Cinétique et stochiométrie

Cintique et stochiomtrieA. GarnierGCH-2103A-2010

Cintique et stochiomtrieDfinitionLes termes de baseLes modes doprationLes relations de baseDtermination thorique Dtermination exprimentaleTaux initiauxCuveChemostatStop flow

Croissance cellulaire - variables

XSPTaux de variation(kg/(m3.s)dX/dtdS/dtdP/dtTaux de production /consommationrxrsrpTaux spcifique(kg/(kg.s) = rx/Xqs= -rs/Xqp= rP/XRendement (kg/kg)Yx/s = rx/rs = /qpYp/x, Yp/s

Mode doprationSystme ferm: cuve (batch)Aucune entre ou sortie

Rgime transitoire

dX/dt = rX, dS/dt = rS

t = 0, X = X0, S = S0

Cuve alimente (Fed-batch)Alimentation seulement

Rgime transitoire

t = 0, V= V0, X= X0, S= S0

F sera contrl de manire maintenir S constant, S=S0=Sc

Si S est constant, m le sera aussi, m= mc

F(t), SinV, X, S

Chemostat (continu, CSTR)F, SinV, X, S, PF, S, X, PUne entre, une sortie

Mlange idal: Xout = X, Sout = S, Pout = P

Aprs une priode initiale dadaptation, ce systme atteindra un rgime permanent: V= cst, X= cst, S= cst, P= cst

Chemostat avec recirculationF F(1+w)V, XBioracteur DcanteurF(1+w)wF, XxFc, XcFex, XxPermet de concentrer les cellules dans le bioracteurPermet de repousser le lavageDveloppement pour X seulement

Croissance cellulaire type de modlesStructur: Tient compte de mtabolites intra-cellulairesSgrg: Tient compte dune distribution de population

STRUCTUR/SGRGNON-STRUCTURSTRUCTURNON-SGRG+ simpleSGRG

Modles de croissanceDu plus simple au plus compliquExponentiel (ordre 0!!)Linaire (logistique)MonodAutresPhnomnes connexesMaintenanceMortalitProductionLuedeking-Piret combin aux diffrents modles

Modle enzymatique - MonodUne variable indpendante, 3 variables dpendantes, trois quations = Une solution!

(1)(2)(3)Pour un systme ferm (cuve) en supposant YX/S constant:

Modle de Monodquation 3 nest peut-tre pas ncessaire:

Xmax-X = Yx/s * SAlors:

Modle de Monod

Modle de MonodSachant que:

Modle de MonodS = (Xmax-X)/Yx/s

Donnesmmax=1Ks=5Yx/s=0,5So=20Xo=0,1

Graph1

0.120

0.219.8

0.319.6

0.419.4

0.519.2

0.619

0.718.8

0.818.6

0.918.4

118.2

1.118

1.217.8

1.317.6

1.417.4

1.517.2

1.617

1.716.8

1.816.6

1.916.4

216.2

2.116

2.215.8

2.315.6

2.415.4

2.515.2

2.615

2.714.8

2.814.6

2.914.4

314.2

3.114

3.213.8

3.313.6

3.413.4

3.513.2

3.613

3.712.8

3.812.6

3.912.4

412.2

4.112

4.211.8

4.311.6

4.411.4

4.511.2

4.611

4.710.8

4.810.6

4.910.4

510.2

5.110

5.29.8

5.39.6

5.49.4

5.59.2

5.69

5.78.8

5.88.6

5.98.4

68.2

6.18

6.27.8

6.37.6

6.47.4

6.57.2

6.67

6.76.8

6.86.6

6.96.4

76.2

7.16

7.25.8

7.35.6

7.45.4

7.55.2

7.65

7.74.8

7.84.6

7.94.4

84.2

8.14

8.23.8

8.33.6

8.43.4

8.53.2

8.63

8.72.8

8.82.6

8.92.4

92.2

9.12

9.21.8

9.31.6

9.41.4

9.51.2

9.61

9.70.8

9.80.6

9.90.4

100.2

10.010.18

10.020.16

10.030.14

10.040.12

10.050.1

10.060.08

10.070.06

10.080.04

10.090.02

10.0910.018

10.0920.016

10.0930.014

10.0940.012

10.0950.01

10.0960.008

10.0970.006

10.0980.004

10.0990.002

X

S

temps (-)

X (-)

S (-)

Modle de Monod

Ordre 0_exponentiel

Courbe exponentielle

AG, nov 2002

Donnes

1tlag=0.5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

avec latence

tXln(X)Xln(X)

00.1-2.3025850930.1-2.302585093

0.10.1105170918-2.2025850930.1-2.302585093

0.20.1221402758-2.1025850930.1-2.302585093

0.30.1349858808-2.0025850930.1-2.302585093

0.40.1491824698-1.9025850930.1-2.302585093

0.50.1648721271-1.8025850930.1-2.302585093

0.60.18221188-1.7025850930.1105170918-2.202585093

0.70.2013752707-1.6025850930.1221402758-2.102585093

0.80.2225540928-1.5025850930.1349858808-2.002585093

0.90.2459603111-1.4025850930.1491824698-1.902585093

10.2718281828-1.3025850930.1648721271-1.802585093

1.10.3004166024-1.2025850930.18221188-1.702585093

1.20.3320116923-1.1025850930.2013752707-1.602585093

1.30.3669296668-1.0025850930.2225540928-1.502585093

1.40.4055199967-0.9025850930.2459603111-1.402585093

1.50.448168907-0.8025850930.2718281828-1.302585093

1.60.4953032424-0.7025850930.3004166024-1.202585093

1.70.5473947392-0.6025850930.3320116923-1.102585093

1.80.6049647464-0.5025850930.3669296668-1.002585093

1.90.6685894442-0.4025850930.4055199967-0.902585093

20.7389056099-0.3025850930.448168907-0.802585093

2.10.8166169913-0.2025850930.4953032424-0.702585093

2.20.9025013499-0.1025850930.5473947392-0.602585093

2.30.9974182455-0.0025850930.6049647464-0.502585093

2.41.10231763810.0974149070.6685894442-0.402585093

2.51.21824939610.1974149070.7389056099-0.302585093

2.61.34637380350.2974149070.8166169913-0.202585093

2.71.48797317250.3974149070.9025013499-0.102585093

2.81.64446467710.4974149070.9974182455-0.002585093

2.91.81741453690.5974149071.10231763810.097414907

32.00855369230.6974149071.21824939610.197414907

3.12.21979512810.7974149071.34637380350.297414907

3.22.45325301970.8974149071.48797317250.397414907

3.32.71126389210.9974149071.64446467710.497414907

3.42.99641000471.0974149071.81741453690.597414907

3.53.31154519591.1974149072.00855369230.697414907

3.63.65982344441.2974149072.21979512810.797414907

3.74.0447304361.3974149072.45325301970.897414907

3.84.47011844931.4974149072.71126389210.997414907

3.94.94024491061.5974149072.99641000471.097414907

45.45981500331.6974149073.31154519591.197414907

4.16.03402875971.7974149073.65982344441.297414907

4.26.66863310411.8974149074.0447304361.397414907

4.37.369979371.9974149074.47011844931.497414907

4.48.14508686652.0974149074.94024491061.597414907

4.59.00171313012.1974149075.45981500331.697414907

4.69.94843156422.2974149076.03402875971.797414907

4.710.12.31253542386.66863310411.897414907

4.810.12.31253542387.369979371.997414907

4.910.12.31253542388.14508686652.097414907

510.12.31253542389.00171313012.197414907

5.110.12.31253542389.94843156422.297414907

5.210.12.312535423810.12.3125354238

5.310.12.312535423810.12.3125354238

5.410.12.312535423810.12.3125354238

5.510.12.312535423810.12.3125354238

5.610.12.312535423810.12.3125354238

5.710.12.312535423810.12.3125354238

5.810.12.312535423810.12.3125354238

5.910.12.312535423810.12.3125354238

610.12.312535423810.12.3125354238

6.110.12.312535423810.12.3125354238

6.210.12.312535423810.12.3125354238

6.310.12.312535423810.12.3125354238

6.410.12.312535423810.12.3125354238

6.510.12.312535423810.12.3125354238

6.610.12.312535423810.12.3125354238

6.710.12.312535423810.12.3125354238

6.810.12.312535423810.12.3125354238

6.910.12.312535423810.12.3125354238

710.12.312535423810.12.3125354238

7.110.12.312535423810.12.3125354238

7.210.12.312535423810.12.3125354238

7.310.12.312535423810.12.3125354238

7.410.12.312535423810.12.3125354238

7.510.12.312535423810.12.3125354238

7.610.12.312535423810.12.3125354238

7.710.12.312535423810.12.3125354238

7.810.12.312535423810.12.3125354238

7.910.12.312535423810.12.3125354238

810.12.312535423810.12.3125354238

8.110.12.312535423810.12.3125354238

8.210.12.312535423810.12.3125354238

8.310.12.312535423810.12.3125354238

8.410.12.312535423810.12.3125354238

8.510.12.312535423810.12.3125354238

8.610.12.312535423810.12.3125354238

8.710.12.312535423810.12.3125354238

8.810.12.312535423810.12.3125354238

8.910.12.312535423810.12.3125354238

Ordre 0_exponentiel

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)

