# A Selection of Chemical Engineering Problems Solved using Mathematica

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A Selection of Chemical Engineering Problems Solved using Mathematica
Housam BINOUS National Institute of Applied Sciences and Technology 1- Chemical Kinetics and Catalysis 2- Applied Thermodynamics

Successive First-Order Reversible Reactions
We consider successive first-order reversible reactions : Governing equations are :

Forward and Backward rate constants:
Steady state solution [Ai] i Forward and Backward rate constants: ki,i+1=1 and ki+1,i=0.9

Transient solution A100, A200, A300, A400, A500,
A600, A700, A800 and A900 A1 A1000

Eley-Rideal Mechanism
Rate expressions for Reaction A + B ’ C 1/ equilibrium constant KA and rate constants are k1 and k2 2/ rate limiting step, rate constant is kp, equilibrium constant KAB 3/ equilibrium constant 1/KC and rate constants are k5 and k6

Adsorption competition with an inert component
Rate expressions for Reaction A + B ’ C Adsorption competition with an inert component 1/ equilibrium constant KA and rate constants are k1 and k2 2/ equilibrium constant KB and rate constants are k3 and k4 3/ equilibrium constant KD and rate constants are k7 and k8 4/ rate limiting step, rate constant is kp, equilibrium constant KAB 5/ equilibrium constant 1/KC and rate constants are k5 and k6

Rate expression when H2 follows dissociative adsorption
Reaction A + H2 ’ AH2 (for example: hydrogenation reactions) Rate expression when H2 follows dissociative adsorption 1/ equilibrium constant KA and rate constants are k1 and k2 2/ equilibrium constant KH2 and rate constants are k3 and k4 3/ rate limiting step, rate constant is kp 4/ equilibrium constant KAH2 and rate constants are k5 and k6 H 2 s catalyst A AH2 s catalyst

Liquid-liquid Equilibrium of Ternary mixture
Liquid phase activity coefficients from NRTL model :

So far we have 5 equations and 6 unknowns, we need one more equation.
We choose values for X1 and X2 than we solve the nonlinear system of 8 equations with 8 unknowns.

Liquid-liquid equilibrium for Water-Benzene-Ethanol at 25 °C
Tie line Plait point

Liquid Liquid Extraction
Liquid Liquid Equilibrium of ternary system Isopropyl ether-water-acetic acid at 20 °C and 1 atm : wt % water wt % acetic acid water rich phase isopropyl ether rich phase tie line

Hunter and Nash Graphical Equilibrium Stage Method
F E1 RN Mixing Point M = F + S= E1 + RN Operating Point P = Ri-1 - Ei = F - E1 = RN - S E1 E2 EN S 1 2 N-1 N F R1 RN-1 RN

Stepping off Equilibrium Stages
wt % water wt % acetic acid P S F E1 RN 5.35 equilibrium stages are needed to achive raffinate specifications

McCabe and Thiele Diagram
wt % Acetic Acid in Raffinate wt % Acetic Acid in Extract Equilibrium Curve Operating Line 5.35 equilibrium stages are needed to achive raffinate specifications

Two Feed Extraction Column
Total Feed FT = F1 + F2 F1 M S EN R1 OP2 OP1 F2 FT Mixing Point M = FT + S= R1 + EN Operating Points OP1 = Ri+1 - Ei = R1 - E0 OP2 = Ek - Rk+1= EN - RN+1 OP1 + OP2 = F2 F2 S=E0 E1 EN-1 EN 1 2 N-1 N R1 R2 RN F1=RN+1

Stepping off Equilibrium Stages
wt % water wt % acetic acid F1 S EN R1 OP2 OP1 F2 FT 2.89 equilibrium stages are needed to achive raffinate specifications

Residue Curve Map vapor y x liquid

Obtaining the boiling temperature :
Liquid phase activity coefficients from Wilson model : Obtaining equilibrium vapor phase mole fractions :

Residue curve map for the ternary system
acetone-methanol-chloroform at P=760 mmHg Azeotrope Residue Curve UN SN SP

y x Simple reactive distillation Chemical reaction Phase equilibrium
Reaction equilibrium

Transformed compositions
Equation for simple distillation with reaction equilibrium

XB XA Residue curve map for the isopropyl acetate chemistry at P=1 atm
water Acetic Acid Isopropanol Isopropyl acetate XA XB Reactive azeotrope Need to take into account acetic acid dimerization

XB XA Residue curve map for the methyl acetate chemistry at P=1 atm
Methanol Methyl acetate XB water Acetic Acid XA Need to take into account acetic acid dimerization

Flash Distillation P and T Vapor V yi Feed F zi Liquid L xi
Rachford and Rice :

Equilibrium constants using virial equation of state:
Equilibrium constants using the equations that fit the DePriester Charts : Equilibrium constants using virial equation of state: Phase Equilibrium :

Hydrocarbon Mixture P=3.5 bars and T=300 K Feed z1=0.2 z2=0.3 z3=0.4

Vapor and Liquid Compositions
Mass Balance equations give vapor and liquid compositions : P=3.5 bars T=300 K Feed F=1 z1=0.2 z2=0.3 z3=0.4 z4=0.05 z5=0.05 Liquid L=0.4330 x1=0.1066 x2=0.3425 x3=0.3790 x4=0.0886 x5=0.0830 Vapor V=0.5770 y1=0.2683 y2=0.2688 y3=0.4153 y4=0.0216 y5=0.0257

Binary ideal mixture with
McCabe and Thiele Method for Distillation of Binary Ideal Mixture feed Zf=0.5 bottom xb=0.05 distillate xd=0.9 Binary ideal mixture with constant relative volatility = a

Pinch Point and Minimum Reflux Ratio
y Feed line : Rectifying operating line :

9 equilibrium stages are needed to achieve the separation
McCabe and Thiele Diagram R=1.5 Rmin x y 9 equilibrium stages are needed to achieve the separation

19 equilibrium stages are needed to achieve the separation
Murphree Liquid Stage Efficiency EML=0.5 y x 19 equilibrium stages are needed to achieve the separation

Multicomponent Distillation
feed Z1=0.3 Z2=0.3 Z3=0.4 bottom xb1=0.05 distillate xd1=0.95 xd2=0.049 xd3=0.001 Ternary ideal mixture of Pentane, Hexane and Heptane with constant relative volatilities = 6.35, 2.47 and 1

8.3 equilibrium stages are needed to achieve the separation
Liquid Compositions Pentane mole fraction Hexane mole fraction Stripping Section Rectifying Section D F B Rectifying operating line : Stripping operating line : R=2.5 and S=1.35 8.3 equilibrium stages are needed to achieve the separation

Enthalpy-Composition Diagram for hexane-octane system at 760 mmHg
Hexane mole fraction Enthalpy of saturated liquid and vapor tie line H(y) h(x) Conjugate line

Ponchon and Savarit method
Enthalpy of saturated liquid and vapor Hexane mole fraction F P1 P2 D B L V feed q=0.41 Z1=0.5 bottom xb1=0.05 distillate xd1=0.95 7 stages are needed to achieve the separation

Conclusion Mathematica’s algebraic, numerical and graphical capabilities can be put into advantage to solve several chemical engineering and chemistry problems including equilibrium-staged separations with McCabe-Thiele, Hunter-Nash and Ponchon-savarit Methods.

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