CHEM-E3205 BIOPROCESS OPTIMIZATION AND SIMULATION

Transcription

1 CHEM-E3205 BIOPROCESS OPTIMIZATION AND SIMULATION TERO EERIKÄINEN ROOM D416d

2 COURSE LECTURES AND EXERCISES Week Day Date Time Place Lectures/Execises 37 Mo :15-11:45 Ke3 Lecture: Bioprocess modeling Tue :15-11:45 Luokka1 Exercise: Matlab bioprocess kinetics simulation 38 Tue :15-11:45 Luokka1 Exercise: Matlab parameter estimation Wed :15-15:45 Ke5 Lecture: Bioprocess measurement and control 39 Tue :15-11:45 Luokka1 Exercise: Matlab PID-control Wed :15-15:45 Ke5 Lecture: Design of experiments 40 Tue :15-11:45 Luokka1 Exercise: Modde design of experiments Wed :15-15:45 Ke5 Lecture: Multivariate modelling 41 Tue :15-11:45 Luokka1 Exercise: Simca exercises Wed :15-15:45 Ke5 Lecture: Neural network and other modelling 41 Tue :15-11:45 Luokka1 Exercise: Neural network 42 Wed :15-15:45 Ke5 Lecture: Quality Control Exam week

3 EXERCISES (MANDATORY) PC CLASSROOM EXERCISES: YOU CAN PERFORM EXERCISES BY BEING PRESENT IN THE PC CLASSROOM. IF CARRIED OUT INDEPENDENTLY BY YOURSELF YOU SHOULD RETURN THE ANSWERS IN A REPORT. EXERCISES SHOULD BE RETURNED AND GET APPROVED BEFORE THE COURSE IS ACCEPTED AS COMPLETED. SEPARATE EXAM IS ALSO HELD. LAB WORK (SMALL GROUPS): FIND OUT HOW THE BIOREACTOR WORKS. MAKE A PLAN TO DEFINE REACTOR k L a-measurement. MAKE A PLAN TO DEFINE KINETIC PARAMETERS FOR AN AERATED YEAST FERMENTATION. REALIZE PLANS USING BIOSTAT C (5L) BIOREACTOR. MAKE A SIMULATION MODEL FROM MEASUREMENT RESULTS MAKE A REPORT OF YOUR WORK

4 MATERIALS FUNDAMENTAL BIOENGINEERING ONLINE VERSION AVAILABLE FREELY CHAPTERS 7,8,14,15 EXTRA ARTICLES LECTURE SLIDES EXERCISES

5 CHEM-E3205 BIOPROCESS OPTIMIZATION AND SIMULATION: MODELING MODELING CATEGORIES BALANCE MODELS KINETIC MODELS BIOREACTOR MODELS (MASS TRANSFER MODELS)* (OTHER METHODS)* *NOT IN THIS LECTURE

6 MODELING DESCRIPTION OF THE PROCESS BY MEANS OF MATHEMATICS REASONS FOR MODELING: PROCESS DESIGN AND OPTIMIZATION SIMULATION THE DESIGN OF EXPERIMENTS AND THE RATIONALIZATION DEFINING PROCESS STATES AND DYNAMICS DESIGN AND TUNING OF PROCESS CONTROLLERS AS PART OF THE CONTROL ALGORITHM (ESTIMATION) QUANTITATIVE MODELING OF BIOPROCESSES ARE BASED ON MATERIAL AND / OR ENERGY BALANCES AND THE KINETICS (SUBSTRATE) RAW MATERIAL PRE-PROCESSING IS AN IMPORTANT VARIABLE BIOLOGICAL SYSTEMS ARE COMPLEX AND NON-LINEAR DYNAMIC CHANGES ARE STRONGLY DEPEND ON THE INITIAL VALUES

