Numerical Library Problems Involving Simultaneous Nonlinear Equations

 

Legend for following Table

 

 

 

 

 

 

 

1L- Lower, A - Average, H - Higher Difficulty Levels

 

 

 

 

 

 

 

2S - Function/Variable Scaling Related Difficulties Exist

 

 

 

 

 

 

 

3DB - Discontinuity/Function Undefined on the Boundary or DI - Inside the Feasible Subspace

 

 

 

 

 

 

4MI - Multiple Solutions Inside or MO - Some Outside of the Feasible Subspace

 

 

 

 

 

 

 

5F - False Solution/s Exist

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Problem Characteristics/Difficulties

No.

File Name - Problem Title

Difficulty

Scaling2

Discontinuity3

Multiple

False

 

 

 

Level1

 

 

Solutions4

Solutions5

 

 

ONE NONLINEAR EQUATION

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

Oneeq1 - Chemical equilibrium calculation

 

 

 

 

 

 

2

Oneeq2a - Bubble Point of a Non-ideal Mixture -ethanol, n-hexane -Wilson equation

 

 

 

 

 

 

3

Oneeq2b - Bubble Pt. of a Non-ideal Mixture -ethanol, n-heptane -Van Laar equation

 

 

 

 

 

 

4

Oneeq3 - Kinetic problem

H

S

 

 

 

 

5

Oneeq4 - Azeotropic point calculation

 

 

 

 

 

 

6

Oneeq5 - Adiabatic flame temperature

 

 

 

 

 

 

7

Oneeq6a - Gas Volume from Beattie Bridgeman Equation of State - Original Form

H

 

DB

 

 

 

8

Oneeq6b - Gas Volume from Beattie Bridgeman Equation of State - Revised Form

 

 

 

 

 

 

9

Oneeq7 - Conversion in a chemical reactor

 

 

DI

 

 

 

10

Oneeq8 - Flow in a smooth pipe

H

 

 

 

 

 

11

Oneeq9 - Pressure drop in a converging diverging nozzle

 

 

DI

MI

 

 

12

Oneeq10 - Batch Distillation at Infinite Reflux

 

 

DI

MI

 

 

13

Oneeq11a - Chemical Equilibrium - 1st Formulation

 

 

DI

 

 

 

14

Oneeq11b - Chemical Equilibrium - 2nd Formulation

 

 

DI

MI

 

 

15

Oneeq12 - Volume from Virial Equation of State

H

 

DB

MI

 

 

16

Oneeq13 - Gas Volume from Redlich-Kwong Equation of State

 

 

 

 

 

 

17

Oneeq14 - Heat duty of a countercurrent flow heat exchanger

H

S

 

 

 

 

18

Oneeq15a - Sinkage depth of sphere in water - 1st form

 

 

 

 

 

 

19

Oneeq15b - Sinkage depth of sphere in water - 2nd form

 

 

 

 

 

 

20

Oneeq16 - Adiabatic Flame Temperature for Natural Gas Combustion

H

 

 

 

 

 

21

Oneeq17 - Global reaction rate in Catalytic Oxidation of Nitrogen

 

 

DI

 

 

 

22

Oneeq18a - Stability of Batch Fluidized Catalytic Reactor - Correct Formulation

 

 

 

MI

 

 

23

Oneeq18b - Stability of Batch Fluidized Catalytic Reactor - Rounded Numbers

 

 

 

 

 

 

24

Oneeq19a - Compressibility factor from the RK equation - three solutions

 

 

 

MI

 

 

25

Oneeq19b - Compressibility factor from the RK equation - one solution

 

 

 

 

 

 

26

Oneeq20a - Equilibrium conversion in a tubular reactor - original form

H

S

DB

 

 

 

27

Oneeq20b - Equilibrium conversion in a tubular reactor - revised form

 

 

 

 

 

 

28

Oneeq21a - General Two-fluid Model Equations - ugs=-0.0295 

 

 

 

MI

 

 

29

Oneeq21b - General Two-fluid Model Equations - ugs=-0.029 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TWO NONLINEAR EQUATIONS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30

Twoeq1 - Pipe diameter calculation for specified pressure drop  

H

 

DB

 

 

 

31

Twoeq2 - Steady state material and energy balance on a reactor

H

 

 

 

 

 

32

Twoeq3 - Equilibrium conversion in a chemical reactor

H

 

 

 

 

 

33

Twoeq4a - Wilson coeff. from azeotropic data (ethyl alcohol - n hexane) - 1st form

 

 

DB

 

 

 

34

Twoeq4b - Wilson coeff. from azeotropic data (ethyl alcohol - n hexane)- 2nd form.

 

 

DB

 

 

 

35

Twoeq5a - Van Laar eqs. coeff. from azeotropic data (ethanol - n heptane) - 1st form.

