14
Effects of Solvent Properties and Injection Strategies on Solvent-Enhanced Steam Flooding for Thin Heavy Oil Reservoirs with Semi-Analytical Approach Hao Liu 1 *, Linsong Cheng 1 , Hao Xiong 1,2 and Shijun Huang 1 1 Department of Petroleum Engineering, China University of Petroleum, Beijing, 18 Fuxue road, Changping 102249 - PR China 2 The University of Oklahoma, 660 Parrington Oval, Norman, OK 73019-0390 - USA e-mail: [email protected] * Corresponding author Abstract Compared with conventional steam ooding and Steam-Assisted Gravity Drainage (SAGD), Solvent-Enhanced Steam Flooding (SESF) is considered a more effective method for improving heavy oil recovery in thin reservoirs in terms of higher thermal efciency and oil production rate. However, there remains a deciency of accurate and efcient methods to evaluate and design an SESF project in the eld. A semi-analytical model is proposed in this paper to predict the recovery performance of SESF and investigate the effects of solvent properties and injection strategies on the SESF process for thin heavy oil reservoirs. The proposed model provides a simple method to simulate not only single solvent injection but also multi-solvent injection by cooperating different values of solvent operating thickness and solvent solubility. To validate the models accuracy, comparisons are made between the proposed model results and the numerical simulation results for a specic heavy oil reservoir case. The results indicate that SESF can achieve a considerably higher oil production rate at the early recovery stage than steam ooding. Moreover, the paper also demonstrates that a higher injection rate results in a lower thermal efciency increment when well spacing is constant. Nevertheless, a high injection rate may also be suitable for longer well spacing owing to the improvement of the viscosity prole beyond the edge of the steam zone caused by longer contact time between the solvent and crude oil. NOMENCLATURE A Area of heated zone, m 2 A d c (t) Solvent diffusion area at time t,m 2 c P Heat capacity at constant pressure within the reser- voir, J/(kg °C) c cap Heat capacity of understrata and overburden rock C si Solvent solubility at the steam front C s Solvent concentration at e C s Average solvent concentration in the solvent pen- etration depth D t Effective diffusion coefcient of solvent at time t, m 2 /d D Solvent molecular diffusion coefcient, m 2 /s dr/dt Radial velocity of steam front, m/s dx/dt Longitudinal velocity of steam front, m/s dd c /dt Solvent diffusion rate, m/s f w Water fractional ow at specic water saturation f 0 w Slope of tangent of the water fractional ow curve at specic water saturation h Reservoir thickness, m h w Enthalpy of saturated water, kJ/kg H o Heat injection rate per unit well length, kJ/md L f Horizontal displacement of cold water front in the second stage, m L e Effective operating thickness of solvent, m L v Latent heat of vaporization of steam, kJ/kg Oil & Gas Science and Technology Rev. IFP Energies nouvelles (2017) 72, 20 Ó H. Liu et al., published by IFP Energies nouvelles, 2017 DOI: 10.2516/ogst/2017015 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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D o s s i e rSecond and Third Generation Biofuels: Towards Sustainability and Competitiveness

Seconde et troisième génération de biocarburants : développement durable et compétitivité

Effects of Solvent Properties and Injection Strategies on

Solvent-Enhanced Steam Flooding for Thin Heavy Oil

Reservoirs with Semi-Analytical Approach

Hao Liu1*, Linsong Cheng

1, Hao Xiong

1,2and Shijun Huang

1

1 Department of Petroleum Engineering, China University of Petroleum, Beijing, 18 Fuxue road, Changping 102249 - PR China2 The University of Oklahoma, 660 Parrington Oval, Norman, OK 73019-0390 - USA

e-mail: [email protected]

* Corresponding author

Abstract—Compared with conventional steam flooding and Steam-Assisted Gravity Drainage (SAGD),Solvent-Enhanced Steam Flooding (SESF) is considered a more effective method for improving heavy oilrecovery in thin reservoirs in terms of higher thermal efficiency and oil production rate. However, thereremains a deficiency of accurate and efficient methods to evaluate and design an SESF project in the field.A semi-analytical model is proposed in this paper to predict the recovery performance of SESF andinvestigate the effects of solvent properties and injection strategies on the SESF process for thin heavyoil reservoirs. The proposed model provides a simple method to simulate not only single solventinjection but also multi-solvent injection by cooperating different values of solvent operating thicknessand solvent solubility. To validate the model’s accuracy, comparisons are made between the proposedmodel results and the numerical simulation results for a specific heavy oil reservoir case. The resultsindicate that SESF can achieve a considerably higher oil production rate at the early recovery stagethan steam flooding. Moreover, the paper also demonstrates that a higher injection rate results in alower thermal efficiency increment when well spacing is constant. Nevertheless, a high injection ratemay also be suitable for longer well spacing owing to the improvement of the viscosity profile beyondthe edge of the steam zone caused by longer contact time between the solvent and crude oil.

NOMENCLATURE

A Area of heated zone, m2

Adc (t) Solvent diffusion area at time t, m2

cP Heat capacity at constant pressure within the reser-voir, J/(kg �C)

ccap Heat capacity of understrata and overburden rock

Csi Solvent solubility at the steam frontCs Solvent concentration at e�Cs Average solvent concentration in the solvent pen-

etration depthDt Effective diffusion coefficient of solvent at time t,

m2/dD Solvent molecular diffusion coefficient, m2/s

dr/dt Radial velocity of steam front, m/s

dx/dt Longitudinal velocity of steam front, m/sddc/dt Solvent diffusion rate, m/sfw Water fractional flow at specific water saturationf 0w Slope of tangent of the water fractional flow curve

at specific water saturationh Reservoir thickness, m

hw Enthalpy of saturated water, kJ/kgHo Heat injection rate per unit well length, kJ/mdLf Horizontal displacement of cold water front in the

second stage, mLe Effective operating thickness of solvent, mLv Latent heat of vaporization of steam, kJ/kg

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20� H. Liu et al., published by IFP Energies nouvelles, 2017DOI: 10.2516/ogst/2017015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

l Length of well, m

qhloss Heat loss rate to understrata and overburden perarea, kJ/m2d

qheff Required heat rate associated with the steam zoneexpansion per unit well length, kJ/md

