Download μ XY dt dP = μ μ

CHEM-E3205 Bioprocess Optimization and Simulation
Exercise 1 (13.9. 2016):
Your task is to explore the Matlab Simulink program and the construction of simulation models.
Start Matlab. Check out first Simulink software on-line manual (press F1 while you are in Matlab
window) (SimulinkGetting Started Tutorials Create a Simple Model.
After the demo, your task is to build a simple model for glucoamylase fermentation. This is a
batch culture, in which Aspergillus niger fungus produces glucoamylase using glucose as a carbon
source. Create a Simulink model and to examine its operations by setting the model parameter
values and the initial state variable values. Run the model and make some tests with various
parameter values and monitor the the model behavior. Here are the batch fermentation kinetic
models which can be put in Simulink format:
dX
 X
dt
dP
 YPS  X
dt
dS
1 dX


dt
Y XS dt

 max  S
KS  S
YPS 
YPS ,max  S
KP  S
Simulink program can be found after the start-up of Matlab. Simulink program opens when you
type the command “simulink” in Matlab command window or by clicking the Simulink icon.
Simulink Library Browser window has icons, which opens different sub-libraries that contain the
necessary components to build the model. We use a basic library called Simulink. Much of the
blocks required can be found Commonly Used Blocks sub-library. The table below shows the
other sub-libraries needed with their suitable blocks, as well as the related definitions, you may
need to build the model.
Sub-library
Sources
Block
Constant
Definitions (double click)
giving the value of the constant
Sinks
Continuous
Math Operations
UserDefined Functions
Signal Routing
Scope
Integrator
Product
Fcn
Mux
graphical monitoring of variables
initial value for a variable
number of inputs
Definition of a function
number of inputs
Start by creating a new simulation window. On this screen you can pick up the blocks you need
from the libraries (by dragging with the mouse from a library window or copying already existing
blocks in the working window by holding down the Ctrl key same time). The blocks can be
connected with the mouse from > sign in each block. The blocks and connecting lines may be
named by double-clicking the icon name area below or directly the workspace.
Each differential equation is presented in graphical form which describes state variable
calculation and plot the simulation results eventually in Scope blocks. The equation calculations
are defined in function blocks (Fcn), or in separate calculation blocks, such as e.g. Product-block
for multiplication etc. See the example in Figure 1, wherein the specific growth rate is already
modeled. Start with the construction of this model. Arrange the blocks from the left to the right
for example: parameters (max, Ks) to Constant-blocks, then Mux (collects and indexes the
incoming signals), then fcn (function, calculate  then multiplied by biomass, then the dX/dt
obtained is integrated and we have finally the value for biomass (state variable X).
Once this first part of the model is complete, the simulation parameters can be set in the menu
Simulation / Model Configuration Parameters (default settings most likely ok, eg. Start time =
0.0, Stop time = 10). Click the Scope block open and run your biomass simulating model. At this
point, substrate concentration is still in a constant block, but now as you continue you change the
block to an integrator block, which changes the substrate concentration from the given the initial
value. Complete the model by adding blocks for substrate consumption and product formation and
simulate the system using subtrate initial levels 10, 30 and 50 g/L and the inoculum concentration,
ie. initial biomass levels of 0.1, 0.3, 0.5, and see the effect of final concentrations (and print the
simulation results if you’re preparing a report). Concentrations of the initial values are placed into
integrators (limits should be used for the substrate integrator so that concentration can not fall
below zero).
Figure 1. A part of the model: the specific growth rate model converted to a Simulink model
Try first with these values:
 max : 1.5 (h-1)
KS : 0.010 (g/l)
YXS : 0.5 (g/g)
YPS,max :0.006 (g/g)
KP : 10 (g/l)
X0: 0.30 g/l
S0: 25 g/l
P0: 0.01 g/l
X
S
P

 max
KS
YPS
YPS,max
KP
YXS
biomass (g/L)
glucose concentration (g/L)
enzyme concentration (g/L)
spesific growth rate (1/h)
maximum spesific growth rate
Monod constant (g/L)
enzyme (product) yield coefficient (g/g)
maximum yield coefficient (g/g)
enzyme production constant (g/L)
biomass yield coefficient (g/g)