Croissance exponentielle

1er ordre_logistique

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

0

0

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0

0

0

0

0

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0

0

0

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0

0

0

0

0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Monod

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

0

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0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)

Croissance exponentielle avec latence

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

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0

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0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Courbe logistique

AG, 11-2002

Donnes

k=1

X0=0.1

Xm=1

tXln(X/(Xmax-X)

00.1-2.1972245773

0.10.1093668704-2.0972245773

0.20.1194946317-1.9972245773

0.30.13042292-1.8972245773

0.40.1421892512-1.7972245773

0.50.154828099-1.6972245773

0.60.168369876-1.5972245773

0.70.1828398332-1.4972245773

0.80.1982568985-1.3972245773

0.90.2146324866-1.2972245773

10.2319693167-1.1972245773

1.10.2502602861-1.0972245773

1.20.2694874524-0.9972245773

1.30.2896211813-0.8972245773

1.40.3106195215-0.7972245773

1.50.3324278617-0.6972245773

1.60.3549789231-0.5972245773

1.70.3781931248-0.4972245773

1.80.4019793473-0.3972245773

1.90.4262360981-0.2972245773

20.4508530604-0.1972245773

2.10.475712984-0.0972245773

2.20.50069385520.0027754227

2.30.5256712630.1027754227

2.40.5505208650.2027754227

2.50.57512085140.3027754227

2.60.59935430220.4027754227

2.70.62311134380.5027754227

2.80.64629102220.6027754227

2.90.66880283160.7027754227

30.69056785770.8027754227

3.10.71151951870.9027754227

3.20.73160390981.0027754227

3.30.75077977491.1027754227

3.40.76901814781.2027754227

3.50.78630171161.3027754227

3.60.80262393691.4027754227

3.70.81798805581.5027754227

3.80.83240593141.6027754227

3.90.84589687351.7027754227

40.85848644981.8027754227

4.10.87020532631.9027754227

4.20.88108817172.0027754227

4.30.89117264272.1027754227

4.40.9004984682.2027754227

4.50.90910663762.3027754227

4.60.91703869872.4027754227

4.70.92433615852.5027754227

4.80.93103998772.6027754227

4.90.93719021682.7027754227

50.94282561862.8027754227

5.10.94798346562.9027754227

5.20.95269935383.0027754227

5.30.95700708353.1027754227

5.40.96093858783.2027754227

5.50.96452390143.3027754227

5.60.96779116163.4027754227

5.70.97076663533.5027754227

5.80.97347476673.6027754227

5.90.97593823943.7027754227

60.97817805123.8027754227

6.10.98021359513.9027754227

6.20.9820627464.0027754227

6.30.98374194964.1027754227

6.40.98526631234.2027754227

6.50.98664968974.3027754227

6.60.98790477334.4027754227

6.70.98904317494.5027754227

6.80.99007550664.6027754227

6.90.99101145784.7027754227

70.99185986794.8027754227

7.10.99262879394.9027754227

7.20.9933255755.0027754227

7.30.99395689225.1027754227

7.40.99452882365.2027754227

7.50.9950468965.3027754227

7.60.99551613275.4027754227

7.70.99594109725.5027754227

7.80.99632593375.6027754227

7.90.99667440465.7027754227

80.99698992435.8027754227

8.10.99727559045.9027754227

8.20.9975342136.0027754227

8.30.997768346.1027754227

8.40.99798028166.2027754227

8.50.99817213196.3027754227

8.60.99834578886.4027754227

8.70.99850297226.5027754227

8.80.99864524026.6027754227

8.90.99877400466.7027754227

90.9988905446.8027754227

9.10.99899601676.9027754227

9.20.99909147167.0027754227

9.30.99917785847.1027754227

9.40.99925603737.2027754227

9.50.99932678717.3027754227

9.60.99939081277.4027754227

9.70.99944875267.5027754227

9.80.99950118457.6027754227

9.90.99954863177.7027754227

100.99959156757.8027754227

0

0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)

Fonction logistique

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

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0

0

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0

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0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X/(Xmax-X)) (-)

Fonction logistique

Modle de Monod

AG, 11-02

Donnes

1

Ks=5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

KY/Xm=0.2475247525

(KY+Xm)/Xm=1.2475247525

tXS

00.120

0.86720597180.219.8

1.37554669360.319.6

1.73697593750.419.4

2.01791808740.519.2

2.24796064830.619

2.4428867710.718.8

2.61211783740.818.6

2.76173105910.918.4

2.8958761258118.2

3.01751304221.118

3.12882755721.217.8

3.23147973591.317.6

3.32676015061.417.4

3.41569205531.517.2

3.49910051721.617

3.57766055471.716.8

3.65193149461.816.6

3.72238202811.916.4

3.7894088342216.2

3.85335065282.116

3.91449908382.215.8

3.97310698212.315.6

4.02939506662.415.4

4.0835571792.515.2

4.13576451092.615

4.1861690342.714.8

4.2349063062.814.6

4.28209778472.914.4

4.3278527506314.2

4.37226991453.114

4.41543877023.213.8

4.45744074023.313.6

4.49835015123.413.4

4.53823506783.513.2

4.57715801143.613

4.61517657983.712.8

4.65234398633.812.6

4.68870952913.912.4

4.7243190026412.2

4.75921505944.112

4.79343752934.211.8

4.82702370264.311.6

4.86000858254.411.4

4.89242510984.511.2

4.92430436614.611

4.95567575554.710.8

4.98656717024.810.6

5.01700514114.910.4

5.0470149754510.2

5.07662088355.110

5.10584609645.29.8

5.13471297515.39.6

5.16324311365.49.4

5.19145743645.59.2

5.21937629155.69

5.24701954015.78.8

5.27440664445.88.6

5.30155675375.98.4

5.328488790368.2

5.35522153656.18

5.38177372296.27.8

5.40816412066.37.6

5.4344116376.47.4

5.46053541786.57.2

5.48655495656.67

5.51249021366.76.8

5.53836174726.86.6

5.5641908586.96.4

5.589999752876.2

5.61581172897.16

5.64165138517.25.8

5.66754486617.35.6

5.6935201467.45.4

5.71960736147.55.2

5.7458392077.65

5.77225140647.74.8

5.79888328137.84.6

5.82577844287.94.4

5.852985640484.2

5.88055981488.14

5.90856341918.23.8

5.93706809198.33.6

5.96615680898.43.4

5.99592668238.53.2

6.02649266298.63

6.05799251848.72.8

6.09059365688.82.6

6.12450268318.92.4

6.159979121792.2

6.19735569459.12

6.23706931619.21.8

6.27971041839.31.6

6.32610538119.41.4

6.37746293339.51.2

6.43565523739.61

6.50381662299.70.8

6.58782029459.80.6

6.70084827979.90.4

6.8849574068100.2

6.912283643710.010.18

6.942683516910.020.16

6.976980255610.030.14

7.016379538210.040.12

7.062750572610.050.1

7.119224825910.060.08

7.19167272810.070.06

7.293273616510.080.04

7.466081711110.090.02

7.492284680310.0910.018

7.521562518310.0920.016

7.554738452310.0930.014

7.593018158110.0940.012

7.638270840910.0950.01

7.693627965510.0960.008

7.764959959410.0970.006

7.865446157810.0980.004

8.037140777810.0990.002

X

S

temps (-)

X (-)

S (-)

Modle de Monod

MBD00059657.unknown

Dtermination thoriqueCintique

Rendement: modles structurs (stochiomtriques et autres)

Une vue trs simplifie du mtabolisme cellulaireLe catabolisme gnre de lATP et du NADHModle stochiomtrique (cliquez ici)

Autres valeurs du coefficient de rendement(Bailey&Ollis, McGraw-Hill, 1986)

Dtermination exprimentaleCoefficient de rendement

CintiqueTaux initiauxStop-flowCuveChemostat

Dtermination exprimentale du coefficient de rendement - YX/S constantS = (Xmax-X)/Yx/s