Sor Residual oil saturationSwc Connate water saturationSwt Water saturation at the end of operating thicknessSwp Water saturation at the production wellT Temperature, �CTr Initial reservoir temperature, �Ctc Time when the first stage ends, dr Radius of steam zone area, mvmc Mass rate of cold steam condensate per unit well

length, kg/mdX Steam quality

x Horizontal displacement of steam front, m

GREEK LETTERS

ar Longitudinal dispersity factordc Solvent penetration depth, me Distance beyond the edge of the steam front, m/ Reservoir porosity

kcap Thermal conduction coefficient of understrata andoverburden rock, kJ/md �C

l Viscosity, mPa sq Density, kg/m3

C(�) Gamma function

SUBSCRIPTS

o Oils Steamw Hot water

r Reservoir rock matrixcap Understrata and overburden rock

INTRODUCTION

Heavy oil resources have an important role in crude oilreserve replacement to meet the world’s future energydemands [1]. However, a considerable portion of the heavyoil resides in thin formations and in some countries more than80% lies in reservoirs with a less than a 10 m pay zone; thishas posed a major challenge for efficient development [2].To date, the predominant in situ recovery methods for reser-voirs with thin pay zone are steam injection by horizontal

wells. Among these, the steam-flooding strategy has beenregarded as a significantly superior technology compared toSteam-Assisted Gravity Drainage (SAGD) operations interms of energy efficiency [3] and has been applied widelyin thin heavy oil reservoirs in China [4-6]. However, signif-icant heat losses to the understrata and overburden can renderthe steam-flooding process uneconomic because of the smallthickness of the reservoir [7]. Solvent-Enhanced SteamFlooding (SESF) requires substantially less steam usageand net injected energy and thus is considered as a highlyeffective method for improving heavy oil recovery in thinreservoirs [7, 8].

Solvent properties and injection strategies are importantfactors that control the performance of SESF and thus deter-mine the economic viability of the process. Therefore, it isnecessary to fully investigate the effects of these factors onproduction performance before implementing in the field.By conducting 63 experiments on a three-dimensionalelemental physical model, Redford [9] first demonstratedthe effects of solvent properties on the production perfor-mance and indicated that naphtha with steam could signifi-cantly reduce oil viscosity. Besides, bitumen recoverycould be improved further by adding CO2 or ethane becausethey can provide more drive energy for the naphtha to enterthe reservoir. Nasr and Pierce [10] conducted a series ofexperiments on steam-CO2 injection strategies in a scaledmodel and revealed that steam-CO2 continuous injectionresults in improved performance compared to steam-CO2

sequential injection. Moreover, oil recovery rates are typi-cally accelerated and improved during the initial stage ofthe process. Although the effects of the solvent propertiesand injection strategies of several solvents on steam floodingcan be identified by well-designed experiments, the numberof solvents tested is limited whereas the experiment require-ments are large. Therefore, the experimental data is difficultto analyse.

Based on laboratory experiments, several attempts usingnumerical simulation have been undertaken to study theSESF process. Shutler and Boberg [11] first used numericalsimulations to delineate the recovery mechanism of thesolvent-steam process. The results indicate that medium-alkane solvents provide the greatest increase in total oilproduction, whereas heavy-alkanes solvents do not improverecovery. They also proposed the corollary that the produc-tion of the process is primarily determined by the placementof the solvent in the reservoir, which in turn is controlled bythe steam movement and solvent volatility. Zhao et al. [8]reported reservoir simulation results on the application ofSESF for a bitumen reservoir with a net pay of 4 m.The results present optimum steam and steam-solvent flood-ing injection strategies by comparing the cumulative Energyinjected to produced Oil Ratio (cEOR) between differentcases. Hence, numerical simulation was proven to be a

Page 2 of 14 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20

powerful method to calculate SESF production. However,the calculation of the numerical simulation is not onlytime-consuming but also relies heavily on a large amountof experimental data, which limits the application of thenumerical simulation method.

For quick calculation and an easy method for the solvent-steam process, several analytical and semi-analyticalmethods were developed. Sharma and Gates [12] consideredmathematical models to calculate the length scales of themass and heat transfer beyond the edge of a co-injectionchamber. Gupta and Gittins [13] developed a semi-analyticalapproach to estimate oil drainage in the co-injection of steamand solvent. The solvent distribution beyond the steam cham-ber calculated by their models can be an indicator of differentsolvents without introducing excessive experimental data.However, their mathematical models are based on Butler’sSAGD model [14, 15] for oil drainage and do not considerthe blocking effects of water on the solvent diffusion, whichmakes the models not applicable for SESF process.

To the best of our knowledge, applying a mathemati-cal model to understand the SESF process for heavy oilreservoirs with thickness less than 10 m has never beenundertaken. In this study, to predict SESF production perfor-mance and study the effects of solvent properties and injec-tion strategies on the SESF process, a new semi-analyticalmodel is proposed based on mass and energy balance princi-ples, diffusion theory, and the theory of Buckley-Leverett.First, the mathematical model is solved in a semi-analyticalmethod. Next, comparisons are made between the calculatedmodel and numerical simulations to verify the proposedmodel. Finally, with the validated model, the effects of thesolvent properties and injection strategies on the productionperformance of SESF are studied in detail.

