pages290_317

290 8 Simulation Examples of Biological Reaction Processes Using Berkeley Madonna

8.4.8 Two Stage Culture with Product Inhibition(STAGED)

System

Products may inhibit growth rates. Under such conditions a multi-stagedcontinuous reactor as shown in Fig. 1 will have kinetic advantages over a singlestage. This is because product concentrations will be lower and consequentlythe rates in the first tank will be higher as compared with a single tank. Thiseffect may be conveniently investigated by simulation. Batch cultures can beexpected to have similar kinetic advantages for product inhibition situations.

Figure 1. Two-stage chemostat with product inhibition.

Model

The inhibition function is expressed empirically as

When product concentrations are low, the equation reduces to the Monodequation.

The product kinetics are according to Luedeking and Piret, with dependenceon both growing and non-growing biomass,

Biological Reaction Engineering, Second Edition. I. J. Dunn, E. Heinzle, J. Ingham, J. E. PfenosilCopyright © 2003 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 3-527-30759-1

8.4 Continuous Reactors 291

rpn = (On + (3n \ln) Xn

In addition, the non-growth term, an, is assumed to be inhibited according to,

a - a"Qn ~ 1 + Pi-r rn

When product concentrations are low, a = ano.

Kinetics for growth:

Kinetics for substrate consumption (neglecting consumption for product):

_ _ rxn

where Y is the yield factor.

Mass balances:

Stage 1,

j- = F[So-Si] +rS iVi

jp = F[P0-Pi] + rp^j

Stage 2 with additional substrate feed FI,

dX2V2 -gjT- = F Xj - [F + F!]X2 + rX2V2

dS2V2 -gj- = F [Si - S2] + FI [Sio - S2] + rS2V2

dP2- =FPl- [F + Fi]P2 + rp2V2

Productivity for product:First stage,


Prodi =

Both stages,

Program

The program is on the CD-ROM.

Nomenclature

Symbols

FKIKS

PProdrSVXYaOC0

P

Indices

Volumetric feed rate m3/hInhibition constantSaturation constant kg/m3

Product concentration kg/m3

Productivity for product kg/m3 hReaction rate kg/m3 hSubstrate concentration kg/m3

Reactor volume m3

Biomass concentration kg/m3

Yield coefficient kg/kgNon-growth product rate term kg P/kg X hNon-growth term with no inhibition kg P/kg X h

Growth dependent product yield kg/kgSpecific growth rate 1/hMaximal specific growth rate 1/h

n01

Refers to tank nRefers to tank 1 inletRefers to tank 1 and inlet of tank 2


210

Refers to tank 2 and system of outflowRefers to inlet concentration of tank 2

Exercises

Results

The startup and approach to steady state for the two stages is shown in Fig. 2.The influence of the inhibition can be tested by varying KI from 0.1 to 10.0, asshown in Fig. 3. The higher the KI the lower is the degree of inhibition and thegreater is the product concentration P2-


4

3.5

3

2.5

,1.5

1

0.5

0

Run 1: 255 steps in 0 seconds

r10

,

10 15TIME

Figure 2. Startup and approach to steady state for the two stages.

Run 4: 255 steps in 0.0167 seconds

1.4.,

1.3

1.2.

1.1I

1

0.9.

0.8

0.7 J

10 12 14 16 18 20 22 24 26TIME

Figure 3. Product concentration P at various values of KI (1 to 5), curves bottom to top.

Reference

Herbert, D. (1961). A Theoretical Analysis of Continuous Culture Systems.Soc. Chem. Ind. Monograph No. 12, London, 2L


8.4.9 Fluidized Bed Recycle Reactor (FBR)

System

A fluidized bed column reactor can be described as 3 tanks-in-series (Fig. 1).Substrate, at concentration SQ, enters the circulation loop at flow rate F. Theflow rate through the reactor due to circulation is FR. Oxygen is absorbed in awell-mixed tank of volume VT. The reaction rate for substrate (r$) depends onboth S and dissolved oxygen (CL)- The rate of oxygen uptake (ro) is related toS by a yield coefficient (Yos)- The gas phase is not included in the model,except via the saturation concentration (CLS)- The oxygen uptake rate ofreactor can be determined by the difference in CL inlet and outlet values.

