09_BioreactorProject_Intro_W12 - Page 1 of 6 SCHOOL OF...

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Unformatted text preview: Page 1 of 6 SCHOOL OF CHEMICAL, BIOLOGICAL, and ENVIRONMENTAL ENGINEERING OREGON STATE UNIVERSITY CHE 361 - TEAM BIOREACTOR PROJECT WINTER Quarter 2012 I. OUTLINE OF PROJECT STEPS This special project is to be performed by TEAMS of students and involves the modeling of a bioreactor using Simulink for dynamic process simulation. Each team will use different kinetic parameters and thus results will not be identical for any two teams. The reactor model has two inputs and two outputs - however each team will study the dynamics of only one combination of 1-output and 1-input. The steps to complete the project can be outlined as follows: 1. Study the ODEs which make up the model of the reactor and choose values of the parameters within the allowable ranges and then pick feasible nominal steady-state inputs, i.e. so that you get positive values of the outputs at steady state - see equations (6a,b), pg.5. After calculating those nominal steady-state outputs, focus on the input (#1 = F, #2 = Ni) / output (#1 = B, #2 = N) pair of variables you are assigned to study. Ranges for the parameters are given on page 5 of this handout and you must remain within those intervals. 2. Linearize the reactor ODEs and find the "local" transfer function for your chosen output/input pair. The parameters in your transfer function obviously depend on the values of process parameters and nominal steady-state inputs that you pick. It is easier to first substitute numerical values of your parameters and the constant input that you do not change into the ODEs and then linearize. Remember that you must use both ODEs, not just the one for your chosen d(output)/dt ! 3. Copy the two (2) "main" files: bio_reacW12.mdl and biorxn_s.p from the class web page bioreactor folder to a folder on a USB jump drive or your network directory. Copy the other auxiliary (xxx.p) files into that same folder. These include sfunykl2.p, errorpx.p, errorp3x.p, fitmodel.p, and step2g.p. Then run MATLAB and set the "Current Folder" to the folder with your copies of the files. Open the model file bio_reacW12.mdl by double-clicking it in the Current Directory window or entering >>bio_reacW12 at the MATLAB prompt. Then modify the "Bio361" block by doubleclicking on it and entering your kinetic parameters and nominal steady-state input and output values. In addition to the "Bio361" block, you must specify steady-state inputs inside the "F_step_in" and "Ni_step_in" blocks. You must specify steady-state outputs in the "Store_tBout" and "Store_tNout" blocks. The "tUin" block must be attached to the lower line for your input step block and the "tYout" must be attached to the output of the Store block for your output. More details are containted in the handout "CHE 361- BIOREACTOR "Simulator". One copy of that handout will be given to each team. Page 2 of 6 4. Perform both step and pulse tests to find experimental transfer function models from the nonlinear dynamic responses of the reactor. You must choose an appropriate size for the input change for each experiment as well as appropriate simulation periods. For each experiment (at least two steps and two pulses), use the supplied "button boxes" to run the MATLAB "step2g" command and other tools to find an "experimentally" determined transfer function which describes the reactor dynamics. 5. Prepare a typed (except equations) report with a complete description of your work and compare the various transfer function models you obtained, i.e. compare at least two step response (time-domain) fitted models and two pulse-test identifications using the frequency response method to the local linearization G(s) derived analytically from the ODEs using partial derivatives for linearization. The derivation equations in your report may be handwritten -- IF DONE NEATLY !! II. SIMULINK S-FILE = biorxn_s.p The file biorxn_s.p contains the Simulink s-file format as shown below. In this version of the bioreactor software, you DO NOT need to modify this file, so it is provided as a .p file instead of .m (which could become corrupted). It is shown here only as a reference for the use of Simulink. The nominal values shown are the default values in the bio_reac.mdl file: V=1 M = 0.1 μmax = 2 Y = 0.5 Ks = 1 The default nominal steady-state inputs: F = 1 and N i = 5.2. The default initial ouputs are the nominal steady-state values: B = 2 and N = 1. function [sys, x0] = biorxn_s(t,x,u,flag,V,M,mumax,Y,Ks,InitialOuts); % biorxn_s(t,x,u,flag) is an S-function for use with SIMULINK % integrators. if abs(flag) == 1 B=x(1); N=x(2); F=u(1); Ni=u(2); Bi=0; mu=(mumax*N)/(Ks+N); sys(1) = (F*Bi - F*B + mu*B)/V; sys(2) = (F*Ni - F*N - mu*B*V/Y - M*B*V)/V; elseif flag == 3 sys(1) = x(1); sys(2) = x(2); elseif flag == 0 sys = [2 0 2 2 0 0]; x0=InitialOuts; end Page 3 of 6 III. SIMULINK BLOCK