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Ex1a: Determination of NRTL Parameters

problem description

Determine NRTL parameters for the isobaric data of ethanol-water system.

data

solving principles

Optimize NRTL parameters (T12, T21) in the following equations by minimizing the error.
NRTL equations
The error is defined as relative errors of activity coefficients. objective function

// ethanol-water by NRTL // DATA REGRESSION GLOBAL n=20 VAR P10(n),P20(n),g1(n),g2(n),x1(n),x2(n),y1(n),y2(n),t(n),g1cal(n),g2cal(n), .. e1(n),e2(n) P*y1=g1*x1*P10 P*y2=g2*x2*P20 x1+x2=1 y1+y2=1 LOG10(P10)=8.21337-1652.05/(t+231.48) // ethanol LOG10(P20)=7.94916-1657.46/(t+227.02) // water LOGE(g1cal)=x2^2*(T21*(G21/(x1+x2*G21))^2+T12*G12/(x2+x1*G12)^2) LOGE(g2cal)=x1^2*(T12*(G12/(x2+x1*G12))^2+T21*G21/(x1+x2*G21)^2) G12=EXP(-alp*T12) G21=EXP(-alp*T21) alp=0.3 // x1,y1,t data x1=(0.0028,0.0118,0.0144,0.0220,0.0302,0.0519,0.0625,0.0715,0.0871,0.1260, .. 0.1720,0.2100,0.2840,0.3240,0.4050,0.5060,0.6630,0.7350,0.8040,0.9170) y1=(0.0320,0.1130,0.1350,0.1860,0.2310,0.3180,0.3390,0.3620,0.4060,0.4680, .. 0.5050,0.5270,0.5670,0.5860,0.6140,0.6610,0.7330,0.7760,0.8150,0.9060) t=(99.3,96.9,96.0,94.8,93.5,90.5,89.4,88.6,87.2,85.4,.. 84.0,83.0,82.0,81.5,80.9,80.0,78.8,78.5,78.5,78.3) P=760 FIND (T12#1[-10,10], T21#0.1[-10,10]) LEAST (e1,e2) UNTIL 0.01% e1=(g1cal-g1)/g1 e2=(g2cal-g2)/g2 SSR=SUM(e1^2+e2^2)

results

tips to tailor to your problems

If you want to change the components, do the following:

[ Change Antoine's parameters ]

[ Change number of data points ]

[ Change VLE data set ]
ethanol liquid mol fraction, ethanol vapor mol fraction, temperature, total pressure:

Ex1b: Calculation of VLE using NRTL parameters

problem description

Calculation of VLE to compare with measured data using NRTL parameters determined in the previous example problem.

results

Ex2: Determination of Reaction Kinetic Constants

problem description

Determine reaction kinetic constants, k1 and k2 for the reaction data below.

Reaction ODEs.

Data

solving principles

Assume k1 and k2 to calculate trend of concentrations of A, B and C and calculate errors with measured data. Optimize k1 and k2 by Marquardt method, non-linear dynamic optimization.

// Reaction Kinetic Constants GLOBAL n=4 //subroutine FUNCTION react(k1,k2,te;Ac,Bc,Cc,tc) VAR Ae(n),Be(n),Ce(n),te(n) // experimentl data VAR Ac(n),Bc(n),Cc(n),tc(n) // calculated values VAR At(n),Bt(n),Ct(n),tt(n) // trend values VAR eA(n),eB(n),eC(n) // error // simulation and sampling A'=-k1*A B'=k1*A-k2*B C'=k2*B A#1; B#0; C#0 INTEGRAL time[0,61] STEP 0.001 Ac#0;Bc#0;Cc#0;tc#0 CHANGE (Ac#A,Bc#B,Cc#C,tc#time) ON (time>te) TREND A,B,C STEP 1 END //main program VAR Ae(n),Be(n),Ce(n),te(n) // experimentl data VAR Ac(n),Bc(n),Cc(n),tc(n) // calculated values VAR At(n),Bt(n),Ct(n),tt(n) // trend values VAR eA(n),eB(n),eC(n) //error react(k1,k2,te,Ac,Bc,Cc,tc) react(k1,k2,te,At,Bt,Ct,tt) with(trend) eA=Ae-Ac;eB=Be-Bc;eC=Ce-Cc FIND (k1#1[0,10],k2#0.5[0,5]) LEAST (eA,eB,eC) OUTPUT k1,k2,te,Ae,Be,Ce,Ac,Bc,Cc,eA,eB,eC // experimental data te=(0,10,30,60) Ae=(1.0000, 0.5077, 0.2808, 0.1385) Be=(0.0000, 0.2808, 0.4654, 0.4154) Ce=(0.0000, 0.2115, 0.2538, 0.4462)

results

tips to tailor to your problems

If you want to change the reaction equations, which are three-component first order series reactions, modification of the codes is not transparent, contact PreFEED for assistance.
Please include your affiliates (company, telephone, and name) in the email.

Other examples of coding the equations

The following sample problems will help you understand how EQUATRAN-G works.

Lesson 1 : Antoine Equation
Lesson 2 : Heat Balance of Heat Exchanger
Lesson 3 : Boiling Point Calculation
Lesson 4 : Reaction Calculation
Lesson 5 : Simple Distillation

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