? So , Fn

FluidizedBed

F,S

Figure 1. Biofilm fluidized bed with external aeration.


Model

The model balance equations are developed by considering the individual tankstages and the absorber separately. The gas phase in the absorber is assumed tobe air.

Substrate balances:For the absorption tank

dS FR

dF =

For each stage n

dSn FR-3T = -^(Sn-!-Sn)- rsn

Oxygen balances:For the absorption tank

For each stage

r = ^(CL3-CL)+KLa(CLs-CL)VT

dCLn FR~dT" = V (CLn-! ~CLn) ~ rOn

Kinetics for stage n:VTm

Kn +Sn K0 +CLn

Program

The program is on the CD-ROM.


Nomenclature

Symbols

CL

CLSFFRKLa

KsKorSVVT

^m

xYT

Dissolved oxygen concentrationSaturation oxygen concentrationFeed flow rateRecycle flow rateTransfer coefficientSaturation constantSaturation constant for oxygenReaction rateSubstrate concentrationReactor volume of one stageVolume of absorber tankMaximum velocityBiomass concentrationYield coefficientInverse liquid residence time

g/m3

g/m3

m3/hm3/h1/hkg/m3

g/m3

kg/m3 hkg/m3

m3

m3

kg/m3 hkg/m3

kg/kg and g/kg1/h

Indices

0l ,2 ,3 ,nmOSTX

Refers to feedRefer to the stage numbersRefers to maximumRefers to oxygenRefers to substrateRefers to aeration tankRefers to biomass

Exercises


Results

Note from the results below that the steady state for oxygen is reached ratherquickly, compared to that of substrate.

Run 1:1003 steps in 0.0333 seconds

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Figure 2. Oxygen concentrations in fluidized bed reactor. Top of column is the lower curve.



35

tf

Figure 3. Substrate concentrations from the run as in Fig. 2.

8.4.10 Nitrification in a Fluidized Bed Reactor(NITBED)

System

Nitrification is an important process for wastewater treatment. It involvesthe sequential oxidation of NFLt"1" to NO2~ and NC>3~ that proceedsaccording to the following reaction sequence:

NH4+ + 1 02 -> N02- + H20 +2H+

NO2~ + O2 -» NO3~The overall reaction is thus

NH4+ + 2O2 NO3- + H2O + 2H+

Both steps are influenced by dissolved oxygen and the corresponding nitrogensubstrate concentration. Owing to the relatively slow growth rates of nitrifiers,

treatment processes benefit greatly from biomass retention.


In this example, a fluidised biofilm sand bed reactor for nitrification, asinvestigated by Tanaka et al. (1981), is modelled as three tanks-in-series with arecycle loop (Fig. 1). With continuous operation, ammonium ion is fed to thereactor, and the products nitrite and nitrate exit in the effluent. The bedexpands in volume because of the constant circulation flow of liquid upwardsthrough the bed. Oxygen is supplied external to the bed in a well-mixed gas-liquid absorber.

Model

The model balance equations are developed by considering, separately, theindividual tank stages and the absorber. Component balances are required for allcomponents in each section of the reactor column and in the absorber, where thefeed and effluent streams are located. Although the reaction actually proceedsin the biofilm phase, a homogeneous model with apparent kinetics is employedrather than a biofilm model, as in the example NITBEDFILM.

03.

Fluidizedbed

Figure 1. Biofilm fluidised-bed recycle loop reactor for nitrification.

