# 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