Reference no: EM131247990

Question 1 - PVT Tests

Oil Composition

Component	Mol %	r (g/cm3)	MW
Nitrogen	0.49	0.8086	28.013
Methane	21.01	0.2997	16.043
Ethane	2.50	0.3562	30.070
Propane	1.67	0.5070	44.097
Iso-Butane	0.98	0.5629	58.123
N-Butane	1.20	0.5840	58.123
Iso-Pentane	0.67	0.6244	72.150
N-Pentane	1.14	0.6311	72.150
Hexanes	2.91	0.6850	84.000
Heptanes +	67.42

Heptanes Plus+ Composition

Component	Mol %	r (g/cm3)	MW
Heptanes	4.500	0.7220	96
Octanes	5.710	0.7450	107
Nonanes	5.390	0.7640	121
Decanes	5.740	0.7780	134
Undecanes	5.940	0.7890	156
Heptadecanes	5.010	0.8470	237
Octadecanes	4.750	0.8520	251
Eicosanes Plus	30.380	0.8380	408
Total	67.420

SEPARATOR FLASH ANALYSIS
Flash Conditions		Gas/Oil	Gas/Oil		Stock Tank	Formation	Separator	Specific	Oil Phase
		Ratio	Ratio		Oil Gravity	Volume	Volume	Gravity of	Density
P	T	scf/bbl	scf/STbbl		at 60 oF	Factor	factor	Flashed Gas	(gm/cc)
psig	oF	(A)	(B)			Bofb(C)	(D)	(Air=1)
945	266								0.7133
200	158	97		106			1.091	0.6682	0.7668
0	122	52		54	40.2	1.196	1.032	1.0512	0.7978
			Rsfb =	159
945	266								0.7136
150	158	105		114			1.084	0.6825	0.7693
0	122	42		44	40.3	1.194	1.032	1.0833	0.7973
			Rsfb =	158
945	266								0.7137
100	158	114		123			1.076	0.7083	0.7725
0	122	32		33	40.4	1.193	1.032	1.0936	0.7969
			Rsfb =	156
945	266								0.7135
50	158	130		139			1.068	0.7672	0.7766
0	122	21		21	40.1	1.197	1.032	1.0457	0.7985
			Rsfb =	160

DIFFERENTIAL   VAPORISATION			@ 266 oF
	Solution	Relative	Relative	Oil
Pressure	Gas/Oil	Oil	Total Oil	Density
psig	Ratio	Volume	Volume	gm/cc
	RsD (A)	BoD (B)	BtD (C)
945	167	1.213	1.213	0.7138
400	82	1.174	1.911	0.7259
300	66	1.167	2.319	0.7282
200	50	1.158	3.130	0.7310
100	33	1.147	5.393	0.7350
0	0	1.116		0.7447
	@ 60 oF =	1.000

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;

component	yi
a) Methane	0.6
b) Ethane	0.22
c) Propane	0.18

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