7 MODELING MECHANISTIC MODELS BASED ON NATURAL PHENOMENA, LAWS OF PHYSICS (BEING "UNIVERSAL ) KINEMATICS, DYNAMICS, STATICS EMPIRICAL MODELS "BLACK-BOX" MODELS, DESCRIBING THE RELATIONS BETWEEN INPUT AND OUTPUT VARIABLES FOR EXAMPLE USING REGRESSION MODELS QUALIFIED IN THE DOMAIN WHERE IDENTIFIED

8 MODELING STATIC MODELS A DESCRIPTION OF THE TIME INDEPENDENT PHENOMENA FOR EXAMPLE PRODUCT QUALITY VS. RAW MATERIALS OR REACTIONS, WHOSE RATE IS VERY HIGH DYNAMIC MODELS TIME DEPENDENT MODELS PROCESSES IN WHICH REACTION (SLOW) RATE AFFECT THE FINAL RESULT TIME SERIES MODELS

9 MODELING CONTINUOUS PROCESSES PROCESS IS TRIED TO ADJUST TO A CERTAIN OPTIMUM -> STATIC MODEL BATCH PROCESS A BATCH PROCESS IS USUALLY TREATED AS A DYNAMIC PHENOMENON, UNLESS ONLY THE FINAL PROCESS STATE MATTERS

10 MODELING NONSEGREGATED MODEL THE CELLS JUST ONE AND THE SAME BIOMASS SEGREGATED MODEL BIOMASS IS DIVIDED INTO SUBPOPULATIONS, WHICH ARE TREATED AS SEPARATE VARIABLES NONSTRUCTURED MODEL A DESCRIPTION OF THE BIOMASS AT THE MACROSCOPIC LEVEL STRUCTURED MODEL THE CELLULAR COMPONENTS ARE HANDLED AS SEPARATE VARIABLES Jakautunut Segregated Nonsegregated Jakautumaton Ei-rakenteellinen Nonstructured Rakenteellinen Structured Monimutkaisuus lisääntyy

11 BALANCE MODELS MASS BALANCE ELEMENTAL BALANCE ENERGY BALANCE REDOX BALANCE

12 MASS BALANCE MASS BLANCE FOR SUBSTANCE A : R A = A ACCUM.RATE = A IN - A OUT + A REACTION

13 ELEMENTAL BALANCE α*c a H b O c + β*o 2 + χ*nh 3 ---> C d H e O f N g + δ*co 2 + ε*h 2 O CARBON: a*α = d + δ HYDROGEN: b*α + 3*χ = e + 2*ε OXYGEN: c*α + 2*β = f + 2*δ + ε NITROGEN: χ = g

14 ENERGY BALANCE Energy accumul. Energy Energy = convection - convection + in out Energy from reaction Energy Energy + conduction - conduction + in out Energy from mixing ± Energy radiation

15 REDOX BALANCE ELECTRON BALANCE CO 2, H 2 O AND NITROGEN COMPOUNDS FORMED IN COMBUSTION REACTIONS VALENCES OF VARIOUS ELEMENTS: CARBON: 4 HYDROGEN: 1 OXYGEN: -2 PHOSPHOROUS: 5 SULPHUR: 6 NITROGEN: -3 (NH 3 ), 0 (N 2 ), 5 (NO 3- )

16 KINETIC MODELS dx/dt, dp/dt, ds/dt ENZYME KINETICS MICROBIAL GROWTH KINETICS BIOCHEMICAL REACTIONS IN LIVING ORGANISMS ARE DEPENDENT INTERACTING ENZYME REACTIONS

17 ENERGY REQUIREMENTS OF A CHEMICAL REACTION Figure 5.2 From Pearson Education, Inc.

18 BASICS OF ENZYME KINETICS QUANTITATIVE EVALUATION OF ALL FACTORS THAT CONDITION ENZYME ACTIVITY MOST IMPORTANT FACTORS: CONCENTRATIONS OF ACTIVE ENZYME, SUBSTRATES AND INHIBITORS ph AND TEMPERATURE KINETICS NEEDED FOR UNDERSTAND THE MOLECULAR MECHANISMS OF ENZYME ACTION DESIGN OF ENZYME REACTORS AND FOR PERFORMANCE EVALUATION DETERMINE INITIAL RATES OF REACTION DETERMINE THE QUANTITATIVE EFFECT OF THE IMPORTANT FACTORS

