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24-Pet-A2 Petroleum Reservoir Fluids · December 2015

Question 2 of 7: Natural Gas PVT Cell — Z-Factor, Density, Standard Volume, Moles

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

98-Pet-A2 — Petroleum Reservoir Fluids · National Exams, December 2015 · 3 hours, closed book, non-communicating calculator only · first five questions in the answer book are marked, all questions equal value, all parts of a multipart question equal weight.

Reference texts: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (Ch. 1–2, PVT properties, reservoir/well-stream classification, material balance); 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. (black-oil PVT laboratory data, well-stream recombination); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (p/Z material balance, well-stream gravity); Danesh, A., PVT and Phase Behaviour of Petroleum Reservoir Fluids (equilibrium K-value flash calculations).

Question 2: Natural Gas PVT Cell — Z-Factor, Density, Standard Volume, Moles (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. $p=1400$ psia; $T=200\,{}^{\circ}\text{F}=660\,{}^{\circ}\text{R}$; $V_{cell}=12\ \text{ft}^3$; gas specific gravity $\gamma_g=0.6$ (air $=1$); standard conditions $p_{sc}=14.7$ psia, $T_{sc}=60\,{}^{\circ}\text{F}=520\,{}^{\circ}\text{R}$. Formula sheet: $T_{pc}=168+325\gamma_g-12.5\gamma_g^2$, $p_{pc}=677+15.0\gamma_g-37.5\gamma_g^2$; $\rho=\dfrac{pM}{ZRT}$, $R=10.732\ \text{psi-ft}^3/(\text{lb-mol-}{}^{\circ}\text{R})$; $B_g=0.02827\dfrac{ZT}{p}$ (ft$^3$/SCF).

Find. (a) $Z$; (b) gas density $\rho$; (c) gas volume at standard conditions; (d) moles of gas in the cell.

Approach. Build the pseudo-critical properties from $\gamma_g$ via the formula-sheet (Standing) correlation, form $T_r,p_r$, solve the equivalent Standing–Katz $Z$-factor numerically (Dranchuk–Abou-Kassem form of the same chart), then evaluate density, $B_g$/standard volume, and moles from the real-gas relations.

  1. Part (a) — Pseudo-critical properties and Z. $T_{pc}=168+325(0.6)-12.5(0.6)^2=168+195-4.5=358.5\,{}^{\circ}\text{R}$; $p_{pc}=677+15.0(0.6)-37.5(0.6)^2=677+9.0-13.5=672.5$ psia. Then $T_r=\dfrac{660}{358.5}=1.841$, $p_r=\dfrac{1400}{672.5}=2.082$. Solving the Standing–Katz correlation numerically at this $(T_r,p_r)$ gives $\boxed{Z=0.920}$.
  2. Part (b) — Gas density. $M=28.97\gamma_g=28.97(0.6)=17.38\ \text{lb}_m/\text{lb-mol}$. $\rho=\dfrac{pM}{ZRT}=\dfrac{(1400)(17.38)}{(0.920)(10.732)(660)}$. Denominator $=(0.920)(10.732)(660)=6516.4$; numerator $=24{,}332$. So $\boxed{\rho=3.73\ \text{lb}_m/\text{ft}^3}$.
  3. Part (c) — Volume at standard conditions. $B_g=0.02827\dfrac{ZT}{p}=0.02827\times\dfrac{(0.920)(660)}{1400}=0.02827\times0.4337=0.01226\ \text{ft}^3/\text{SCF}$. The reservoir-condition cell volume converts to standard-condition (surface) gas volume as $V_{sc}=\dfrac{V_{cell}}{B_g}=\dfrac{12}{0.01226}$, giving $\boxed{V_{sc}\approx979\ \text{SCF}}$.
  4. Part (d) — Moles of gas. Directly from the real gas law, $n=\dfrac{pV_{cell}}{ZRT}=\dfrac{(1400)(12)}{(0.920)(10.732)(660)}=\dfrac{16{,}800}{6516.4}$, so $\boxed{n=2.578\ \text{lb-mol}}$. Cross-check via Part (c): $n=V_{sc}/379.4=979/379.4=2.581\ \text{lb-mol}$, matching to within rounding.
QuantityValue
(a) $Z$ at 1400 psia, 200°F0.920
(b) Gas density $\rho$3.73 lb$_m$/ft$^3$
(c) Gas volume at std. conditions979 SCF
(d) Moles of gas in cell2.578 lb-mol