flow rate. This could mean that the turbine law is not correct. The latterwill thus be checked in the next section.

4.2 Second comparison point: December 7, 17:19

The second comparison point is at approximately 50% of the nominal load. The resultsare globally more accurate compared to the last point at 62% of load. The same conclusionabout the error on Qev can be drawn. Furthermore, one can again observe the same erroron the hot source outlet temperature, and the same order of magnitude of the error for Tcdand Ptu,out.

However, there is a big difference with the operating points of November 21 regarding theCD and PR powers. For those variables, the simulation is very accurate. This comes fromthe fact that the computed refrigerant mass flow rate is 3% more accurate than in the lastoperating point. This has a positive repercussion on the exchanged powers. One can alsonotice that the electrical power output is, in this case, surprisingly close to the measurement.

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Variables Model Results Measurements Relative errors [%]Mwf [kg/s] CF CF +4Qcd [kW] 12749 12598 +1.2Qev [kW] 2818 2637 +6.9Qpr [kW] 11545 11538 +0.1Mcs [kg/s] 343.63 338 +1.7Wtu,el [kW] CF CF -0.8η [%] CF CF -2.1Ptu,in [bar] 12.22 12.95 -5.6Ptu,out [bar] 1.88 1.99 -5.5ηis [%] CF CF +4.8THS,out [◦C] 99.9 135.7 -26.3xpr,out [%] 74.8 75.3 -0.7

Absolute errors [K]Tcd [◦C] 31.4 33.1 -1.7Tvap [◦C] 99.9 101.9 -2

Table 5.2: Comparison of the results of the simulation with the mean value of the measure-ments between 16:59 and 17:19 of December 7. CFstands for ”Confidential”.

4.3 Third comparison point: October 31, 00:00The third comparison point is at 30% partial load. This is very far from the nominal

point and larger errors are expected. However, despite numerous trials with all possiblecombinations of guess values, it was impossible for the solver to make the solution converge.

This can be explained by observing in the two last tables that the EV inlet quality isincreasing as the load is decreasing. At 30% of charge, the quality that is measured is at91%. This is an approximated value, and the real quality could be even greater. As can beseen in Fig.5.12, in the night between October 31 and November 1, the quality oscillatedmostly between 100% and 90%. The fact that the fluid at the inlet is near from vapour statemakes the solver crash.

Indeed, when the solver is looking for a solution, it is trying to solve the system by iter-ating on guess values. These values are usually near from the initial guesses. In this case,one of the iteration runs with a guess on the EV inlet quality greater than 1. This causesthe thermodynamic state calculation to crash and it stops the resolution.

It has been considered to detect when Xev,in,guess gets out of the range [0,1] and to re-place it by Tev,in if need be, with Tev,in,guess = Tsat,dew. But this is not sufficient to solvethe problem. Indeed, if a temperature is provided as guess, the solver will keep iterating onthis temperature. However, the guess on temperature being very close from the saturation

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temperature, the solver could ”jump” the two-phase state. In practice, the solver will trya solution with a Tev,in,guess slightly lower. Unfortunately, this temperature will correspondto a liquid phase at this pressure, causing the computed enthalpy to subsequently drop.This will lead to completely wrong computed powers, and thus wrong temperature profiles,ultimately causing the solver to crash.

Figure 5.12: Evaporator inlet quality versus time in the night between October 31 andNovember 1. The red point represents the considered operational point.

Without further improvements, this operational point thus remains impossible to solveand no comparison can be made. This demonstrates one of the weaknesses of the model.Simulating operational point with EV inlet temperature near to the saturation temperatureis problematic.

5 Part load laws discussionThe last section has highlighted some possible sources of errors. The error on Qev is one

of the largest. This can be a consequence of a wrong Aev,d overrating. The latter couldbe overestimated. Indeed, if Aev,d was decreased, it would lead to a lower EV power, andtherefore might solve the problem of THS,out. Nevertheless, if Qev decreases, so do Tvap andPtu,in, widening the gap with the measured values. Yet, one way to find a solution with adecreased Qev but an unchanged Tvap is to modify the way in which the exchange coefficientsare changing at part load. Moreover, the part load law was a really simplified equation anddeserves to be checked.

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Secondly, it has been observed in the first comparison point that an error could comefrom the turbine law. A modification of this law could completely change the behaviour ofthe simulation and lead to other results. It is thus also important to validate it.

This section is thus dedicated to two discussions about the turbine law and the HEXexchange coefficients law. The simulation equations will be checked, and improvements willbe investigated.

5.1 TurbineIn theory, it is very simple to check the validity of the turbine law. Based on the three

samples of data, a scatter plot can be drawn of the mass flow rate versus the inlet pressure.It is then easy to check if the approximated linear turbine law that is used (see Eq.4.5) fitsthe dots distribution.

As can be observed in Fig.5.13, in practice, conclusions are difficult to draw due to theuncertainty on the mass flow rate measurement. In the figure are represented the threesamples with the linear turbine law in black. For recall, the coefficients a0 and a1 arecomputed automatically to draw the black line. Their computed values in Eq.4.5 when Mis in kg/s and Pin in Pa are:

a0,auto = 0 (5.3)a1,auto = 22611 (5.4)

The blue dots represent the mass flow rate calculated thanks to CFD coefficients. Thismeans that, in this case, Mwf is computed with the same equation but with coefficients thatwere predicted by the CFD analysis. In practice, one has:

a0,cfd = 40000 (5.5)a1,cfd = 22370 (5.6)

The green dots represent the mass flow rate computed thanks to a power balance atthe turbine. The electrical power output being measured, one can obtain the mechanicalpower Ptu,mec by dividing it by the generator efficiency (approximated by its nominal effi-ciency). The in/outlet enthalpies being computed by mean of the in/outlet pressures andtemperatures, on can obtain the mass flow rate with:

M = Pmechin − hout

(5.7)

Finally, the red dots correspond to the measured mass flow rate. In fact, the measurementis volumetric and it must be corrected by the density (based on measurements of pressureand temperature).

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Figure 5.13: Turbine law check on the three different comparison points.

