Dynamic model for Steel purification in AOD converter

%print("Dynamic Model for Evaluating Mass and Concentration variation");

%Pre-alloacation of Arrays

XbFe=zeros(1,i);

XbCr=zeros(1,i);

XbO2=zeros(1,i);

XbFeO=zeros(1,i);

XbCr2O3=zeros(1,i);

CbFe=zeros(1,i);

CbCr=zeros(1,i);

CbO2=zeros(1,i);

CbFeO=zeros(1,i);

CbCr2O3=zeros(1,i);

keq_FeO=zeros(1,i);

keq_Cr2O3=zeros(1,i);

val=zeros(1,i);

XiFe=zeros(1,i);

XiCr=zeros(1,i);

CiFe=zeros(1,i);

CiCr=zeros(1,i);

JFe=zeros(1,i);

JCr=zeros(1,i);

MolesTransFe=zeros(1,i);

MolesTransCr=zeros(1,i);

MolesTransfFeO=zeros(1,i);

MolesTransfCr2O3=zeros(1,i);

MolesTransO2=zeros(1,i);

MFe=zeros(1,i);

MCr=zeros(1,i);

MO2InMetal=zeros(1,i);

Moxy=zeros(1,i);

MCr2O3=zeros(1,i);

MFeO=zeros(1,i);

MassOfFe=zeros(1,i);

MassOfCr=zeros(1,i);

MassofO2=zeros(1,i);

MassOfFeO=zeros(1,i);

MassOfCr2O3=zeros(1,i);

TotalMolesInMetal=zeros(1,i);

TotalMolesInSlag=zeros(1,i);

TotalMassOfMetal=zeros(1,i);

TotalMassOfSlag=zeros(1,i);

VolOfMetal=zeros(1,i);

VolOfSlag=zeros(1,i);

MolarVolumeofMetal=zeros(1,i);

MolarVolumeofSlag=zeros(1,i);

PerFeInMetal=zeros(1,i);

PerCrInMetal=zeros(1,i);

PerO2InMetal=zeros(1,i);

PerFeOInSlag=zeros(1,i);

PerCr2O3InSlag=zeros(1,i);

time=zeros(1,i);

%Input from User

TotalMassOfMetal(1) = input("Input Total Mass of Metal:" );

TotalMassOfSlag(1) = input("Input Total Mass of Slag: ");

DensityOfMetal(1) = input("Input Density of Metal: ");

DensityOfSlag(1) = input("Input Density of Slag: ");

PerFeInMetal(1) = input("Input Percentage of Fe in Metal: ");

PerCrInMetal(1) = input("Input Percentage of Cr in Metal: ");

PerO2InMetal(1)= input("Input Percentage of O2 in Metal: ");

PerFeOInSlag(1) = input("Input Percentage of FeO in Slag: ");

PerCr2O3InSlag(1) = input("Input Percentage of Cr2O3 in Slag: ");

O2AddedFromTop(1) = input("Input Oxygen added from Top: ");

O2AddedFromBottom(1) = input("Input Oxygen added from bottom: ");

Del_T = input("Input time step of each calculation: ");

Temp=input("Operating range of Temperature:" );

MassTransCoeffFe=input("Mass transfer Coefficients of Fe: ");

MassTransCoeffCr=input("Mass transfer Coefficients of Cr: ");

AssumedArea=input("Area Assumed: ");

%Standard Known Values/ Given Inputs

AtomicMassofFe= 56;

AtomicMassofCr= 52;

AtomicMassofO2= 16;

AtomicMassofFeO= 72;

AtomicMassofCr2O3= 152;

%Volume of Metal and Slag

VolOfMetal(1)=TotalMassOfMetal(1)/DensityOfMetal;

VolOfSlag(1)=TotalMassOfSlag(1)/DensityOfSlag;

%Initial Moles of Metal and Slag in kmoles

MFe(1)=TotalMassOfMetal(1)*(PerFeInMetal(1)/100)*(1/AtomicMassofFe);

MCr(1)=TotalMassOfMetal(1)*(PerCrInMetal(1)/100)*(1/AtomicMassofCr);

MFeO(1)=TotalMassOfSlag(1)*(PerFeOInSlag(1)/100)*(1/AtomicMassofFeO);

MCr2O3(1)=TotalMassOfSlag(1)*(PerCr2O3InSlag(1)/100)*(1/AtomicMassofCr2O3);

MO2InMetal(1)=TotalMassOfMetal(1)*(PerO2InMetal(1)/100)*(1/AtomicMassofO2);

%Moles of Oxygen Added in kmoles

MO2Added=((O2AddedFromBottom+O2AddedFromTop)*2*(273/298)/(22.4*60));

Moxy(1)=MO2InMetal(1)+MO2Added;

%Total Moles in Metal and Slag in kMoles

TotalMolesInMetal(1)=MCr(1)+MFe(1)+Moxy(1);

TotalMolesInSlag(1)=MCr2O3(1)+MFeO(1);

%Molar Volume

MolarVolumeofMetal(1)=TotalMolesInMetal(1)/VolOfMetal(1);

MolarVolumeofSlag(1)=TotalMolesInSlag(1)/VolOfSlag(1);

time(1)=0;

for i= 1:1200

%Mole Fractions of elements

XbFe(i)=MFe(i)/TotalMolesInMetal(i);

XbCr(i)=MCr(i)/TotalMolesInMetal(i);

XbO2(i)=Moxy(i)/TotalMolesInMetal(i);

