Generating our own data with the help of Aspen-Hysys®
Consider a steady-state ternary mixture of benzene (), toluene (), and cumene () at . This mixture, with a thermal quality equal to 1.0 (i.e. saturated liquid), is fed to a 19-stage column with a total condenser and partial reboiler. The feed is at stage 10. The feed flow rate is set to .
Following Wankat’s textbook (Ref. 1), we desire 99% recovery of benzene in the distillate stream and 93% recovery of toluene in the bottom stream. Hence, the values of the reflux and reboil ratios ( and , respectively) are found to be equal to 2.087 and 0.9718.
We computes the temperature and composition profiles using a rigorous approach, which includes both the energy and mass balances. These profiles are successfully compared to those given by HYSYS (http://www.aspentech.com/hysys/).
HYSYS data is shown with colored curves while our data are represented with dashed black lines. We find perfect agreement between both sets of data.
Consider a steady-state ternary mixture of benzene (
23.33%mole
33.33%mole
43.34%mole
101.325kPa
1kmol/hr
Following Wankat’s textbook (Ref. 1), we desire 99% recovery of benzene in the distillate stream and 93% recovery of toluene in the bottom stream. Hence, the values of the reflux and reboil ratios (
R
s
We computes the temperature and composition profiles using a rigorous approach, which includes both the energy and mass balances. These profiles are successfully compared to those given by HYSYS (http://www.aspentech.com/hysys/).
HYSYS data is shown with colored curves while our data are represented with dashed black lines. We find perfect agreement between both sets of data.
Feed stream composition and flow rate
Benzene (component 1), Toluene (component 2) and Cumene (component 3)
Benzene (component 1), Toluene (component 2) and Cumene (component 3)
In[]:=
F=1;(*inkmol/hr*)
In[]:=
z1F=0.2333;z2F=0.3333;z3F=0.4334;
Total pressure in kPa
In[]:=
P=101.325;
Antoine constants and equation
Aa1=169.65;Ba1=-10314.8;Ca1=0.0;Da1=-23.5895;Ea1=2.0944210^-005;Fa1=2.0;Aa2=76.45110;Ba2=-6995.0;Ca2=0.0;Da2=-9.16350;Ea2=6.225010^-006;Fa2=2.0;Aa3=136.712;Ba3=-9687.70;Ca3=0.0;Da3=-19.305;Ea3=1.770310^-002;Fa3=1.0;
In[]:=
PSat1[i_]:=Exp[Aa1+Ba1/(T[i]+Ca1)+Da1Log[T[i]]+Ea1T[i]^Fa1];PSat2[i_]:=Exp[Aa2+Ba2/(T[i]+Ca2)+Da2Log[T[i]]+Ea2T[i]^Fa2];PSat3[i_]:=Exp[Aa3+Ba3/(T[i]+Ca3)+Da3Log[T[i]]+Ea3T[i]^Fa3];
Feed is saturated liquid and feed temperature is equal to 109.763°C
In[]:=
TF=.