In the absorber, oxygen is transferred from the air to the liquid phase. Thenitrogen compounds are referred to as Si, 82, and 83, respectively. Dissolved


oxygen is referred to as O. Additional subscripts, as seen in Fig. 1, identify thefeed (F), recycle (R) and the flows to and from the tanks 1, 2 and 3, each withvolume V, and the absorption tank with volume VA-

The fluidised bed reactor is modelled by considering the componentbalances for the three nitrogen components (i) and also for dissolved oxygen.For each stage n, the component balance equations have the form

Similarly for the absorption tank, the balance for the nitrogen-containingcomponents include the input and output of the additional feed and effluentstreams, giving

The oxygen balance in the absorption tank must account for mass transfer fromthe air, but neglects the low rates of oxygen supply and removal of the feed andeffluent streams. This gives

For the first and second biological nitrification rate steps, the reaction kineticsfor any stage n were found to be described by

r = vml Sin Qn

K + S K + O

r2n = Vm2 S2n °n

K2+S2n KO2+°n

The oxygen uptake rate is related to the above reaction rates by means of theconstant yield coefficients, YI and ¥2, according to

ron = - H n Y i -r2nY2

The reaction stoichiometry provides the yield coefficient for the first step


and for the second stepYI = 3.5 mg O2/(mg NNH4)

Y2 = LI mg O2/(mg NNO2)

Program

The program is found on the CD-ROM.

Nomenclature

Symbols

F Feed and effluent flow rate L/hFR Recycle flow rate L/hKj^a Transfer coefficient hK Saturation constants mg/LKI Saturation constant for ammonia mg/LK2 Saturation constant for ammonia mg/LO Dissolved oxygen concentration mg/LOs and O* Oxygen solubility, saturation cone. mg/LOUR Oxygen uptake rate mg/Lr Reaction rate mg/L hS Substrate concentration mg/LV Volume of one reactor stage LVA Volume of absorber tank Lvm Maximum velocity mg/L hY Yield coefficient mg/mg

Indices

1,2,31,2,3AFijm

Refer to ammonia, nitrite and nitrate, resp.Refer to stage numbersRefers to absorption tankRefers to feedRefers to substrate i in stage jRefers to maximum


Ol and O2S1,S2S and *

Refer to oxygen in first and second reactionsRefer to substrates ammonia and nitriteRefer to saturation value for oxygen

Exercises


Results

Run 1: 519 steps in 0.2 seconds6

10 15 20 25 30 35 40 45 50

Figure 2. Dynamic startup of continuous operation showing oxygen concentrations andnitrogen compounds at the top of the column.

280

270

260

250

1^240.

£,230-<

220

210

200

190

180


P2.5

5 c

M I

0.5

15 20 25 30 35 40

KLA

Figure 3. Parametric run of continuous operation showing oxygen and ammonia in the effluentversus


8.4.11 Continuous Enzymatic Reactor (ENZCON)

System

This example, schematically shown in Fig. 1 involves a continuous, constantvolume, enzymatic reactor with product inhibition in which soluble enzyme isfed to the reactor.

EO.FE

Figure 1. Continuous enzymatic reactor with enzyme feed.

Model

I» S1f P1§ F1

The mass balance equations are formulated by noting the two separate feedstreams and the fact that the enzyme does not react but is conserved.

Total flow:

Mass balances:dSi

FS + FE =

= FsSo-FiS 1 + r s V


r = -F iP 1 + rpV

Kinetics with product inhibition:

rS - -vmKM + S + (P/Ki)

vm = EI K2

rP = -2rs

Program

The program is found on the CD-ROM.

Nomenclature

Symbols

E Enzyme concentration kg/m3

F Flow rate m3/hKI Inhibition constantKM Saturation constant kg/m3

K2 Rate constant 1/hP Product concentration kg/m3

r Reaction rate kg/(m3 h)S Substrate concentration kg/m3

V Reactor volume m3

vm Maximum rate kg /(m3 h)

Indices

0 Refers to inlet values


1EPS

Refers to reactor and outlet valuesRefers to enzymeRefers to productRefers to substrate

Exercises

Results

Variations in the flows FE (Fig. 2) or Fs (Fig. 3) cause the product levels tochange.


