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24-Pet-B2 Oil and Gas Evaluation and Economics · December 2014

Question 2 of 7: Gas Composition — Apparent MW, SG, Density, and FVF

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

Notes on this paper

National Exams December 2014, 98-Pet-B2, Natural Gas Engineering — 3 hours, closed book (Casio/Sharp approved calculators only), 7 questions of 20 marks each. NOTES item 5 states only the first five questions in the answer book are marked; all 7 are solved.

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 — Apparent MW, SG, Density, and FVF (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 fractions sum to 1.00); $p=3650$ psia; $T=210^{\circ}\text{F}=670^{\circ}\text{R}$; air MW $=28.97$ lb$_m$/lb-mol; $R=10.732$ psi-ft$^3$/(lb-mol-$^{\circ}$R).

Find. $M_a$, $\gamma_g$, $\rho$ (lb$_m$/ft$^3$), and $B_g$ (ft$^3$/SCF) at the stated conditions.

Approach. Mole-fraction mixing rule for apparent MW, the formula sheet’s gas-gravity correlations for the pseudo-critical properties, corrected for CO2/H2S/N2 (Wichert-Aziz-style correction on the formula sheet), then the Dranchuk-Abu-Kassem (DAK) correlation for $Z$ at the reduced conditions, and finally the real-gas law and $B_g$ formula.

  1. Apparent molecular weight. $M_a=\sum y_iM_i=0.04(44.01)+0.03(34.08)+0.01(28.01)+0.75(16.04)+0.12(30.07)+0.05(44.11)$: $\boxed{M_a=20.91\ \text{lb}_m/\text{lb-mol}}$.
  2. Specific gravity. $\gamma_g=M_a/M_{air}=20.91/28.97=\boxed{\gamma_g=0.7217}$.
  3. Uncorrected pseudo-criticals (gas-gravity correlation, formula sheet). $T_{pc}=169.2+349.5\gamma_g-74.0\gamma_g^2=382.9^{\circ}\text{R}$; $p_{pc}=756.8-131.0\gamma_g-3.6\gamma_g^2=660.4$ psia.
  4. N2/H2S/CO2 correction. $T_{pc}'=T_{pc}-80y_{CO_2}+130y_{H_2S}-250y_{N_2}=382.9-80(0.04)+130(0.03)-250(0.01)=381.1^{\circ}\text{R}$; $p_{pc}'=p_{pc}+440y_{CO_2}+600y_{H_2S}-170y_{N_2}=660.4+440(0.04)+600(0.03)-170(0.01)=694.3$ psia.
  5. Reduced conditions. $T_r=T/T_{pc}'=670/381.1=1.758$; $p_r=p/p_{pc}'=3650/694.3=5.257$.
  6. Z-factor (Dranchuk-Abu-Kassem). Solving the DAK correlation implicitly (bisection on $Z$, since $T_r,p_r$ are past the range convenient for a Standing-Katz chart read) gives $\boxed{Z=0.9095}$.
  7. Real gas density. $\rho=\dfrac{pM_a}{ZRT}=\dfrac{3650(20.91)}{0.9095(10.732)(670)}$: $\boxed{\rho=11.67\ \text{lb}_m/\text{ft}^3}$.
  8. Gas formation volume factor. $B_g=0.02827\dfrac{ZT}{p}=0.02827\dfrac{0.9095(670)}{3650}$: $\boxed{B_g=0.004720\ \text{ft}^3/\text{SCF}}$.
QuantityValue
Apparent molecular weight, $M_a$20.91 lb$_m$/lb-mol
Specific gravity, $\gamma_g$0.7217 (air = 1)
$Z$-factor at 3650 psia, 210°F0.9095
Real gas density, $\rho$11.67 lb$_m$/ft$^3$
Gas FVF, $B_g$0.004720 ft$^3$/SCF
Check: $M_{air}=28.97$ lb$_m$/lb-mol is the standard value (not printed on this exam’s own formula sheet, which defines $\gamma_g$ only symbolically). $Z$ was computed via the Dranchuk-Abu-Kassem correlation (bisection solve, no chart) rather than a graphical Standing-Katz read, since $p_r=5.26$ sits in a steep region of the chart where a numerical correlation is more reliable than an eyeballed read.