24-Pet-B2 Oil and Gas Evaluation and Economics · Undated paper
Question 3 of 7: Sour Gas Mixture Properties
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams May 2019, 17-Pet-B2, Natural Gas Engineering — 3 hours, open book (non-communicating calculator permitted), 7 questions of equal (10-mark) value. 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.; McCain, The Properties of Petroleum Fluids, 3rd ed.; Mohitpour et al., Pipeline Design and Construction, 3rd ed. (ASME Press); GPSA Engineering Data Book (component critical-property tables); Wichert & Aziz (1972), “Calculate Z's for Sour Gases,” Hydrocarbon Processing; Mandhane, Gregory & Aziz (1974), “A Flow Pattern Map for Gas-Liquid Flow in Horizontal Pipes,” Int. J. Multiphase Flow.
Question 3: Sour Gas Mixture Properties (10 marks)
Check: this exam's own formula sheet does not tabulate individual component critical properties (needed for Kay's rule) or state the Wichert–Aziz $\varepsilon$-factor equation explicitly. Component $T_c$/$P_c$ are taken from the standard GPSA Engineering Data Book / McCain physical-property table (part a). For part (b), “the approach of Wichert and Aziz” is implemented as the linear N$_2$/CO$_2$/H$_2$S correction to the gravity-based $T_{pc}$/$p_{pc}$ correlation that this exam's own formula sheet prints immediately below that correlation. Both parts use the Dranchuk–Abu-Kassem (DAK) numerical fit of the Standing–Katz $Z$-chart (the standard stand-in for “read $Z$ off the Katz chart”), cross-checked against the independent Hall–Yarborough correlation (agreement within 1.5% at these $T_{pr}$, consistent with both correlations' known accuracy near the low-$T_{pr}$ trough of the chart, which is where this sour mixture happens to sit).
Given.
Quantity
Value
Composition
see table above (N$_2$, CO$_2$, H$_2$S, C$_1$–n-C$_4$)
Pressure, $p$
10.19 MPa
Temperature, $T$
271 K
Gas flow rate
$2800\times10^3$ Sm$^3$/d
Find. (a) $V_m$, $\rho$ via Kay's rule + Katz(DAK) correlation; (b) $V_m$, $\rho$ via the gravity correlation with Wichert–Aziz-style sour-gas correction; (c) mass flow rate.
Approach. Build the apparent molecular weight once; get pseudocritical properties two different ways (true-property mixing vs. gravity correlation + acid-gas correction); solve each for $Z$ via DAK; convert to molar volume and density; then use the standard-condition molar volume to turn the volumetric flow rate into a mass flow rate.
Apparent molecular weight and gas gravity.
$$M_a=\sum y_iM_i=0.0050(28.01)+0.2250(44.01)+0.1000(34.08)+0.6610(16.04)+0.0070(30.07)+0.0015(44.10)+0.0003(58.12)+0.0002(58.12)$$
$$\boxed{M_a=24.36\ \text{lb}_m/\text{lb-mole}\ (=\text{kg/kmol})}, \qquad \gamma_g=\frac{M_a}{28.97}=\boxed{0.8409}$$
Flowing conditions in field units: $p=10.19\ \text{MPa}=1477.9$ psia, $T=271\ \text{K}=487.8\ ^\circ\text{R}$.
(a) Kay's rule pseudocriticals. Mole-fraction-weight each component's own critical temperature and pressure (GPSA table):
$$T_{pc}=\sum y_iT_{ci}=423.5\ ^\circ\text{R}, \qquad p_{pc}=\sum y_iP_{ci}=820.1\ \text{psia}$$
$$T_{pr}=\frac{487.8}{423.5}=1.152, \qquad p_{pr}=\frac{1477.9}{820.1}=1.802$$
Solving the DAK equation of state at these reduced coordinates: $\boxed{Z_a=0.496}$.
(a) Molar volume and density. With $R=8.314\ \text{kPa}\cdot\text{m}^3/(\text{kmol}\cdot\text{K})$:
$$V_{m,a}=\frac{Z_aRT}{p}=\frac{0.496(8.314)(271)}{10{,}190}=\boxed{0.1097\ \text{m}^3/\text{kmol}}$$
$$\rho_a=\frac{pM_a}{Z_aRT}=\frac{10{,}190(24.36)}{0.496(8.314)(271)}=\boxed{222.1\ \text{kg/m}^3}$$
(b) Gravity-correlation pseudocriticals, corrected for acid gas. From the formula sheet, $T_{pc}=169.2+349.5\gamma_g-74.0\gamma_g^2=410.8\ ^\circ\text{R}$ and $p_{pc}=756.8-131.0\gamma_g-3.6\gamma_g^2=644.1$ psia (uncorrected). Applying the printed N$_2$/H$_2$S/CO$_2$ correction (Wichert–Aziz-style) with $y_{CO_2}=0.225$, $y_{H_2S}=0.100$, $y_{N_2}=0.005$:
$$T_{pc}'=410.8-80(0.225)+130(0.100)-250(0.005)=\boxed{404.5\ ^\circ\text{R}}$$
$$p_{pc}'=644.1+440(0.225)+600(0.100)-170(0.005)=\boxed{802.2\ \text{psia}}$$
$$T_{pr}'=\frac{487.8}{404.5}=1.206, \qquad p_{pr}'=\frac{1477.9}{802.2}=1.842 \ \Rightarrow\ \boxed{Z_b=0.587}$$
(b) Molar volume and density.
$$V_{m,b}=\frac{Z_bRT}{p}=\boxed{0.1299\ \text{m}^3/\text{kmol}}, \qquad \rho_b=\frac{pM_a}{Z_bRT}=\boxed{187.5\ \text{kg/m}^3}$$
The corrected route gives a $\sim$16% higher $Z$ (and correspondingly lower density) than Kay's rule — the acid-gas correction pushes $T_{pc}'$ down and $p_{pc}'$ up relative to the naive gravity correlation, moving the state point away from the deep trough of the $Z$-chart. Part (b), not part (a), is the intended production-facility design value, since it is the method that accounts for the mixture's 32.5 mol% acid-gas content.
(c) Mass flow rate. Convert the standard-condition volumetric rate to a molar rate using the standard molar volume ($T_{sc}=60^\circ\text{F}=288.7$ K, $p_{sc}=14.7$ psia $=101.35$ kPa, $Z_{sc}\approx1$):
$$V_{m,sc}=\frac{RT_{sc}}{p_{sc}}=\frac{8.314(288.7)}{101.35}=23.68\ \text{m}^3/\text{kmol}$$
$$\dot n=\frac{q_{sc}}{V_{m,sc}}=\frac{2800\times10^3}{23.68}=118{,}230\ \text{kmol/d}$$
$$\dot m=\dot nM_a=118{,}230(24.36)=2{,}880{,}144\ \text{kg/d}=\boxed{33.34\ \text{kg/s}}$$
