Question 1 - PVT Tests

Oil Composition

Heptanes Plus+ Composition

a) Find the heptanes + molecular weight and density using a simple ideal mixing rule.

b) Estimate the specific gravity of the gas at standard conditions.

c) Estimate the bubble point pressure given a GOR = 77 scf/stb and T_reservoir = 122 ^oF.

d) Explain the difference between constant volume depletion and differential liberation tests.

e) Estimate the oil and total formation volume factor when the reservoir falls to 500 psi below the bubble point?

f) Physically, what does the Y-factor mean? Why do we use it? Explain its significance with respect to the relative volume? When is the Y-factor = 1?

g) Estimate the oil density at 13.79 bar using correlations.

h) Explain the difference between the results using correlations vs constant volume depletion tests vs separator tests (with details).

Question 2 - Thermodynamics

a) Justify the following equations:

i) (∂lnΦ_i/∂P) = V¯_i^R/RT

ii) (∂lnΦ^_i/∂T) = -H¯_i^R/RT²

iii) G^R/RT = Σ_ix_ilnΦ^_i

iv) Σ_ix_id lnΦ^_i = 0 (at const T, P)

b) Fugacity and fugacity coefficients

For a natural gas, three component system at T = 203^oF and P = 5000 psi, estimate the solution fugacities ( f^_i ) and fugacity coefficients (Φ^_i ) for each component assuming;

i) Estimate the solution fugacities ( f^{^}_i ) and fugacity coefficients ( Φ^{^}i ) for each component using the general equation for the fugacity coefficient from the virial equation of state:

ii) Is the above estimation reliable? Why or why not? How do we prove it.

iii) Explain why assuming an ideal solution will give different results.

iv) What is the overall fugacity coefficient and fugacity of the solution?

Bonus: How would you find the virial coefficients (B values) experimentally?

c) The fugacity of pure component can be related rigorously to measurable properties using thermodynamic relations (hint: prove both equalities):

RTlnΦ = _v∫^∞ [∂P/∂n - RT/v]dV - RTlnZ + RT(Z-1)(Prausnitz, 1969)

Using the real gas law as PV = ZnRT, prove that the fugacity for a pure compound is

ln Φ = ₀∫^P Z-1/P. dP = 1/RT _∞∫^v (RT/v - P) dv + (Z-1) -lnZ