1.8

1.6

Run 3: 8004 steps in 0.1 83SeC°ndS

0.8

.0.6 / /

tS

s--- P1:2(0.2)— P1:3(0.3)

,-'"

0.4

0.2

0 10 20 30 40TIME

50 60 70 80

Figure 2. Performance for three values of FE.

r4.5Run 3: 8004 steps in 0.233seconds

• 3.5

•3

• 2.5

.2

-1.5

jft•<*/r

0 10

x--'

r *>"* -^ -» **" ~ ""

I—. P1:2(1.5).. P1:3(2)

20 30 40 50 60 70 80TIME

Figure 3. Performance for three values of Fs.

8.4.12 Reactor Cascade with Deactivating Enzyme(DEACTENZ)

System

Biocatalysts usually deactivate during their use, and this has to be considered inthe bioreactor design. One of the methods to keep productivity fluctuationslow, and hence to efficiently utilize the biocatalyst, is to use a series of reactorswith biocatalyst batches having different times-on-stream in each reactor. In


this example a series of three stirred tanks of a constant equal volume withbiocatalyst deactivating by first order reaction kinetics is investigated (Fig. 1).After a time period ILAG? ̂ e biocatalyst from the tank with longest time-on-stream (first tank in the cascade) is discarded and replaced by a fresh batch.The streams are switched over so that tank 1 becomes tank 3, the last reactor inthe series. Other tanks are switched over correspondingly. This is equivalent toreplacing the used enzyme with fresh enzyme in tank 3 and moving the usedenzyme upstream from tank 3 to tank 2 to tank 1, which is easier to simulate.(3-galactosidase was taken as an example of the biocatalyst. This obeysMichaelis-Menten kinetics with competitive product inhibition, and the kineticconstants were determined with considerable accuracy. The same constants areused also in this substrate inhibition model.

F,S0

F,Si F,S2 F,S3

Figure 1. Tanks in series reactor with immobilized enzyme.

Model

Using the stoichiometry, S —> P, the mass balances for the ith tank (i = 1, 2, 3)with the volume V can be written

Substrate

Product

Enzyme (active)

= F(PM-Pi)dt


=rE ivwhere rate of substrate consumption is given by product inhibition(competitive)

sirSi = ' vmaxbi - 7 - Z~^\

V Kinh

According to the molar stoichiometry

RPi= -RSi

The rate of enzyme deactivation is assumed to be:

rEi = - kD EI

For each batch of enzyme in tank i

dEi i c-

This equation can be applied by changing the initial conditions for each tankwhen the enzyme is moved from tank to tank. Thus the final value in tank nbecomes the initial condition in tank i-1. The initial conditions can also becalculated by analytical integration of the enzyme deactivation equation attimes corresponding to the respective ages of the biocatalysts in the respectivereactors (multiples of TLAG)- Fresh enzyme with the activity EQ is in the thirdtank. The other tanks start with the following enzyme activities:

EI = E0 e C- (3 - i) ko TLAG]

Program

In the program on the CD-ROM note that the cost calculation at the end of theprogram is included only as a comment but could be incorporated into theprogram with the corresponding values for the constants.


Nomenclature

Symbols

COSTEECOSTFICOSTkD

KinhKmOCOSTPRCmrsST

t

TDOWNTLAGvmax

Indices

0i

Specific product costsEnzyme concentrationEnzyme costFlow rateInvestment costDeactivation constantInhibition constantMichaelis - Menten constantOperating costTotal amount of productReactor refill costReaction rate of deactivationReaction rate of substrateSubstrate concentrationResidence timeTimeDown timeTime-on-stream differenceMaximum specific reaction rate

Refers to initial, feedRefers to reactor number

$/kgkg/m3

$/kgm3/h$/kg1/hmol/m3

mol/m3

$/kgmol$/kgkg/(m3 h)mol/(m3 h)mol/m3

hhhhmol/kg h

Exercises


Results

The results from DEACTENZ show an exponential decrease of the biocatalystactivity (Fig. 2), which causes dynamic changes in the substrate and productconcentrations (Fig. 3) in all three reactors.


Run 1: 50000 steps in 0.917 seconds0.5-,

0.45-

0.4-

0.35-

a 0 3 '.0.25-

"* 0.2-

0.15-

0.1-

0.05-

0-

\

\\

%*.

