Areal Displacement Efficiency

Key Takeaways

• Flood pattern geometry is the primary determinant of areal displacement efficiency at a given mobility ratio, and the most common patterns differ significantly in their sweep characteristics: The five-spot pattern (one injection well at the centre of a square with four production wells at the corners, or equivalently inverted with producers at centre and injectors at corners) achieves theoretical areal sweep efficiency at breakthrough of approximately 72 percent at unit mobility ratio (M = 1), meaning 28 percent of the pattern area is never contacted by injected water before breakthrough at any production well. The nine-spot pattern (one injector at centre, 8 producers surrounding it) achieves slightly higher areal sweep at breakthrough because the larger number of surrounding producers creates a more uniform pressure gradient across the pattern. A direct line-drive pattern (rows of injectors and producers aligned parallel to the regional structural trend) achieves higher areal sweep efficiency (80 to 88 percent at unit mobility ratio) but is less efficient per well because the producer-to-injector ratio is 1:1, requiring more total wells than the 5-spot (4:1 producer-to-injector ratio). The staggered line-drive pattern, which offsets the production rows by half the well spacing relative to the injection rows, provides a compromise between line-drive sweep and 5-spot well efficiency and is used in the Pembina Cardium waterflood where the structural dip (0.8 degrees northeast) creates an asymmetry that the staggered geometry partially compensates.
• Mobility ratio is the single most important fluid property parameter controlling areal displacement efficiency and flood front stability: Mobility ratio M = (k_rw / mu_w) / (k_ro / mu_o) compares the mobility of water (its ability to flow in the presence of residual oil) to the mobility of oil (its ability to flow at connate water saturation). When M is close to 1.0 or below 1.0, water advances as a stable, nearly piston-like front, and areal sweep efficiency improves steadily with injection. When M is much greater than 1.0 (typically greater than 3 to 5), water is much more mobile than oil, and the flood front becomes unstable: fingers of high-mobility water channel through the most permeable paths, leaving large pockets of undisplaced oil behind and achieving poor areal sweep at breakthrough. For Cardium light oil (mu_o = 3 to 6 mPa·s at reservoir temperature) with water viscosity mu_w = 0.6 mPa·s and typical end-point relative permeabilities (k_rw = 0.3, k_ro = 0.8), M = (0.3/0.6) / (0.8/5) = 0.5 / 0.16 = 3.1, indicating moderately unfavourable mobility ratio that requires careful pattern design and injection rate management to maintain reasonable areal sweep. For viscous heavy oil in the Cold Lake or Peace River areas (mu_o = 1,000 to 100,000 mPa·s), M exceeds 100 to 10,000 at the flood front, essentially guaranteeing very poor areal sweep by cold water injection and motivating the use of thermal recovery (SAGD, CSS) or polymer flooding to reduce the effective mobility ratio to manageable levels.
• Areal permeability heterogeneity reduces areal displacement efficiency by creating preferential flow channels that bypass lower-permeability zones: In a real reservoir with heterogeneous areal permeability, injected water moves preferentially through high-permeability channels and sand bodies (where the resistance to flow is lowest), bypassing oil in adjacent lower-permeability zones. The Dykstra-Parsons coefficient (V_DP) quantifies the permeability variation from the permeability distribution on a log-normal probability plot: V_DP = (k_50 - k_84) / k_50 (where k_50 is the median permeability and k_84 is the 84th percentile permeability). A V_DP of 0 represents a perfectly homogeneous reservoir; V_DP of 0.7 to 0.85 is typical of heterogeneous sandstones; V_DP approaching 1.0 represents extreme heterogeneity with a few high-permeability streaks dominating flow. In the Cardium Formation at Pembina, V_DP ranges from 0.40 to 0.65 across different pool areas, reflecting the variation in depositional facies from channel-confined sand bodies (higher V_DP) to more uniform shoreface sands (lower V_DP). The Dykstra-Parsons mobility ratio-heterogeneity correlation predicts areal sweep efficiency at waterflood breakthrough of 50 to 65 percent for the Cardium at M = 3.1, consistent with field-observed waterflood recovery factors of 15 to 22 percent OOIP for the Pembina Cardium compared to the theoretical 35 to 40 percent for a homogeneous reservoir at the same mobility ratio.
• Polymer flooding improves areal displacement efficiency by reducing the effective mobility ratio toward unity and suppressing viscous fingering at the flood front: Polymer flooding adds a high-molecular-weight polymer (typically partially hydrolyzed polyacrylamide, or HPAM, at 400 to 2,000 mg/L concentration) to the injection water, increasing the viscosity of the injected fluid from 0.6 mPa·s (plain water) to 2 to 10 mPa·s (polymer solution), reducing the effective mobility ratio from 3.1 to 0.9 to 1.5 for Cardium conditions. The reduced mobility ratio suppresses viscous fingering, delays water breakthrough, and increases the areal sweep at breakthrough from approximately 60 percent (water alone at M = 3.1) to 75 to 85 percent (polymer at M = 1.0 to 1.5), improving the volumetric recovery factor by 5 to 12 percent OOIP for a typical Cardium well. The incremental cost of the polymer (CAD 0.80 to 1.50 per m³ of injection water at 600 to 1,200 mg/L HPAM concentration, plus injection plant modifications of CAD 2 to 5 million per facility) must be justified by the incremental oil recovery. At CAD 60 to 80/bbl WTI-equivalent recovered, a polymer flood that adds 8 percent OOIP recovery over water alone in a pool with 10 MMbbl OOIP per section generates 800,000 bbl incremental recovery worth CAD 48 to 64 million per section, substantially exceeding the polymer cost of CAD 8 to 15 million per section over the project life, providing the economic justification for polymer pilot projects in the Pembina Cardium that have been operational since the 1980s.
• Surveillance data from producing wells (water cuts, production rates, and tracer tests) allows ongoing calibration of the areal displacement efficiency model and guides pattern balancing decisions: The actual areal displacement efficiency achieved in a waterflood is monitored indirectly through production surveillance rather than direct measurement. Rising water cuts in production wells indicate the flood front has swept through the inter-well path between the injector and that producer; the rate of water cut increase (percent water cut per year) indicates the sweep rate and the remaining oil volumes ahead of the front. Tracers (radioactive isotopes or chemical tracers such as deuterium-labelled water, sulfonated naphthalene, or nitrate) injected with the water allow quantification of the areal sweep by identifying which injector's water is arriving at each producer, at what concentration, and with what time lag. In a 5-spot pattern at 400-metre well spacing, tracer breakthrough at 90 days indicates rapid channelling through a high-permeability streak (the expected breakthrough for a homogeneous pattern at M = 3 is approximately 180 to 240 days), alerting the reservoir engineer to implement pattern rebalancing by reducing injection in the offending injector and increasing injection in adjacent injectors whose flood fronts are lagging behind. This dynamic injection rebalancing, calibrated against the tracer and water-cut surveillance data, is the primary operational method for improving areal displacement efficiency in a producing waterflood project without drilling new wells.