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

Question 2 of 7: Average Gas Velocity in a Flow Line

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

Notes on this paper

National Exams May 2015, 98-Pet-B2, Natural Gas Engineering — 3 hours, closed book (non-communicating calculator permitted), 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: Average Gas Velocity in a Flow Line (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 (per-component critical properties supplied directly); $q_{sc}=10$ MMSCFD; $d=4$ in; $\bar p=2500$ psia; $\bar T=120^{\circ}\text{C}=707.67^{\circ}\text{R}$; $T_{sc}=60^{\circ}\text{F}=519.67^{\circ}\text{R}$, $p_{sc}=14.7$ psia.

Find. Average gas velocity $V$ inside the flow line (ft/sec).

Approach. Because exact per-component critical properties are given, use Kay’s mixing rule directly (no sweet-gas correction needed) to get $T_{pc},p_{pc}$, solve for $Z$ at flowing conditions (Dranchuk-Abu-Kassem), then apply the real-gas continuity relation to convert the standard-condition rate to an actual volumetric rate at $\bar p,\bar T$ and divide by the pipe cross-sectional area.

  1. Apparent molecular weight and pseudo-criticals (Kay’s rule). $M_a=\sum y_iM_i=0.92(16.04)+0.05(30.07)+0.03(44.11)=\boxed{M_a=17.58\ \text{lb}_m/\text{lb-mol}}$. $T_{pc}=\sum y_iT_{ci}=0.92(343.33)+0.05(549.92)+0.03(666.06)=363.3^{\circ}\text{R}$; $p_{pc}=\sum y_ip_{ci}=0.92(666.4)+0.05(706.5)+0.03(616.4)=666.9$ psia.
  2. Reduced conditions. $\bar T=120^{\circ}\text{C}=248.0^{\circ}\text{F}=707.67^{\circ}\text{R}$. $T_r=\bar T/T_{pc}=707.67/363.3=1.948$; $p_r=\bar p/p_{pc}=2500/666.9=3.749$.
  3. Z-factor (Dranchuk-Abu-Kassem). Solving the DAK correlation implicitly (bisection on $Z$) at $T_r=1.948,\ p_r=3.749$ gives $\boxed{Z=0.9300}$.
  4. Standard-to-flowing volume conversion. By the real-gas continuity relation, the actual volumetric rate at $\bar p,\bar T$ is $Q_{actual}=q_{sc}\left(\dfrac{p_{sc}}{\bar p}\right)\left(\dfrac{\bar T}{T_{sc}}\right)Z=10\times10^6\left(\dfrac{14.7}{2500}\right)\left(\dfrac{707.67}{519.67}\right)(0.9300)$: $Q_{actual}=8.531\times10^4\ \text{ft}^3/\text{day}$.
  5. Velocity. Pipe area $A=\pi d^2/4=\pi(4/12)^2/4=0.08727\ \text{ft}^2$. $V=\dfrac{Q_{actual}}{A\times86{,}400}$: $\boxed{V=9.88\ \text{ft/sec}}$.
QuantityValue
Apparent molecular weight, $M_a$17.58 lb$_m$/lb-mol
Pseudo-critical $T_{pc}$, $p_{pc}$ (Kay’s rule)363.3°R, 666.9 psia
$T_r$, $p_r$ at flowing conditions1.948, 3.749
Z-factor0.9300
Average gas velocity, $V$9.88 ft/sec
Check: the source clearly and legibly states the flow-line average temperature as “120 degree C” — this is unusually hot for a surface gathering flow line (typical range roughly 10–65°C), but nothing in the data is self-contradictory, so it is used as printed rather than assumed to be a typo for °F. Kay’s mixing rule (mole-fraction-weighted average of the given per-component critical properties) was used in place of the formula sheet’s SG-only $T_{pc}/p_{pc}$ correlation, since exact component critical properties are supplied here — the more accurate choice when full composition and per-component criticals are both available (no CO$_2$/H$_2$S/N$_2$ present, so no sour-gas correction applies).