Donnesmmax=1Ks=5Yx/s=0,5So=20Xo=0,1

Graph1

0.120

0.219.8

0.319.6

0.419.4

0.519.2

0.619

0.718.8

0.818.6

0.918.4

118.2

1.118

1.217.8

1.317.6

1.417.4

1.517.2

1.617

1.716.8

1.816.6

1.916.4

216.2

2.116

2.215.8

2.315.6

2.415.4

2.515.2

2.615

2.714.8

2.814.6

2.914.4

314.2

3.114

3.213.8

3.313.6

3.413.4

3.513.2

3.613

3.712.8

3.812.6

3.912.4

412.2

4.112

4.211.8

4.311.6

4.411.4

4.511.2

4.611

4.710.8

4.810.6

4.910.4

510.2

5.110

5.29.8

5.39.6

5.49.4

5.59.2

5.69

5.78.8

5.88.6

5.98.4

68.2

6.18

6.27.8

6.37.6

6.47.4

6.57.2

6.67

6.76.8

6.86.6

6.96.4

76.2

7.16

7.25.8

7.35.6

7.45.4

7.55.2

7.65

7.74.8

7.84.6

7.94.4

84.2

8.14

8.23.8

8.33.6

8.43.4

8.53.2

8.63

8.72.8

8.82.6

8.92.4

92.2

9.12

9.21.8

9.31.6

9.41.4

9.51.2

9.61

9.70.8

9.80.6

9.90.4

100.2

10.010.18

10.020.16

10.030.14

10.040.12

10.050.1

10.060.08

10.070.06

10.080.04

10.090.02

10.0910.018

10.0920.016

10.0930.014

10.0940.012

10.0950.01

10.0960.008

10.0970.006

10.0980.004

10.0990.002

X

S

temps (-)

X (-)

S (-)

Modle de Monod

Ordre 0_exponentiel


AG, nov 2002

Donnes

1tlag=0.5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

avec latence

tXln(X)Xln(X)

00.1-2.3025850930.1-2.302585093

0.10.1105170918-2.2025850930.1-2.302585093

0.20.1221402758-2.1025850930.1-2.302585093

0.30.1349858808-2.0025850930.1-2.302585093

0.40.1491824698-1.9025850930.1-2.302585093

0.50.1648721271-1.8025850930.1-2.302585093

0.60.18221188-1.7025850930.1105170918-2.202585093

0.70.2013752707-1.6025850930.1221402758-2.102585093

0.80.2225540928-1.5025850930.1349858808-2.002585093

0.90.2459603111-1.4025850930.1491824698-1.902585093

10.2718281828-1.3025850930.1648721271-1.802585093

1.10.3004166024-1.2025850930.18221188-1.702585093

1.20.3320116923-1.1025850930.2013752707-1.602585093

1.30.3669296668-1.0025850930.2225540928-1.502585093

1.40.4055199967-0.9025850930.2459603111-1.402585093

1.50.448168907-0.8025850930.2718281828-1.302585093

1.60.4953032424-0.7025850930.3004166024-1.202585093

1.70.5473947392-0.6025850930.3320116923-1.102585093

1.80.6049647464-0.5025850930.3669296668-1.002585093

1.90.6685894442-0.4025850930.4055199967-0.902585093

20.7389056099-0.3025850930.448168907-0.802585093

2.10.8166169913-0.2025850930.4953032424-0.702585093

2.20.9025013499-0.1025850930.5473947392-0.602585093

2.30.9974182455-0.0025850930.6049647464-0.502585093

2.41.10231763810.0974149070.6685894442-0.402585093

2.51.21824939610.1974149070.7389056099-0.302585093

2.61.34637380350.2974149070.8166169913-0.202585093

2.71.48797317250.3974149070.9025013499-0.102585093

2.81.64446467710.4974149070.9974182455-0.002585093

2.91.81741453690.5974149071.10231763810.097414907

32.00855369230.6974149071.21824939610.197414907

3.12.21979512810.7974149071.34637380350.297414907

3.22.45325301970.8974149071.48797317250.397414907

3.32.71126389210.9974149071.64446467710.497414907

3.42.99641000471.0974149071.81741453690.597414907

3.53.31154519591.1974149072.00855369230.697414907

3.63.65982344441.2974149072.21979512810.797414907

3.74.0447304361.3974149072.45325301970.897414907

3.84.47011844931.4974149072.71126389210.997414907

3.94.94024491061.5974149072.99641000471.097414907

45.45981500331.6974149073.31154519591.197414907

4.16.03402875971.7974149073.65982344441.297414907

4.26.66863310411.8974149074.0447304361.397414907

4.37.369979371.9974149074.47011844931.497414907

4.48.14508686652.0974149074.94024491061.597414907

4.59.00171313012.1974149075.45981500331.697414907

4.69.94843156422.2974149076.03402875971.797414907

4.710.12.31253542386.66863310411.897414907

4.810.12.31253542387.369979371.997414907

4.910.12.31253542388.14508686652.097414907

510.12.31253542389.00171313012.197414907

5.110.12.31253542389.94843156422.297414907

5.210.12.312535423810.12.3125354238

5.310.12.312535423810.12.3125354238

5.410.12.312535423810.12.3125354238

5.510.12.312535423810.12.3125354238

5.610.12.312535423810.12.3125354238

5.710.12.312535423810.12.3125354238

5.810.12.312535423810.12.3125354238

5.910.12.312535423810.12.3125354238

610.12.312535423810.12.3125354238

6.110.12.312535423810.12.3125354238

6.210.12.312535423810.12.3125354238

6.310.12.312535423810.12.3125354238

6.410.12.312535423810.12.3125354238

6.510.12.312535423810.12.3125354238

6.610.12.312535423810.12.3125354238

6.710.12.312535423810.12.3125354238

6.810.12.312535423810.12.3125354238

6.910.12.312535423810.12.3125354238

710.12.312535423810.12.3125354238

7.110.12.312535423810.12.3125354238

7.210.12.312535423810.12.3125354238

7.310.12.312535423810.12.3125354238

7.410.12.312535423810.12.3125354238

7.510.12.312535423810.12.3125354238

7.610.12.312535423810.12.3125354238

7.710.12.312535423810.12.3125354238

7.810.12.312535423810.12.3125354238

7.910.12.312535423810.12.3125354238

810.12.312535423810.12.3125354238

8.110.12.312535423810.12.3125354238

8.210.12.312535423810.12.3125354238

8.310.12.312535423810.12.3125354238

8.410.12.312535423810.12.3125354238

8.510.12.312535423810.12.3125354238

8.610.12.312535423810.12.3125354238

8.710.12.312535423810.12.3125354238

8.810.12.312535423810.12.3125354238

8.910.12.312535423810.12.3125354238

Ordre 0_exponentiel

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)



0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Monod

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)


0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Courbe logistique

AG, 11-2002

Donnes

k=1

X0=0.1

Xm=1

tXln(X/(Xmax-X)

00.1-2.1972245773

0.10.1093668704-2.0972245773

0.20.1194946317-1.9972245773

0.30.13042292-1.8972245773

0.40.1421892512-1.7972245773

0.50.154828099-1.6972245773

0.60.168369876-1.5972245773

0.70.1828398332-1.4972245773

0.80.1982568985-1.3972245773

0.90.2146324866-1.2972245773

10.2319693167-1.1972245773

1.10.2502602861-1.0972245773

1.20.2694874524-0.9972245773

1.30.2896211813-0.8972245773

1.40.3106195215-0.7972245773

1.50.3324278617-0.6972245773

1.60.3549789231-0.5972245773

1.70.3781931248-0.4972245773

1.80.4019793473-0.3972245773

1.90.4262360981-0.2972245773

20.4508530604-0.1972245773

2.10.475712984-0.0972245773

2.20.50069385520.0027754227

2.30.5256712630.1027754227

2.40.5505208650.2027754227

2.50.57512085140.3027754227

2.60.59935430220.4027754227

2.70.62311134380.5027754227

2.80.64629102220.6027754227

2.90.66880283160.7027754227

30.69056785770.8027754227

3.10.71151951870.9027754227

3.20.73160390981.0027754227

3.30.75077977491.1027754227

3.40.76901814781.2027754227

3.50.78630171161.3027754227

3.60.80262393691.4027754227

3.70.81798805581.5027754227

3.80.83240593141.6027754227

3.90.84589687351.7027754227

40.85848644981.8027754227

4.10.87020532631.9027754227

4.20.88108817172.0027754227

4.30.89117264272.1027754227

4.40.9004984682.2027754227

4.50.90910663762.3027754227

4.60.91703869872.4027754227

4.70.92433615852.5027754227

4.80.93103998772.6027754227

4.90.93719021682.7027754227

50.94282561862.8027754227

5.10.94798346562.9027754227

5.20.95269935383.0027754227

5.30.95700708353.1027754227

5.40.96093858783.2027754227

5.50.96452390143.3027754227

5.60.96779116163.4027754227

5.70.97076663533.5027754227

5.80.97347476673.6027754227

5.90.97593823943.7027754227

60.97817805123.8027754227

6.10.98021359513.9027754227

6.20.9820627464.0027754227

6.30.98374194964.1027754227

6.40.98526631234.2027754227

6.50.98664968974.3027754227

6.60.98790477334.4027754227

6.70.98904317494.5027754227

6.80.99007550664.6027754227

6.90.99101145784.7027754227

70.99185986794.8027754227

7.10.99262879394.9027754227

7.20.9933255755.0027754227

7.30.99395689225.1027754227

7.40.99452882365.2027754227

7.50.9950468965.3027754227

7.60.99551613275.4027754227

7.70.99594109725.5027754227

7.80.99632593375.6027754227

7.90.99667440465.7027754227

80.99698992435.8027754227

8.10.99727559045.9027754227

8.20.9975342136.0027754227

8.30.997768346.1027754227

8.40.99798028166.2027754227

8.50.99817213196.3027754227

8.60.99834578886.4027754227

8.70.99850297226.5027754227

8.80.99864524026.6027754227

8.90.99877400466.7027754227

90.9988905446.8027754227

9.10.99899601676.9027754227

9.20.99909147167.0027754227

9.30.99917785847.1027754227

9.40.99925603737.2027754227

9.50.99932678717.3027754227

9.60.99939081277.4027754227

9.70.99944875267.5027754227

9.80.99950118457.6027754227

9.90.99954863177.7027754227

100.99959156757.8027754227

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)