1 MATHEMATICAL MODEL

A simplified diagram of the SESF process is presented inFigures 1 and 2. To decouple the primary mechanisms fromthe other complexities that accompany the SESF process,important assumptions and simplifications are providedbelow:1. based on the position of the steam front, the entire pro-

duction process is divided into three stages: before thesteam front reaches the upper and lower boundary (steamfront rising stage) (Fig. 1b), after the steam front reachesthe boundary without steam condensate reaching the pro-duction well (steam front spreading stage) (Fig. 2b), afterthe cold steam condensate reaches the production well(steam condensate-producing stage). The pressure insidethe steam zone is constant during all stages [16, 17];

2. an interface model proposed by van Lookeren [18] hasbeen used widely to describe the shape of the steam front

without considering heat loss. It is a reasonable model forthe steam-flooding process in thick reservoirs; however, itis not applicable for thin reservoirs with considerablymore severe heat losses to the understrata and overbur-den. Thus, according to the reservoir numerical simula-tion results, the geometries of the steam and waterfronts are assumed to be a cosine curve and circularshaped, respectively;

3. all mobile oil is assumed to be displaced by the steam andhot water; thus, only residual oil is left in the steam andhot water zone;

4. the gas-phase solvent can move freely in the hot waterzone owing to the high temperature and low oil saturation[17, 19], whereas the cold steam condensate may blockthe diffusion of solvent into the heavy oil. By investigat-ing VAPor-EXtraction (VAPEX) experiments, Das andButler [20] proposed that the contact area of the solventand crude oil was directly related to the rate of the masstransfer, as indicated in Figure 3a. Thus, it is assumed thatthe diffusion coefficient is proportional to the contact areain a limited distance beyond the edge of the steam front,as illustrated in Figure 3b. The limited distance is definedas the effective operating thickness of the solvent, whichis determined by the volatility of solvent;

5. medium solvents (C6-C12) are considered to provide thegreatest increase in total oil production because theycan both travel with the steam in a vaporized phase andcondense in the cooler regions of the reservoir and diffusein the crude oil [21]. Light solvents (CO2, C1-C5), whichhave considerably higher volatility, are believed totransport further into the reservoir and thus increase theoperating thickness when co-injecting with mediumsolvents. Therefore, the solvents used in this model areassumed to be medium solvents and a combination ofmedium and light solvents;

6. local equilibrium is assumed along the steam front suchthat the equilibrium state inside the steam zone is notaffected by the phase behaviour at the steam front [22].Other assumptions, such as no mutual solubility betweenthe water and hydrocarbon components and no variationin the rock-fluid properties along the horizontal section ofthe well are identical to those proposed by Keshavarzet al. [23].The mathematical model is divided into three parts based

on the three stages (steam front rising stage, steam frontspreading stage, steam condensate-producing stage). Theseare introduced in detail in the following.

1.1 Steam Front Rising Stage

The process of the steam front rising stage is short because ofthe small thickness of the reservoir, which makes the gener-ating of steam condensate negligible. Therefore, the velocity

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20 Page 3 of 14

of the steam front can be calculated by the energy conserva-tion equation:

Ho ¼hqrcPr

ð1� /Þ/

þ qoSorcPo þ qsDSocPs

þ qwSwccPwi/dlðT s � T rÞ dAdt

¼ 2p qrcPrð1� /Þ

/þ qoSorcPo þ qsDSocPs

þ qwSwccPw

�/dlðT s � T rÞrU ð1Þ

DSo ¼ 1� Sor � Swc ð2Þ

where Ho is the heat injection rate per unit well length; A isthe area of the steam front; qr, qo, qs, and qw are the densitiesof the rock, crude oil, steam, and water, respectively; cPr, cPo,

cPs, and cPw are the heat capacities of the rock, crude oil,steam, and water, respectively; / is the reservoir porosity;Sor is the residual oil saturation; Swc is the connate watersaturation; dl is the unit length of well; Ts is the steam tem-perature; Tr is the initial reservoir temperature; r is the radiusof steam zone area; and U is the velocity of steam front.

The unsteady-state solvent concentration distributionalong the steam front can be described by Equation (3) [24]:

ooe

ðDþ aLUÞ oCs

oe

� �þ U

oCs

oe¼ oCs

otð3Þ

The corresponding boundary conditions are:

Cs ¼ 0; ts ¼ 0

Cs ¼ Csi; e ¼ 0

Cs ¼ 0; e ! 1

8><>: ð4Þ

where e is the distance beyond the edge of the steam front;Csi is the solvent solubility at the steam front; Cs is the

i

j

k

Injection WellProduction Well

Understrata

Overburden

Oil Layer

i

k

Steam zone

Solvent zone

a) b)

Figure 1

Illustration of steam front rising stage. a) Three-dimensional diagram of the stage; b) two-dimensional diagram of the stage.

i

j

k

i

k

Hot water zone

Cold water zone

a) b)

Figure 2

Illustration of steam front spreading stage. a) Three-dimensional diagram of the stage; b) two-dimensional diagram of the stage.

Page 4 of 14 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20

solvent concentration at e; D is the solvent molecular diffu-sion coefficient; aL is the longitudinal dispersity factor; andts is the solvent injection time.

Owing to the nonlinearity of Equation (3), the Heat Inte-gral Method (HIM) is used to determine the concentrationprofile. This method is a powerful approximation methodfor solving a variety of diffusion problems [25, 26]. RabieiFaradonbeh et al. [24] realized that the exponential formof the HIM method provides more accurate predictions ofthe concentration profile than the polynomial form; there-fore, the exponential form of the concentration distributionis used for the calculations of the fluid mixture and oil flowrate in this study.

The concentration distribution in exponential form aheadof the interface can be expressed as:

Cs ¼ Csie� e

dc ð5Þ

where dc is the solvent penetration depth. TransformingEquation (3) into integral form in the domain of the solventpenetration depth and substituting Equation (5) for Cs,Equation (3) can be simplified into:

Dþ aLUð Þ 1dc

� U ¼ odcot

; t ¼ 0; dc ¼ 0ð Þ ð6Þ

According to the Butler’s theory, all mobile oil is dis-placed by the steam and only residual oil is left in the steam

zone. Therefore, based on the mass conservation equationand assumption (6), the oil production rate in this stagecan be expressed as:

qoi ¼ qo/DSodldr

dtþ qo/ 1� Swcð Þdl�Cs

dAdc tð Þdt

ð7Þ

�Cs ¼R dc0 Csie

� edcde

dcð8Þ

where Adc is the solvent diffusion area at time t and �Cs is theaverage solvent concentration in the solvent penetrationdepth.

