1. 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

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

3. 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

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

5. 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

6. 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

7. 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

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

9. 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.

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

11. 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

12. Hunter and Nash Graphical Equilibrium Stage MethodF 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

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

14. 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

15. 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

16. 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

17. Residue Curve Map
vapor y x
liquid

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

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

20. y x Simple reactive distillation Chemical reaction Phase equilibrium
Reaction equilibrium

21. Transformed compositions
Equation for simple distillation with reaction equilibrium

22. 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

23. 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

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

25. 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 :

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

27. 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

28. 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

29. Pinch Point and Minimum Reflux Ratioy
Feed line :
Rectifying operating line :

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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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