Several observations can be made on this figure. Firstly, the black line and the blue dotsare close, thus the coefficients a0 and a1 computed automatically are correctly approximatingthe CFD coefficients. The model of turbine is thus consistent with the CFD forecasting.

Secondly, the linear CFD law does not fit the calculated nor the measured mass flowrates. The mass flow rate seems overestimated by the CFD line. This effect gets more obvi-ous as the cycle load is getting further from its nominal value.

Finally, the calculated mass flow rate is most of the time larger than the measured one,and the difference is sometimes significant. In this context, it is difficult to know which valueis correct.

In order to improve the accuracy of the model results, an optimal turbine law has beenfitted on the measured values (the three samples being gathered in one plot). The result isrepresented in Fig.5.14. The yellow line represents the best fit in a least square sense. Theoptimal coefficients are:

a0,fit = 91100 (5.8)a1,fit = 23780 (5.9)

Using the simulation model with the optimal turbine law, one gets for November 21 theresults displayed in Tab.5.3. The results are mitigated. One one hand, one can observe agreat improvement in the computed value of the refrigerant mass flow rate. Nevertheless,it goes along with a turbine inlet pressure that is further from the measurement. This canmean two things. Either the measurement of the refrigerant mass flow rate is not reliable(and the adjusted turbine law is still not relevant), or the improvement of the turbine law isnot sufficient in itself to obtain very precise results. Other improvements needs to be added.

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Figure 5.14: Turbine law fitting on the measured values of the three samples.

For example, on can observe that the same kind of errors on EV power and hot source outlettemperature are still observable. Nevertheless, the correction of the turbine law globallyimproves the accuracy.

5.2 Heat exchangersIt is very difficult to make experimental analysis on HEX exchange coefficient without

having a completely instrumented HEX. In this ORC, the only variables that are measuredare at the in/outlets of the STHEX. Therefore, it is impossible to have an idea of the precisevalue of the real exchange coefficients.

However, if a quantitative analysis cannot be carried, a qualitative one is still possible.Indeed, a global LMTD can be computed with the measurements at the in/outlets of theSTHEX. Therefore, a global exchange coefficient based on the nominal total exchange areafrom the datasheets can be deduced. This approach is rather gross because, in the LMTDmethod, the heat capacity is not supposed to vary. Therefore, this method might not giveusable exchange coefficients, but it could give an idea of the evolution of the latter withrespect to the mass flow. This way, one could draw conclusion to validate or not Eq.4.14.Indeed, this equation was a grossly simplified approach, and could give totally wrong results.

The analysis is carried at the condenser, because it is a more standard STHEX than the

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Variables Model Results Measurements Relative errors [%]Mwf [kg/s] CF CF +2.2Qcd [kW] 15436 15537 -0.6Qev [kW] 3480 3269 +6.45Qpr [kW] 14075 14330 -1.78Tout,cs [◦C] 32.16 32.2 -0.1Wel [kW] CF CF +4.4η [%] CF CF +4.7Ptu,in [bar] 16.88 16.04 +5.2Ptu,out [bar] 2.22 2.356 -5.8ηis [%] CF CF +4.7THS,out [◦C] 114.6 147.33 -22.2Xpr,out [%] 63 66.1 -4.6

Absolute errors [K]Tcd [◦C] 36.3 38.1 -1.8Tvap [◦C] 114.6 111.76 +2.84

Table 5.3: Comparison of the result obtained with the optimal turbine law with the mea-surements of November 21. CFstands for ”Confidential”.

evaporator and preheater. The global exchange coefficients are thus computed the followingway:

Ucd,global = Qcd,measured

Acd,datasheet ∗ LMTDmeasured

(5.10)

The results with the three samples are represented in Fig.5.15. In this figure are com-pared the measured U (the blue dots, calculated with Eq.5.10) with the exchange coefficientsthat would have been obtained thanks to Eq. 4.14 (the red and green curves). The Ud fromEq. 4.14 has been computed with the nominal LMTD, the power from section 5.3 and theexchange area from the datasheets. The green and red curves are obtained with differentCHEX . The green curve corresponds to CHEX = 0.785, the value used when a phase changeoccurs in the cell. The red stands for CHEX = 0.645, the value of no phase change.

Surprisingly, the evolution of U is not so badly predicted by Eq.4.14. As usual, the ap-proximation gets worse as the operational point is getting further from the nominal point.Still, both curves are quite well in accordance with the scatter plot, considered the simplicityof the law. If the data are gathered, an optimal law can be fitted, as for the turbine law.This is represented in Fig.5.16. The best coefficient in the least square sense is CHEX = 0.69.The optimal curve is placed right between the two previous curves.

Changing the CHEX in the simulation for the optimal value is not necessary. Indeed,as can be seen in Fig.5.16, the value of the exchange coefficient will barely change and the

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Figure 5.15: Exchange coefficient part load law check with the three samples.

Figure 5.16: Exchange coefficient part load law fitted on the measurements.

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results will be quite similar. Therefore, to improve the simulation model results, it shouldbe considered either to change completely the exchange coefficient law into something morecomplex, or act on another variable.

With the assumptions that have been made to conduct this analysis, definitive conclusionscannot be drawn. One must be careful with the validity of the approach. However, theresults tend to prove that Eq.4.14 provides a rather good approximation of the evolution ofthe exchange coefficient. If a simplified law has to be used, the proposed equation (with theproposed coefficients) seems to be a quite good compromise.

6 ConclusionIn the light of the above analysis, the model can be criticized and discussed. This

conclusion is divided in two parts. First, the model forces and weaknesses will be objectivelyhighlighted. Then, possible improvements will be suggested and solutions to some issues willbe proposed.

6.1 Model forces and weaknessesThis model review will be based on the model objectives stated in section 1 of Chapter

2. The achievement of those objectives will be discussed one by one.

• Possibility of design and simulation: Indeed, the model is well divided in twoparts. The two modes are implemented and work perfectly in combination with eachother. It results in a model that is more global and that could be a good tool formanufacturers.