19 ENZYME KINETICS Activity proportional to the concentration of active enzyme k 1 k S + E ES P + E k 2 Henri kinetics K1 dissoc. const ES K2 dissoc. const EP v= ds dt = dp dt = k [ ES] = k cat [ ES] P=0 or insignificant v= ke0s k2 + S k 1 VmaxS = K + S Michaelis- Menten Rapid equilibrium K= equilibrium constant The binding step in equilibrium and much faster than the conversion step v= ke0s k2 + k + S k 1 = V K max D S + S Briggs- Haldane Steady state hypothesis K D = dissociation constant

20 v= k ES ES ES BRIGGS-HALDANE APPARENT STEADY STATE After a very short transient state the enzyme substrate complex reaches steady state, so that its concentration remains constant throughout the reaction [ ES] formation dissociation formation [ E][ S] k + k) [ ES] k1[ E][ S] = ( k2 + k) [ ES] [ ] [ E][ S] [ E][ S] ES = = ( k = k = ( In steady state: = ES + k) [ E] = [ E ] [ ES] dissociation k 1 K D d[ ES] = 0 dt [ ES] ([ E ] [ ES] )[ S] [ ES] K M + [ ES][ S] = [ E0][ S] [ ] [ E0][ S] ES = K D + [ S] [ E0][ S] [ S] v= k = Vmax K + [ S] K + [ S] when v= V when max D 0 S >> K [ S] [ E ] 0 S << K D D D D (0 order reaction kinetics) v= Vmax (1st order reaction kinetics) K D K D is the dissociation constant of the ES complex into E and S = = k K

21 K M and V max Whatever the hypothesis, the rate equation is expressed in terms of two parameters: K M is Michaelis constant, (not being dependent on either enzyme or substrate concentration) V max is a lumped parameter containing the enzyme concentration (e or [E 0 ]) and the catalytic rate constant (k or k cat ). (dimension of k or k cat will be determined by the enzyme concentration dimension) When defining kinetic parameter, the value of the determined parameter K M should be in the midpoint of that range. K M corresponds the substrate concentration in which reaction rate in half of the maximum. 18,0 16,0 14,0 Irreversible reaction v (g/l s) 12,0 10,0 8,0 6,0 4,0 2,0 Km K m =10 v = (V max *s)/(k m +s) V max = 20 0,0 0,0 20,0 40,0 60,0 s (g/l) With small substrate concentration 1st order kinetics With large substrate concentration zero order kinetics

22 LINEARIZATION METHODS [ S] [ S] v = v max + K v m max Langmuir v v v K m Eadie = max [ S] Hofstee 1 v = 1 v max + K v m max 1 [ S] Lineweaver Burk

23 LACTOSE HYDROLYSIS WITH β-galactosidase: EMPIRICAL K m AND v max VALUES: experime nt Lactose mmol l-1 reaction rate mmol l-1 min- 1 S v 0,50 0,106 1,00 0,376 2,00 0,764 4,00 1,152 6,00 1,386 8,00 1,388 14,00 1,500 20,00 1,438 Best result with nonlinear parameter estimation (not shown here) K m v max Logaritmic 5,6 2,3 Lineweaver-Burk -38-8,9 Langmuir 3,8 1,8 v 1,8 1,6 1,4 1,2 1 0,8 0,6 0,4 0,2 0 Logaritmic y = Ln(x) S Lineweaver-Burk 1/v 1/v=Km/vmax *1/s + 1/vmax Langmuir-plot s/v=km/vmax + s/vmax 1/V y = x /S S/v y = x S

