Oneeq19a

Name: Oneeq19a - Compressibility factor from the RK equation - three solutions
       
Source: Cutlip, M. B. and Shacham, M, Problem Solving in Chemical
  Engineering with Numerical Methods (2nd Ed), Prentice Hall Inc.,
Reference/s      
       
Model: 1 implicit equation, indep. variable name: z
  Average difficulty level
  Constraints: z>0
  Discontinuities: none in the range of interest
  Initial range: zmin=-0.5, zmax=1.2
       
Solved by Shacham, M., POLYMATH 5.1, build 19, April 1, 2001
       
Model Eqs. Compressibility factor from the RK equation - three solutions |POLVER05_1

EXCEL FILE 

f(z)=z^3-z^2-Q*z-r #    

TEXT FILE 

P = 200 #

POLYMATH FILE 

Pc=33.5 #
  T= 631*2 #
  Tc=126.2 #
  Pr=P/Pc #
  Tr=T/Tc #
  Asqr=0.4278*Pr/(Tr^2.5) #
  B=0.0867*Pr/Tr #
  Q=B^2+B-Asqr #
  r=Asqr*B #
  p=(-3*Q-1)/3 #
  q=(-27*r-9*Q-2)/27 #
  R=(p/3)^3+(q/2)^2 #
  V=if(R>0)then((-q/2+sqrt(R))^(1/3))else(0) #
  WW=if(R>0)then(-q/2-sqrt(R))else(0) #
  psi1 = if(R<0)then(arccos(sqrt((q^2/4)/(-p^3/27))))else(0) #
  W = if(R>0)then(sign(WW)*(abs(WW))^(1/3))else(0) #
  z1 = if(R<0)then(2*sqrt(-p/3)*cos((psi1/3)+2*3.1416*0/3)+1/3)else(0) #
  z2 = if(R<0)then(2*sqrt(-p/3)*cos((psi1/3)+2*3.1416*1/3)+1/3)else(0) #
  z3 = if(R<0)then(2*sqrt(-p/3)*cos((psi1/3)+2*3.1416*2/3)+1/3)else(0) #
  z0=if(R>0)then(V+W+1/3)else(0) #
  z(min)=-.5, z(max)=1.2
       
Variable/function values Variable Value

f(x)
  z 0.35

-9.6270E-02
  P 200  
  Pc 33.5  
  T 1262  
  Tc 126.2  
  Pr 5.970149254  
  Tr 10  
  Asqr 0.008076552  
  B 0.051761194  
  Q 0.046363864  
  r 0.000418052  
  p -0.379697197  
  q -0.089946747  
  R -4.83753E-06  
  V 0  
  WW 0  
  psi1 0.048870067  
  W 0  
  z1 1.044760488  
  z2 -0.032420632  
  z3 -0.012336754  
  z0 0  
       
Root1 Variable Value

f(x)
  z -0.03241692071380

-6.10E-16
  P 200  
  Pc 33.5  
  T 1262  
  Tc 126.2  
  Pr 5.970149254  
  Tr 10  
  Asqr 0.00807655154040  
  B 0.05176119402990  
  Q 0.04636386369680  
  r 0.00041805195140  
  p -0.37969719703020  
  q -0.08994674725770  
  R -0.00000483752560  
  V 0.00000000000000  
  WW 0.00000000000000  
  psi1 0.048870067  
  W 0.00000000000000  
  z1 1.044760488  
  z2 -0.032420632  
  z3 -0.012336754  
  z0 0.00000000000000  
       
Root2 Variable Value

f(x)
  z -0.01234360708030

-1.28E-13
  (The other variables have the same value as in Root1)    
       
Root3 Variable Value

f(x)
  z 1.04476050281300

3.7405E-18
  (The other variables have the same value as in Root1)    
       
Function plot