• User friendliness: All along the model implementation, particular attention hasbeen devoted to use simplified correlations that do not require too much upstreaminformation research. This is an advantage and a drawback at the same time. Indeed,the model is quite easy to use, which is a good point for any manufacturer. However,the simplifying assumptions and some correlations used can seem gross and can leadto a limited accuracy.It should also be reminded that an interface has been developed for an easy usage of themodel. The interface will not be described in this work but a user-guide is presentedin the appendices. It is designed for the ”everyday” usage of the model and is veryconvenient. But even without the interface, the code has been written in a way whichis meant to be easy to understand and to use. The object oriented structure and thepython language makes it clear and readable.

• Robustness: The design model is very robust, even with the nested solver structure.Most of the time, the automatic guesses are sufficient to make it run without failure.However, it is possible that, if the pinch point is provided as input for CD and EV,

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Figure 5.17: Robustness test of the model. Representation of the number of iterationsnecessary to solve the model with a given guess value. Each graph represents the test withonly one of the guess value that changes.

the automatic guess variables are not sufficient. One should therefore impose themmanually.

For the simulation model, convergence is trickier to achieve. The problem being morecomplex, the solver is more sensitive to the guess values. Still, the solver is most of thetime quite robust. The ORC analyzed in this chapter is not a good example, becauseof the hot source outlet temperature problem. Nevertheless, the model has been usedto simulate other cycles than the one presented here and has shown a good flexibilityregarding the guesses choice. In general, the more complex the temperature profiles,the more difficult it is to solve the problem. The robustness really depends on theproblem and will be different for every project. For standard ORC cycle, the modelconverges easily.

In order to have an idea of the robustness of the model, several simulation of the ORChave been carried out with different guesses. To get rid of the THS,out issue, it hasbeen decided to use the datasheet areas as nominal areas for the simulation, becausethey are smaller than the ones used in this chapter. The rest of the inputs are thesame as in the simulation for the 7th of December at 16:00 (second comparison point).The result is depicted in Fig.5.17. The three guess variables are tested independently.The range of the graphs is the range in which convergence could be reached given atolerance of 1e−8 with the hybrid solver method. The red dot on the figure correspondsto the exact value of the solution. Imposing the guess at its right value will logicallyresult in the best convergence rapidity. It can be seen in the figure that the guessescan be included into a quite wide range. Of course, if the guesses are not changedindividually, the result will be different and the robustness is difficult to quantify.

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• Accuracy: The resulting precision comes in this case from a compromise between theeasiness of use and the complexity of the correlations. The user-friendliness has beenemphasized, so that the model could be a real convenient tool for industrial. However,this is achieved at the expense of the accuracy.Nevertheless, this being considered, the model is quite reliable and can provide goodorders of magnitude in simulation and in design. Yet, it is very difficult to have a goodidea of the real accuracy of the model. Indeed, as discussed, the sensors accuracy is notwell known. Moreover, a more complete database would have been necessary to confirmthe conclusions. Indeed, the simulations have been conducted on this particular caseonly. Other configurations should be tested, to see the real potential of the model. Moreoperational points could also be tested to check if the observed accuracy is reproducible.Also, the overrating of the HEX makes the model more difficult to apply rigorously.

• Versatility: This objective is totally achieved. Not only the model can be usedfor simulation and design problems, but it is also applicable to the 5 most commoncycle configurations that can be met on the market. Furthermore, it also contains aMBM that is very well working and that allows to use the model even with very exotictemperature profiles. Finally, the most convenient input options has been implemented.The tool that has been developed is thus very versatile and general, and is applicablefor a very wide range of medium to large scale ORC projects. The model also offersthe possibility to use either Refprop or Coolprop. However, during the different teststhat have been carried out, the Refprop library has been proved to be less robustthan its rival. Indeed, it can have some problems with the evaluation of the turbineoutlet isentropic enthalpy based on the entropy and pressure. It is thus better to useCoolprop.

• Easiness of improvement: Thanks to the object oriented structure, it is very easyto implement further developments to the model. This will be explained in the nextsection.

Globally, the model fulfilled its initial objectives. Nevertheless, it is obvious that it canbe improved in many ways, especially concerning the accuracy. The possible improvementsare developed in the next section.

6.2 Possible improvementsThere is a fundamental improvement that must be implemented in order to have a really

physically correct model. Instead of the subcooling, the total mass of fluid in the cycle mustbe provided as input. To this purpose, a complete analysis must be carried in order todevelop an accurate model of mass computation in STHEX. The spatial distribution of thedifferent phases must be better determined and the void fraction correlation must be testedto check its accuracy.

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Of course, this is not the only thing that can be improved. One should neverthelessbe cautious when changing the existing code in the model. Indeed, it could happen that amodification of an object makes it incompatible with the other objects or with the globalmodel in which it is included. Nevertheless, there are several ways to ”safely” improve themodel thanks to the object oriented structure. Each of them will be described with precisepropositions of improvement:

• Creation of new cycles with the existing classes: One easy way to complete themodel is to use the existing objects into new configurations. One could for examplebuild a double-stage cycle with the existing components. If we take a wider point ofview than ORC, it could also be possible to create a heat pump with some of theexisting objects.

• Adding new component classes: Adding new components will never compromisethe existing codes. For example, the model could be completed by a dedicated modelof hot/cold source. In these new components could be computed the state of the fumesin the chimney, the pump power in the secondary loops, the consumption of the air-condenser,etc. But a multi-stage turbine object could also be created for regenerativerankine cycles.

• Adding new methods in the existing classes: It is also completely safe to addnew methods without touching the existing ones. A lot of improvements could be donein this way. For example, a big assumption is the fact that the pressure drops in thecycle are imposed and kept constant in simulation. This is of course false in practice.One could add a method to the STHEX or the pipes to compute the pressure drops,given the flow pattern and the geometry of the component. One could also add a newmethod aside from the MBM in the HEX classes to compute the state of the fluid incase of super-critical cycle. New methods can also be added in the turbine and thepump to get into more details in terms of operating regimes and geometry. This couldhelp in the evaluation of the mass of fluid trapped in the components.

