Numerical Library Problems Involving Simultaneous Nonlinear Equations

Legend for following Table 







^{1}L Lower, A  Average, H  Higher Difficulty
Levels 







^{2}S  Function/Variable Scaling Related
Difficulties Exist 







^{3}DB  Discontinuity/Function Undefined on the
Boundary or DI  Inside the Feasible Subspace 







^{4}MI  Multiple Solutions Inside or MO  Some
Outside of the Feasible Subspace 







^{5}F  False Solution/s Exist 
















Problem Characteristics/Difficulties 

No. 
File Name  Problem Title 
Difficulty 
Scaling^{2} 
Discontinuity^{3} 
Multiple 
False 



Level^{1} 


Solutions^{4} 
Solutions^{5} 


ONE NONLINEAR EQUATION 














1 
Oneeq1
 Chemical equilibrium calculation 






2 
Oneeq2a  Bubble Point of a Nonideal Mixture
ethanol, nhexane Wilson equation 






3 
Oneeq2b  Bubble Pt. of a Nonideal Mixture
ethanol, nheptane 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 RedlichKwong 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 Twofluid Model Equations 
ugs=0.0295 



MI 


29 
Oneeq21b  General Twofluid 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 liquidliquid equilibrium
data 
H 


MI 



















THREE NONLINEAR EQUATIONS 














42 
Threeq1  Dew point of a nonideal binary mixture
(isobutanolwater) 






43 
Threeq2  Two phase flash of a nonideal binary
mixture (isobutanolwater) 
H 


MO 
F 

44 
Threeq3  Multiple steady states in a cooled
exothermic CSTR 



MI 


45 
Threeq4a  Eq. composition in a constant volume
gasphase batch reactor  orig. form 
H 

DB 



46 
Threeq4b  Eq. composition in a constant volume
gasphase 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 nonideal binary mixture
(isobutanolwater) 




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 







^{1}L Lower, A  Average, H  Higher Difficulty
Levels 







^{2}S  Function/Variable Scaling Related
Difficulties Exist 







^{3}DB  Discontinuity/Function Undefined on the
Boundary or DI  Inside the Feasible Subspace 







^{4}MI  Multiple Solutions Inside or MO  Some
Outside of the Feasible Subspace 







^{5}F  False Solution/s Exist 