Fonction logistique

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X/(Xmax-X)) (-)

Fonction logistique

Modle de Monod

AG, 11-02

Donnes

1

Ks=5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

KY/Xm=0.2475247525

(KY+Xm)/Xm=1.2475247525

tXS

00.120

0.86720597180.219.8

1.37554669360.319.6

1.73697593750.419.4

2.01791808740.519.2

2.24796064830.619

2.4428867710.718.8

2.61211783740.818.6

2.76173105910.918.4

2.8958761258118.2

3.01751304221.118

3.12882755721.217.8

3.23147973591.317.6

3.32676015061.417.4

3.41569205531.517.2

3.49910051721.617

3.57766055471.716.8

3.65193149461.816.6

3.72238202811.916.4

3.7894088342216.2

3.85335065282.116

3.91449908382.215.8

3.97310698212.315.6

4.02939506662.415.4

4.0835571792.515.2

4.13576451092.615

4.1861690342.714.8

4.2349063062.814.6

4.28209778472.914.4

4.3278527506314.2

4.37226991453.114

4.41543877023.213.8

4.45744074023.313.6

4.49835015123.413.4

4.53823506783.513.2

4.57715801143.613

4.61517657983.712.8

4.65234398633.812.6

4.68870952913.912.4

4.7243190026412.2

4.75921505944.112

4.79343752934.211.8

4.82702370264.311.6

4.86000858254.411.4

4.89242510984.511.2

4.92430436614.611

4.95567575554.710.8

4.98656717024.810.6

5.01700514114.910.4

5.0470149754510.2

5.07662088355.110

5.10584609645.29.8

5.13471297515.39.6

5.16324311365.49.4

5.19145743645.59.2

5.21937629155.69

5.24701954015.78.8

5.27440664445.88.6

5.30155675375.98.4

5.328488790368.2

5.35522153656.18

5.38177372296.27.8

5.40816412066.37.6

5.4344116376.47.4

5.46053541786.57.2

5.48655495656.67

5.51249021366.76.8

5.53836174726.86.6

5.5641908586.96.4

5.589999752876.2

5.61581172897.16

5.64165138517.25.8

5.66754486617.35.6

5.6935201467.45.4

5.71960736147.55.2

5.7458392077.65

5.77225140647.74.8

5.79888328137.84.6

5.82577844287.94.4

5.852985640484.2

5.88055981488.14

5.90856341918.23.8

5.93706809198.33.6

5.96615680898.43.4

5.99592668238.53.2

6.02649266298.63

6.05799251848.72.8

6.09059365688.82.6

6.12450268318.92.4

6.159979121792.2

6.19735569459.12

6.23706931619.21.8

6.27971041839.31.6

6.32610538119.41.4

6.37746293339.51.2

6.43565523739.61

6.50381662299.70.8

6.58782029459.80.6

6.70084827979.90.4

6.8849574068100.2

6.912283643710.010.18

6.942683516910.020.16

6.976980255610.030.14

7.016379538210.040.12

7.062750572610.050.1

7.119224825910.060.08

7.19167272810.070.06

7.293273616510.080.04

7.466081711110.090.02

7.492284680310.0910.018

7.521562518310.0920.016

7.554738452310.0930.014

7.593018158110.0940.012

7.638270840910.0950.01

7.693627965510.0960.008

7.764959959410.0970.006

7.865446157810.0980.004

8.037140777810.0990.002

X

S

temps (-)

X (-)

S (-)

Modle de Monod

MBD00059657.unknown

Estimation des rendements en cuveAvec des donnes de t, X, S, on peut calculer, Yx/s par un graphe de X vs S:

Ici, Yx/s = 0,5

Graph2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

8

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.01

10.02

10.03

10.04

10.05

10.06

10.07

10.08

10.09

10.091

10.092

10.093

10.094

10.095

10.096

10.097

10.098

10.099

X

S (-)

X (-)

Modle de Monod -X vs S

Ordre 0_exponentiel


AG, nov 2002

Donnes

1tlag=0.5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

avec latence

tXln(X)Xln(X)

00.1-2.3025850930.1-2.302585093

0.10.1105170918-2.2025850930.1-2.302585093

0.20.1221402758-2.1025850930.1-2.302585093

0.30.1349858808-2.0025850930.1-2.302585093

0.40.1491824698-1.9025850930.1-2.302585093

0.50.1648721271-1.8025850930.1-2.302585093

0.60.18221188-1.7025850930.1105170918-2.202585093

0.70.2013752707-1.6025850930.1221402758-2.102585093

0.80.2225540928-1.5025850930.1349858808-2.002585093

0.90.2459603111-1.4025850930.1491824698-1.902585093

10.2718281828-1.3025850930.1648721271-1.802585093

1.10.3004166024-1.2025850930.18221188-1.702585093

1.20.3320116923-1.1025850930.2013752707-1.602585093

1.30.3669296668-1.0025850930.2225540928-1.502585093

1.40.4055199967-0.9025850930.2459603111-1.402585093

1.50.448168907-0.8025850930.2718281828-1.302585093

1.60.4953032424-0.7025850930.3004166024-1.202585093

1.70.5473947392-0.6025850930.3320116923-1.102585093

1.80.6049647464-0.5025850930.3669296668-1.002585093

1.90.6685894442-0.4025850930.4055199967-0.902585093

20.7389056099-0.3025850930.448168907-0.802585093

2.10.8166169913-0.2025850930.4953032424-0.702585093

2.20.9025013499-0.1025850930.5473947392-0.602585093

2.30.9974182455-0.0025850930.6049647464-0.502585093

2.41.10231763810.0974149070.6685894442-0.402585093

2.51.21824939610.1974149070.7389056099-0.302585093

2.61.34637380350.2974149070.8166169913-0.202585093

2.71.48797317250.3974149070.9025013499-0.102585093

2.81.64446467710.4974149070.9974182455-0.002585093

2.91.81741453690.5974149071.10231763810.097414907

32.00855369230.6974149071.21824939610.197414907

3.12.21979512810.7974149071.34637380350.297414907

3.22.45325301970.8974149071.48797317250.397414907

3.32.71126389210.9974149071.64446467710.497414907

3.42.99641000471.0974149071.81741453690.597414907

3.53.31154519591.1974149072.00855369230.697414907

3.63.65982344441.2974149072.21979512810.797414907

3.74.0447304361.3974149072.45325301970.897414907

3.84.47011844931.4974149072.71126389210.997414907

3.94.94024491061.5974149072.99641000471.097414907

45.45981500331.6974149073.31154519591.197414907

4.16.03402875971.7974149073.65982344441.297414907

4.26.66863310411.8974149074.0447304361.397414907

4.37.369979371.9974149074.47011844931.497414907

4.48.14508686652.0974149074.94024491061.597414907

4.59.00171313012.1974149075.45981500331.697414907

4.69.94843156422.2974149076.03402875971.797414907

4.710.12.31253542386.66863310411.897414907

4.810.12.31253542387.369979371.997414907

4.910.12.31253542388.14508686652.097414907

510.12.31253542389.00171313012.197414907

5.110.12.31253542389.94843156422.297414907

5.210.12.312535423810.12.3125354238

5.310.12.312535423810.12.3125354238

5.410.12.312535423810.12.3125354238

5.510.12.312535423810.12.3125354238

5.610.12.312535423810.12.3125354238

5.710.12.312535423810.12.3125354238

5.810.12.312535423810.12.3125354238

5.910.12.312535423810.12.3125354238

610.12.312535423810.12.3125354238

6.110.12.312535423810.12.3125354238

6.210.12.312535423810.12.3125354238

6.310.12.312535423810.12.3125354238

6.410.12.312535423810.12.3125354238

6.510.12.312535423810.12.3125354238

6.610.12.312535423810.12.3125354238

6.710.12.312535423810.12.3125354238

6.810.12.312535423810.12.3125354238

6.910.12.312535423810.12.3125354238

710.12.312535423810.12.3125354238

7.110.12.312535423810.12.3125354238

7.210.12.312535423810.12.3125354238

7.310.12.312535423810.12.3125354238

7.410.12.312535423810.12.3125354238

7.510.12.312535423810.12.3125354238

7.610.12.312535423810.12.3125354238

7.710.12.312535423810.12.3125354238

7.810.12.312535423810.12.3125354238

7.910.12.312535423810.12.3125354238

810.12.312535423810.12.3125354238

8.110.12.312535423810.12.3125354238

8.210.12.312535423810.12.3125354238

8.310.12.312535423810.12.3125354238

8.410.12.312535423810.12.3125354238

8.510.12.312535423810.12.3125354238

8.610.12.312535423810.12.3125354238

8.710.12.312535423810.12.3125354238

8.810.12.312535423810.12.3125354238

8.910.12.312535423810.12.3125354238

Ordre 0_exponentiel

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)