• Slight modification of existing methods: It is also possible to change some lit-tle details or to add some equations to the exiting methods. Some equations mightdeserve to be improved. As previously said, the part load laws seem to provide goodapproximation with rather simple equations. However, if more accuracy is needed,these equations should be replaced by better performing ones, with more inputs andthat require a better knowledge of the HEX geometry.

• Adding new correlations to the dedicated library: The correlations that areused in this model (for the correction factor of the LMTD, the ε−NTU method, thevoid fraction determination,etc.) were gathered in a library. New correlations thatcould provide more precise results for specified HEX can be added in order to computemore exactly the exchange area or the mass of refrigerant. It could also be useful toadd in this library a method that could provide the nominal exchange coefficient of a

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HEX in the different phase configuration, given the nominal conditions and the HEXgeometry. This way, one could avoid using standard U values and being obliged tokeep the AU product consistency instead of using the A and the U independently.

The solver performances could also be improved. No bounded solver has been imple-mented here, but it is a possibility to investigate. It could help the solver to not go intodangerous zones, like the one that was met on the third comparison point. One could alsoconsider changing the guess variables in order to avoid this problem. For example, theevaporator inlet enthalpy could be the iteration variable instead of the temperature or qual-ity. But in this case, the guess variable is less intuitive and would be more difficult to choose.

For now, the model has been presented and confronted. To complete the analysis of it,it is important to show its capability through an industrial application. This is the purposeof the next chapter.

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Chapter 6

Model application on a geothermalORC with air-condenser

In this chapter, the model will be used to answer to a practical issue about a geothermalORC with air-condenser. The purpose of this case study is to show the capabilities of themodel and to propose an example of application.

First, the problem that is faced is described. The approach that was adopted to solveit using the model is presented in the second section. In a third part, the results obtainedusing this approach are analyzed in order to find the best answer to the initial question.Finally, conclusion about the global approach and the results are drawn.

1 Problem descriptionA project of a geothermal ORC working with R245fa in C1 configuration is to be studied.

The hot fluid could enter the EV at 185◦C and 1.6 MPa with a mass flow rate of 95.47 kg/s.The heat that should be dissipated at the condenser is about 41 MW. The global view ofthe nominal point of the cycle is presented in Fig.6.1, with its T-s diagram.

The heat sink would be the ambient air. The R245fa would be cooled in an air-condenser.According to the mean ambient temperature at the site location, the nominal heat sink inlettemperature has been set at 10◦C. The fans of the air-condenser should thus produce a highmass flow rate of more than 2700 kg/s to dissipate the heat in case of an air temperaturerise of 15 K. However, to produce such a mass flow rate, the fans must consume electricalpower. Yet, in a geothermal power plant, the CAPEX is usually important and the price ofelectricity is also very high thanks to green energy policies. It is therefore very importantto produce as much electricity as possible. Moreover, the power will obviously also fluctuatewith the ambient temperature. In summer, the cycle might not be able to produce as muchpower as in winter. Should the air mass flow rate be changed in this case?

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Figure 6.1: Nominal operational point of the geothermal cycle and T-s diagram representa-tion.

In this context, how should the fans be controlled in order to produce as much electricityas possible yearly? Indeed, if the fans consumption rises, the air mass flow rate increases aswell as and the power released by the working fluid in the condenser. The condensing pres-sure thus decreases and the power production at the turbine rises, all other things remainingequal. The question is thus: is it economically interesting to pay more in fans consumptionto produce more electricity?

The goal of the analysis is thus to find out what would be the best way to control the fansspeed in order to retrieve the most electrical power from the cycle. The adopted approachto answer to this question is presented in the next section.

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2 Adopted approachA model of air-condenser is obviously needed to solve the problem. The analysis being

purely quantitative, a simplified model is sufficient. Moreover, numerous simulations have tobe carried and the model must not be slowed down by heavy calculations at the air-condenser.

First, the volume flow rate Vair can be computed thanks to the nominal mass flow rateMair and the mean air density ρ. Considering a given nominal fans consumption Wfan,d

and a fans efficiency ηfan, provided as inputs, the pressure drop across the fans can beapproximated by:

∆P = Wfan,d ∗ ηfanVair

(6.1)

The air speed vair can be deduced with the simplified equation:

vair =√

2 ∗∆Pρ

(6.2)

Finally, the cross-sectional area of the air flow Afan can be calculated with:

Afan = Vairvair

(6.3)

Substituting ∆P from Eq.6.1 to Eq.6.2 and vair from Eq.6.3 to Eq.6.2 gives an equationthat links the power consumption to the air volume flow rate thanks to the nominal crosssectional area:

Vair =(

2Wfanηfanρ

∗ A2fan

) 13

(6.4)

The nominal fans consumption has been set at 270 kW for the considered design massflow rate, with an efficiency of 90%. This results in a pressure drop of 109 Pa, an air speedof 13.3 m/s and a nominal Afan of 166 m2.

This nominal Afan is an input of the simulation model. Considering that the fans effi-ciency does not vary much until a certain part load, ηfan is considered constant regardlessof the operation point. Two different strategies of fans control are compared:

• The fans consumption remains at its maximum value: The goal of this strategyis to produce as much power as possible, regardless of the ambient temperature, witha constant fans consumption of 270kW. The nominal cross-sectional area remainingthe same, the volume flow rate can be determined with Eq.6.4. Thus, the only thingchanging with time is the heat sink inlet temperature and the mass flow rate. Theimplemented simulation doesn’t even need any modification.

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• The condensing pressure remains at its nominal value: In this strategy, thepower consumption of the fans decreases if 270kW are not needed to maintain thecondensing pressure at its nominal value. To compute this, the simulation model hasto be modified. The condensing pressure becomes the new input instead of the heatsink mass flow rate and the heat sink mass flow rate becomes the iteration variableinstead of Tcd. Once the system has converged and the right mass (and thus volume)flow rate is found, the fans consumption can be computed by reversing Eq.6.4. Ofcourse, the fans consumption can only be lowered if the ambient temperature is lessthan 10◦C. If Tamb ≥ 10◦C, the problem is the same as in the first strategy because thefans are limited by their maximum performances. The same calculation as in the firststrategy will then be used.

