Gas Stream z-Factor, Density and Formation Volume Factor: 24-Pet-A2 Petroleum Reservoir Fluids, Undated paper, Q6

Question 6: Gas Stream z-Factor, Density and Formation Volume Factor (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Gas composition and critical properties
Component	y_i	T_c (°F)	P_c (psia)	M
Methane	0.82	−116.5	673.1	16.04
Ethane	0.05	90.09	708.3	30.07
Propane	0.04	206.26	617.4	44.10
n-Butane	0.03	305.62	550.7	58.12
CO₂	0.03	88.0	1073	44.01
N₂	0.03	−232.8	492	28.01

P_res = 2400 psia, T_res = 180°F (639.67°R), gas rate = 1.5 MMSCFD, V_sc = 379.4 SCF/lb-mol.

Find. (a) z; (b) M_av; (c) ρ_g; (d) lb-mol/day; (e) lb/day; (f) specific volume; (g) B_g in reservoir bbl/SCF.

Approach. Build pseudo-critical properties with Kay's mixing rule from the given component data, get T_r, P_r, read z (here, via the Dranchuk & Abou-Kassem correlation as the verifiable proxy for the Standing-Katz chart), then work through the real-gas-law quantities in sequence.

Check: part (a) explicitly calls for the Standing-Katz graphical z-factor correlation. The numeric value below uses the Dranchuk & Abou-Kassem (1975) equation of state, the standard analytical fit to the same Standing-Katz data (accurate to within about 1% over this T_r, P_r range) – the accepted numerical substitute for this chart.

(b) Apparent molecular weight via Kay's rule, $M_{av}=\sum y_iM_i$: $$M_{av}=0.82(16.04)+0.05(30.07)+0.04(44.10)+0.03(58.12)+0.03(44.01)+0.03(28.01)=\boxed{20.32\text{ lb/lb-mol}}$$
Pseudo-critical properties (Kay's mixing rule, T_c converted °F→°R by $+459.67$): $$T_{pc}=\sum y_iT_{ci}=381.7^\circ\text{R},\qquad P_{pc}=\sum y_iP_{ci}=675.5\text{ psia}$$
Reduced conditions. $$T_r=\frac{639.67}{381.7}=1.676,\qquad P_r=\frac{2400}{675.5}=3.553$$
(a) z-factor from the Dranchuk & Abou-Kassem correlation at this T_r, P_r: $$z\approx\boxed{0.853}$$
(c) Gas density via $\rho=pM/(zRT)$: $$\rho_g=\frac{(2400)(20.32)}{(0.853)(10.732)(639.67)}=\boxed{8.33\text{ lb/ft}^3}$$
(d) Daily moles produced via $V_{sc}=n\times379.4$: $$n=\frac{1{,}500{,}000}{379.4}=\boxed{3954\text{ lb-mol/day}}$$
(e) Daily mass produced. $$\dot m=n\times M_{av}=3954\times20.32=\boxed{80{,}355\text{ lb/day}}$$
(f) Specific volume (reciprocal of density): $$v=\frac{1}{\rho_g}=\frac{1}{8.33}=\boxed{0.1201\text{ ft}^3/\text{lb}}$$
(g) Gas formation volume factor. From the real gas law, 1 SCF of gas at standard conditions ($p_{sc}\approx14.7$ psia, $T_{sc}\approx520^\circ$R, $z_{sc}\approx1$) occupies, at reservoir conditions: $$B_g=\frac{V_{res}}{V_{sc}}=\frac{z\,T/p}{z_{sc}T_{sc}/p_{sc}}=0.02827\frac{zT}{p}\ \left[\frac{\text{ft}^3}{\text{SCF}}\right]$$ $$B_g=0.02827\times\frac{(0.853)(639.67)}{2400}=0.006428\ \text{ft}^3/\text{SCF}$$ Converting to barrels ($1\text{ bbl}=5.615\text{ ft}^3$): $$B_g=\frac{0.006428}{5.615}=\boxed{0.001145\text{ reservoir bbl/SCF}}$$

Question 6 – results
Quantity	Value
(a) z-factor	0.853
(b) Apparent MW	20.32 lb/lb-mol
(c) Gas density	8.33 lb/ft³
(d) Moles produced	3954 lb-mol/day
(e) Mass produced	80,355 lb/day
(f) Specific volume	0.1201 ft³/lb
(g) B_g	0.001145 rb/SCF (0.006428 ft³/SCF)

Topic. Pseudo-critical properties by Kay's mixing rule, z-factor determination, and the full chain of real-gas-law quantities (density, moles, mass, specific volume, B_g) for a produced gas stream.

Key relations. $M_{av}=\sum y_iM_i$; $T_{pc}=\sum y_iT_{ci}$, $P_{pc}=\sum y_iP_{ci}$; $\rho=pM/(zRT)$; $B_g=0.02827\,zT/p$ ft³/SCF.

Why this works. Every quantity asked for in (b)–(g) is a direct consequence of the single z-factor found in (a) – it is the one correction that turns the ideal gas law into a real-gas description, and every downstream density/rate/FVF calculation simply substitutes it into the real-gas-law relations.

Common pitfall. Using T_c values straight from the table (°F) in the T_r=T/T_pc ratio without first converting both T and T_pc to an absolute scale (°R) – reduced properties are only meaningful on an absolute temperature/pressure basis.

Source. Standing, Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems (pseudo-critical correlations, Z-factor); Ahmed, Reservoir Engineering Handbook, Ch.2 (real-gas-law applications).

Question 6 of 6: Gas Stream z-Factor, Density and Formation Volume Factor

Question 6: Gas Stream z-Factor, Density and Formation Volume Factor (20 marks)