0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Monod

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)


0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Courbe logistique

AG, 11-2002

Donnes

k=1

X0=0.1

Xm=1

tXln(X/(Xmax-X)

00.1-2.1972245773

0.10.1093668704-2.0972245773

0.20.1194946317-1.9972245773

0.30.13042292-1.8972245773

0.40.1421892512-1.7972245773

0.50.154828099-1.6972245773

0.60.168369876-1.5972245773

0.70.1828398332-1.4972245773

0.80.1982568985-1.3972245773

0.90.2146324866-1.2972245773

10.2319693167-1.1972245773

1.10.2502602861-1.0972245773

1.20.2694874524-0.9972245773

1.30.2896211813-0.8972245773

1.40.3106195215-0.7972245773

1.50.3324278617-0.6972245773

1.60.3549789231-0.5972245773

1.70.3781931248-0.4972245773

1.80.4019793473-0.3972245773

1.90.4262360981-0.2972245773

20.4508530604-0.1972245773

2.10.475712984-0.0972245773

2.20.50069385520.0027754227

2.30.5256712630.1027754227

2.40.5505208650.2027754227

2.50.57512085140.3027754227

2.60.59935430220.4027754227

2.70.62311134380.5027754227

2.80.64629102220.6027754227

2.90.66880283160.7027754227

30.69056785770.8027754227

3.10.71151951870.9027754227

3.20.73160390981.0027754227

3.30.75077977491.1027754227

3.40.76901814781.2027754227

3.50.78630171161.3027754227

3.60.80262393691.4027754227

3.70.81798805581.5027754227

3.80.83240593141.6027754227

3.90.84589687351.7027754227

40.85848644981.8027754227

4.10.87020532631.9027754227

4.20.88108817172.0027754227

4.30.89117264272.1027754227

4.40.9004984682.2027754227

4.50.90910663762.3027754227

4.60.91703869872.4027754227

4.70.92433615852.5027754227

4.80.93103998772.6027754227

4.90.93719021682.7027754227

50.94282561862.8027754227

5.10.94798346562.9027754227

5.20.95269935383.0027754227

5.30.95700708353.1027754227

5.40.96093858783.2027754227

5.50.96452390143.3027754227

5.60.96779116163.4027754227

5.70.97076663533.5027754227

5.80.97347476673.6027754227

5.90.97593823943.7027754227

60.97817805123.8027754227

6.10.98021359513.9027754227

6.20.9820627464.0027754227

6.30.98374194964.1027754227

6.40.98526631234.2027754227

6.50.98664968974.3027754227

6.60.98790477334.4027754227

6.70.98904317494.5027754227

6.80.99007550664.6027754227

6.90.99101145784.7027754227

70.99185986794.8027754227

7.10.99262879394.9027754227

7.20.9933255755.0027754227

7.30.99395689225.1027754227

7.40.99452882365.2027754227

7.50.9950468965.3027754227

7.60.99551613275.4027754227

7.70.99594109725.5027754227

7.80.99632593375.6027754227

7.90.99667440465.7027754227

80.99698992435.8027754227

8.10.99727559045.9027754227

8.20.9975342136.0027754227

8.30.997768346.1027754227

8.40.99798028166.2027754227

8.50.99817213196.3027754227

8.60.99834578886.4027754227

8.70.99850297226.5027754227

8.80.99864524026.6027754227

8.90.99877400466.7027754227

90.9988905446.8027754227

9.10.99899601676.9027754227

9.20.99909147167.0027754227

9.30.99917785847.1027754227

9.40.99925603737.2027754227

9.50.99932678717.3027754227

9.60.99939081277.4027754227

9.70.99944875267.5027754227

9.80.99950118457.6027754227

9.90.99954863177.7027754227

100.99959156757.8027754227

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)

Fonction logistique

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X/(Xmax-X)) (-)

Fonction logistique

Modle de Monod

AG, 11-02

Donnes

1

Ks=5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

KY/Xm=0.2475247525

(KY+Xm)/Xm=1.2475247525

tXS

00.120

0.86720597180.219.8

1.37554669360.319.6

1.73697593750.419.4

2.01791808740.519.2

2.24796064830.619

2.4428867710.718.8

2.61211783740.818.6

2.76173105910.918.4

2.8958761258118.2

3.01751304221.118

3.12882755721.217.8

3.23147973591.317.6

3.32676015061.417.4

3.41569205531.517.2

3.49910051721.617

3.57766055471.716.8

3.65193149461.816.6

3.72238202811.916.4

3.7894088342216.2

3.85335065282.116

3.91449908382.215.8

3.97310698212.315.6

4.02939506662.415.4

4.0835571792.515.2

4.13576451092.615

4.1861690342.714.8

4.2349063062.814.6

4.28209778472.914.4

4.3278527506314.2

4.37226991453.114

4.41543877023.213.8

4.45744074023.313.6

4.49835015123.413.4

4.53823506783.513.2

4.57715801143.613

4.61517657983.712.8

4.65234398633.812.6

4.68870952913.912.4

4.7243190026412.2

4.75921505944.112

4.79343752934.211.8

4.82702370264.311.6

4.86000858254.411.4

4.89242510984.511.2

4.92430436614.611

4.95567575554.710.8

4.98656717024.810.6

5.01700514114.910.4

5.0470149754510.2

5.07662088355.110

5.10584609645.29.8

5.13471297515.39.6

5.16324311365.49.4

5.19145743645.59.2

5.21937629155.69

5.24701954015.78.8

5.27440664445.88.6

5.30155675375.98.4

5.328488790368.2

5.35522153656.18

5.38177372296.27.8

5.40816412066.37.6

5.4344116376.47.4

5.46053541786.57.2

5.48655495656.67

5.51249021366.76.8

5.53836174726.86.6

5.5641908586.96.4

5.589999752876.2

5.61581172897.16

5.64165138517.25.8

5.66754486617.35.6

5.6935201467.45.4

5.71960736147.55.2

5.7458392077.65

5.77225140647.74.8

5.79888328137.84.6

5.82577844287.94.4

5.852985640484.2

5.88055981488.14

5.90856341918.23.8

5.93706809198.33.6

5.96615680898.43.4

5.99592668238.53.2

6.02649266298.63

6.05799251848.72.8

6.09059365688.82.6

6.12450268318.92.4

6.159979121792.2

6.19735569459.12

6.23706931619.21.8

6.27971041839.31.6

6.32610538119.41.4

6.37746293339.51.2

6.43565523739.61

6.50381662299.70.8

6.58782029459.80.6

6.70084827979.90.4

6.8849574068100.2

6.912283643710.010.18

6.942683516910.020.16

6.976980255610.030.14

7.016379538210.040.12

7.062750572610.050.1

7.119224825910.060.08

7.19167272810.070.06

7.293273616510.080.04

7.466081711110.090.02

7.492284680310.0910.018

7.521562518310.0920.016

7.554738452310.0930.014

7.593018158110.0940.012

7.638270840910.0950.01

7.693627965510.0960.008

7.764959959410.0970.006

7.865446157810.0980.004

8.037140777810.0990.002

X

S

temps (-)

X (-)

S (-)

Modle de Monod

X

S (-)

X (-)


MBD00059657.unknown

Effet de maintenanceS = S(croissance) + S(maintenance)

rS = 1/YG* rX + m * X

qs = 1/YG* m + m

1/Yx/s = qs/m = 1/YG + m/ m

Effet de maintenance1/Yx/s = qs/m = 1/YG + m/ m

Graph2

2.2

2.1

2.0666666667

2.05

2.04

2.0333333333

2.0285714286

2.025

2.0222222222

2.02

2.0181818182

2.0166666667

2.0153846154

1/Yx/s

1/mu

1/(Yx/s)

1/Yx/s vs 1/mu

Ordre 0_exponentiel


AG, nov 2002

Donnes

m=1tlag=0.5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

avec latence

tXln(X)Xln(X)