To have a clear comparison of the two strategies, all the other inputs than the ones men-tioned above are kept constant, including superheating and subcooling.

To solve this kind of problem, it is very useful to have a model that can be coupled witha database. Indeed, with Python, contrarily to EES, it is very easy to implement a loop thatwill launch the simulation thousands of times, using the hourly ambient temperature profilealong the year that available in an Excel file. This is also one of the forces of this model.

However, an issue still needs to be solved. If the system is launched thousands of times,with inputs varying quite strongly, how is it possible to set guesses that ensuring convergencefor any operating point? The key is actually to implement in the loop an algorithm thatwill find a reasonable guess for each simulation. Considering that the temperature is notexpected to change much from one hour to another, the first approximation of the guess isto use the result of the last iteration. This works pretty well, but it still fails for some pointswhen the temperature suddenly drops or rises. In this case, the algorithm tries to increaseor decrease the guess (depending on the temperature variation from the last iteration) stepby step until the system converges. It should be noted that, even with these precautions,the system still fails sometimes. The guess has then to be imposed manually.

3 ResultsThe main difference between the two strategies is the heat sink mass flow rate. In the

Fig.6.2 are represented the heat sink mass flow rate along the year with the two differentstrategies. If the fans power consumption is kept at 270 kW, the red curve is obtained. Themass flow rate is quite constant and only changes through the air density variation. If thefans power is adapted to keep Pcd constant, the mass flow rate varies strongly, as shown bythe blue curve. This section aims to investigate the impact of the heat sink mass flow rateand inlet temperature changes on the cycle behaviour and performances.

First, let’s compare the temperature profiles obtained with the two different strategies,represented in Fig.6.3. The right side diagram shows the results when the maximum fans

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Figure 6.2: Mass flow rate variation using the two different strategies.

power is kept constant. The ambient temperature (thus the heat sink inlet temperature) isrepresented in yellow. The time scale starts on January 1st and covers the whole year, sothat the differences between the winter and the summer regimes are easy to observe. Theblue line is the condensing pressure and it clearly follows the ambient temperature trend.The vaporizing temperature (in red) is also almost constant. The variation of the latter canonly be seen with a zoom on the curve. Nevertheless, the hot source outlet temperature(in green) fluctuates during the year. Indeed, if the condensing temperature changes, thesubcooling being imposed, the evaporator inlet temperature will change as well. The hotsource inlet temperature and mass flow being fixed, the power exchange will be reinforced(or diminished) and the hot source outlet temperature will decrease (or rise).

The left side figure illustrate the results obtained if the condensing pressure is kept con-stant by adjusting the fans power. As can be observed, the results are actually quite similar.This comes from the fact that the ambient temperature is very often greater than the designtemperature of 10◦C. Therefore, the fans power is set at its maximal value and the problemis the same as on the right graph. As can be seen, the condensing pressure (in blue) ismaintained mainly during the cold months. One can also notice an error in the value of Tcdand Tvap around t = 8250h. These are neither physical values nor solver failure. They justcomes from mistakes in the dealing of the results files.

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Figure 6.3: Temperature regimes during the whole year using two different strategies.

The best strategy being the one that will allow to obtain as much electricity as possible, itis necessary to compare the power produced and the power consumed. The power producedby the turbine is represented in Fig.6.4 on the right side graph.The power consumed by thefans is shown in the left side figure. As can be observed, the fans consumption can be muchreduced in winter if it can be adapted. But during a big part of the year, the consumption isat 270 kW anyway. When Pcd is constant, nothing changes in the cycle and thus the powerproduction is also constant. Otherwise, the production fluctuates accordingly to the outlettemperature variations. During the summer, the production decreases because Pcd rises.The fans being at maximal power, the blue and red lines are superimposed on each other.

Using these data, one can obtained the performances of the cycle by mean of integration.The results are summarized in Tab.6.1. As expected, the constant Pcd strategy allows thefans to consume less electricity (annual gain of 693 MWh annually). This comes mainly fromthe cold months, as can be observed in the table. However, the gain in electricity productionof the turbine with the maximal fan power compensates this over-consumption. Indeed, thenet electricity production is 1225 MWh less important for the constant Pcd strategy. Thus,it seems better to purchase fans that will constantly work at their nominal speed and powerconsumption. However, the fans are only working at maximal power consumption during53% of the year with the constant Pcd strategy. It could thus be interesting to change thedesign value of the cycle to see if this conclusion would be the same with larger fans.

If the design value of the heat sink inlet temperature is set at 15◦C, everything else being

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Figure 6.4: Consumption and production of electricity: comparison of the results obtainedwith the two strategies.

equal (including Wfan), the nominal Afan becomes 308 m2. The fans size is almost doubled.Using this new value in the simulation, different results are obtained.

First, as can be noticed in Fig.6.5, the power consumption of the fans further decreases(in constant Pcd strategy) if the design ambient temperature is 15◦C. In this case, the fansare less often at their maximum value (34% of the year).

Then, the power production curves can also be compared. As can be seen in Fig.6.6,a design ambient temperature at 15◦C allows to produce more power in the constant Wfan

strategy. Indeed, Afan being larger, the volumetric flow rate is higher. The refrigerant isthus cooler and Pcd decreases and the production of the turbine rises. The same conclusioncan be drawn in the other strategy when Tamb ≥ 15◦C. One can also notice that the powerproduction can be kept constant more often with the design ambient temperature at 15◦C.

The electrical energy produced and consumed during the year are displayed in Tab.6.2.For the constant Wfan strategy, the fans consumption naturally remains the same. Theproduction is nevertheless increased by 3478 MWh annually. For the constant Pcd strategy,the turbine production also increases by 2065 MWh. The fans consumption decreases by581 MWh. Globally, the net production increases in both cases, but gains are larger for theconstant Wfan strategy. Therefore, the conclusion is the same as for the design at 10◦C: the

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Results [MWh]Strategy Constant Pcd Constant Wfan

Fans consumption (Annual) 1672 2365Fans consumption ([March;August]) 1109 1182Fans consumption ([September;March]) 563 1182Turbine production (Annual) 62076 63994Turbine production ([March;August]) 29693 29827Turbine production ([September;March]) 32383 34167Net production (Annual) 60404 61629

Table 6.1: Consumption and production of electricity: comparison of the results obtainedwith the two strategies.

