Question 3 of 4: Miscible Flood — Gravity Segregation vs. Viscous Instability

Question 3: Miscible Flood — Gravity Segregation vs. Viscous Instability (30 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.

Find. $R_{v/g}$ for project-a and project-b; which force (viscous or gravity) dictates each project's displacement, which project sweeps better, and a recommendation for the weaker project.

Approach. Compute the effective permeability $k=\sqrt{k_vk_h}$, the 5-spot interstitial velocity $v=1.25\,i/(hL)$, and $R_{v/g}$ for each case; $R_{v/g}\gg1$ means viscous forces control the displacement (gravity segregation negligible), $R_{v/g}\ll1$ means gravity dominates.

1. Project-a — effective permeability and velocity. $k=\sqrt{k_vk_h}=\sqrt{100\times400}=\sqrt{40{,}000}=200\text{ mD}$. $v=\dfrac{1.25\,i}{hL}=\dfrac{1.25\times1500}{50\times1000}=\dfrac{1875}{50{,}000}=0.0375\text{ bbl/day-ft}^2$.
2. Project-a — viscous-to-gravity ratio. $$R_{v/g,a}=\frac{2050\,(0.0375)(1.2)(1000)}{(200)(0.25)(50)}=\frac{92{,}250}{2500}=\boxed{36.9}$$ Since $R_{v/g,a}=36.9\gg1$, viscous instability dictates the displacement performance in project-a; gravity segregation is a secondary effect.
3. Project-b — effective permeability and velocity. With $k_v=k_h=5$ mD, $k=\sqrt{5\times5}=5\text{ mD}$. The thinner interval raises the interstitial velocity fivefold: $v=\dfrac{1.25\times1500}{10\times1000}=\dfrac{1875}{10{,}000}=0.1875\text{ bbl/day-ft}^2$.
4. Project-b — viscous-to-gravity ratio. $$R_{v/g,b}=\frac{2050\,(0.1875)(1.2)(1000)}{(5)(0.25)(10)}=\frac{461{,}250}{12.5}=\boxed{36{,}900}$$ $R_{v/g,b}=36{,}900\gg1$ as well, so viscous instability again dictates project-b's performance — and does so about 1000× more emphatically than project-a, because both the sharply lower permeability ($k$ falls 40×) and the thinner interval (raising $v$ 5× and shrinking $h$) push $R_{v/g}$ far higher.
5. (c) Relative sweep efficiency. A higher $R_{v/g}$ means gravity-driven override/underride of the gas is even more thoroughly suppressed relative to the viscous forces holding the flood front together, so project-b achieves the higher sweep efficiency of the two: with $R_{v/g,b}\approx1000\times R_{v/g,a}$, gravity tonguing is essentially negligible in project-b, giving a more uniform, near-piston-like vertical and areal displacement, whereas project-a — though still viscous-dominated — retains a comparatively larger (if still secondary) gravity-segregation contribution that mildly degrades its vertical sweep relative to project-b.
6. (d) Recommendation for project-a (the lower-recovery project). Since $v\propto i$ and $R_{v/g}\propto v$, the most direct, quantitative lever is to increase the gas injection rate in project-a: doubling $i$ doubles $R_{v/g,a}$ toward project-b's viscous-dominated regime and further suppresses residual gravity override, at the cost of a higher pressure drop/faster breakthrough that must be checked against fracture-pressure and voidage-replacement constraints. Complementary measures that reduce the effective gravity term without raising rate: convert to WAG (water-alternating-gas) injection to reduce the mobile gas column and dampen override; complete injectors low in the interval (with producers completed higher) so buoyancy works with, not against, the intended flow path; and consider a smaller inter-well spacing $L$ (infill pattern) or a horizontal injector along the base of the pay to raise the effective velocity for the same total voidage rate.