As indicated in Figures 4a and 4b, the steam front risingstage can be divided into two secondary stages according tothe position of the solvent boundary. They can be describedby Equations (9) and (10), respectively.

dAdcðtÞdt

¼d p

2 r þ @dc@t

� �2 � r2h in o

dt; r þ @dc

@t� h

2

� �ð9Þ

see equation (10) at the bottom of this page

1.2 Steam Front Spreading Stage

The steam front spreading stage is schematically presentedin Figure 2. In this stage, the steam is already touching the

dAdcðtÞdt

¼d h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir þ @dc

@t

� �2 � h2

� �2qþ r þ @dc

@t

� �2p� 2 arccos h

2 rþ@dc@tð Þ

� �� �� pr2

2

dt

; r þ @dc@t

>h

2

� �ð10Þ

Vaporized Solvent

&Steam

Time Line

Rock matrix

Average water saturation within operating thickness

Water

Oil

0t 1t

0wS 1wS

Vaporized Solvent

&Steam

0t 1t

Time Line

Rock matrix

Water

Oil

0wSAverage water saturation within operating thickness

1wS

a) b)

Figure 3

Schematic of contact area change at interface. a) Das and Butler’s perspective; b) simplification based on the Das and Butler’s perspective.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20 Page 5 of 14

understrata and overburden; therefore, the heat injected isdivided into two parts based on the energy conservationequation:

Ho ¼ qheff þ qhloss ð11Þ

where qhloss is the heat loss rate to the understrata and over-burden per area and qheff is the required heat rate associatedwith the steam zone expansion per unit well length.

The heat consumption rate used to expand the steam zoneis expressed by the energy increase of the area. As describedin assumption (2) and Figure 2b, the area of the steam zone istwice that of the hot water zone. Therefore, the required heatrate associated with the steam expansion per unit well lengthin this stage can be expressed as:

qheff ¼2

3qrcPr

ð1� /Þ/

þ qoSorcPoþqsDSocPsþ qwSwccPw

��

� T s � T rð Þ/qoDSodA

dt

þ 1

3qrcPr

ð1� /Þ/

þ qoSorcPo þ qsDSocPw

��

� Tw � T rð Þ/qoDSodA

dtð12Þ

According to assumption (2), the geometry of the waterfront is assumed to be a diameter-constant circular shape;thus, the change of the heated area can be transformed tothe change of distance:

dA

dt¼ h

dx

dtð13Þ

Carslaw and Jaeger [27] built and solved the heat lossmodel of a semi-infinite plate with a constant temperatureboundary. As the hot water mainly contacts the understrataand overburden, the heat loss rate is written as:

qhloss ¼ 2

Z t

tc

ðTw � T rÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikcapqcapccappðt � sÞ

sdx

dsds ð14Þ

where Ts and Tw are the temperature of the steam and hotwater, respectively; qcap is the density of the understrata

and overburden rock; kcap is the thermal conduction coeffi-cient of the understrata and overburden rock; ccap is the heatcapacity of the understrata and overburden rock; x is thehorizontal displacement of the steam front; and tc is the timewhen the first stage terminates.

Rabiei Faradonbeh et al. [28] also employed HIM todetermine the temperature profile. Therefore, the tempera-ture of the hot water can be expressed as:

Tw ¼R dcT0 T s � T rð Þe� e

dcT de

dcTþ T r ð15Þ

Based on the mass conservation law, the generating rateof the cold steam condensate per unit well length can begiven as:

vmc ¼Ho

XLv þ hw� qsdl

dAs

dt� qwdl

dAw

dtð16Þ

where vmc is the mass rate of cold steam condensate per unitwell length; X is the steam quality; Lv is the latent heat ofsteam vaporization; hw is the enthalpy of saturated water;and As and Aw are the areas of the steam zone and hot waterzone, respectively.

The areas of the steam zone and hot water zone inEquation (16) can be rewritten as Equation (17) andEquation (18) because of the cosine curve and circular shapeof the steam and water fronts, respectively:

As ¼ 2h

ph

2þ x

� �ð17Þ

Aw ¼ xhþ ph2

8� As ð18Þ

Shutler and Boberg [11] proposed that piston-like flowthrough a thin layer is assumed; therefore, the isothermaltwo-phase flow theory of Buckley and Leverett [29] can beintroduced into isothermal zones. Based on Shutler’s theory,the horizontal displacement of the cold water front can beexpressed as:

Lf ¼ f 0wðSwf Þ/hdl

Z t

tc

vmc

qwdt þ x ð19Þ

a) b)

Figure 4

Schematic of solvent diffusion process in first stage. a) Before solvent reaches boundary; b) after solvent reaches boundary.

Page 6 of 14 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20

where f 0wðSwf Þ is the slope of the tangent of the waterfractional flow curve at the cold water front. Because thesolvent penetration depth is extremely thin when the coldwater begins to generate, the horizontal displacement ofthe steam front is assumed to be not affected by the viscosityreduction by the solvent.

Cold water is assumed to block the diffusion of thesolvent into the crude oil. Based on assumption (4), theeffective diffusion coefficient of the solvent can be givenby Figure 5 and Equations (20)-(22):

�Sw ¼Swc þ 1

Le/hdl

Z t

tc

vmc

qwdt; ðLf � x2Þ

Swt þ 1

Le/hdl1� fwðSwtÞ½ �

Z t

tc

vmc

qwdt; ðLf > x2Þ

8>>><>>>:

ð20Þ

Le ¼ x2 � x1 ð21Þ

Dt ¼ D1� �Sw1� Swc

ð22Þ

where Le is the effective operating thickness of the solvent;�Sw is the average water saturation in Le; x1 and x2 are thecoordinates of the steam edge and the effective operatingfront, respectively; and Dt is the effective diffusion coeffi-cient of solvent at time t.

The solvent diffusion rate and oil production rate can alsobe calculated by Equations (6) and (7).

1.3 Steam Condensate-Producing Stage

The steam condensate-producing stage begins when thesteam condensate is produced from the production well.The water saturation profile between the steam edge andproduction well is determined by the oil viscosity profile,which is in turn influenced by the solvent concentrationprofile.

The following mixing rule is used for calculating themixture viscosity of the oil phase [30]:

ln lm ¼ 1� Csie� e

dc

� �ln lo þ Csie

� edc ln ls ð23Þ

where lo, ls, and lm are the viscosities of the heavy oil,solvent, and mixture of heavy oil and solvent, respectively.

