PET 509E Hydrocarbon Thermodynamics - Fall 2010
     

 
 Instructor:    
     
    Dr. Şenol Yamanlar
    Petroleum and Natural Gas Engineering
    Department 

Component assignments:

505101505    Mehmet A. Torcuk    CH₄ (Methane)

505101506    Tolga Kilcigil           C₂H₆ (Ethane)

505101507    Yasin Demiralp        C₃H₈ (Propane)

Term Project #2

AD z factor correlation control points

Tr=1.1         Pr=1.2            z=0.5881

Tr=2.0         Pr=6.0            z=0.9857

Tr=2.0         Pr=2.8            z=0.9382

Composite Simpson's Rule for Numerical Integration

         

Code Fragment :

IMPLICIT DOUBLE PRECISION(A-H,O-Z)

N=500                                    !  NUMBER OF INTERVALS

A=0.D0                                   !  LOWER INTEGRAL BOUNDARY

B=10.D0                                 !  UPPER INTEGRAL BOUNDARY

SUM = 0.D0

.............................

DO K = 1, N - 1, 2                   ! EVALUATE ODD VALUES

    PR = A + DBLE(K) * (B - A) / DBLE(N)

    SUM = SUM + 4.D0 * F(TR, PR)

ENDDO


DO K = 2, N - 2, 2                                     ! EVALUATE EVEN VALUES

    PR = A + DBLE(K) * (B - A) / DBLE(N)

    SUM = SUM + 2.D0 * F(TR, PR)

ENDDO


RESULT = (B - A) * ( F(TR, A) + SUM + F(TR, B)) / (3.D0 * DBLE(N) )                ! VALUE OF INTEGRAL
 

........................

DOUBLE PRECISION FUNCTION F(TR,PR)                     ! FUNCTION TO BE INTEGRATED

IMPLICIT DOUBLE PRECISION (A-H,O-Z)


! F= DZ_DTR (TR, PR) / PR                                            ! IN CASE OF H^R

F= 2.D0*PR+1.D0                                                        ! A SIMPLE FUNCTION TO TEST THE ALGORIHM

END FUNCTION
 

Assignment #1 (due 02 December 2010)

Use van der Waals EOS and compute residual properties for H, S, U, and G between P=0 to 100 Bar (ΔP=5 Bar). Do this computations for T= 1.5 T_c and T= 3 T_c for your assigned component.

vdW EOS is cubic in V and Z. To find the gaseous root from the cubic polynomial, use Newton-Raphson iterative sequence, and use an appropriate initial estimate. For Z⁰, usually an initial estimate of 0.8 to 1.0 will converge to the gaseous root. If you want to solve for molar volume V, then you should calculate a V⁰ value from PV=RT ideal gas equation of state.

Plot your H^R, S^R, U^R, G^R results as a function of P.

Bring your results on a CD to the class, so that you can share your findings with your classmates.

Term Project #1

Assignment #1 (due 28 October 2010)

_{Use B-truncated virial equation of state (Z= 1 + BP/RT)  and write a computer program and plot P vs Z graph for temperatures and pressures given below:}

_{Methane T= 220 K and 300 K    (P=0.5 to 200 bar)}

_{Ethane T= 330 K and 400 K      (P=0.5 to 200 bar)}

_{Propane T= 420 K and 500 K    (P=0.5 to 200 bar)}

_{Predict second virial coefficient from the corresponding states correlation. Use NIST Webbook internet base program to calculate and plot reference curves. Repeat the same tasks using C-truncated virial equation of state. You may solve the cubic equation either for Z or V. Use Newton-Raphson algorithm in your program :}

If you choose to use 

     
form of the B-truncated virial EOS and solve for V, your program will fail around 50 bar, since this form of the EOS is only valid  at low pressures.

Assignment #2 (due 04 November 2010)

_{Use B-truncated virial equation of state (Z= 1 + BP/RT)  and write a computer program to compute z factor of equimolar binary mixtures of n-Butane.}

505101505    Mehmet A. Torcuk    CH₄ - nC₄H₁₀ (Methane+n-Butane)  @ 400 K

505101506    Tolga Kilcigil           C₂H₆ - nC₄H₁₀ (Ethane+n-Butane)    @ 450 K

505101507    Yasin Demiralp        C₃H₈ - nC₄H₁₀ (Propane+n-Butane)   @ 500 K
 

Reference data for each binary mixture is given below:

Assignment #3 (due 11 November 2010)

Use B-truncated and C-Truncated virial equation of state and compute z factor of n-Butane at your assigned temperatures ( in case of methane there will be condensation at 400 K. To stay in the single phase region use 450 K instead). Plot the results. Use NIST Webbook internet base program to calculate the reference curve and then plot P-Z curve on the same graph.

Compute and plot your assigned component and n-Butane mixtures at your assigned temperature and composition in the reference curves. The reference curves are given below: