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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 1output and 1input. 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 steadystate
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 steadystate 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 steadystate 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 doubleclicking 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 steadystate input and
output values. In addition to the "Bio361" block, you must specify steadystate inputs
inside the "F_step_in" and "Ni_step_in" blocks. You must specify steadystate 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 (timedomain) fitted models and two pulsetest 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 SFILE = biorxn_s.p
The file biorxn_s.p contains the Simulink sfile 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 steadystate inputs: F = 1 and N i = 5.2.
The default initial ouputs are the nominal steadystate 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 Sfunction 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 growthlimiting
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 Monodtype 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 steadystate forms of the two ODEs [2,4] are two algebraic equations which can be
solved to yield the two steadystate outputs given the two steadystate inputs: D
N = KS µ −D max D
= and B Y ( N i − N ) D+M Y (6a,b) This is a classical, wellestablished 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 steadystate inputs and parameters from the following ranges: The volume
of the reactor for everyone is V = 1.0 liter.
Steadystate 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 h1
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
bioreac.mdl
Setup input and output
subsystems. Not yet ! Straightline
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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This note was uploaded on 03/01/2012 for the course CHE 361 taught by Professor Staff during the Winter '08 term at Oregon State.
 Winter '08
 Staff

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