No reaction

[Jaundre Venter]

Hi all

Can someone please explain to me the following:

I am busy with a project of simulation the production of penicillin in a bio
reactor. Now i have 9 ODE's which i want to simulate.

now for some reason the last three graphs i am getting doesn't show any
response what so ever. i am using the following code.

dx(1)=(((mu)*(x(1)))-(((x(1))/(x(6)))*((dx_6)))*(CO)*(HION)), //biomass
concentration X
dx(2)=((z*(((mu)*(x(1)))-(((F)*(x(1)))/(x(6)))))+(QQ)), //hydrogen ion
concentration H+
dx(3)=((((mupp)*(x(1)))-((K)*(x(3)))-((x(3))/(x(6)))*(dx_6))*(HION)),
//Penicilin concentration P
dx(4)=((-((mu)/(Yxs))*(x(1)))-(((mupp)/(Yps))*(x(1)))-((mx)*(x(1)))+((Fsf)/(x(6)))-((x(4)/(x(6)))*(dx_6))),
//Substrate concentration S
dx(5)=(-(((mu)/(Yxo))*(x(1)))-(((mupp)/(Ypo))*(x(1)))-(((mo))*(x(1)))+((kla)*(cll-(x(5))))-(((x(5))/(x(6)))*(dx_6))),
//dissolved oxygen
dx(6)=((F+Fab+Floss)*(HION)),  // culture Volume V
dx(7)=(((rq1)*(dx_1)*(x(6)))+(rq2)*(x(1))*(x(6))), //Heat generation Qrxn
dx(8)=((((F)/(sf))*(Tf-(x(8))))+(1/((x(6))*(pcp)))*(QT)),  //  Temperature T
dx(9)=(((a1)*(dx_1))+((a2)*(x(1)))+(a3)),  //  CO2 evolution, CO2
endfunction

now when i ask for plotting the graphs i am using the following.:

//  initial values
x0=[0.1, 1e-5, 0, 15, 1.16, 100,0,297,0.5]';
t=0:0.005:400;
y=ode(x0, 0, t, f);

// the plots of each variable
da.title.text="BIOMASS CONCENTRATION"
da.x_label.text="Time, hours";
da.y_label.text="X,g/l ";
scf(1);clf; //Opens and clears figure 1
plot(t,y(1,:))

da.title.text="HYDROGEN ION H+ CONCENTRATION"
da.y_label.text="H+,mol/l ";
scf(2);clf; //Opens and clears figure 2
plot(t,y(2,:))

da.title.text="PENICILLIN CONCENTRATION"
da.y_label.text="P,g/l ";
scf(3);clf; //Opens and clears figure 3
plot(t,y(3,:))

da.title.text="SUBSTRATE CONCENTRATION"
da.y_label.text="S,g/l ";
scf(4);clf; //Opens and clears figure 4
plot(t,y(4,:))

da.title.text="DISSOLVED OXYGEN CONCENTRATION"
da.y_label.text="C_l,g/l ";
scf(5);clf; //Opens and clears figure 5
plot(t,y(5,:))

da.title.text="CULTURE VOLUME"
da.y_label.text="V,l";
scf(6);clf; //Opens and clears figure 6
plot(t,y(6,:))

da.title.text="HEAT OF REACTION"
da.y_label.text="Qrxn,cal";
scf(7);
clf; //Opens and clears figure 7
plot(t,y(7),:)

da.title.text="TEMPERATURE"
da.y_label.text="T,Kelvin";
scf(8);
clf; //Opens and clears figure 8
plot(t,y(8),:)

da.title.text="CO2 EVOLUTION"
da.y_label.text="CO2,mmol/l/";
scf(9);
clf; //Opens and clears figure 9
plot(t,y(9),:)

