24-Pet-B2 Oil and Gas Evaluation and Economics · May 2016
Question 3 of 7: Pipeline Suitability Check
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams May 2016, 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.
Check: the paper lists “Average operating pressure, 60°F” — a °F value cannot be a pressure, and no other temperature is given anywhere in this question, while “Standard temperature, 60°F” is already stated separately just above it. Read as a misprint for “average operating temperature, 60°F” (the only reading that supplies the $T$ the general flow equation needs) and used as such below.
Given.
Quantity
Value
Pipe I.D., $d$
12 in
Length, $L$
100 mi $=528{,}000$ ft
Inlet / outlet pressure
$p_1=400$, $p_2=200$ psia
Gas gravity, $\gamma_g$
0.6
Avg. temperature, $T$
$60^\circ\text{F} = 519.67\ ^\circ\text{R}$ (see the check note)
Avg. $Z$-factor
0.90
Roughness, $\varepsilon$
0.0006 in
Viscosity, $\mu$
0.011 cp
Required rate
24 MMSCFD
Find. Whether the 12-in line can deliver 24 MMSCFD between the stated end pressures.
Pipeline schematic: fixed inlet/outlet pressures and diameter set a maximum deliverable capacity, checked here against the 24 MMSCFD demand.
Approach. Compute the pipeline’s maximum steady-state capacity from the general flow equation with a Colebrook friction factor (iterated against Reynolds number, since $q$ and $f$ are mutually dependent), then compare that capacity to the 24 MMSCFD requirement.
Set up the general flow equation. From the formula sheet,
$$q_{sc}=5.634\,\frac{T_{sc}}{p_{sc}}\sqrt{\frac{(p_1^2-p_2^2)\,d^5}{\gamma_g\,Z\,T\,L\,f}}, \qquad N_{Re}=710.39\,\frac{p_{sc}}{T_{sc}}\,\frac{\gamma_g\,q_{sc}}{\mu\,d}$$
with $q_{sc}$ in MSCFD, $T$ in $^\circ\text{R}$, $d$ in inches, $L$ in ft.
Iterate friction factor via Colebrook. Starting from an assumed $f$, compute $q_{sc}$, then $N_{Re}$, then update $f$ from Colebrook’s equation $1/\sqrt{f}=-2\log_{10}(\varepsilon/(3.7d)+2.51/(N_{Re}\sqrt{f}))$, repeating to convergence:
$$N_{Re}=2.39\times10^{6}\ (\text{fully turbulent}), \qquad \boxed{f=0.01164}$$
Solve for pipeline capacity.
$$q_{sc}=5.634\left(\frac{519.67}{14.7}\right)\sqrt{\frac{(400^2-200^2)(12)^5}{0.6(0.90)(519.67)(528{,}000)(0.01164)}}$$
$$\boxed{q_{sc}=26{,}200\ \text{MSCFD}=26.2\ \text{MMSCFD}}$$
Compare to the requirement. Capacity (26.2 MMSCFD) exceeds the required 24 MMSCFD by about 9% — the 12-in line is suitable, with a modest margin rather than a comfortable one.
