Gas Z-Factor, Original Gas In Place, and Gas Viscosity: 24-Pet-A2 Petroleum Reservoir Fluids, December 2019, Q4

Question 4: Gas Z-Factor, Original Gas In Place, and Gas Viscosity (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 component properties
Component	mol%	$T_c$, °R	$P_c$, psia	M, lb/lb-mol	$\mu$ @ 1 atm, cp
Methane	97.12	343.33	666.4	16.04	0.0128
Ethane	2.42	549.92	706.5	30.07	0.0110
Propane	0.31	666.06	616.0	44.10	0.0098
i-Butane	0.05	734.46	527.9	58.12	0.0091
n-Butane	0.02	765.60	550.6	58.12	0.0094
i-/n-Pentane	trace	—	—	72.15	0.0080/0.0082
Hexanes	0.02	913.60	436.9	86.18	0.0078
Heptanes+	0.06	1082	372	128	0.0068

$h=21$ ft, $\phi=0.18$, $S_w=0.33$, spacing $=700$ acres, $P_i=3810$ psia, $T=194\,{}^{\circ}\text{F}$.

Find. (i) $Z$ at initial conditions, (ii) original gas in place per well drainage area, (iii) gas viscosity at 1 atm and 194°F.

Approach. Mix pseudo-criticals directly from the composition (Kay's rule, given as-is since Tc/Pc are supplied per component, including for the heptanes-plus fraction); solve for $Z$ via the DAK correlation; convert drainage-area bulk rock volume to hydrocarbon pore volume and divide by $B_g$ for OGIP; combine atmospheric-pressure component viscosities with the Herning–Zipperer mixing rule (per the formula sheet).

(i) Gas Z-factor at initial reservoir condition

Pseudo-critical properties. $$T_{pc}=\sum y_iT_{ci} = 0.9712(343.33)+0.0242(549.92)+0.0031(666.06)+0.0005(734.46)+0.0002(765.60)+0.0002(913.60)+0.0006(1082) = 350.2\,{}^{\circ}\text{R}$$ $$P_{pc}=\sum y_iP_{ci} = 666.9\text{ psia}$$
Reduced properties. $$T_r=\frac{194+460}{350.2}=1.868\qquad P_r=\frac{3810}{666.9}=5.713$$
Solve DAK for $Z$: $$\boxed{Z \approx 0.951}$$

Check: the heptanes-plus specific gravity is printed in the paper as "0.0758," an order of magnitude too low for a C7+ fraction (physically plausible range ≈0.68–0.85) – almost certainly a misprint for 0.758. This does not affect the calculation above, since $T_c$ and $P_c$ for heptanes-plus (1082°R, 372 psia) are given directly in the table rather than derived from the SG/MW via a correlation.

(ii) Original gas in place, single well's 700-acre drainage area

Bulk and pore volume. $$V_b = 700\text{ ac}\times43{,}560\text{ ft}^2/\text{ac}\times21\text{ ft} = 6.403\times10^8\text{ ft}^3$$ $$V_p = V_b\phi = 1.153\times10^8\text{ ft}^3\qquad V_{hc}=V_p(1-S_w)=7.722\times10^7\text{ ft}^3$$
Gas FVF at initial conditions. $$B_{gi}=0.02827\frac{ZT}{p}=0.02827\times\frac{0.951\times654}{3810}=0.004615\ \text{ft}^3/\text{scf}$$
Original gas in place. $$G = \frac{V_{hc}}{B_{gi}} = \frac{7.722\times10^7}{0.004615} = \boxed{1.673\times10^{10}\ \text{scf} \approx 16.73\ \text{Bscf}}$$

(iii) Gas viscosity at 1 atm, 194°F – Herning–Zipperer rule

Mixing rule (formula sheet). $$\mu_g = \frac{\sum_j \mu_{gj}\,y_j\sqrt{M_j}}{\sum_j y_j\sqrt{M_j}}$$ Trace i-/n-pentane contribute negligibly and are omitted.
Evaluate. Using the table's atmospheric-pressure component viscosities and molecular weights: $$\boxed{\mu_g(1\text{ atm}, 194\,{}^{\circ}\text{F}) \approx 0.01271\ \text{cp}}$$

Quantity	Value
$T_{pc}$, $P_{pc}$	350.2°R, 666.9 psia
(i) $Z$ (initial conditions)	0.951
(ii) $G$ (single well, 700 ac)	1.673×10¹⁰ scf (16.73 Bscf)
(iii) $\mu_g$ (1 atm, 194°F)	0.01271 cp

Topic. Real-gas Z-factor correlations, volumetric OGIP estimation, and the Herning–Zipperer gas-viscosity mixing rule.

Key relations. Kay's rule for $T_{pc},P_{pc}$; DAK implicit $Z(T_r,P_r)$; $B_g=0.02827\,ZT/p$; $G=V_{hc}/B_{gi}$; Herning–Zipperer $\mu_g=\sum \mu_j y_j\sqrt{M_j}/\sum y_j\sqrt{M_j}$.

Why this works. At $P_r\approx5.7$ the gas is well above the "hump" of minimum $Z$ on the Standing-Katz chart (compressibility effects dominate over attraction), consistent with $Z>0.9$; the Herning-Zipperer rule weights each component's viscosity by $y_i\sqrt{M_i}$ because lighter molecules diffuse and dominate momentum transfer disproportionately to their mole fraction.

Common pitfall. Using a simple mole-fraction-weighted average for gas viscosity (ignoring $\sqrt{M_i}$ weighting) systematically under-weights methane's dominant contribution to a light gas's viscosity.

Source. Standing, Volumetric and Phase Behavior; Ahmed, Reservoir Engineering Handbook Ch.2 (Z-factor, gas viscosity correlations).

Question 4 of 7: Gas Z-Factor, Original Gas In Place, and Gas Viscosity

Question 4: Gas Z-Factor, Original Gas In Place, and Gas Viscosity (20 marks)

(i) Gas Z-factor at initial reservoir condition

(ii) Original gas in place, single well's 700-acre drainage area

(iii) Gas viscosity at 1 atm, 194°F – Herning–Zipperer rule