"%xx

s••-. -'*"">cr^r "'"'"•-j+ '"•*«._/• "••|«.»

— ^ — — -" • — •

sj**

r*i**

"''— . — E2:1

_-— Totalproduct:1

-i..••••••

***

—i...

-4000

-3500

-3000

^-2500 3

I-2000 Q_

-1500 pH

-1000

.500

-0

0 100 200 300 400 500 600 700 800 900 1000

TIME

Figure 2. Exponential biocatalyst deactivation and total product during one run.

140-i

120-

100-

°l 8°-

C/l^ 60cn

40-

20

0

Run 1: 50000 steps in 0.933 seconds120

100

80

a-40

20

0 100 200 300 400 500 600 700 800 900 1000

TIME

Figure 3. Dynamic changes in the substrate and product concentrations.


References

Prenosil, I.E., Peter, J., Bourne, J.R. (1980). Hydrolytische Spaltung desMilchzuckers der Molke durch immobilisierte Enzyme im Festbett-Reaktor.Verfahrenstechnik 14, 392.

Prenosil, J.E. (1981). Optimaler Betrieb fur einen Festbett- und einen Fliessbett-Reaktor mit desaktivierendem Katalysator. Chimia 35, 226 .

Prenosil, J.E., Hediger, T. (1986). An Improved Model for Capillary-Membrane, Fixed-Enzyme Reactors. In Membranes and Membrane Processes,Plenum, N. Y., 515.

8.4.13 Continuous Production of PHB in a Two-TankReactor Process (PHBTWO)

System

This example considers a two-stage process for the production of PHB, abiopolymer. The kinetics of this fermentation is presented in the example PHB.The structured kinetic model involves a Luedeking-Piret-type expression andalso an inhibition by the product. From this it might be expected that two stageswould be better than one, and it is the goal of this example to optimize theprocess. The volume ratio and the feed rate are the obvious design andoperating parameters.

Sfeed,

> 82, F0

Figure 1. Configuration of the two-tank system.


Model

The details of the structured model will not be repeated here (See PHB). Thebiomass consists of a synthesis part R and the intracellular product P. Thebiomass growth rate of R is proportional to the specific growth rate, which isgiven by a two-part expression

S (S/Ks,2)n

(KS,i + S) -*

The synthesis rate of PHB is given by a two-part expression

The term -kiP represents a product inhibition.

The model requires component balances for P, R and S for both tanks, as seenin the program. The relative reactor volumes are determined by the parameterVrat. The volumetric productivities are calculated to compare the results.

Program

The program is found on the CD-ROM

Nomenclature

Symbols

FO Feed flow rate m3/hKI Inhibition constant, for (NH4>2SO4 kg/m3

KS Saturation constant kg/m3

n Hill CoefficientP Product concentration (PHB) kg/m3

PROD Productivity kg/(m3h)R Residual biomass concentration kg/m3

rp Rate of synthesis of PHB kg/m3

TR Rate of synthesis of R kg/m3


Sfeed

Vi and V2

XYP/RYR/S

MP

Indices

Rate of substrate uptake kg/(m3 h)Limiting substrate cone. NH4+ as

(NH4)2S04 kg/m3

Feed concentration kg/m3

Reactor volumes m3

Biomass concentration kg/m3

Yield coefficient kg/kgYield coefficient, kg/kgSpecific rate of synthesis of R (rR/R) 1/h

Specific rate of synthesis of P (rp/P) 1/h

12m

Refers to reaction 1 and tank 1Refers to reaction 2 and tank 2Refers to maximum

Exercises


Results


4

90 100

Figure 2. A run showing the dynamic approach to steady state for X, S, P in both tanks.

Run 20: 20380 steps in 5.78 seconds

0.2

Figure 3. Here with FO set at the optimum value of 1.24, the influence of VRAT is investigatedgiving a value for the maximum in PROD corresponding to the OPTIMIZE results. VRAT is seennot to be very important. Thus equal-sized tanks are adequate.

Documents

pages290_317