Results [MWh]Strategy Constant Pcd Constant Wfan

Fans consumption (Annual) 1672/1091 2365/2365Fans consumption ([March;August]) 1109/893 1182/1182Fans consumption ([September;March]) 563/198 1182/1182Turbine production (Annual) 62076/64141 63994/67472Turbine production ([March;August]) 29693/31424 29827/31879Turbine production ([September;March]) 32383/32716 34167/35592Net production (Annual) 60404/63049 61629/65107

Table 6.2: Consumption and production of electricity: comparison of the results obtainedwith the two strategies. Results in blue/red corresponds to design ambient temperature(Tamb) at Tamb =10◦C /Tamb =15◦C

constant Wfan strategy performs better. 2057 MWh can be saved annually by choosing thisoption with a design ambient temperature at 15◦C.

4 ConclusionIn conclusion, the best strategy is to maintain the maximum power at the fans to lower

the condensing pressure as much as possible in order to produce more electricity at the tur-bine. The price of the fans electrical consumption is worth to be paid. Of course, this resulthas been obtained with the assumptions explained in Section 2 and can thus be criticized.Moreover, let’s remember that subcooling and superheating are fixed in the simulations. Thiscauses no trouble when Pcd is kept constant. However, when the condensing pressure varies,subcooling is supposed to change according to the mass of fluid in the cycle. To be sureof the validity of the conclusion, one should carry the same analysis with a charge-sensitive

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Figure 6.5: Electrical power consumption of the fans for a design ambient temperature at10 and 15◦C in the constant Pcd strategy.

model.

The choice of the design of the air-condenser is in reality much more complex than thesimplified approach adopted here. Indeed, it depends on many other variables than the crosssectional area and the nominal consumption. In practice, a complete technico-economicanalysis must be conducted. However, this kind of simplified model can still help in findinganswers to specific questions, like the ones considered in this chapter. Moreover, carryingthis kind of analysis can lead to useful results than can be reused after. For example, theanalysis allows to highlight the relation between the ambient temperature and the powerproduction, everything else remaining constant. This relation is represented in Fig.6.7 forthe two design temperatures and the two strategies. This curve profile can then be reusedto answer to other questions the manufacturer may have without launching any simulation.

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Figure 6.6: Electrical power production for both design design temperatures and both strate-gies.

Figure 6.7: Electrical power production for both design temperatures and both strategies.

This chapter presented one of the many possibilities offered by the model. This particularapplication has been chosen to highlight the ease of using the model into a loop to answera specific problem. The use of Python instead of EES allows to launch easily hundreds ofsimulations to solve optimization and control problems. Of course, this is only one of themany applications that can be made with the model and its whole potential of it could not

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be completely presented in this thesis.

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Chapter 7

Conclusion

1 Overall retrospective of the modelThe model presented in this paper is able to design and simulate medium to large scale

Organic Rankine Cycles (ORC) with shell and tubes heat exchangers in different configura-tions. It allows to add a recuperator and/or a preheater in parallel or in series. In designmode, the calculations are based on the condensing/vaporizing temperatures or the heat ex-changer pinch points, the superheating and subcooling, the hot/cold sources specifications,the pump/turbine efficiencies and the pressure drops in pipes and heat exchangers. The sim-ulation mode uses the cold/hot sources inlets and the mass flow rates, the superheating andsubcooling, the pressure drops and the nominal heat exchanger exchange areas. Those ar-eas can be computed in design mode if appropriate global exchange coefficients are provided.

The part load equations that have been used are rather simple in order to obtain auser-friendly tool that does not require too much upstream research or information to getacceptable results. Of course, this implies a limited accuracy. In the analysis carried inChapter 5, the model exhibited sufficient precision after the turbine part load law calibra-tion. However, if more accuracy is needed, it is necessary to develop some new methods thatwill go into more details concerning the shell and tubes heat exchangers. Still, it has beenshown that the turbine part load law and the exchange coefficient part load laws providerather good order of magnitude, considering their apparent simplicity.

The Moving Boundary Model that has been implemented allows to simulate almost alltemperature profiles. Nevertheless, it has been demonstrated that the present model is some-times not able to simulate operational points corresponding to a fluid entering or leavinga heat exchanger near to saturated state. Moreover, in the considered ORC, the modelreturned a completely wrong hot source outlet temperature. This comes probably from anoverestimation of the nominal exchange area and of the complex shape of the temperatureprofile. In other ORC simulations made for Enertime (but not developed in this paper), thisproblem never appeared.

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The model is in general quite robust. In simulation mode, the choice of the guess valuesis usually flexible, except for very exotic temperature profiles. In design mode, the automaticgeneration of guess values works well and the computation hardly ever fails. Nevertheless,the nested solver structure can lead to long computational time and it should always bepreferred, when possible, to use the condensing/vaporizing temperatures instead of the heatexchangers pinch points.

Of course, the model needs further improvements. Its main weakness is the use of subcool-ing instead of the mass of refrigerant in simulation mode. This choice was justified becausethe mass of refrigerant was not known and was very difficult to determine. However, solvingsimulations in this way is not physical and this weakness must be considered when usingthe model. Among other possible improvements, one can also mention the pressure dropscomputation in the different components and the exchange coefficient computation in shelland tubes heat exchangers.

It should also be noted that the database used for the model validation was quite poor.Indeed, the sensors were not especially installed at the optimal location to validate the model.Moreover, the choice of operational points in the available data was quite restricted due tothe fact that it is very difficult to find a stable point. Also, no data base were available fornominal operational point, making it impossible to evaluate the heat exchangers overratingconsequences on the nominal conditions. Finally, the precision of some sensors still remainedunknown. Therefore, the model should be confronted to another case study to confirm theconclusions of this paper. Especially, it could be interesting to test the model on a regener-ative cycle in order to check if it still works well in other ORC configurations.