By employing the theory of Buckley and Leverett, theslope of the tangent of the water fractional flow curveat the production well can be written as:

f 0w Swp� � ¼ e/hdlR t

tcvmcqw

dtð24Þ

The oil production rate can be rewritten from Equation (7)by considering the water and solvent production:

qoi ¼ qo/DSodldr

dtþ qo/ 1� Swcð Þdl�Cs

dAdc tð Þdt

� �

� fw Swp� �

1� Csð Þ ð25Þ

where Swp is the water saturation at the production well,which is determined by f 0wðSwoÞ and lm, and fwðSwpÞ is thefractional flow of water at the production well, which canbe acquired by considering lm and Swp.

2 CALCULATION FOR MATHEMATICAL MODEL

2.1 Model Treatment

A semi-analytical method is used to solve the model dueto the complexity of the equations. To solve the semi-analytical model conveniently, several equations must firstbe solved.

The equation describing the movement of the steam frontcan be obtained by integrating Equations (11)-(14):

Ho � 2

Z t

0ðTw � T rÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikcapqcapccappðt � sÞ

sdx

dsds

¼ 2

3qrcPr

ð1� /Þ/

þ qoSorcPo þ qsDSocPs þ qwSwccPw

� �

� T s � T rð Þ/ dAT

dt

þ 1

3qrcPr

ð1� /Þ/

þ qoSorcPo þ qsDSocPw

��

� Tw � T rð Þ/ dAT

dtð26Þ

Swf

Swc

SwOperatingThickness

Le

Sw1 Sw2

Sw3

Swt

x2x1

Swm

xt

Figure 5

Schematic of solvent operating thickness.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20 Page 7 of 14

Equation (26) belongs to the Volterra integral equations ofthe second kind, which makes it difficult to solve directly.In this article, Equation (26) is solved with the support ofa Laplace transform and the displacement of the steam frontis given as:

x ¼Z t

tc

Ho

Be

ABC 0:5ð Þ½ �2s

� �erfc

A

BC 0:5ð Þ ffiffiffi

sp� �

ds ð27Þ

where

A ¼ 2 Tw � T rð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikcapqcapccapp t � sð Þ

sð28Þ

B ¼ 2

3qrcPr

ð1� /Þ/

þ qoSorcPo þ qs�SocPs þ qwSwccPw

� �

� T s � T rð Þ/þ 1

3qrcPr

ð1� /Þ/

þ qoSorcPo þ qs�SocPw

� �

� Tw � T rð Þ/ ð29Þ

2.2 Calculation Flow for Mathematical Model

Because the solvent diffusion rate and steam front velocitychange with time, time is first discretized into small inter-vals. As mentioned above, the following steps are used forthe calculation of the oil production rate:1. for a given heat injection rate and solvent component,

Equations (1), (2), (5), and (6) are coupled and solvedfor the steam front velocity U, radius of the steam zonearea r, solvent diffusion rate ddc/dt, and solvent penetra-tion depth dc;

2. the production rate in the first stage is calculated usingEquations (7)-(10);

3. repeat steps 2 and 3 substituting dc calculated in step 2into Equation (6) until the steam front reaches the under-strata and overburden, i.e., when the process enters thenext stage;

4. the steam front velocity dx/dt and the steam front dis-placement x in the second stage are calculated usingEquations (15) and (27);

5. the cold steam condensate generating rate vmc is calcu-lated using Equations (16)-(18). Then, Equations (5),(6), and (19)-(22) are coupled and solved for the solventddc/dt, dc, and the cold steam condensate distributionbeyond the edge of the steam front;

6. the production rate in the second stage is also calculatedusing Equations (7)-(10);

7. repeat steps 5-7 substituting dc calculated in step 6 intoEquation (6) until the cold steam condensate reachesthe production well, when the process enters the thirdstage;

8. vmc , ddc/dt, and dc are calculated in the same manner asstep 6. The water fractional flow fw(Swo) in the third stageis calculated using Equations (5), (23), and (24). Then,the oil production rate of the third stage can be calculatedusing Equation (25);

9. repeat steps 9 substituting dc calculated in step 9 intoEquation (6) until fw(Swo) = 1, when the process ends.

3 RESULTS AND DISCUSSION

3.1 Model Validation

It is difficult to address all combinations of different solventsby experiments and numerical simulation, making thevalidation of the SESF process far from comprehensive.Given this situation, the model with solvent concentrationvalue of zero is validated to ensure that the proposed modelis a credible base model for the SESF calculation. Thismethod of validation is considered as reasonable in this arti-cle because the major objective of the model is to investigatethe effects of the solvent properties on the production ofSESF, not that of a specific solvent.

STARS is an effective thermal recovery reservoir numer-ical simulator developed by the CMG Company. As theresults of STARS are exact numerical solutions that canclosely reveal the real reservoir production process, it fre-quently serves as a reference to test and verify the correct-ness of other models. Hence, to validate the correctness ofthe proposed model, the results of the model are comparedwith those of STARS. The parameters used in the proposedmodel and STARS are all based on the average propertyparameters of one oil field in China. The well spacingbetween the production well and injection well is 40 m.The thickness of the reservoir is 7 m. The steam injectionrate per unit length is 0.09 t/md, which is low because ofthe thin thickness of the reservoir. The temperature of thesteam is 300 �C and the oil viscosity is 300 mPa s at thereservoir condition. Table 1 lists the reservoir propertiesand injection parameters used in the calculation of both thenew model and STARS.

The steam zone development comparison between theproposed model and STARS is made using Figure 6. Thegeometries and movements of the steam front and hot waterfront predicted by the proposed model are similar to thenumerical simulation results, which also proves the reason-ability of assumption (2). Figure 7 depicts the cold steamcondensate front position at the end of the steam frontspreading stage. The difference of the condensate front

Page 8 of 14 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20

position between the two methods is only 2 m, which alsoproves the feasibility of the Buckley-Leverett theory in thesteam-flooding process in a thin layer.

Figure 8 displays the oil production rate as a function ofthe steam-flooding production time. The oil production rateincreases before the steam front reaches the understrata andoverburden. In the second stage, the production rate remainsvirtually stable because the hot water zone between thesteam zone and boundaries alleviates the heat loss. Afterthe steam condensate reaches the production well, the oilproduction rate begins to decrease sharply; in this stage thesteam zone and hot water zone stop expanding at the pointwhen the heat loss rate to the overburden and understrataequals the heat injection rate [31, 32].

