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