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24-Pet-A2 Petroleum Reservoir Fluids · May 2018

Question 6 of 7: Recombining Separator Gas and Liquid Compositions

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

Notes on this paper

17-Pet-A2 — Petroleum Reservoir Fluids · National Exams, May 2018 · 3 hours, closed book, Casio/Sharp approved calculators only · a formula sheet is provided; FIVE (5) questions constitute a complete exam paper (the first five as submitted are marked); all questions equal value, all parts of a multipart question equal weight; oilfield-unit questions must be answered in field units.

Reference texts: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (Ch. 1–2, PVT properties, reservoir/well-stream classification); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed. (Standing–Katz Z-factor correlation, gas properties); McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (phase behaviour, black-oil PVT laboratory data, gas hydrates/waxes/asphaltenes); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (material balance, well-stream gravity, pseudo-critical property correlations); Danesh, A., PVT and Phase Behaviour of Petroleum Reservoir Fluids (equilibrium K-value flash calculations, Gibbs' phase rule).

Question 6: Recombining Separator Gas and Liquid Compositions (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.

ComponentGas phase (mol%)Liquid phase (mol%)MW (lb$_{mass}$/lb-mole)
Methane71716.043
Ethane10530.074
Propane91544.097
i-Butane3758.123
n-Butane42558.123
i-Pentane21872.150
n-Pentane12372.150
Total100100—

Separator gas : separator liquid mass ratio = 0.5 : 1 (lb$_{mass}$).

Find. Recombined (well-stream) mole-percent composition for all seven components.

Approach. Compute each phase's own average molecular weight from its own composition, convert the given mass basis (0.5 lb$_{mass}$ gas : 1 lb$_{mass}$ liquid) into moles of each phase, then sum each component's moles from both phases and renormalize to get the recombined mole fractions.

  1. Average molecular weight of each phase. $MW_{gas}=\sum y_iMW_i=0.71(16.043)+0.10(30.074)+0.09(44.097)+0.03(58.123)+0.04(58.123)+0.02(72.150)+0.01(72.150)$, giving $\boxed{MW_{gas}=24.60\ \text{lb}_{mass}/\text{lb-mole}}$. Likewise $MW_{liq}=\sum x_iMW_i=0.07(16.043)+0.05(30.074)+0.15(44.097)+0.07(58.123)+0.25(58.123)+0.18(72.150)+0.23(72.150)$, giving $\boxed{MW_{liq}=57.42\ \text{lb}_{mass}/\text{lb-mole}}$ (much heavier, as expected for the liquid phase).
  2. Moles of each phase (basis: 0.5 lbmass gas + 1 lbmass liquid). $n_{gas}=\dfrac{0.5}{24.60}=0.02033\ \text{lb-mole}$; $n_{liq}=\dfrac{1}{57.42}=0.01741\ \text{lb-mole}$. Total moles $n_{tot}=0.02033+0.01741=0.03774\ \text{lb-mole}$.
  3. Recombine each component and renormalize. For each component $i$, total moles $=n_{gas}y_i+n_{liq}x_i$, and the recombined mole fraction is $z_i=\dfrac{n_{gas}y_i+n_{liq}x_i}{n_{tot}}$. Carrying this through for all seven components (values below) reproduces the well-stream (wellhead) composition that flashed into this separator's gas and liquid.
ComponentRecombined well-stream mole %
Methane41.47%
Ethane7.69%
Propane11.77%
i-Butane4.85%
n-Butane13.69%
i-Pentane9.38%
n-Pentane11.15%
Total100.00%

The recombined stream sits, as expected, between the light gas composition (71% methane) and the much heavier liquid composition (7% methane, dominated by butanes/pentanes) — methane drops from 71 mol% in the gas alone to 41.5 mol% once the (much lower-mole-count, but far heavier per mole) liquid phase is folded back in.