Am i doing something wrong? before the ODE's i have just programmed the
initial values and constants :

funcprot(0);
function dx = f(t,x)
K1=1.0e-10         //mol/l
K2=7.0e-05         //mol/l
Kx=0.15            // Contois saturation constant, g/l
Kox=2e-02          // oxygen limitation constant
mux=0.092          // maitenance coefficient on subsrate
p=3                //constant
Kp=0.0002          //   inhibition constant
Kop=2e-02      // oxygen limitation constant
K=0.04     //  Penicillin hydrolysis constant, per h
Yxs=0.45  //   yield constant,g biomass/g glucose = dimensionless
Yps=0.90  //   yield constant, g pinicillin/ g glucose = dimensionless
mx= 0.014  //   Maintenance coefficient on substrate, per h
Yxo=0.04  //   yield constant, g biomass/g oxygen = dimensionless
Ypo=0.20  //   yield constant, g penicillin/g oxygen= dimensionless
mo= 0.467  //   maintenance coefficient of oxygen, per h
mup=0.0005  // specific rate of penicilline production (per h)
sf=600 // Feed substrate concentration, g/l
kla=23     // function of agitation power input and oxugen flow rate,
dimensional
cll=1.16   //  dissolved oxygen concentration, g/l
Cab=3      // concentrations in both solutions
Fa=5     // acid flow rate, l/h  !!
Fb=5      // base flow rate, l/h !!
delta_t=0.01   //  time step in digital PID controller - arbitrary value!!!
z=10e-5     // constant
F=0.042       //  feed substrate flow rate l/h
T0=273         //  temperature at freezing, K
Tv=373       //  temperature at boiling
T=298  //  feed temp of substrate
h=(2.5e-4)     //  constant
Floss=(x(6)*(h)*(exp(5)*((T-T0)/(Tv-T0))))
Fab=Fa+Fb  // volume increase due to influx of acid Fa and base Fb
Fsf=((sf)*(F))
kg= 7e-3 //  Arrhenius constant for growth
kd=10e33  //  Arrhenius constant for cell death
Eg= 5100  //  Activation energy for growth, cal/mol
Ed= 50000  //  Activation energy for cell death, cal/mol
R= 1.987  //  gas constant, cal/mol k
T= 297  //  Temperature
RT= R*T
alpa= 70  //  constant in Kla
betha= 0.4  //  constant in Kla
Pw= 30  //  Agitation power input, W
fg= 8.6  //  Flow rate of oxygen
V=100  //  Volume
QE= ((kg*exp(-(Eg/RT)))-(kd*exp(-(Ed/RT))))
kla= alpa*((sqrt(fg)*(Pw/x(6)))^betha)
mu
=(((mux)/(1+((K1)/(x(2)))+((x(2))/(K2))))*((x(3))/(((Kx)*(x(1)))+(x(3))))*((x(5))/(((Kox)*(x(1)))+(x(5))))*(QE))
//  Specific growth rate
mupp =
((mup)*((x(4))/((Kp)+(x(4))+(x(4)^2)/(K1)))*((x(5)^p)/((Kop)*(x(1)))+(x(5)^p)))
// Specific penicillin production rate
B =(((1e-14/x(2)-x(2))*x(6)-Cab*(Fa+Fb)*delta_t)/(x(6)+(Fa+Fb)*delta_t))
QQ =((-B+sqrt(B^2+4e-14))/2-(x(2)))*(1/delta_t)
dx_6 = (F+Fab+Floss) //Culture Volume V
dx_1 = (((mu)*(x(1)))-((x(1))/(x(6)))*(dx_6)) //biomass concentration X
rq1 = 60  //  yield of heat generation, cal/g biomass
rq2 = 1.6783e-4  //  Constant, cal/g biomass h
Tf = 296  //  substrate feed temperature, Kelvin
a = 1000   //  heat transfer coefficient of cooling/heating liquid, cal/h
degree C
b = 0.60   //  constant
Fc=0.1   //  Cooling water flow rate, not sure about value, l/h
pcCpc = 1/2000   //  Density times heat capacity of cooling liquid, per l
degree C
pcp = 1/1500   //  density times heat capacity of medium
QT = ((x(7)-(((a)*(Fc^b+1))/((Fc)+((a)*(Fc^b))/2*pcCpc))))
a1=0.143  //  constant relating CO2 to growth, mmol CO2/g biomass
a2=4e-7  //  Constant relating CO2 to mainteneance energy, mmol CO2/g
biomass h
a3=1e-4 //  Constant relating CO2 to penicillin production, mmol CO2/l h
CO= (((a1)*(dx_1))+((a2)*(x(1)))+(a3)),  //  CO2 evolution, CO2
HION=((z*(((mu)*(x(1)))-(((F)*(x(1)))/(x(6)))))+(QQ))

Thanks.
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