Question 3 of 7: Reservoir Fluid Phase Envelope — Depletion Paths

Question 3: Reservoir Fluid Phase Envelope — Depletion Paths (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. Phase envelope of the reservoir fluid, with critical point at $T_c=100\,{}^{\circ}\text{F}$, $p_c=2450$ psi. The bubble-point branch runs from about $(-180\,{}^{\circ}\text{F},970\text{ psi})$ up to a maximum near $(40\,{}^{\circ}\text{F},2550\text{ psi})$ and down to the critical point. The dew-point branch runs from the critical point out to a maximum temperature near $(220\,{}^{\circ}\text{F},1400\text{ psi})$, then back down and left to low pressure near $(10\,{}^{\circ}\text{F},\sim0\text{ psi})$. Path B is a vertical line at $T\approx175$–$180\,{}^{\circ}\text{F}$, from about 3400 psi down to about 950 psi. Path A is a curved line from the same high-pressure, high-temperature corner (about $178\,{}^{\circ}\text{F}$, 3200 psi) down to about $(10\,{}^{\circ}\text{F},450\text{ psi})$.

Find. (a) Phase behaviour along A and B; (b) which is the reservoir path and which the production-tubing path; (c) cricondenbar and cricondentherm; (d) effect of dry-gas injection on both.

Approach. Reservoir depletion happens at a fixed reservoir temperature, since only pressure falls as fluid is withdrawn, so it plots as a vertical line on a $p$–$T$ diagram. Flow up the production tubing to the surface loses pressure and temperature together, so it plots as a diagonal path. Identify each path by its shape, follow each across the envelope, read the envelope's extreme points for (c), and reason from the effect of composition on the envelope for (d).

[Figure not reproduced: Phase envelope as read from the source diagram (solid: bubble-point branch; dashed: dew-point branch), critical point at (100°F, 2450 psi). Path B, vertical at the reservoir temperature, is the reservoir depletion path. Path A, with pressure and temperature falling together, is the production-tu. See the official exam paper.]

1. Part (b) — identify the paths first, since that fixes the reading of part (a). Reservoir depletion removes fluid at essentially constant reservoir temperature, with only pressure falling, so it must plot as a vertical line: that is Path B, at $T\approx175$–$180\,{}^{\circ}\text{F}$. Flow from the reservoir up the production tubing to the surface loses pressure and cools at the same time, so $p$ and $T$ fall together: that is Path A. Both paths start from the same initial reservoir condition at the top right of the diagram. $\boxed{\text{B = reservoir path};\ \text{A = production tubing path}}$.
2. Part (a), Path B (reservoir, isothermal at $T\approx175$–$180\,{}^{\circ}\text{F}$). This temperature lies between the critical temperature ($100\,{}^{\circ}\text{F}$) and the cricondentherm ($\approx220\,{}^{\circ}\text{F}$), so the fluid is a retrograde gas condensate. From about 3400 psi down to the upper dew point (about 2100 psi) it is single-phase gas. Below the dew point, liquid condenses in the reservoir even though pressure is falling (retrograde condensation), and the liquid dropout grows as depletion continues. The path ends at about 950 psi, still inside the envelope, because the lower dew-point branch at this temperature is only about 550 psi. Condensed liquid therefore remains in the reservoir at the end of the path, and most of it is immobile and lost to production. Only if depletion continued down towards the lower dew point would part of it re-vaporize.
3. Part (a), Path A (production tubing). Starting from reservoir conditions (about $178\,{}^{\circ}\text{F}$, 3200 psi) as single-phase gas, pressure and temperature both fall as the stream rises. The path crosses the envelope at about $140\,{}^{\circ}\text{F}$ and 2300 psi, to the right of the critical point, so it crosses the dew-point branch and the first liquid condenses there. Inside the two-phase region more liquid condenses as the stream cools and expands. It reaches the surface/separator end of the path (about $10\,{}^{\circ}\text{F}$, 450 psi) well inside the envelope, as a two-phase gas + condensate stream that the separator splits into gas and stock-tank liquid.
4. Part (c) — cricondenbar and cricondentherm. The highest point of the envelope lies a little left of the critical point, at about $40\,{}^{\circ}\text{F}$: $\boxed{p_{cricondenbar}\approx2550\text{ psi}}$. The rightmost point of the envelope lies on the dew-point branch at mid pressure (about 1400 psi): $\boxed{T_{cricondentherm}\approx220\,{}^{\circ}\text{F}}$. As expected for a gas condensate, the cricondentherm is well to the right of the critical point and the reservoir temperature lies between the two.
5. Part (d) — effect of large-volume dry-gas injection. Dry gas is essentially methane plus a little ethane and nitrogen. Mixing a large volume of it into the reservoir fluid makes the overall composition much lighter.
   Cricondentherm: the envelope's right-hand extent is set by the heavy ends, and diluting them moves the whole envelope towards lower temperature, so the cricondentherm decreases.
   Cricondenbar: adding a light, volatile gas to a fluid that contains intermediates and heavy ends raises its saturation pressure. This is what a swelling test measures: the saturation pressure climbs with each increment of injected gas. The same effect appears in binary systems, where the critical locus of methane with a heavier hydrocarbon rises far above the critical pressure of either pure component. The upper part of the envelope therefore moves up while the envelope shifts left, and the cricondenbar increases.
   $\boxed{\text{cricondenbar INCREASES; cricondentherm DECREASES}}$. Only in the limit where the mixture becomes almost entirely injected gas does the envelope finally collapse towards the dry gas's own small envelope, at which point the cricondenbar would fall again. Operationally, lean-gas cycling in a condensate reservoir keeps pressure up and re-vaporizes some dropped-out condensate.