XbFeO(i)=MFeO(i)/TotalMolesInSlag(i);

XbCr2O3(i)=MCr2O3(i)/TotalMolesInSlag(i);

%Bulk Concentration of elements

CbFe(i)=XbFe(i)*MolarVolumeofMetal(i);

CbCr(i)=XbCr(i)*MolarVolumeofMetal(i);

CbO2(i)=XbO2(i)*MolarVolumeofMetal(i);

CbFeO(i)=XbFeO(i)*MolarVolumeofSlag(i);

CbCr2O3(i)=XbCr2O3(i)*MolarVolumeofSlag(i);

%Equilibriium Constant Identfication

keq_FeO(i)=exp((-121009.9+(53.114*Temp)+ (8.314* Temp*log(0.5585/16)))/(-8.314*Temp));

keq_Cr2O3(i)=exp((-274347+(120.55*Temp)+ (8.314* Temp*log(0.5585/16)))/(-8.314*Temp));

%Interface concentration calculation of Fe and Cr

val(i)=keq_Cr2O3(i)*XbO2(i);

XiFe(i)=XbFeO(i)/(keq_FeO(i)*XbO2(i));

XiCr(i)=(XbCr2O3(i)^(0.5))/(val(i)^(1.5));

CiFe(i)=XiFe(i)*MolarVolumeofMetal(i);

CiCr(i)=XiCr(i)*MolarVolumeofMetal(i);

%Mass Flux Balance

JFe(i)=-MassTransCoeffFe*(CbFe(i)-CiFe(i));

JCr(i)=-MassTransCoeffCr*(CbCr(i)-CiCr(i));

%Moles Transfered

MolesTransFe(i)=JFe(i)*Del_T*AssumedArea;

MolesTransCr(i)=JCr(i)*Del_T*AssumedArea;

MolesTransfFeO(i)=MolesTransFe(i);

MolesTransfCr2O3(i)=0.5*MolesTransCr(i);

MolesTransO2(i)=MolesTransFe(i)+1.5*MolesTransCr(i);

%Moles of elements after this iteration

MFe(i+1)=MFe(i)+MolesTransFe(i);

MCr(i+1)=MCr(i)+MolesTransCr(i);

MO2InMetal(i+1)=MO2InMetal(i)+MolesTransO2(i);

Moxy(i+1)=Moxy(i)+MolesTransO2(i)+MO2Added;

MCr2O3(i+1)=MCr2O3(i)-MolesTransfCr2O3(i);

MFeO(i+1)=MFeO(i)-MolesTransfFeO(i);

%Mass of each elements

MassOfFe(i+1)=MFe(i+1)*AtomicMassofFe;

MassOfCr(i+1)=MCr(i+1)*AtomicMassofCr;

MassofO2(i+1)=Moxy(i+1)*AtomicMassofO2;

MassOfFeO(i+1)=MFeO(i+1)*AtomicMassofFeO;

MassOfCr2O3(i+1)=MCr2O3(i+1)*AtomicMassofCr2O3;

%Total Moles in metal and Slag

TotalMolesInMetal(i+1)=MCr(i+1)+MFe(i+1)+Moxy(i+1);

TotalMolesInSlag(i+1)=MCr2O3(i+1)+MFeO(i+1);

%Total Mass of Metal and Slag

TotalMassOfMetal(i+1)=MassOfFe(i+1)+MassofO2(i+1)+MassOfCr(i+1);

TotalMassOfSlag(i+1)=MassOfCr2O3(i+1)+MassOfFeO(i+1);

%Molar Volumes

VolOfMetal(i+1)=TotalMassOfMetal(i+1)/DensityOfMetal;

VolOfSlag(i+1)=TotalMassOfSlag(i+1)/DensityOfSlag;

MolarVolumeofMetal(i+1)=TotalMolesInMetal(i+1)/VolOfMetal(i);

MolarVolumeofSlag(i+1)=TotalMolesInSlag(i+1)/VolOfSlag(i);

%Percentage of elements

PerFeInMetal(i+1)=(MFe(i+1)*100*AtomicMassofFe)/TotalMassOfMetal(i+1);

PerCrInMetal(i+1)=(MCr(i+1)*100*AtomicMassofCr)/TotalMassOfMetal(i+1);

PerO2InMetal(i+1)=(Moxy(i+1)*100*AtomicMassofO2)/TotalMassOfMetal(i+1);

PerFeOInSlag(i+1)=(MFeO(i+1)*100*AtomicMassofFeO)/TotalMassOfSlag(i+1);

PerCr2O3InSlag(i+1)=(MCr2O3(i+1)*100*AtomicMassofCr2O3)/TotalMassOfSlag(i+1);

time(i+1)=time(i)+i/10;

%temperature iterations

Temp=Temp+0.02;

end

I am constantly getting :

Error using zeros

Size vector must be a row vector with real elements.

Error in dynamic_model (line 5)

XbFe=zeros(1,i);

[Prasanth Warrier]

Hi Community... need help badly to know how to resolve above mentioned error

Answer 1

[Star Strider]

The problem with this assignment (and the others like it):

XbFe=zeros(1,i);

is that ‘i’ needs to be defined as a scalar double. It does not appear to be in the code you posted. In that absence, MATLAB interprets ‘i’ as the imaginary operator and it throws the error you got.

[Prasanth Warrier]

Thanks Star Strider... i made the corrections and program worked

[Star Strider]

As always, my pleasure!