In[]:=
PSat1f=Exp[Aa1+Ba1/(TF+Ca1)+Da1Log[TF]+Ea1TF^Fa1];PSat2f=Exp[Aa2+Ba2/(TF+Ca2)+Da2Log[TF]+Ea2TF^Fa2];PSat3f=Exp[Aa3+Ba3/(TF+Ca3)+Da3Log[TF]+Ea3TF^Fa3];
In[]:=
FindRoot[z1FPSat1f+z2FPSat2f+z3FPSat3f==P,{TF,350}]
Out[]=
{TF382.913}
In[]:=
TF=382.913;
In[]:=
TF-273.15
Out[]=
109.763
Latent heat of vaporization for Benzene, Toluene and Cumene
C1A=4.750010^7;C2A=0.45238;C3A=0.0534;C4A=-0.1181;C1B=5.014410^7;C2B=0.3859;C3B=0;C4B=0;C1C=5.79510^7;C2C=0.3956;C3C=0;C4C=0;(*criticaltemperatures*)TcA=562.16;TcB=591.8;TcC=631.15;(*expressionsavailableinAspen-HysysorPerry'sCHEHandbook*)λA=10^-3C1A(1-Ti1/TcA)^(C2A+C3ATi1/TcA+C4A(Ti1/TcA)^2);λB=10^-3C1B(1-Ti2/TcB)^(C2B+C3BTi2/TcB+C4B(Ti2/TcB)^2);λC=10^-3C1C(1-Ti3/TcC)^(C2C+C3CTi3/TcC+C4C(Ti3/TcC)^2);(*normalboilingpoints*)Ti1=80.1+273.15;Ti2=110.6+273.15;Ti3=152.39+273.15;
Liquid and vapor-phase Enthalpies in kJ/kmol
H[i_]:=y1[i](λA+138.2(Ti1-80.1-273.15)+96.3(T[i]-Ti1))+y2[i](λB+167.5(Ti2-80.1-273.15)+138.2(T[i]-Ti2))+(1-y1[i]-y2[i])(λC+214.4(Ti3-80.1-273.15)+206.1(T[i]-Ti3));h[i_]:=x1[i](138.2(T[i]-80.1-273.15))+x2[i](167.5(T[i]-80.1-273.15))+(1-x1[i]-x2[i])(214.4(T[i]-80.1-273.15));
Feed stream enthalpy
In[]:=
hF=z1F(138.2(TF-80.1-273.15))+z2F(167.5(TF-80.1-273.15))+z3F(214.4(TF-80.1-273.15));
In[]:=
hF
Out[]=
5368.73
Distillate stream enthalpy
h0=y1[1](138.2(T[0]-80.1-273.15))+y2[1](167.5(T[0]-80.1-273.15))+(1-y1[1]-y2[1])(214.4(T[0]-80.1-273.15));
MESH equations
In[]:=
eq1=Di+L[0]V[1];eq2=Dih0+L[0]h0V[1]H[1]+Qc;(*energybalancearoundthecondenser*)eq1b=x1[0]y1[1];eq2b=x2[0]y2[1];eq3[i_]:=V[i]+L[i]V[i+1]+L[i-1];eq4[i_]:=V[i]y1[i]+L[i]x1[i]V[i+1]y1[i+1]+L[i-1]x1[i-1];eq5[i_]:=V[i]y2[i]+L[i]x2[i]V[i+1]y2[i+1]+L[i-1]x2[i-1];eq6[i_]:=y1[i]Px1[i]PSat1[i];(*Raoult'slaw*)eq7[i_]:=y2[i]Px2[i]PSat2[i];eq8[i_]:=V[i]H[i]+L[i]h[i]V[i+1]H[i+1]+L[i-1]h[i-1];eq3[10]:=V[10]+L[10]V[11]+L[9]+F;(*feedstagematerialbalance*)eq4[10]:=V[10]y1[10]+L[10]x1[10]V[11]y1[11]+L[9]x1[9]+Fz1F;eq5[10]:=V[10]y2[10]+L[10]x2[10]V[11]y2[11]+L[9]x2[9]+Fz2F;eq6[10]:=y1[10]Px1[10]PSat1[10];eq7[10]:=y2[10]Px2[10]PSat2[10];eq8[10]:=V[10]H[10]+L[10]h[10]V[11]H[11]+L[9]h[9]+FhF;eq45=V[20]+BL[19];eq46=V[20]y1[20]+Bx1[20]L[19]x1[19];eq47=V[20]y2[20]+Bx2[20]L[19]x2[19];eq48=y1[20]Px1[20]PSat1[20];eq49=y2[20]Px2[20]PSat2[20];eq50=V[20]H[20]+Bh[20]L[19]h[19]+Qr;(*energybalancearoundthereboiler*)eq51=L[0]/DiRR;(*refluxratiodefinition*)eq52=x2[20]B0.93z2FF;(*93%recoveryofTolueneinthebottomstream*)eq53[i_]:=PSat1[i]x1[i]+PSat2[i]x2[i]+PSat3[i]x3[i]P;(*bubblepointequations*)(*summationrules*)x3[i_]:=1-x1[i]-x2[i];y3[i_]:=1-y1[i]-y2[i];
Reflux ratio is equal to 2.087
In[]:=
RR=2.087;
Forming the system of 147 nonlinear algebraic equations and initial guess for the 147 unknowns