00.1-2.3025850930.1-2.302585093

0.10.1105170918-2.2025850930.1-2.302585093

0.20.1221402758-2.1025850930.1-2.302585093

0.30.1349858808-2.0025850930.1-2.302585093

0.40.1491824698-1.9025850930.1-2.302585093

0.50.1648721271-1.8025850930.1-2.302585093

0.60.18221188-1.7025850930.1105170918-2.202585093

0.70.2013752707-1.6025850930.1221402758-2.102585093

0.80.2225540928-1.5025850930.1349858808-2.002585093

0.90.2459603111-1.4025850930.1491824698-1.902585093

10.2718281828-1.3025850930.1648721271-1.802585093

1.10.3004166024-1.2025850930.18221188-1.702585093

1.20.3320116923-1.1025850930.2013752707-1.602585093

1.30.3669296668-1.0025850930.2225540928-1.502585093

1.40.4055199967-0.9025850930.2459603111-1.402585093

1.50.448168907-0.8025850930.2718281828-1.302585093

1.60.4953032424-0.7025850930.3004166024-1.202585093

1.70.5473947392-0.6025850930.3320116923-1.102585093

1.80.6049647464-0.5025850930.3669296668-1.002585093

1.90.6685894442-0.4025850930.4055199967-0.902585093

20.7389056099-0.3025850930.448168907-0.802585093

2.10.8166169913-0.2025850930.4953032424-0.702585093

2.20.9025013499-0.1025850930.5473947392-0.602585093

2.30.9974182455-0.0025850930.6049647464-0.502585093

2.41.10231763810.0974149070.6685894442-0.402585093

2.51.21824939610.1974149070.7389056099-0.302585093

2.61.34637380350.2974149070.8166169913-0.202585093

2.71.48797317250.3974149070.9025013499-0.102585093

2.81.64446467710.4974149070.9974182455-0.002585093

2.91.81741453690.5974149071.10231763810.097414907

32.00855369230.6974149071.21824939610.197414907

3.12.21979512810.7974149071.34637380350.297414907

3.22.45325301970.8974149071.48797317250.397414907

3.32.71126389210.9974149071.64446467710.497414907

3.42.99641000471.0974149071.81741453690.597414907

3.53.31154519591.1974149072.00855369230.697414907

3.63.65982344441.2974149072.21979512810.797414907

3.74.0447304361.3974149072.45325301970.897414907

3.84.47011844931.4974149072.71126389210.997414907

3.94.94024491061.5974149072.99641000471.097414907

45.45981500331.6974149073.31154519591.197414907

4.16.03402875971.7974149073.65982344441.297414907

4.26.66863310411.8974149074.0447304361.397414907

4.37.369979371.9974149074.47011844931.497414907

4.48.14508686652.0974149074.94024491061.597414907

4.59.00171313012.1974149075.45981500331.697414907

4.69.94843156422.2974149076.03402875971.797414907

4.710.12.31253542386.66863310411.897414907

4.810.12.31253542387.369979371.997414907

4.910.12.31253542388.14508686652.097414907

510.12.31253542389.00171313012.197414907

5.110.12.31253542389.94843156422.297414907

5.210.12.312535423810.12.3125354238

5.310.12.312535423810.12.3125354238

5.410.12.312535423810.12.3125354238

5.510.12.312535423810.12.3125354238

5.610.12.312535423810.12.3125354238

5.710.12.312535423810.12.3125354238

5.810.12.312535423810.12.3125354238

5.910.12.312535423810.12.3125354238

610.12.312535423810.12.3125354238

6.110.12.312535423810.12.3125354238

6.210.12.312535423810.12.3125354238

6.310.12.312535423810.12.3125354238

6.410.12.312535423810.12.3125354238

6.510.12.312535423810.12.3125354238

6.610.12.312535423810.12.3125354238

6.710.12.312535423810.12.3125354238

6.810.12.312535423810.12.3125354238

6.910.12.312535423810.12.3125354238

710.12.312535423810.12.3125354238

7.110.12.312535423810.12.3125354238

7.210.12.312535423810.12.3125354238

7.310.12.312535423810.12.3125354238

7.410.12.312535423810.12.3125354238

7.510.12.312535423810.12.3125354238

7.610.12.312535423810.12.3125354238

7.710.12.312535423810.12.3125354238

7.810.12.312535423810.12.3125354238

7.910.12.312535423810.12.3125354238

810.12.312535423810.12.3125354238

8.110.12.312535423810.12.3125354238

8.210.12.312535423810.12.3125354238

8.310.12.312535423810.12.3125354238

8.410.12.312535423810.12.3125354238

8.510.12.312535423810.12.3125354238

8.610.12.312535423810.12.3125354238

8.710.12.312535423810.12.3125354238

8.810.12.312535423810.12.3125354238

8.910.12.312535423810.12.3125354238

Ordre 0_exponentiel

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)



0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Monod

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)


maintenance

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

ln(X) (-)


Courbe logistique

AG, 11-2002

Donnes

k=1

X0=0.1

Xm=1

tXln(X/(Xmax-X)dX/dt

00.1-2.19722457730.09

0.10.1093668704-2.09722457730.0974057581

0.20.1194946317-1.99722457730.1052156647

0.30.13042292-1.89722457730.113412782

0.40.1421892512-1.79722457730.1219714681

0.50.154828099-1.69722457730.1308563587

0.60.168369876-1.59722457730.1400214609

0.70.1828398332-1.49722457730.1494094286

0.80.1982568985-1.39722457730.1589511007

0.90.2146324866-1.29722457730.1685653823

10.2319693167-1.19722457730.1781595528

1.10.2502602861-1.09722457730.1876300753

1.20.2694874524-0.99722457730.1968639654

1.30.2896211813-0.89722457730.2057407527

1.40.3106195215-0.79722457730.2141350344

1.50.3324278617-0.69722457730.2219195785

1.60.3549789231-0.59722457730.2289688873

1.70.3781931248-0.49722457730.2351630851

1.80.4019793473-0.39722457730.2403919516

1.90.4262360981-0.29722457730.2445588868

20.4508530604-0.19722457730.2475845783

2.10.475712984-0.09722457730.2494101409

2.20.50069385520.00277542270.2499995186

2.30.5256712630.10277542270.2493409863

2.40.5505208650.20277542270.2474476422

2.50.57512085140.30277542270.2443568577

2.60.59935430220.40277542270.2401287226

2.70.62311134380.50277542270.234843597

2.80.64629102220.60277542270.2285989368

2.90.66880283160.70277542270.221505604

30.69056785770.80277542270.2136838916

3.10.71151951870.90277542270.2052594932

3.20.73160390981.00277542270.196359629

3.30.75077977491.10277542270.1871095045

3.40.76901814781.20277542270.1776292362

3.50.78630171161.30277542270.16803133

3.60.80262393691.40277542270.1584187528

3.70.81798805581.50277542270.1488835963

3.80.83240593141.60277542270.1395062968

3.90.84589687351.70277542270.1303553529

40.85848644981.80277542270.1214874653

4.10.87020532631.90277542270.1129480163

4.20.88108817172.00277542270.1047718054

4.30.89117264272.10277542270.0969839636

4.40.9004984682.20277542270.0896009771

4.50.90910663762.30277542270.0826317591

4.60.91703869872.40277542270.0760787238

4.70.92433615852.50277542270.0699388246

4.80.93103998772.60277542270.064204529

4.90.93719021682.70277542270.0588647144

50.94282561862.80277542270.0539054715

5.10.94798346562.90277542270.0493108146

5.20.95269935383.00277542270.0450632951

5.30.95700708353.10277542270.0411445257

5.40.96093858783.20277542270.0375356183

5.50.96452390143.30277542270.034217545

5.60.96779116163.40277542270.0311714291

5.70.97076663533.50277542270.0283787751

5.80.97347476673.60277542270.0258216453

5.90.97593823943.70277542270.0234827923

60.97817805123.80277542270.0213457513

6.10.98021359513.90277542270.0193949031

6.20.9820627464.00277542270.0176155089

6.30.98374194964.10277542270.0159937262

6.40.98526631234.20277542270.0145166061

6.50.98664968974.30277542270.0131720795

6.60.98790477334.40277542270.0119489322

6.70.98904317494.50277542270.0108367731

6.80.99007550664.60277542270.0098259979

6.90.99101145784.70277542270.0089077483

70.99185986794.80277542270.0080738704

7.10.99262879394.90277542270.0073168715

7.20.9933255755.00277542270.006629877

7.30.99395689225.10277542270.0060065886

7.40.99452882365.20277542270.0054412426

7.50.9950468965.30277542270.0049285707

7.60.99551613275.40277542270.0044637622

7.70.99594109725.50277542270.0040424281

7.80.99632593375.60277542270.0036605675

7.90.99667440465.70277542270.0033145358

80.99698992435.80277542270.0030010152

8.10.99727559045.90277542270.0027169872

8.20.9975342136.00277542270.0024597069

8.30.997768346.10277542270.0022266797

8.40.99798028166.20277542270.0020156391

8.50.99817213196.30277542270.001824527

8.60.99834578886.40277542270.0016514748

8.70.99850297226.50277542270.0014947868

8.80.99864524026.60277542270.0013529244

8.90.99877400466.70277542270.0012244924

90.9988905446.80277542270.0011082251

9.10.99899601676.90277542270.0010029753

9.20.99909147167.00277542270.000907703

9.30.99917785847.10277542270.0008214657

9.40.99925603737.20277542270.0007434092

9.50.99932678717.30277542270.0006727597

9.60.99939081277.40277542270.0006088162

9.70.99944875267.50277542270.0005509435

9.80.99950118457.60277542270.0004985666

9.90.99954863177.70277542270.0004511646

100.99959156757.80277542270.0004082657

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

temps (-)

