24-Pet-A2 Petroleum Reservoir Fluids · December 2018
Question 3 of 7: Dry Gas Reservoir — Z-Factor, Density, In-Place Volume and Moles
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
17-Pet-A2 — Petroleum Reservoir Fluids · National Exams, December 2018 · 3 hours, closed book, Casio/Sharp approved calculators only · a formula sheet is provided; FIVE (5) questions constitute a complete exam paper (the first five as submitted are marked); all questions equal value, all parts of a multipart question equal weight; oilfield-unit questions must be answered in field units.
Reference texts: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (Ch. 1–2, PVT properties, reservoir/well-stream classification); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed. (Standing–Katz Z-factor correlation, gas properties); McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (phase behaviour, black-oil PVT laboratory data); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (material balance, pseudo-critical property correlations, gas/oil PVT relations); Danesh, A., PVT and Phase Behaviour of Petroleum Reservoir Fluids (equilibrium K-value flash calculations, Gibbs' phase rule).
Question 3: Dry Gas Reservoir — Z-Factor, Density, In-Place Volume and Moles (20 marks)
Find. (a) $Z$; (b) $\rho_g$; (c) $V_{sc}$; (d) moles of gas $n$.
Approach. Get the pseudo-critical properties from the formula-sheet Standing correlation, form $T_{pr}$ and $p_{pr}$, and read $Z$ off the Standing–Katz chart (page 5). Because the chart cannot be read to more than about two significant figures by eye, $Z$ is reproduced here with the Dranchuk–Abou-Kassem equation of state, the standard numerical fit to that same chart, then used directly in the real gas law for density, moles, and (via the standard-condition ideal-gas limit) the surface-equivalent volume.
Pseudo-critical properties and reduced conditions. $T_{pc}=168+325\gamma_g-12.5\gamma_g^2=168+325(0.6)-12.5(0.6)^2=168+195-4.5=358.5\ ^\circ\text{R}$. $p_{pc}=677+15.0\gamma_g-37.5\gamma_g^2=677+9-13.5=672.5\ \text{psia}$. With $T=659.67\ ^\circ\text{R}$ and $p=1400\ \text{psia}$: $T_{pr}=\dfrac{T}{T_{pc}}=\dfrac{659.67}{358.5}$, so $\boxed{T_{pr}\approx1.840}$; $p_{pr}=\dfrac{p}{p_{pc}}=\dfrac{1400}{672.5}$, so $\boxed{p_{pr}\approx2.082}$.
Part (a) — gas deviation factor Z. At $T_{pr}=1.840$, $p_{pr}=2.082$, the Standing–Katz chart (reproduced numerically via Dranchuk–Abou-Kassem) gives $\boxed{Z\approx0.920}$.
Part (b) — gas density. Apparent molecular weight: $M=\gamma_g\times M_{air}=0.6\times28.97=17.38\ \text{lb}_{mass}/\text{lbmol}$. $\rho=\dfrac{pM}{ZRT}=\dfrac{1400\times17.38}{0.920\times10.732\times659.67}$, so $\boxed{\rho\approx3.74\ \text{lb}_{mass}/\text{ft}^3}$.
Part (d) — moles of gas in place. (Solved before part (c), which needs it.) Real gas law: $n=\dfrac{pV}{ZRT}=\dfrac{1400\times12.394\times10^6}{0.920\times10.732\times659.67}$, so $\boxed{n\approx2.665\times10^6\ \text{lbmol}}$.
Part (c) — reservoir gas volume at standard conditions. At $p_{sc}=14.7\ \text{psia}$, standard conditions are close enough to atmospheric that $Z_{sc}\approx1$, so the ideal gas law applies: $V_{sc}=\dfrac{nRT_{sc}}{p_{sc}}=\dfrac{2.665\times10^6\times10.732\times519.67}{14.7}$, so $\boxed{V_{sc}\approx1.011\times10^9\ \text{ft}^3}$ (about 1.011 Bcf of gas in place at surface conditions).
Quantity
Value
(a) Gas deviation factor, $Z$
0.920
(b) Gas density, $\rho_g$
3.74 lb$_{mass}$/ft$^3$
(c) Reservoir gas volume at standard conditions, $V_{sc}$
$1.011\times10^9$ ft$^3$ (1.011 Bcf)
(d) Moles of gas in place, $n$
$2.665\times10^6$ lbmol
Check: Part (a) is nominally a chart reading; the value above is the Dranchuk–Abou-Kassem numerical fit to the Standing–Katz chart at the computed $T_{pr},p_{pr}$, which the project treats as the defensible stand-in for an eye reading off the printed chart (page 5 of the source) — both should agree to about $\pm0.01$–$0.02$ in $Z$.