DIAGRAM = bio_reacW12.mdl bio_reac.mdl G(s) = B(s)/F(s) setup CHE 361 - OSU Chemical Engineering Fin Bout tYout tUin F_step_in t_u_u' M ux Demux Store_tBout t_y_y' Bio361 Alt_output Store_tNout Ni_step_in Alt_input M ux DOUBLE Click to RUN step2g Demux GO TO Command Window !! Nout Nin Step_Analysis F = input B = output DOUBLE click to RUN pulsec GO TO Command Window !! Pulse_Analysis Double click on the “Bio361” block opens this window for reactor parameters: Page 4 of 6 IV. THE BIOREACTOR MODEL (from "Computer Games and Simulation for Biochemical Engineering", H.R. Bungay, J. WileyInterscience, 1985. The analysis of the continuous cultivation of microorganisms starts with the mass balance equation for any component: rate of change of = component in reactor input - output + net generated In the special case of the device termed a chemostat (mixed flow reactor), there is a chosen (manipulated) volumetric rate for feeding sterile medium (food) to organisms in a vessel of constant volume. The mass balance for the organisms (bugs) can be written: V with B V F μ = = = = dB = FBi − FB + µ B V dt ≡ grams of Bugs hour 1 organism (bugs) concentration in g/liter at time t the constant liquid volume, liters the volumetric feed rate at time t, liters/h the specific growth rate coefficient (additional g of bugs grown/h.)/g of bugs present at time t , depends on N below concentration of bugs in the feed = 0 Bi = With excellent mixing, B in the vessel is assumed to be the same as in the product stream. A new term, the dilution rate D(t) = F(t) / V, is introduced and the first ODE of the bioreactor model is obtained as: dB FB = µ B − D B =µ B − dt V 2 A mass balance for the nutrient in lowest proportions for growth (the growth-limiting nutrient) gives: V with N = Ni = Y = M = dN µ BV = FN i − FN − − MB V dt Y ≡ grams of Nutrient hour 3 the concentration of the limiting nutrient (food) in the bioreactor, g/liter the concentration of the limiting nutrient in the feed stream the "yield coefficient", g of bugs produced per gram of food used to produce new bugs the "maintenance coefficient" to keep bugs alive even if no more bugs were produced, g of food used per hour for maintenance per gram of bugs in the bioreactor Page 5 of 6 Dividing by V yields the second ODE required for the bioreactor model: dN µB = DN i − DN − −M B dt Y 4 The specific growth rate coefficient ( µ ) depends on the concentration of food and exhibits substrate inhibition. With K1=0 for this project, we obtain Monod-type kinetics. N N = µ max 2 K S + N + K1 N KS + N µ = µ max with μmax = Ks = K1 = 5 the maximum specific growth rate possible with excess food present a constant with appropriate units a constant with appropriate units K1= 0 for this project (Monod kinetics) The steady-state forms of the two ODEs [2,4] are two algebraic equations which can be solved to yield the two steady-state outputs given the two steady-state inputs: D N = KS µ −D max D = and B Y ( N i − N ) D+M Y (6a,b) This is a classical, well-established analysis that applies to any continuous culture that meets the assumptions of perfect mixing and constant volume. However the nomenclature here follows conventions which evolved in the biological sciences rather than chemical engineering. In CHE 443 you will learn the general approach used by chemical engineers to describe any process which can be characterized as a chemical conversion via both sequential and parallel reactions. In particular Chapters 29 & 30 of Prof. Levenspiel's Chemical Reaction Engineering, 3rd Ed., contain descriptions of enzyme and microbial reactions. The bioreactor in our project is an example of microbial fermentation with substrate limiting behavior (Chap. 29). Choose your steady-state inputs and parameters from the following ranges: The volume of the reactor for everyone is V = 1.0 liter. Steady-state inputs (ranges): 0.5 - 5 liters / hour F 1 - 100 g / liter Ni "Bug" characteristics (ranges): M 0.001 - 0.2 (g food/h) / g bugs μmax 0.1 - 3.0 h-1 Y 0.2 - 0.7 g bugs / g food used to produce bugs Ks 0.2 - 10. g food / liter Page 6 of 6 Tasks for CHE 361 Bioreactor Project Analysis Pick nominal inputs and parameter values to obtain feasible nominal steadystate outputs. Derive G(s)local Make changes to bio-reac.mdl Setup input and output subsystems. Not yet ! Straight-line simulation ? Perform Step Tests using tYout.dat, step2g.p and fitmodel.p files via Button Box Gstep1, Gstep2 , etc. Perform Pulse Tests using uin.dat, yout.dat and pulsec.p files to create freq.dat and plot a Bode plot using chebode.p via Button Box Gpulse1, Gpulse2 , etc. Run freqg.p to specify a transfer function, generate it’s frequency response via the short cut method and store in a frequency data file like freqg2.dat Use chebode2i.p to make Bode plots with freqg.dat from pulse experiment versus Glocal frequency response file calculated by freqg.p ...
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