X (-)

Fonction logistique

temps (-)

ln(X/(Xmax-X)) (-)

Fonction logistique

temps (-)

dX/dt (-)

Fonction logistique

Modle de Monod

AG, 11-02

Donnes

mmax=1

Ks=5

Yx/s=0.54.9995

So=20Estimation des paramtres

Xo=0.1ln(X/X0)/t

Calculs

Xmax =10.1

KY/Xm=0.2475247525

(KY+Xm)/Xm=1.2475247525

tXSln(X/X0)/tln

00.120

0.86720597180.219.80.7992878314-0.810877161

1.37554669360.319.60.7986732066-0.8133602452

1.73697593750.419.40.7981079825-0.8156437507

2.01791808740.519.20.7975734607-0.8178032187

2.24796064830.6190.7970599799-0.8198776811

2.4428867710.718.80.796561745-0.8218905504

2.61211783740.818.60.7960749366-0.8238572563

2.76173105910.918.40.7955968667-0.8257886584

2.8958761258118.20.7951255485-0.8276927839

3.01751304221.1180.7946594561-0.8295757975

3.12882755721.217.80.7941973804-0.831442583

3.23147973591.317.60.7937383388-0.8332971112

3.32676015061.417.40.7932815142-0.8351426827

3.41569205531.517.20.7928262142-0.8369820946

3.49910051721.6170.792371842-0.8388177582

3.57766055471.716.80.791917875-0.8406517849

3.65193149461.816.60.7914638493-0.842486049

3.72238202811.916.40.7910093475-0.8443222362

3.7894088342216.20.79055399-0.8461618804

3.85335065282.1160.7900974274-0.8480063933

3.91449908382.215.80.789639335-0.8498570866

3.97310698212.315.60.789179408-0.8517151918

4.02939506662.415.40.7887173578-0.8535818746

4.0835571792.515.20.7882529089-0.8554582482

4.13576451092.6150.7877857962-0.8573453835

4.1861690342.714.80.7873157627-0.8592443185

4.2349063062.814.60.7868425579-0.8611560662

4.28209778472.914.40.7863659354-0.8630816209

4.3278527506314.20.7858856522-0.865021965

4.37226991453.1140.7854014669-0.8669780738

4.41543877023.213.80.7849131385-0.8689509206

4.45744074023.313.60.7844204254-0.8709414816

4.49835015123.413.40.7839230843-0.8729507396

4.53823506783.513.20.7834208692-0.8749796884

4.57715801143.6130.7829135305-0.8770293367

4.61517657983.712.80.782400814-0.8791007116

4.65234398633.812.60.7818824598-0.8811948625

4.68870952913.912.40.7813582017-0.883312865

4.7243190026412.20.7808277663-0.8854558241

4.75921505944.1120.7802908716-0.8876248788

4.79343752934.211.80.7797472264-0.8898212054

4.82702370264.311.60.7791965293-0.8920460218

4.86000858254.411.40.7786384673-0.8943005919

4.89242510984.511.20.7780727153-0.8965862301

4.92430436614.6110.7774989342-0.8989043057

4.95567575554.710.80.7769167701-0.9012562487

4.98656717024.810.60.7763258528-0.9036435547

5.01700514114.910.40.7757257943-0.906067791

5.0470149754510.20.7751161874-0.9085306029

5.07662088355.1100.7744966037-0.9110337209

5.10584609645.29.80.7738665921-0.9135789678

5.13471297515.39.60.7732256765-0.9161682671

5.16324311365.49.40.7725733534-0.9188036524

5.19145743645.59.20.7719090899-0.9214872766

5.21937629155.690.7712323209-0.9242214237

5.24701954015.78.80.7705424455-0.9270085203

5.27440664445.88.60.7698388244-0.9298511494

5.30155675375.98.40.7691207759-0.9327520654

5.328488790368.20.7683875717-0.9357142105

5.35522153656.180.7676384322-0.938740734

5.38177372296.27.80.7668725215-0.9418350131

5.40816412066.37.60.7660889415-0.9450006765

5.4344116376.47.40.7652867249-0.9482416315

5.46053541786.57.20.7644648282-0.9515620942

5.48655495656.670.7636221227-0.9549666244

5.51249021366.76.80.7627573849-0.9584601652

5.53836174726.86.60.7618692851-0.962048088

5.5641908586.96.40.7609563749-0.9657362454

5.589999752876.20.7600170715-0.969531031

5.61581172897.160.7590496411-0.9734394501

5.64165138517.25.80.7580521778-0.9774692016

5.66754486617.35.60.7570225808-0.9816287737

5.6935201467.45.40.7559585253-0.9859275579

5.71960736147.55.20.75485743-0.9903759827

5.7458392077.650.7537164171-0.9949856749

5.77225140647.74.80.7525322645-0.9997696516

5.79888328137.84.60.7513013481-1.0047425537

5.82577844287.94.40.7500195717-1.0099209304

5.852985640484.20.7486822801-1.0153235884

5.88055981488.140.747284152-1.0209720258

5.90856341918.23.80.7458190654-1.0268909756

5.93706809198.33.60.7442799273-1.0331090937

5.96615680898.43.40.7426584551-1.0396598412

5.99592668238.53.20.7409448934-1.0465826306

6.02649266298.630.7391276395-1.0539243365

6.05799251848.72.80.7371927425-1.0617413203

6.09059365688.82.60.735123219-1.0701021953

6.12450268318.92.40.7328980983-1.0790916827

6.159979121792.20.7304910587-1.0888161228

6.19735569459.120.7278684214-1.0994115774

6.23706931619.21.80.7249861029-1.1110561442

6.27971041839.31.60.7217847944-1.1239894306

6.32610538119.41.40.7181819632-1.1385448685

6.37746293339.51.20.7140577592-1.1552066528

6.43565523739.610.7092282018-1.1747180646

6.50381662299.70.80.7033886783-1.1983097395

6.58782029459.80.60.695976404-1.2282553279

6.70084827979.90.40.6857519613-1.2695620764

6.8849574068100.20.6688741722-1.3377483444

6.912283643710.010.180.6663745187-1.3478469444

6.942683516910.020.160.6636004907-1.3590540175

6.976980255610.030.140.6604814011-1.3716551394

7.016379538210.040.120.6569146071-1.3860649875

7.062750572610.050.10.6527425371-1.4029201502

7.119224825910.060.080.6477042614-1.4232747839

7.19167272810.070.060.6413175313-1.4490771736

7.293273616510.080.040.6325195787-1.4846209019

7.466081711110.090.020.618012246-1.543230526

7.492284680310.0910.0180.6158640825-1.5519091067

7.521562518310.0920.0160.6134799934-1.5615408268

7.554738452310.0930.0140.6107990682-1.5723717644

7.593018158110.0940.0120.6077328125-1.5847594373

7.638270840910.0950.010.604145289-1.5992530324

7.693627965510.0960.0080.5998112229-1.6167626594

7.764959959410.0970.0060.594313875-1.6389719448

7.865446157810.0980.0040.5867337192-1.6695957744

8.037140777810.0990.0020.5742118534-1.7201841123

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X

S

temps (-)

X (-)

S (-)

Modle de Monod

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X (-)


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X

Modle de Monod - Estimation des paramtres

YG =0.5

m=0.1g de S/g de X / s

mu1/mu1/Yx/s

0

0.522.2

112.1

1.50.66666666672.0666666667

20.52.05

2.50.42.04

30.33333333332.0333333333

3.50.28571428572.0285714286

40.252.025

4.50.22222222222.0222222222

50.22.02

5.50.18181818182.0181818182

60.16666666672.0166666667

6.50.15384615382.0153846154

1/Yx/s

1/mu

1/(Yx/s)

1/Yx/s vs 1/mu

MBD00059657.unknown

MBD0004CCC4.unknown

Effet de mortalitLe taux de mortalit cellulaire: rd = - kd*X o kd=cste

Donc en cuve: dX/dt = m*X kd*X = (m kd)*X

En gnral, on nglige la maintenance et la mortalit en cuve

Mcanisme de dbordement: effet sur la cintique et le rendementglutamine

Dtermination de la cintique Taux initiauxvaluation de qglc, qgln, qlact et qNH3

Systmes danalyse de cintique rapideMthode de flux arrt (Stopped-flow): Un moteur va actionner 2 ou 3 seringues contenant les ractifs qui seront mlangs.Le mlange est ensuite aspir dans la cuvette dobservation par la seringue stop.