24 MICROBIAL GROWTH KINETICS BIOCHEMICAL REACTIONS IN LIVING ORGANISMS ARE OFTEN ENZYMATIC REACTIONS DEPENDENT ON EACH OTHER. CELL GROWTH IS AN AUTOCATALYTIC REACTION: THE GROWTH RATE IS DIRECTLY PROPORTIONAL TO THE AMOUNT OF PREFORMED GROWTH OF CELLS. THE SPECIFIC GROWTH RATE MAY BE DETERMINED WHEN THE CELL CONCENTRATION CHANGE RATE dx/dt IS DIVIDED WITH CELL CONCENTRATION μμ = dddd dddd 1 XX

25 MICROBIAL GROWTH stationary phase IN BATCH CULTIVATION: LAG-PHASE 10 ACCELERATING PHASE X (kg/m3) Exponential growth Lag-phase time (d) EXPONENTIAL GROWTH DECELERATING GROWTH STATIONARY PHASE CELL DEATH 1 ST ORDER KINETICS

26 MONOD EQUATION SUITABLE FROM EXPONENTIAL TO STATIONARY PHASE SPECIFIC GROWTH RATE µ IS GIVEN AS A FUNCTION OF SUBSTRATE CONCENTRATION. PARAMETERS ARE MAXIMUM SPECIFIC GROWTH RATE µ MAX AND MONOD CONSTANT K S : µ = S = µ max S K + S s s S << K S >> K K s s µ µ µ µ K µ µ 2 max max s max S

27 MONOD CONSTANT IF AN ANALYSIS OF FERMENTATION DATA BY THE MONOD MODEL GIVES A KM VALUE SUBSTANTIALLY DIFFERENT FROM THE LITERATURE VALUES, THERE IS REASON TO BELIEVE THAT THE WRONG STRUCTURE OF THE KINETIC EXPRESSION HAS BEEN CHOSEN. THUS, IF K M IS FOUND TO BE 1 g/l, THIS IS A SIGN THAT THE WRONG LIMITING SUBSTRATE HAS BEEN CHOSEN OR THE REACTION SUFFERS FROM PRODUCT INHIBITION.

28 EXPANDED MONOD KINETICS THE SIMPLE MONOD MODEL CAN ALSO BE EXPANDED TO INCLUDE BOTH SUBSTRATE INHIBITION (7.21) AND PRODUCT INHIBITION (7.22) OR (7.23) ALL THREE EQUATIONS ARE EMPIRICAL IN NATURE, AND THEIR FORM JUST MIMICS ORAL MODELS FOR, RESPECTIVELY, SUBSTRATE AND PRODUCT INHIBITION OF CELL REACTIONS IN WINE FERMENTATION, EQ. (7.22) GIVES A GOOD REPRESENTATION OF FERMENTATION DATA WHEN p p max g ethanol/l FOR MOST WINE YEASTS.

29 EFFECT OF SUBSTRATE INHIBITION TO SPECIFIC GROWTH RATE WITH VARIOUS K S AND K I VALUES, WHEN µ MAX =1.0 H -1 : A) K S =1; K I =10 B) K S =0.1; K I =10 C) K S =1; K I =20 D) K S =0.1; K I =20 UNITS FOR S, K S, K I : kg m -3 Non-competitive substrate inhibition : µ = 1 + K S [ S] µ max 1 + [ S] K I

30 IN A MORE COMPLEX KINETIC MODELS ONE MAY TAKE INTO CONSIDERATION: CELL DEATH SUBSTRATE AND PRODUCT INHIBITION MAXIMUM CELL DENSITY (POPULATION) PREFERENCE OF CARBON SOURCE TEISSIER, CONTOIS, MOSER, LOGISTIC EFFECT OF MANY LIMITING CARBON SOURCES: µ = µ max K [ S ] 1 + [ S ] [ S ] 2 K I1 K I 2 + [ S ] K + [ I ] K [ I ] S 1 1 K S 2 2 I1 1 I 2 + 2