The possible applications of the model are numerous. It is therefore impossible to presentall its potential uses in this document. An example of problem resolution has been proposedin Chapter 6, but it is far from being the only possibility of the model. Using the model inother situations is important to check the good functioning of every features and to propose,if needed, further improvements.

2 AcknowledgementsI would like to thank all the members of Enertime for their welcome in their team. I

couldn’t expect such a better first experience for an internship. I really enjoyed the groupatmosphere and the dynamism of the company (not to mention the wild table soccer games).

More especially, I’m grateful to Hayato Hagi, Benoit Obert and Evgueni Touliankine fortheir availability and their help for any questions I had. Of course, I also warmly thank LeaVerge, my industrial supervisor, for guiding me through the project and for her pertinentadvice in any situations. It was really great for me having in the same time such a flexible

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way of working and a permanently available help and guidance from her. I wish other internsto work with Lea in the same conditions as I did.

A special thanks goes to Pr. Vincent Lemort, who gave me the opportunity to work atEnertime and helped me in the realization of this Master Thesis. From the ThermodynamicLaboratory, I also wish to thank Remi Dickes for the documents and information he providedto me about ORC modelling.

I also warmly thank all the friends I made in the Cite Universitaire of Paris, who mademy stay a real pleasure.

Finally, I am very grateful to my relatives for their support during the redaction andtheir attentive reading of the paper. Without them, this document would probably be anorthographic mine field.

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Appendices

1 Interface user GuideThe interface of the model has been developed with the dedicated open-access library

wxPython. It is split into two different windows: one for the cycle design and the other forthe simulation. This appendix is dedicated to the description of these windows. First, theobjective of the interface is reviewed. Then, a description and a user guide of the designwindow is proposed. Finally, the same thing is done for the simulation window.

1.1 Objective of the interfaceThe model that was presented in this paper is written in Python 3.4 on Eclipse. How-

ever, the model user may not know how to code in this language. Moreover, it is sometimesquite difficult to comprehend and use someone else’s code. This is the fundamental reasonfor the need of an interface. It has to allow anyone to interact with the model in a clear andrelevant way.

Another reason is that the model will be used mainly to answer everyday questions. It isthus interesting to have a tool from which one can get rapidly the answer for any questions,without manipulating the source code. It is also a safety measure because the code of themodel does not change when the interface is used.

Finally, in such a large model involving a lot of variables and features, it is important tohave a complete and clear display of the results of the calculations. This way, the user caneasily target the source of a problem and can rapidly have access to the information he islooking for.

1.2 Design windowWhen the application is launched, the first thing that pop on the screen is the Design

window, represented in Fig.7.1. It is divided in several parts that will be explained indepen-dently.

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Figure 7.1: Global Design window.

Configuration choice

In the top left of Fig.7.1 appears the cycle configuration choice. A zoom of it is proposedin Fig.7.2. It is the first thing to select before entering any input. Indeed, the window contentwill change accordingly to the chosen configuration, as the inputs are different in each ofthem. A scheme of the configuration is proposed in order to have a visual representation ofthe cycle.

Figure 7.2: Cycle configuration choice.

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Option choice

The next inputs to give to the interface are in the box in the bottom left of Fig.7.1. Azoom is once again proposed in Fig.7.3. In this figure appear the options referring to a C5cycle. Again, other options can appear if a different configuration is selected. Clicking on thegrey buttons gives access to the different possibilities for computing the cycle. For example,clicking on the option that relates to the evaporator specification gives the possibility toprovide the vaporizing temperature, the vaporizing pressure or the EV pinch point as input.In the white box, the user must write the corresponding value in the corresponding unit. Ascan be observed, there is an Explain me button in the bottom right of the figure. This kindof button will appear in other places of the interface to provide further explanation aboutspecific options when relevant.

Figure 7.3: Design input options.

Inputs

The largest part of the Design window is taken by the input box, represented in Fig.7.4.It contains all the inputs that the user needs to provide in order to compute the cycle. Theyare classified according to their referring component. They are represented by their names,their values (in the white boxes) and their descriptions (including the unit).

As can be observed, some variables have two names, like the first one for example. Itmeans that two different variables can be given. In the example of the first variable, the user

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can enter in the white space the value of the EV inlet temperature in Kelvin or the valueof the inlet quality in % if the inlet is two-phase. The solving algorithm will automaticallydetect if it is a quality or a temperature depending on the provided value.

One can also see an Ignore button above the preheater inputs. By clicking on it, the solverwill compute the cycle as if the preheater was not there. This allows to easily compare anycycle with or without the preheater, without having to duplicate the cycle in another con-figuration. The same option exists on the recuperator, if relevant.

On the right of Fig.7.4 appear the exchange coefficient matrices. They must be completedlike presented in Fig.3.15.

Figure 7.4: Design input options.

Buttons

By scrolling the Design window, one can access to buttons that facilitate the use of theinterface. They are represented in Fig.7.5. Each of them will be described hereafter, fromthe left to the right.

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The Compute button triggers the solving algorithm of the cycle with the given inputs.First, the solver will check if the inputs are consistent. Indeed, the user might choose awrong option, use wrong units, leave some inputs empty, enter negative values for the pow-ers, etc. If something is wrong, a message appears to help the user to correct the mistake.Then, the solver computes the cycle itself. If something goes wrong (like a not computablethermodynamic property), a message appears with the error source. This might happen forinstance if the user imposes super-critical conditions. If everything works fine, a new tabcontaining the resulting cycle is opened.

The Save Inputs button allows to save the inputs of a cycle in a file at a chosen locationon the computer. The file will be saved under a ”.C5” format in this case. The next buttoncan load the inputs of a previously saved cycle. If the configuration selection is on 5 forinstance, only the ”.C5” cycles can be loaded. This is very useful for the everyday use of themodel but also for working on bigger projects.

As can be observed in Fig.7.4, there are a lot of inputs to provide. Some of them are notespecially known or are not very interesting in a first computation (like the length of thepipes). By clicking on the Default Parameters button, these inputs are filled with standardvalues, so that the user can focus on relevant variables.