 

 

DB

 

 

 

36

Twoeq5b - Van Laar eqs. coeff. from azeotropic data (ethanol - n heptane) - 2nd form.

 

 

DB

 

F

 

37

Twoeq6 - Conversion in a chemical reactor

H

 

DB

 

 

 

38

Twoeq7 - Chemical equilibrium - 3rd formulation

 

 

 

MI

 

 

39

Twoeq8 - Global reaction rate in Catalytic Oxidation of Nitrogen

H

 

DB

 

 

 

40

Twoeq9 - Pipe flow velocity calculation for a specified pressure drop

 

 

DB

 

 

 

41

Twoeq10 - Correlation of liquid-liquid equilibrium data

H

 

 

MI

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

THREE NONLINEAR EQUATIONS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

42

Threeq1 - Dew point of a nonideal binary mixture (isobutanol-water)

 

 

 

 

 

 

43

Threeq2 - Two phase flash of a nonideal binary mixture (isobutanol-water)

H

 

 

MO

F

 

44

Threeq3 - Multiple steady states in a cooled exothermic CSTR 

 

 

 

MI

 

 

45

Threeq4a - Eq. composition in a constant volume gas-phase batch reactor - orig. form

H

 

DB

 

 

 

46

Threeq4b - Eq. composition in a constant volume gas-phase batch reactor - rev. form 

H

 

 

MO

 

 

47

Threeq5 - Exothermic reversible reaction in a CSTR

 

 

DB

 

 

 

48

Threeq6 - Consecutive reactions in a CSTR

 

 

 

 

 

 

49

Threeq7 - Steady state operation of an adiabatic CSTR

 

 

 

MI

 

 

50

Threeq8 - Pipe and Pump Network  

 

 

 

MO

 

 

 

 

 

 

 

 

 

 

 

SEVERAL NONLINEAR EQUATIONS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

51

Foureq1 - Steady state operation of an adiabatic CSTR

 

 

 

MI

 

 

52

Fiveq1 - Steady state operation of an exothermic CSTR

 

 

 

 

 

 

53

Sixeq1 - Poorly scaled chemical equilibrium problem

H

S

 

MO

 

 

54

Sixeq2a - Steady state solution for reaction rate equations - 1st parameter set

 

 

 

MO

 

 

55

Sixeq2b - Steady state solution for reaction rate equations - 2nd parameter set

 

 

 

MO

 

 

56

Sixeq2c - Steady state solution for reaction rate equations - 3rd parameter set

 

 

 

 

 

 

57

Sixeq3 - Bubble point of a non-ideal binary mixture (isobutanol-water)

 

 

 

 

F

 

58

Sixeq4a - Modeling of a CSTR for a complex sequence of reactions - original form.

H

S

DI

 

 

 

59

Sixeq4b - Modeling of a CSTR for a complex sequence of reactions- revised form.

 

 

 

MO

 

 

60

Seveneq1 - Chemical Equilibrium 

 

 

 

MO

 

 

61

Seveneq2a - Esterification Reaction in Two Consecutive CSTRs - Original Form.

H

 

 

 

 

 

62

Seveneq2b - Esterification Reaction in Two Consecutive CSTRs - Revised Form.

H

 

 

 

F

 

63

Seveneq3a - Flow Distribution in a Pipeline Network - Constant Friction Factor

 

 

 

MI

 

 

64

Seveneq3b - Flow Distribution in a Pipeline Network - Calculated Friction Factor

 

 

 

 

 

 

65

Seveneq4 - Water Distribution Network

 

 

 

 

 

 

66

Nineq1 - Three phase flash - ethanol, benzene and water mixture

H

 

 

MO

 

 

67

Teneq1a - Chemical Equilibrium Problem - R = 10

 

 

DB

 

 

 

68

Teneq1b - Chemical Equilibrium Problem - R =40

H

 

DB

 

 

 

69

Teneq2a - Combustion of Propane in Air - R = 10

 

 

DB

 

 

 

70

Teneq2b - Combustion of Propane in Air - R = 40

H

 

DB

 

 

 

71

Teneq3 - Small flow sheeting system with recycle

 

 

 

 

 

 

72

11eq1 - Stirred pot reactor process

 

 

 

 

 

 

73

13eq1 - Gibbs energy minimization

H

 

DB

 

 

 

74

14eq1 - Three stage, two component distillation column

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Legend

 

 

 

 

 

 

 

1L- Lower, A - Average, H - Higher Difficulty Levels

 

 

 

 

 

 

 

2S - Function/Variable Scaling Related Difficulties Exist

 

 

 

 

 

 

 

3DB - Discontinuity/Function Undefined on the Boundary or DI - Inside the Feasible Subspace

 

 

 

 

 

 

4MI - Multiple Solutions Inside or MO - Some Outside of the Feasible Subspace

 

 

 

 

 

 

 

5F - False Solution/s Exist

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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