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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle
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 (-)
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle avec latence
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle
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 (-)
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle avec latence
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle
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 (-)
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle avec latence
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 (-)
Modle de Monod -X vs S
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
Courbe exponentielle
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 (-)
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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) (-)
Croissance exponentielle
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 (-)
Croissance exponentielle avec latence
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) (-)
Croissance exponentielle avec latence
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
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
X
S
temps (-)
X (-)
S (-)
Modle de 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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
X
S (-)
X (-)
Modle de Monod -X vs S
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
8.110.12.312535423810.12.31253
Top Related