31 YIELD COEFFICIENTS Y X/S, Y X/O2 Y X/ATP YIELD COEFFICIENTS DEFINE THE RELATIONSHIP OF FORMATION AND CONSUMPTION OF DIFFERENT PRODUCTS AND SUBSTRATES (INCLUDING ENERGY) Y X / S = dc dt dc dt X S C C X S

32 EXAMPLE: KINETIC MODEL FOR BIER FERMENTATION

33 Yeast suspension consists of three components in a segregated model From Lag-phase to active yeast, reaction (1) Dead yeast sedementation rate µ SD, half of the inoculation amount is dead, reaction (2) Active yeast grows, a part will die, a part is in a lag-phase (1,3,4)

34 Specific sedimentation rate Specific growth rate Effect of temperature Specific substrate consumption rate Ethanol inhibition effect and specific product formation rate

35 EXPERIMENTAL ARRANGEMENTS

36 PILOT-SCALE CULTIVATION ALONG THE TEMPERATURE PROFILE AND THE ESTIMATES FROM THE KINETIC MODELS

37 BIOREACTOR MODELING BATCH CULTIVATION CONTINUOUS CULTIVATION FED-BATCH CULTIVATION PLUG-FLOW REACTOR

38 BATCH CULTIVATION Aeration Exhaust gas Batch cultivation Total volume: dv dt V V = ds dt dx dt 0 Substrate: Biomass: µ X = ( Y X / S = µ XV mx) V

39 CONTINUOUS CULTIVATION µ µ µ = = + = + = = = V F D XV FX dt dx V V mx Y X S S F dt ds V F F dt dv S X in out in ) ( ) ( 0 / Total volume: Substrate: Biomass: Dilution rate: Chemostat Exhaust gas Aeration Product Substrate

40 Chemostat variables as a function of dilution rate

41 FED-BATCH CULTIVATION XV X F dt dx V V mx Y X S S F dt ds V F dt dv in S X in in µ µ + = + = = ) ( ) ( / Total volume: Substrate: Biomass: Exhaust gas Aeration Substrate Fed-batch cultivation

42 STATE-SPACE REPRESENTATION FIRST ORDER DIFFERENTIAL EQUATIONS CAN BE REPRESENTED BY STATE-SPACE EQUATIONS THE SYSTEM STATE x, CONTROLS u AND OUTPUT y VALUES ARE REPRESENTED IN A MATRIX FORM MATRIX REPRESENTATION ENABLES THE STABILITY ESTIMATION AND HELPS TO CALCULATE TRANSFER FUNCTIONS HERE IS DESCRIBED CONTINUOUS CULTIVATION THE STATE EQUATION : x = y = missä Ax + Bu Cx X( t) x = ( ) S t u = [ S ( t) ] in µ D A = µ m YX / S 0 B = D C = [ 1 0] 0 D

43 PLUG-FLOW REACTOR Substraatti Tu o t e CONTINUOUS PROCESS CAN BE MODELLED WITH STATIC OR DYNAMIC MODELS STATIC MODEL RESEMBLES BATCH CULTIVATION THE CONCENTRATION IS FUNCTION OF THE POSITION DYNAMIC MODEL IS CREATED DIVIDING THE REACTOR LENGTH/HEIGHT TO FINITE ELEMENTS

44 THE PLUG FLOW REACTOR CONCENTRATION CHANGES AS A FUNCTION OF THE POSITION Z IN AN EQUILIBRIUM: A) NO REACTION B) WITH THE REACTION, AND C) DYNAMIC FINITE ELEMENT MODEL a) b) c)

45 OVERVIEW OF DIFFERENT TYPES OF DATA FOR ODE-BASED KINETIC MODELS OF METABOLISM