[scilab-Users] No reaction
Jaundre Venter
jaundreventer at gmail.com
Wed Oct 5 15:00:55 CEST 2011
Hi Adrien
i am new to SCILAB! I just want to say that.
Yes dx_1 is equal to dx1 but the only reason why i have programmed it like
that is becasue the ODE's looks as follows - (see word file attached that
can explain the ODE"s better. with regards to the HION and CO it actually
refers to [H+] and CO2 as you said. the only reason why n multiplied HION
and CO wit hsome ODE's is because some does have a influence on some ODE's.
This is the first time i am working with SCILAB thus i am struggling to
understand how SCILAB wants the code so that all 9 ODE's are shown and so
that the ODE's that is having a effect on other does happen. I though if you
refer to dx(1) for example in a other ODE it means that SCILAb will know the
dx(1) has a influence on the other ODE.
The main goal of my assesment is to deliver similar results obtained from
MATLAB on SCILAB. all i got was how the grpahs should look like and the
ODE's.
On Wed, Oct 5, 2011 at 2:43 PM, Adrien Vogt-Schilb <vogt at centre-cired.fr>wrote:
> Hi
>
> Try to isalote your problem
> if i understood well, the following code
>
>
> // 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);
>
> returns y such that sum(y(6:9,:)>x0) == 0 ?
> if this is true, we do not need the plots to solve the problem
> can you check that ?
>
> I believe the f function is erroneous.
> It seems that dx_1 should be equal to dx(1) at each time step, and that
> HION should be equal to x(2) at each time step, etc.
>
> in other terms, some of your phisical variables seem to be represented by
> to variables (i am guessing HION=[H+] and x(2)=[H+] also) but scilab does
> not have any chance to know that.
> if my guess is right, you have to rewrite the f function in a way that
> eliminates all references to HION, dx_1, dx_6 and so on
>
>
> On 05/10/2011 14:27, Jaundre Venter wrote:
>
> 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.
>
>
>
> --
> Adrien Vogt-Schilb (Cired)
> Tel: (+33) 1 43 94 *73 77*
>
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