Systmes danalyse de cintique rapideMoteurMlangeurMoteurMoteurTemps mort :Temps pour lequel on ne peut avoir de donnes (temps de mlange)De lordre de 1 milliseconde.

Ractif 1Ractif 2

Les composs seront analyss par des mthodes spectrophotomtriques laide de :Systmes danalyse de cintique rapide Photodiodes Dichrosme circulaire Tube photomultiplicateur Matrice CCD (2048 longueurs dondes analyses en 3,5 millisecondes)

Systmes danalyse de cintique rapideMthode de flux tanch (Quenched-flow) : Mthode utilises lorsquon ne dispose pas de mthodes optiques satisfaisantes pour tudier lapparition des produits et des intermdiaires.Il faut arrter rapidement les ractions enzymatiques pour pouvoir collecter les mlanges et les analyser.

Systmes danalyse de cintique rapideMthode de flux tanch (Quenched-flow) : Types dtanchage :

tanchage chimique : Ajout dacide ou de base (ex. HCl 1M) tanchage physique : Conglation ultra-rapide.

MoteurMlangeurMoteurMlangeurRcupration des fractionsSystmes danalyse de cintique rapideDlai ractionnel de lordre de 2 100 millisecondesChambre ractionnelle linaireRactif 1Ractif 2Agent tanchant

Spectroscopie de masse en ligne Chromatographie HPLC ou en phase gazeuse lectrophorse sur gel, Comptage scintillation, etcSystmes danalyse de cintique rapideLes fractions recueillies sont analyses par des mthodes non-optiques :

Estimation des paramtres de Monod en cuvePuis on peut reformuler lquation de X pour isoler des termes relis linairement:ttY = b + m X

Monod estimation des paramtresmmax = 1m = 0,2475 = Ks*Yx/s/Xmax

Ks= 0,2475*10,1/0,5

Ks= 5

Graph4

0.7992878314

0.7986732066

0.7981079825

0.7975734607

0.7970599799

0.796561745

0.7960749366

0.7955968667

0.7951255485

0.7946594561

0.7941973804

0.7937383388

0.7932815142

0.7928262142

0.792371842

0.791917875

0.7914638493

0.7910093475

0.79055399

0.7900974274

0.789639335

0.789179408

0.7887173578

0.7882529089

0.7877857962

0.7873157627

0.7868425579

0.7863659354

0.7858856522

0.7854014669

0.7849131385

0.7844204254

0.7839230843

0.7834208692

0.7829135305

0.782400814

0.7818824598

0.7813582017

0.7808277663

0.7802908716

0.7797472264

0.7791965293

0.7786384673

0.7780727153

0.7774989342

0.7769167701

0.7763258528

0.7757257943

0.7751161874

0.7744966037

0.7738665921

0.7732256765

0.7725733534

0.7719090899

0.7712323209

0.7705424455

0.7698388244

0.7691207759

0.7683875717

0.7676384322

0.7668725215

0.7660889415

0.7652867249

0.7644648282

0.7636221227

0.7627573849

0.7618692851

0.7609563749

0.7600170715

0.7590496411

0.7580521778

0.7570225808

0.7559585253

0.75485743

0.7537164171

0.7525322645

0.7513013481

0.7500195717

0.7486822801

0.747284152

0.7458190654

0.7442799273

0.7426584551

0.7409448934

0.7391276395

0.7371927425

0.735123219

0.7328980983

0.7304910587

0.7278684214

0.7249861029

0.7217847944

0.7181819632

0.7140577592

0.7092282018

0.7033886783

0.695976404

0.6857519613

0.6688741722

0.6663745187

0.6636004907

0.6604814011

0.6569146071

0.6527425371

0.6477042614

0.6413175313

0.6325195787

0.618012246

0.6158640825

0.6134799934

0.6107990682

0.6077328125

0.604145289

0.5998112229

0.594313875

0.5867337192

0.5742118534

X

Modle de Monod - Estimation des paramtres

Ordre 0_exponentiel


AG, nov 2002

Donnes

1tlag=0.5

Yx/s=0.5

So=20

Xo=0.1

Calculs

Xmax =10.1

avec latence

tXln(X)Xln(X)

00.1-2.3025850930.1-2.302585093

0.10.1105170918-2.2025850930.1-2.302585093

0.20.1221402758-2.1025850930.1-2.302585093

0.30.1349858808-2.0025850930.1-2.302585093

0.40.1491824698-1.9025850930.1-2.302585093

0.50.1648721271-1.8025850930.1-2.302585093

0.60.18221188-1.7025850930.1105170918-2.202585093

0.70.2013752707-1.6025850930.1221402758-2.102585093

0.80.2225540928-1.5025850930.1349858808-2.002585093

0.90.2459603111-1.4025850930.1491824698-1.902585093

10.2718281828-1.3025850930.1648721271-1.802585093

1.10.3004166024-1.2025850930.18221188-1.702585093

1.20.3320116923-1.1025850930.2013752707-1.602585093

1.30.3669296668-1.0025850930.2225540928-1.502585093

1.40.4055199967-0.9025850930.2459603111-1.402585093

1.50.448168907-0.8025850930.2718281828-1.302585093

1.60.4953032424-0.7025850930.3004166024-1.202585093

1.70.5473947392-0.6025850930.3320116923-1.102585093

1.80.6049647464-0.5025850930.3669296668-1.002585093

1.90.6685894442-0.4025850930.4055199967-0.902585093

20.7389056099-0.3025850930.448168907-0.802585093

2.10.8166169913-0.2025850930.4953032424-0.702585093

2.20.9025013499-0.1025850930.5473947392-0.602585093

2.30.9974182455-0.0025850930.6049647464-0.502585093

2.41.10231763810.0974149070.6685894442-0.402585093

2.51.21824939610.1974149070.7389056099-0.302585093

2.61.34637380350.2974149070.8166169913-0.202585093

2.71.48797317250.3974149070.9025013499-0.102585093

2.81.64446467710.4974149070.9974182455-0.002585093

2.91.81741453690.5974149071.10231763810.097414907

32.00855369230.6974149071.21824939610.197414907

3.12.21979512810.7974149071.34637380350.297414907

3.22.45325301970.8974149071.48797317250.397414907

3.32.71126389210.9974149071.64446467710.497414907

3.42.99641000471.0974149071.81741453690.597414907

3.53.31154519591.1974149072.00855369230.697414907

3.63.65982344441.2974149072.21979512810.797414907

3.74.0447304361.3974149072.45325301970.897414907

3.84.47011844931.4974149072.71126389210.997414907

3.94.94024491061.5974149072.99641000471.097414907

45.45981500331.6974149073.31154519591.197414907

4.16.03402875971.7974149073.65982344441.297414907

4.26.66863310411.8974149074.0447304361.397414907

4.37.369979371.9974149074.47011844931.497414907

4.48.14508686652.0974149074.94024491061.597414907

4.59.00171313012.1974149075.45981500331.697414907

4.69.94843156422.2974149076.03402875971.797414907

4.710.12.31253542386.66863310411.897414907

4.810.12.31253542387.369979371.997414907

4.910.12.31253542388.14508686652.097414907

510.12.31253542389.00171313012.197414907

5.110.12.31253542389.94843156422.297414907

5.210.12.312535423810.12.3125354238

5.310.12.312535423810.12.3125354238

5.410.12.312535423810.12.3125354238

5.510.12.312535423810.12.3125354238

5.610.12.312535423810.12.3125354238

5.710.12.312535423810.12.3125354238

5.810.12.312535423810.12.3125354238

5.910.12.312535423810.12.3125354238

610.12.312535423810.12.3125354238

6.110.12.312535423810.12.3125354238

6.210.12.312535423810.12.3125354238

6.310.12.312535423810.12.3125354238

6.410.12.312535423810.12.3125354238

6.510.12.312535423810.12.3125354238

6.610.12.312535423810.12.3125354238

6.710.12.312535423810.12.3125354238

6.810.12.312535423810.12.3125354238

6.910.12.312535423810.12.3125354238

710.12.312535423810.12.3125354238

7.110.12.312535423810.12.3125354238

7.210.12.312535423810.12.3125354238

7.310.12.312535423810.12.3125354238

7.410.12.312535423810.12.3125354238

7.510.12.312535423810.12.3125354238

7.610.12.312535423810.12.3125354238

7.710.12.312535423810.12.3125354238

7.810.12.312535423810.12.3125354238

7.910.12.312535423810.12.3125354238

810.12.312535423810.12.3125354238

8.110.12.312535423810.12.31253

Documents

Cinétique et stochiométrie