RMSRE (Rooting-Mean-Square of Relative Error)(Eq. 30) and RE (Relative Error) (Eq. 31) are employedto evaluate the accuracy of the proposed model in calculatingthe cumulative oil production and oil production rate [33]:

RMSRE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

NPTS

XNPTSi¼1

ycali � ysimiysimi

� �2vuut � 100% ð30Þ

REi ¼ ycali � ysimiysimi

� 100% ð31Þ

where NPTS is the number of data points; ycali is the calcu-lated value at point i by the proposed model; and ysimi isthe calculated value at point i by STARS.

In Figure 9, the cumulative oil calculated by the proposedmodel and STARS are compared. The RE of the cumulativeoil for each point is less than 7%; the RMSRE is only 3.5%.Thus, the proposed model is accurate in calculating thesteam-flooding process. Figure 10 indicates the RE distribu-tion of the oil production rate with time. It can be clearlyobserved that the RE is significantly higher in the third stagethan in the first and second stages. According to ouranalyses, the greater difference between the two results inthe third stage is largely due to the one-dimensional assump-tion of the Buckley-Leverett theory. The RE and absoluteerror (difference between the calculated oil production rateby the proposed model and STARS) in the later portion ofthe third stage is less than that in the middle of the samestage. As is known from a previous study, the solvent mainlyaffects the early and late stages of the steam injection process[10, 34], which is consistent with the low RE stage in theproposed model. Therefore, the proposed model is suffi-ciently accurate to calculate the SESF process.

After the validation of the proposed model, the oilproduction rate of the steam flooding is compared with thatof SESF, as illustrated in Figure 11. The solubility of thesolvent at the steam front is 0.2, the diffusion coefficientof the solvent into the heavy oil is 5.5 9 10�2 m2/d, which

TABLE 1

Average property parameters of X oil field in China.

Parameter Value

Porosity 0.32

Initial oil saturation 0.75

Residual water saturation 0.25

Pay thickness, m 7

Initial reservoir temperature, �C 80

Density of sand rock, kg/m3 2.5 9 103

Density of understrata and overburden, kg/m3 2.5 9 103

Density of oil, kg/m3 1.0 9 103

Density of water, kg/m3 1.0 9 103

Thermal conductivity of understrata and overburden, J/m2 day �C 1.94 9 103

Conductivity of understrata and overburden, J/kg �C 1.0 9 103

Thermal capacity of sand rock, J/kg �C 1.0 9 103

Thermal capacity of oil, J/kg �C 3.0 9 103

Thermal capacity of water, J/kg �C 4.2 9 103

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20 Page 9 of 14

is one order of magnitude greater than the Das and Butler’sresults that pertain to Heleshaw laboratory models ofVAPEX [35]. Gupta and Gittins [13] regard the higher diffu-sion coefficient as reasonable because of the higher temper-ature and existence of a blanket layer. The longitudinaldispersity factor is 5 9 10�3 m and the viscosity of solventis 4.5 mPa s. It can be seen that oil rate increases rapidly in

the first stage with the contact area increasing until the steamfront reaches the boundaries when the oil rate reaches itshighest point. Then, it begins to decline owing to the lowersolvent concentration gradient beyond the steam front andthe blocking effects of the steam condensate on the solventdiffusion. Moreover, the production time is shortenedbecause of the improvement of the oil viscosity profilebeyond the edge of the steam caused by the dissolution ofthe solvent into the heavy oil. These are consistent withthe working stage of the solvent mentioned in other litera-tures [10, 34], which in turn verifies the proposed model.

3.2 Effects of Solvent Properties on SESF

Figure 12 displays the effects of different effective operatingthicknesses of the solvent on both the production rate andreduced steam oil ratio. The reduced steam oil ratio is

a)

b)

c)

Figure 6

Comparison of steam front movement between proposed modeland STARS. a) Steam flooding time = 46 days; b) steam flood-ing time = 200 days; c) steam flooding time = 400 days.

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100 STARS Semi-analytical Model

Time (day)

Oil

prod

uctio

n ra

te (1

0-3m

3 ·(m·d

)-1)

Figure 8

Comparison of calculated oil production with STARS results.

0 500 1000 1500 2000 2500 3000 35000

500

1000

1500

2000

2500

3000

3500 0% RE 5% RE Cumulative oil production

STAR

S re

sult

(10-3

m3 ·(m

·d)-1

)

Semi-analytical model result (10-3m3·(m·d)-1)

Figure 9

RE distribution along cumulative oil production.

Figure 7

Comparison of steam condensate front between proposedmodel and STARS.

Page 10 of 14 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20

defined as the steam oil ratio difference between SESF andsteam flooding, which represents the thermal efficiencyincrement by the solvent. We can see that the oil ratedecreases slower with higher effective operating thickness,while the production time remains unaffected. The largerthe effective operating thickness, the greater the thermal effi-ciency increment. This means that by pushing the solventfurther into the reservoir, the thermal efficiency can beincreased without additional consumption of solvent, thusincreasing the economic benefits. This is similar to the phe-nomenon in the experiments of Redford [9].

Figure 13 indicates that the solvent solubility in heavy oilalso has significant effects on the SESF process. It can beobserved that both the oil production rate in the early stageand thermal efficiency increment increase with the solvent

solubility. Moreover, according to Equations (23) and (24),for the benefit of a lower mixture viscosity beyond the steamedge, a higher solvent solubility tends to result in a shorterproduction time without decreasing the cumulative oilproduction, such that heavy oil is recovered considerablymore efficiently.

However, it should be noted that a larger operatingthickness always means a lower solvent solubility in termsof a single solvent. Consequently, an optimal solvent mustbe carefully selected for the best performance of SESF wheninjecting a single solvent with steam. Multi-solvent injection,which is rarely mentioned in other analytical models, isprovided with a simple method to simulate in the proposedmodel using different values of operating thickness andsolubility.