Finally, the New Model button simply opens a new tab in the Design window like theone in Fig.7.1. The user can thus work on two designs in parallel.

Figure 7.5: Design buttons.

Result tab

The results tab is divided in 3 parts. The first one is dedicated to the display of theglobal results, like represented in Fig.7.6. A large representation of the cycle is filled withcorresponding values and variables. It is important to have such a representation to clearlyidentify the relevant information. It also helps to spot the possible issues of the computedcycle. As can be observed, a pie chart of the working fluid mass distribution is also provided,as well as a T-S diagram.

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Figure 7.6: Global results display.

Figure 7.7: HEX results display.

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Under the global results are displayed the details of the HEX moving boundary model.As can be seen in Fig.7.7, the temperature profile, the State Matrix and the Zone Matrix ofeach HEX is given. If further details are needed about the cycle, the complete list of all thevariables with their raw values is also accessible in the results tab.

In the result tab, two buttons are also available. The first one just closes the tab. Theother one gives access to the Simulation window. This means that the computed cycle in thedesign window will be the basis of the simulations that will be described in the next section.

1.3 Simulation windowAs previously said, the Simulation window can be accessed when a design is computed.

The window is represented in Fig.7.8. It is divided in different boxes that are explainedhereafter.

Figure 7.8: Simulation window.

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Design variable box

This list of variable is automatically filled when the window opens. It contains everydesign values that will be used in the part load laws of the simulation. It also contains thevariables that will be used to compute the residuals. The value of those variables are notfixed, and can be changed in any simulation. If they are modified, the simulation will notrelate to the designed cycle anymore.

Parameter box

This list contains all the parameters that are considered constant from design to simula-tion, due to simplifying assumptions. For instance, the pressure drops are in this box. Onceagain, this list is automatically filled, but it can be changed at any time.

Option box

Like in the design window, the user can choose between several input options. Theseoptions are almost the same as in the design window. A turbine law option and a solveroption have been added. It offers the possibility to impose a0 and a1 manually or to computeautomatically. The solver option allows to choose the solver algorithm and tolerance.

Guess box

The guess box is right under the option box and it obviously contains the iterative variablenames and their initial values. Some buttons were added to help the user to impose relevantguesses. Automatic Guesses imposes automatically initial values based on the hot and coldsource temperatures. This method does not always succeed. The button Update Guessesimposes as initial values the resulting iterative variables of the last simulation. This is usefulwhen the user wants to simulate operational points close to each other.

Input box

The input box contains the rest of the fundamental inputs of the simulation or the inputsneeded in the part load laws (like the different coefficients).

Button box

The same buttons as in the Design window are available in simulation, except that thebutton Compute is now the button !! Solve !!. Two new buttons also appear in the list.The first one is the Reload Cycle button, which automatically fills the first two boxes withthe values of the referring design cycle. Then, the Variable Description button opens anexplanation window in which every simulation input is described. Indeed, the user mightnot understand what the name of the variables refer to.

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When all the variables are correctly filled, the cycle can be solved. By clicking on the!! Solve !! button, the chosen root solver method is launched with the given guess values.From there, three different messages can pop up, represented in Fig.7.9.

The message A) indicates that the solver has found a solution that brings the residual tozero. The message contains the number of iteration that were needed. Clicking on ok willopen a result tab like the one in the Design window. In the two other messages, somethingwrong occurred. Message B) means that the solver has found a solution which is not thecorrect one. Indeed, the convergence criterion in the MINPACK library is not always relevantand the solver sometimes stops before the residues have reached zero. This usually comesfrom not relevant guesses. Because the solver still finds a solution, a result tab is opened,even if the results are wrong. This is quite convenient because the result tab helps to findwhich guess was wrong (for example by spotting a temperature cross in a HEX). It is alsopossible to force the solver to search further for the solution by decreasing the tolerance.Finally, the message C) indicates that the solver stopped during the process. Usually, itrefers to a thermodynamic property that could not be found. This often comes from wronginputs or not relevant guesses. This is the most embarrassing error, as no result tab isopened. Therefore, it is harder to find the source of the problem.

Figure 7.9: Simulation status messages.

1.4 ConclusionFor now, the interface was only tested in the context of the Master Thesis. It is therefore

important for Enertime to adapt it to their specific needs. However, the interface is alreadypretty complete and can be used to solve a lot of problems quite easily. More than a tool touse the model, this interface is a real part of it because it also helps to identify the modelpossible improvements and its weaknesses.

It should be noticed that the interface code is not easy to understand, especially forsomeone who never used wxPython; modifications must be done carefully.

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Nomenclature

Acronyms

C1, 2, 3, 4, 5 Design Cycle configuration 1,2,3,4,5

CAPEX Capital Expenses (initial investment)

CD Condenser

CF Confidential

CFD Computational fluid dynamics

CS Cold Source

DN Nominal Diameter

EV Evaporator

GWP Global Warming Potential

HEX Heat Exchangers

HS Hot Source

LMTD Logarithmic Mean Temperature Difference

NPSH Net Positive Suction Head

NTU Number of Transfer Unit

ODP Ozone Depletion Potential

ORC Organic Rankine Cycles

PR Preheater

PU Pump

RE Recuperator

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SimC1, 2, 3, 4, 5 Simulation Cycle configuration 1,2,3,4,5

SISO Single Input Single Output

SM State Matrix

STHEX Shell and tubes heat exchangers

TU Turbine

WHR Waste Heat Recovery

Subscripts

b0 Related to Block 0

b1 Related to Block 1

b2 Related to Block 2

b3 Related to Block 3

c Cold side

cd Condenser

d design

ev Evaporator

h Hot side

in inlet

out outlet

pr Preheater

pu Pump

re Recuperator

tot total

tu Turbine

wf Working fluid (refrigerant)

Variables

Q Heat

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W Power

ε Efficiency

η Cycle efficiency

ρ Density

h Enthalpy

P Pressure

s Entropy

T Temperature

U Global HEX exchange coefficient

x Quality

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