Question 1 of 4: EOR Fundamentals — Short Answer

Question 1: EOR Fundamentals — Short Answer (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.

1. Snap-off. Snap-off is the pore-scale mechanism that leaves oil trapped as isolated, disconnected blobs (ganglia) after a waterflood, and it is the principal reason residual oil saturation $S_{or}$ is non-zero in a water-wet rock. As the water phase advances through a pore body-and-throat network, water preferentially occupies the corners and crevices of a water-wet pore (thin films coat the grain surfaces) while oil retreats to the centre of the pore. At a pore throat, the water film thickens faster than the oil filament in the throat can drain; once the constricting water annulus closes completely across the throat, the oil thread ahead of it necks down under capillary instability (a Rayleigh-type instability of the oil cylinder) and pinches off, "snapping" the continuous oil filament into a disconnected droplet trapped in the adjacent pore body. Because the trapped blob is now surrounded by water on all sides, it can only be re-mobilized by a viscous or capillary force large enough to push it through the pore throat again — a very high capillary number is normally needed, which is exactly the target of surfactant/chemical EOR (Q1.5). Snap-off is most severe in water-wet systems with a favourable pore-body-to-pore-throat aspect ratio; oil-wet or mixed-wet rocks trap oil predominantly by a different mechanism (film drainage / bypassing) rather than snap-off.

2. Wettability characterization. Two standard laboratory methods, both run on a cleaned, restored-state core plug:

• Contact-angle method. A drop of oil (or water) is placed on a flat, polished mineral (or crude-oil-aged) surface immersed in the other fluid, and the angle $\theta$ measured through the water phase is read at equilibrium. Water-wet: $\theta \approx 0^{\circ}$–$75^{\circ}$ (strongly water-wet near $0^{\circ}$). Oil-wet: $\theta \approx 105^{\circ}$–$180^{\circ}$ (strongly oil-wet near $180^{\circ}$). Intermediate/neutral wettability spans roughly $75^{\circ}$–$105^{\circ}$.
• Amott-Harvey index. A core at irreducible water saturation is subjected to spontaneous imbibition of water then forced (waterflood) displacement, and the reverse sequence with oil, giving a water index $I_w$ and oil index $I_o$; the Amott-Harvey index is $I_{AH}=I_w-I_o$, ranging $-1$ to $+1$. Water-wet: $I_{AH}$ close to $+1$ (typically $0.3$ to $1.0$, spontaneous water imbibition dominates). Oil-wet: $I_{AH}$ close to $-1$ (typically $-1.0$ to $-0.3$, spontaneous oil imbibition dominates). Neutral wettability: $I_{AH}\approx 0$.

(The USBM index, from the ratio of areas under the forced-displacement capillary-pressure curves, is a common third method: positive $\log(A_1/A_2)$ indicates water-wet, negative indicates oil-wet.)

3. Oil viscosity and breakthrough recovery. The fractional-flow curve $f_w(S_w)=\left[1+\dfrac{k_{ro}\mu_w}{k_{rw}\mu_o}\right]^{-1}$ shows explicitly that increasing $\mu_o$ (at fixed $k_{ro}$, $k_{rw}$, $\mu_w$) increases the ratio $k_{ro}\mu_w/(k_{rw}\mu_o)$'s sensitivity — in practice a higher $\mu_o$ makes water the relatively more mobile phase everywhere, so the whole $f_w$ curve shifts upward/left: $f_w$ rises more steeply at low $S_w$ and the curve becomes more strongly S-shaped (less favourable, higher mobility ratio $M=\lambda_w/\lambda_o$). Applying the Welge tangent construction from $(S_{wc},0)$ to a "steeper/higher" curve moves the tangent point to a lower front saturation $S_{wf}$ and a higher $f_w(S_{wf})$ at breakthrough. Physically this means: water breaks through earlier (at fewer pore volumes injected, since $Q_{i,BT}=1/f_w'(S_{wf})$ falls as the curve steepens) and it breaks through carrying a smaller swept oil bank ($\bar S_{w2}-S_{wc}$ is smaller), so cumulative oil recovery at breakthrough is lower for a more viscous oil. This is the classical unfavourable-mobility-ratio result: viscous oils give earlier water breakthrough, lower breakthrough sweep efficiency, and a longer, more expensive high-water-cut tail to reach the same ultimate recovery — the motivation for viscosity-reducing EOR (thermal, miscible, polymer) ahead of or during a waterflood on heavy oil.

4. Gravity segregation. Gravity segregation (override/underride) is the vertical separation of the displacing fluid from the oil bank caused by a density contrast between them, superimposed on the intended areal/vertical sweep. A less dense displacing fluid (steam, CO2, hydrocarbon gas, or even fresh injection water into a denser formation brine) rises and rides along the top of the interval (override); a denser fluid sinks to the base (underride, e.g. water injected below a lighter oil column). Either way the injected fluid channels through only part of the pay thickness, bypassing oil in the rest of the interval and giving early breakthrough with poor vertical sweep efficiency. To minimize gravity segregation: (i) increase the injection/displacement rate so viscous forces dominate density forces — exactly the viscous-to-gravity ratio $R_{v/g}$ used in Question 3, keeping $R_{v/g}\gg 1$; (ii) reduce the density contrast where practical (e.g. WAG – water-alternating-gas – injection, which alternates a denser slug with the lighter gas to counteract override); (iii) place completions to work with, not against, gravity (e.g. inject gas high/produce low in a gravity-stable displacement, or use horizontal wells along the top/base of the pay); and (iv) favour thinner, higher-permeability-contrast intervals with vertical flow barriers that limit cross-flow, since gravity segregation scales with permeability and formation thickness.

5. Optimal salinity in surfactant/chemical flooding. Anionic surfactant/chemical (ASP, surfactant-polymer) floods depend on generating an ultra-low oil-water interfacial tension (IFT, $\sim 10^{-3}$ mN/m or lower) so that the capillary number $N_c=v\mu/\sigma$ rises enough to mobilize snap-off-trapped residual oil (Q1.1). Winsor's phase-behaviour classification shows that a given surfactant's IFT-vs-salinity curve passes through a minimum only within a narrow "optimal salinity" window: below it the system is Winsor Type I (oil-in-water microemulsion, surfactant partitions mostly to the aqueous phase, IFT still relatively high); above it, Type II(-) (water-in-oil microemulsion, surfactant partitions to the oil phase); only near the optimum does the system form a Type III middle-phase microemulsion in equilibrium with both excess oil and excess brine, where IFT with both phases is simultaneously minimized. Reservoir/injection brine salinity (and its dilution/mixing with connate brine and any preflush as the slug propagates) must therefore be engineered and monitored to stay within this optimal window along the entire flood path; missing it — even by a modest salinity swing — can raise IFT by an order of magnitude or more and largely defeat the flood's oil-mobilization purpose, on top of the surfactant retention/adsorption and phase-stability issues that also depend on salinity.