0 150 300 450 600 750 9000

30

60

90

120

150

Oil

prod

uctio

n ra

te (1

0-3m

3 ·(m·d

)-1)

Time (day)

0.50.40.30.20.1

0.1 0.2 0.3 0.4 0.50.00.20.40.60.81.01.21.4

Red

uced

ste

am-o

il ra

tio

Solvent solubility

Figure 13

Effects of solvent solubility on production performance ofSESF.

0 200 400 600 800 10000

20

40

60

80

100

120

Oil

prod

uctio

n ra

te (1

0-3m

3 ·(m·d

)-1)

Time (day)

Steam flooding SESF

Figure 11

Comparison of calculated oil production rate between steamflooding and SESF.

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

Oil

prod

uctio

n ra

te (1

0-3m

-3·(m

·d)-1

)

Time (day)

1m2m3m4m5m

1 2 3 4 50.00.10.20.30.40.50.6

Red

uced

ste

am-o

il ra

tio

Operating thickness,m

Figure 12

Effects of solvent operating thickness on production perfor-mance of SESF.

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100

datum point (0%)

Lowest point (-100%)

highest point (100%)

Calculated REi

Semi-analytical Model

Time (day)

Oil

prod

uctio

n ra

te (1

0-3m

3 ·(m·d

)-1)

Figure 10

RE distribution along oil production rate and time.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20 Page 11 of 14

3.3 Effects of Injection Strategy on SESF

Figure 14 illustrates the effects of different injection rates onSESF production. It can be concluded that the differencesbetween the largest oil rate and the stable oil rate are virtuallythe same among different injection rates. The reason is thatthe diffusion rate is largely determined by the concentrationgradient and contact area, not the interface velocity. Further,the generating of water within the operating thickness accel-erates with an increasing injection rate, which results in asharp decline of oil production rate at an early recovery stagefor a high injection rate. Moreover, Figure 14 indicates thatthe thermal efficiency increment increases with a decrease ofthe injection rate because of the longer contacting time of thesolvent with the oil and thus relatively shorter productiontimes compared with steam flooding.

Figure 15 displays the effects of different well spacing onboth the production rate and reduced steam oil ratio. It isclear that the oil rates in the early stage are identical for dif-ferent well spacing. Moreover, the larger the well spacing,the lower the thermal efficiency increment. This is becausethe diffusion rates are the same with different well spacingand thus the oil is unaffected by the solvent increases relatedto the well spacing. Therefore, solvents with higher operat-ing thickness, which means wider working range, are moresuitable for longer well spacing.

From Figures 14 and 15, it can also be concluded thatdespite the fact that a higher injection rate may result inlower thermal efficiency increment when well spacing isconstant, it may be more suitable for longer well spacingowing to the improvement of saturation and oil viscosityprofiles beyond the steam edge caused by the longer contacttime. Thus, an optimal injection rate must be carefullyselected for the best performance of SESF with a given wellspacing.

CONCLUSION

In this study, a semi-analytical model for predicting SESFproduction performance was established. Then the theoreti-cal model was validated using STARS results and error anal-ysis. The production performances of steam flooding andSESF were also compared. Moreover, with the theoreticalmodel, the effects of solvent properties, injection strategieson oil production rate, and thermal efficiency incrementwere investigated. The findings can be summarized as fol-lows:1. compared with the STARS results for one case based on

average reservoir parameters, the proposed model provedto be sufficiently accurate in calculating the SESF pro-duction performance;

2. SESF can achieve a considerably higher oil productionrate at the early recovery stage than steam flooding. Fur-ther, the production time is shortened owing to theimprovement of the viscosity profile beyond the edgeof the steam, which is caused by the solvent dissolutioninto the heavy oil;

3. the operating thickness and solubility of a singlesolvent are proportional to the oil production incrementof SESF; however, they cannot be increased simul-taneously. Thus, an optimal solvent must be carefullyselected for the best performance of SESF when injectinga single solvent with steam. The proposed model alsoprovided a simple method to simulate multi-solventinjection using different values of operating thicknessand solubility;

4. a higher injection rate can result in a lower thermalefficiency increment when well spacing is constant.

0 200 400 600 800 1000 1200 1400 16000

20

40

60

80

100

120

140O

il pr

oduc

tion

rate

(10-3

m3 ·(m

·d)-1

)

Time (day)

0.11t/(m·d)0.09t/(m·d)0.07t/(m·d)0.05t/(m·d)

0.05 0.07 0.09 0.110.00.10.20.30.40.50.6

Red

uced

ste

am-o

il ra

tio

Injection rate t/(m·d)

Figure 14

Effects of injection rate on production performance of SESF.

0 200 400 600 800 1000 1200 1400 16000

20

40

60

80

100

120

140

Oil

prod

uctio

n ra

te (1

0-3m

3 ·(m·d

)-1)

Time (day)

20m40m60m80m

20 40 60 800.00.10.20.30.40.50.6

Red

uced

ste

am-o

il ra

tio

Well spacing m

Figure 15

Effects of well spacing on production performance of SESF.

Page 12 of 14 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20

However, it may be suitable for longer well spacingowing to the improvement of the viscosity profile beyondthe steam edge, which is caused by longer contact timebetween the solvent and crude oil.

ACKNOWLEDGMENTS

The authors wish to thank the Research Institute ofPetroleum Exploration & Development, Liaohe OilfieldCompany, PetroChina (2013-JS-9399). This work was alsosupported in part by a grant from the National Science andTechnology Major Projects of China (2016ZX05012-005-004) for financial support. Discussions with colleagues ofan oil reservoir numerical simulation group provided greatinsight for our paper.

REFERENCES

1 Besson C. (2005) Resources to Reserves: Oil & GasTechnologies for the Energy Markets of the Future, OECDPublishing, Paris.

2 Adams D. (1982) Experiences with waterfloodingLloydminster heavy-oil reservoirs, J. Petro. Technol. 34, 8,1643-1650.

3 Stalder J.L. (2007) Unlocking bitumen in thin and/orlower pressure pay using cross SAGD (XSAGD), Proceedingsof the Canadian International Petroleum Conference,F. Petroleum Society of Canada.