In[]:=
sys=Flatten[Join[{eq1,eq2,eq1b,eq2b},Table[{eq3[i],eq4[i],eq5[i],eq6[i],eq7[i],eq8[i]},{i,1,9}],{eq3[10],eq4[10],eq5[10],eq6[10],eq7[10],eq8[10]},Table[{eq3[i],eq4[i],eq5[i],eq6[i],eq7[i],eq8[i]},{i,11,19}],{eq45,eq46,eq47,eq48,eq49,eq50,eq51,eq52},Table[eq53[i],{i,0,20}]]];
In[]:=
Length[sys]
Out[]=
147
In[]:=
guess=Flatten[Join[Table[{{x1[i],0.1},{x2[i],0.2}},{i,0,20}],Table[{{y1[i],0.1},{y2[i],0.1}},{i,1,20}],{{{Qc,-8.410^4},{Qr,8.510^4}},{{Di,0.5},{B,0.5}},{{L[0],0.50},{L[1],0.49},{L[2],0.49},{L[3],0.48},{L[4],0.47},{L[5],0.47},{L[6],0.47},{L[7],0.47},{L[8],0.46},{L[9],0.46},{L[10],1.47},{L[11],1.48},{L[12],1.49},{L[13],1.49},{L[14],1.49},{L[15],1.49},{L[16],1.48},{L[17],1.48},{L[18],1.47},{L[19],1.47}}},{{{V[1],1.0},{V[2],1.0},{V[3],1.0},{V[4],1.0},{V[5],1.0},{V[6],1.0},{V[7],1.0},{V[8],1.0},{V[9],1.0},{V[10],1.0},{V[11],1.0},{V[12],1.0},{V[13],1.0},{V[14],1.0},{V[15],1.0},{V[16],1.0},{V[17],1.0},{V[18],1.0},{V[19],1.0},{V[20],1.0}},{{T[0],92+273.15},{T[1],101+273.15},{T[2],105+273.15},{T[3],108+273.15},{T[4],109+273.15},{T[5],111+273.15},{T[6],112+273.15},{T[7],113+273.15},{T[8],113+273.15},{T[9],114+273.15},{T[10],114+273.15},{T[11],117+273.15},{T[12],119+273.15},{T[13],121+273.15},{T[14],121+273.15},{T[15],122+273.15},{T[16],123+273.15},{T[17],125+273.15},{T[18],127+273.15},{T[19],150+273.15},{T[20],152+273.15}}}],1];
In[]:=
Length[guess]
Out[]=
147
Solution is obtained using FindRoot command
Reboil ratio is found equal to 0.9718
Reboiler and condenser duties in kJ/hr
Liquid-phase composition profile (present calculation versus Aspen-Hysys results)
Counting from the bottom (i.e., reboiler stage 1)
Counting from the bottom (i.e., reboiler stage 1)
Vapor-phase composition profile (present calculation versus Aspen-Hysys results)
Counting from the bottom (i.e., reboiler stage 1)
Counting from the bottom (i.e., reboiler stage 1)
Temperature profile (present calculation versus Aspen-Hysys results)
Counting from the bottom (i.e., reboiler stage 1)
Counting from the bottom (i.e., reboiler stage 1)
Liquid and vapor flow rates versus stage number (present calculation versus Aspen-Hysys results)
Counting from the bottom (i.e., reboiler stage 1)
Counting from the bottom (i.e., reboiler stage 1)
References
References
◼
[1] P. C. Wankat, Separation Process Engineering, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2007.
CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Separation of a Ternary Ideal Mixture at 101.325 kPa
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, January 21, 2024
https://community.wolfram.com/groups/-/m/t/3106496
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, January 21, 2024
https://community.wolfram.com/groups/-/m/t/3106496