Schematic Black-Oil PVT Property Trends vs. Pressure: 24-Pet-A2 Petroleum Reservoir Fluids, December 2018, Q6

Question 6: Schematic Black-Oil PVT Property Trends vs. Pressure (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.

Approach. All five properties are governed by the same physical picture: above the bubble point $p_b$ the oil is a single-phase undersaturated liquid holding a fixed dissolved-gas content $R_{sob}$, so its behaviour is that of an ordinary (weakly compressible) liquid; below $p_b$ gas evolves out of solution as pressure falls, and every property's trend changes character exactly at $p_b$. Each panel below marks $p_b$ with a dashed vertical line.

Schematic black-oil PVT property trends vs. pressure at constant reservoir temperature, bubble point $p_b$ marked with a dashed line on every panel. (a) $\mu_o$ falls as pressure declines toward $p_b$ (more dissolved gas thins the oil), reaching a minimum exactly at $p_b$, then rises again below $p_b$ as the oil loses light ends to the evolving gas. (b) $B_o$ rises from 1 (surface) up to a maximum $B_{ob}$ at $p_b$ as more gas dissolves with increasing pressure below $p_b$, then falls slightly above $p_b$ as the single-phase liquid is isothermally compressed. (c) $B_t=B_o+B_g(R_{sob}-R_{so})$ coincides with $B_o$ above $p_b$ (no free gas, $R_{so}=R_{sob}$) but diverges sharply upward below $p_b$ as the evolved free-gas volume $B_g$ grows rapidly with falling pressure. (d) $R_{so}$ rises with pressure below $p_b$ as more gas dissolves, then is CONSTANT (=$R_{sob}$) above $p_b$, since no more gas is available to dissolve into an already-saturated oil. (e) $c_o$ is defined only above $p_b$ (single-phase liquid), decreasing mildly as pressure rises further above $p_b$; approaching $p_b$ from above it, and immediately below it, the system's effective compressibility rises sharply because the free gas phase near saturation is far more compressible than the liquid alone.

Property	Trend vs. pressure (constant T)
(a) $\mu_o$	Falls to a minimum at $p_b$, then rises below $p_b$
(b) $B_o$	Rises to a maximum $B_{ob}$ at $p_b$, then falls slightly above $p_b$
(c) $B_t$	Equals $B_o$ above $p_b$; diverges upward sharply below $p_b$
(d) $R_{so}$	Rises with $p$ below $p_b$; constant $=R_{sob}$ above $p_b$
(e) $c_o$	Defined only above $p_b$; decreases mildly with increasing $p$, spikes approaching $p_b$

Topic: Black-oil PVT property behaviour above and below the bubble point.

Key relations: $B_t=B_o+B_g(R_{sob}-R_{so})$ (formula sheet); $c_o=-\dfrac{1}{B_{ob}}\left(\dfrac{dB_o}{dp}\right)_T$ (defined only for undersaturated, single-phase oil).

Why this works: The bubble point is the single physical boundary between two completely different systems — a single-phase compressible liquid above it, a liquid in equilibrium with an expanding free-gas phase below it — so every PVT property that depends on gas solubility or the presence of a free gas phase must have a slope or kink exactly at $p_b$, even though the properties themselves (viscosity, volume, compressibility) are physically distinct.

Common pitfall: Drawing $R_{so}$ as continuing to rise above $p_b$ (it must flatten — an undersaturated oil cannot hold more gas than $R_{sob}$ at a fixed temperature); drawing $B_t$ and $B_o$ as different curves above $p_b$ (they are identical there, since $R_{so}=R_{sob}$ makes the gas term vanish).

Source: McCain, The Properties of Petroleum Fluids, 3rd ed., Ch. 3–4 (black-oil PVT properties); Ahmed, Reservoir Engineering Handbook, 5th ed., Ch. 2.

Question 6 of 7: Schematic Black-Oil PVT Property Trends vs. Pressure

Question 6: Schematic Black-Oil PVT Property Trends vs. Pressure (20 marks)