4 Fu C. (2007) The research and implementation of Qi40steamflood techniques, Petrol. Geol. Eng. 21, 2, 39-42.

5 Zhao S. (2012) Research and application on key technique ofefficient development of heavy oil resources in ultra-thin layerin south region of Chenjiazhuang oilfield, Petrol. Geol. Reco.Effic. 19, 3, 98-100.

6 Song Y. (2013) Optimization design of steam flooding forhorizontal well in thin heavy oil reservoir, Fault-Block Oil &Gas Field 2, 239-241.

7 Zhao D.W., Wang J., Gates I.D. (2014) Thermal recoverystrategies for thin heavy oil reservoirs, Fuel 117, 431-441.

8 Zhao D.W., Wang J., Gates I.D. (2013) Optimized solvent-aided steam-flooding strategy for recovery of thin heavy oilreservoirs, Fuel 112, 50-59.

9 Redford D. (1982) The use of solvents and gases with steam inthe recovery of bitumen from oil sands, J. Can. Pet. Technol.21, 1, 45-53.

10 Nasr T., Pierce G. (1995) Steam-CO2 recovery processesfor bottom water oil reservoirs, J. Can. Pet. Technol. 34, 7,42-49.

11 Shutler N., Boberg T. (1972) A one-dimensional analyticaltechnique for predicting oil recovery by steamflooding, SPEJ. 12, 6, 489-498.

12 Sharma J., Gates I.D. (2010) Steam-solvent coupling at thechamber edge in an in situ bitumen recovery process,Proceedings of the SPE Oil & Gas India Conference &Exhibition, Mumbai, F. Society of Petroleum Engineers.

13 Gupta S.C., Gittins S. (2012) An investigation into optimalsolvent use and the nature of vapor/liquid interface insolvent-aided SAGD process with a semianalytical approach,SPE J. 17, 4, 1255-1264.

14 Butler R.M. (1985) A new approach to the modelling ofsteam-assisted gravity drainage, J. Can. Pet. Technol. 24, 3,42-51.

15 Butler R.M. (1994) Steam-assisted gravity drainage: concept,development, performance and future, J. Can. Pet. Technol.33, 2, 44-50.

16 Thomas S. (2008) Enhanced oil recovery – an overview, OilGas Sci. Technol. – Rev. IFP 63, 1, 9-19.

17 He C., Mu L., Fan Z., Xu A., Zeng B., Ji Z., Han H. (2017)An improved steam injection model with the considerationof steam override, Oil Gas Sci. Technol. – Rev. IFP 72,6, 1-14.

18 van Lookeren J. (1983) Calculation methods for linear andradial steam flow in oil reservoirs, SPE J. 23, 3, 427-439.

19 de Haas T.W., Fadaei H., Guerrero U., Sinton D. (2013)Steam-on-a-chip for oil recovery: the role of alkalineadditives in steam assisted gravity drainage, Lab Chip 13, 19,3832-3839.

20 Das S.K., Butler R.M. (1998) Mechanism of the vaporextraction process for heavy oil and bitumen, J. Pet. Sci. Eng.21, 1, 43-59.

21 Shu W., Hartman K. (1988) Effect of solvent on steam recoveryof heavy oil, SPE Reserv. Eng. 3, 2, 457-465.

22 Edmunds N.R. (2013) Observations on the mechanisms ofsolvent-additive SAGD processes, Proceedings of the SPEHeavy Oil Conference-Canada, F. Society of PetroleumEngineers.

23 Keshavarz M., Okuno R., Babadagli T. (2015) A semi-analytical solution to optimize single-component solventcoinjection with steam during SAGD, Fuel 144, 400-414.

24 Rabiei Faradonbeh M., Harding T.G., Abedi J. (2012)Semi-analytical modeling of steam-solvent gravity drainageof heavy oil and bitumen, part 1: enhanced flow rate atmobile zone. Proceedings of the SPE Annual TechnicalConference and Exhibition, F. Society of PetroleumEngineers.

25 Goodman T.R. (1958) The heat-balance integral and itsapplication to problems involving a change of phase, Trans.ASME 80, 2, 335-342.

26 Closmann P.J., Smith R.A. (1983) Temperature observationsand steam-zone rise in the vicinity of a steam-heated fracture,SPE J. 23, 4, 575-586.

27 Carslaw H.S., Jaeger J.C. (1988) Conduction of heat in solids,2nd edn., Oxford University Press, New York, USA.

28 Rabiei Faradonbeh M., Harding T.G., Abedi J. (2014)Semi-analytical modeling of steam-solvent gravity drainageof heavy oil and bitumen, Proceedings of the SPE Heavy OilConference-Canada, F. Society of Petroleum Engineers.

29 Buckley S.E., Leverett M. (1942) Mechanism of fluiddisplacement in sands, Trans. ASME 146, 1, 107-116.

30 Poling B.E., Prausnitz J.M., O’connell J.P. (2001) Theproperties of gases and liquids, McGraw-Hill, New York.

31 Mandl G., Volek C. (1969) Heat and mass transport insteam-drive processes, SPE J. 9, 1, 59-79.

32 Chandra S. (2006) Improved steamflood analytical model,Texas A&M University.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles (2017) 72, 20 Page 13 of 14

33 Wang X., Cai W., Lu J., Sun Y., Zhao L. (2015) Model-based optimization strategy of chiller driven liquiddesiccant dehumidifier with genetic algorithm, Energy 82,939-948.

34 Hedden R., Verlaan M., Lastovka V. (2014) Solvent enhancedsteam drive, Proceedings of the SPE Improved Oil RecoverySymposium, F. Society of Petroleum Engineers.

35 Das S.K., Butler R.M. (1996) Diffusion coefficients of propaneand butane in peace river bitumen, Can. J. Chem. Eng. 74, 6,985-992.

Manuscript submitted in August 2016

Manuscript accepted in May 2017

Published online in August 2017

Cite this article as: H. Liu, L. Cheng, H. Xiong and S. Huang (2017). Effects of Solvent Properties and Injection Strategies onSolvent-Enhanced Steam Flooding for Thin Heavy Oil Reservoirs with Semi-Analytical Approach, Oil Gas Sci. Technol 72, 20.

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