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24-Pet-B2 Oil and Gas Evaluation and Economics · December 2015

Question 2 of 7: Gas Composition — Pseudocriticals, Density, FVF, and Gas-in-Place

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

Notes on this paper

National Exams December 2015, 98-Pet-B2, Natural Gas Engineering — 3 hours, closed book (non-communicating calculator permitted), 7 questions of 20 marks each (only the first five as they appear in the answer book are officially marked). All 7 questions are solved, not just the first five.

Reference texts: Katz et al., Handbook of Natural Gas Engineering; Lee & Wattenbarger, Gas Reservoir Engineering (SPE Textbook Series Vol. 5); Ahmed, Reservoir Engineering Handbook, 5th ed.; Mohitpour et al., Pipeline Design and Construction, 3rd ed. (ASME Press); McCain, The Properties of Petroleum Fluids, 3rd ed.

Question 2: Gas Composition — Pseudocriticals, Density, FVF, and Gas-in-Place (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. Composition table above (mole % sums to 100.00, no N$_2$/CO$_2$/H$_2$S); $p=2500$ psia; $T=200^{\circ}\text{F}=659.67^{\circ}\text{R}$; $\phi=0.25$; $S_{wc}=0.10$; standard conditions $14.7$ psia, $60^{\circ}\text{F}$; air MW $=28.97$ lb$_m$/lb-mol; $R=10.732$ psi-ft$^3$/(lb-mol-$^{\circ}$R).

Find. $T_{pc}$, $p_{pc}$; $\rho$ (lb$_m$/ft$^3$); $B_g$ (ft$^3$/SCF); gas-in-place per acre-ft (SCF).

Approach. Apparent MW from the composition, Sutton’s correlation (this exam’s formula sheet) for pseudocriticals since no N$_2$/CO$_2$/H$_2$S correction is needed, the Dranchuk-Abu-Kassem (DAK) equation of state for $Z$ at the reduced conditions, then the real-gas law, $B_g$, and the standard SCF-per-acre-ft volumetric formula.

  1. (a) Apparent molecular weight and pseudocriticals. $M_a=\sum y_iM_i=0.9267(16.04)+0.0529(30.07)+0.0138(44.11)+0.0018(58.12)+0.0034(58.12)+0.0014(72.15)$: $\boxed{M_a=17.47\ \text{lb}_m/\text{lb-mol}}$. $\gamma_g=M_a/28.97=0.6029$. Sutton’s correlation: $T_{pc}=169.2+349.5\gamma_g-74.0\gamma_g^2$ and $p_{pc}=756.8-131.0\gamma_g-3.6\gamma_g^2$: $\boxed{T_{pc}=353.0^{\circ}\text{R}}$, $\boxed{p_{pc}=676.5\ \text{psia}}$ (no N$_2$/CO$_2$/H$_2$S present, so no further correction).
  2. Reduced conditions. $T_{pr}=T/T_{pc}=659.67/353.0=\boxed{T_{pr}=1.869}$; $p_{pr}=p/p_{pc}=2500/676.5=\boxed{p_{pr}=3.695}$.
  3. Z-factor (Dranchuk-Abu-Kassem). Solving the DAK correlation implicitly for the reduced density (fixed-point iteration) gives $\boxed{Z=0.9120}$.
  4. (b) Real gas density. $\rho=\dfrac{pM_a}{ZRT}=\dfrac{2500(17.47)}{0.9120(10.732)(659.67)}$: $\boxed{\rho=6.763\ \text{lb}_m/\text{ft}^3}$.
  5. (c) Gas formation volume factor. $B_g=0.02827\dfrac{ZT}{p}=0.02827\dfrac{0.9120(659.67)}{2500}$: $\boxed{B_g=0.006803\ \text{ft}^3/\text{SCF}}$.
  6. (d) Gas-in-place per acre-foot. Hydrocarbon pore volume per acre-ft $=43{,}560\,\phi(1-S_{wc})=43{,}560(0.25)(0.90)=9801\ \text{ft}^3$ (reservoir conditions); converting to standard conditions via $B_g$: $G=43{,}560\,\phi(1-S_{wc})/B_g=9801/0.006803$: $\boxed{G=1{,}440{,}606\ \text{SCF per acre-ft}}$ ($=1.441$ MMSCF/acre-ft).
QuantityValue
Apparent molecular weight, $M_a$17.47 lb$_m$/lb-mol
Pseudocritical temperature, $T_{pc}$353.0°R
Pseudocritical pressure, $p_{pc}$676.5 psia
Z-factor at 2500 psia, 200°F0.9120
Real gas density, $\rho$6.763 lb$_m$/ft$^3$
Gas FVF, $B_g$0.006803 ft$^3$/SCF
Gas-in-place, $G$ (per acre-ft)1,440,606 SCF (1.441 MMSCF)
Check: the exam’s own formula sheet gives Sutton’s pseudocritical correlation but no explicit $Z$-factor chart/correlation for this question (unlike Q6/Q7, which supply a graphical pseudopressure function); $Z$ was computed via the standard Dranchuk-Abu-Kassem equation of state rather than a Standing-Katz chart read, since $p_{pr}=3.70$ sits in a region a numerical correlation resolves more precisely than an eyeballed chart.