Well-Stream Specific Gravity from a Separator Test: 24-Pet-A2 Petroleum Reservoir Fluids, May 2018, Q5

Question 5: Well-Stream Specific Gravity from a Separator Test (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.

Check: the source prints "1 lb$_{mass}$ of gas = 379.4 SCF" — this is the standard oilfield molar-volume constant (1 lb-mole of ideal gas occupies 379.4 SCF at 14.696 psia, 60°F), not a per-lb$_{mass}$ figure; treated here as a misprint and used correctly as SCF per lb-mole, consistent with every other quantity on this problem's formula sheet being expressed per lb-mole.

Given.

Quantity	Value
Gas specific gravity, $\gamma_g$ (air=1)	0.7
Oil specific gravity, $\gamma_o$ (water=1)	0.8
Oil molecular weight, $MW_o$	80 lb$_{mass}$/lb-mole
MW of air	28.97 lb$_{mass}$/lb-mole
Molar volume, standard conditions	379.4 SCF/lb-mole
Producing gas-oil ratio (from figure)	15,000 SCF/STB

Find. Specific gravity of the recombined well-stream fluid, $\gamma_{wf}=MW_{wf}/MW_{air}$.

[Figure not reproduced: Separator schematic (per the source figure): the well-stream fluid flashes into 15,000 SCF of gas per STB of separator oil — the basis for the recombination below. See the official exam paper.]

Approach. Take 1 STB of separator oil as the basis; convert both the oil and its associated gas (via the given GOR) into masses and lb-moles, then form the apparent molecular weight of the whole (recombined) well-stream fluid as total mass over total moles, and finally its specific gravity relative to air.

Oil mass and moles (basis: 1 STB). $m_{oil}=350\gamma_o=350\times0.8=280\ \text{lb}_{mass}$. $n_{oil}=\dfrac{m_{oil}}{MW_o}=\dfrac{280}{80}=3.5\ \text{lb-mole}$.
Gas mass and moles. $MW_{gas}=\gamma_g\times MW_{air}=0.7\times28.97=20.28\ \text{lb}_{mass}/\text{lb-mole}$. From the figure's producing GOR of 15,000 SCF/STB and the molar-volume constant: $n_{gas}=\dfrac{15{,}000}{379.4}=39.54\ \text{lb-mole}$, so $m_{gas}=n_{gas}\times MW_{gas}=39.54\times20.28=801.8\ \text{lb}_{mass}$.
Recombined well-stream apparent molecular weight. $MW_{wf}=\dfrac{m_{oil}+m_{gas}}{n_{oil}+n_{gas}}=\dfrac{280+801.8}{3.5+39.54}=\dfrac{1081.8}{43.04}$, so $\boxed{MW_{wf}\approx25.14\ \text{lb}_{mass}/\text{lb-mole}}$.
Well-stream specific gravity. $\gamma_{wf}=\dfrac{MW_{wf}}{MW_{air}}=\dfrac{25.14}{28.97}$, so $\boxed{\gamma_{wf}\approx0.868}$. As expected, this lands between the pure gas gravity (0.7) and a value that reflects the oil's heavier contribution per mole, weighted toward the gas since the well stream here is overwhelmingly gas by mole count ($n_{gas}\gg n_{oil}$) — consistent with production from a wet gas reservoir.

Quantity	Value
Oil: mass / moles (1 STB basis)	280 lb$_{mass}$ / 3.5 lb-mole
Gas: mass / moles	801.8 lb$_{mass}$ / 39.54 lb-mole
Apparent MW of well-stream fluid	25.14 lb$_{mass}$/lb-mole
Well-stream specific gravity, $\gamma_{wf}$	0.868

Topic: Recombining a separator oil + gas stream into a single well-stream apparent molecular weight and specific gravity.

Key relations: $MW=m/n$; $MW_{gas}=\gamma_g\,MW_{air}$; $MW_{wf}=\dfrac{\sum m_i}{\sum n_i}$; $\gamma_{wf}=MW_{wf}/MW_{air}$.

Why this works: An "apparent molecular weight" of a mixture is defined exactly the way any average molecular weight is — total mass divided by total moles — so recombining two streams needs only their individual masses and mole counts on a common basis, here 1 STB of separator liquid.

Common pitfall: Using the molar-volume constant per lb-mass instead of per lb-mole (see the check callout above), or forgetting that $\gamma_{wf}$ must be computed from the recombined $MW_{wf}$, not by simply averaging $\gamma_g$ and $\gamma_o$ on a mole basis (mixing a gas-phase and liquid-phase specific-gravity definition would be dimensionally inconsistent).

Source: Ahmed, Reservoir Engineering Handbook, 5th ed., Ch. 1 (well-stream gravity, recombination); McCain, The Properties of Petroleum Fluids, 3rd ed., Ch. 5.

Question 5 of 7: Well-Stream Specific Gravity from a Separator Test

Question 5: Well-Stream Specific Gravity from a Separator Test (20 marks)