Mobility Ratio

What Is Mobility Ratio?

Mobility ratio (symbol M) is a dimensionless number used in reservoir engineering to quantify the stability of a displacement flood, defined as the mobility of the displacing fluid divided by the mobility of the displaced fluid, where mobility is the ratio of relative permeability to viscosity for each fluid phase. A mobility ratio of 1.0 (unit mobility) represents a theoretically stable, piston-like displacement front; values below 1.0 produce stable, efficient sweeps; and values above 1.0 cause the displacing fluid to finger through the slower, more viscous oil, bypassing significant volumes and reducing recovery efficiency. Mobility ratio is the single most important parameter governing areal and vertical sweep efficiency in waterfloods, gas floods, and enhanced oil recovery (EOR) projects.

Key Takeaways

Mobility ratio M = (k_rw / mu_w) / (k_ro / mu_o), where k_r is relative permeability at residual saturation conditions and mu is viscosity in centipoise.
M less than 1 (favorable ratio) produces stable displacement with high sweep efficiency; M greater than 1 (unfavorable ratio) produces viscous fingering and poor recovery.
Polymer flooding works by increasing the effective viscosity of the displacing water phase, reducing M toward or below 1.0 and improving sweep efficiency.
CO₂ floods typically have very unfavorable mobility ratios (M of 10-100) because CO₂ viscosity is extremely low, requiring WAG (water-alternating-gas) injection or foam to control mobility.
Craig's areal sweep efficiency curves quantify the relationship between mobility ratio and volumetric sweep at breakthrough and ultimate recovery for five-spot and other well patterns.

How Mobility Ratio Governs Displacement Stability

The physics behind mobility ratio is rooted in the stability of a moving fluid interface. When a less viscous fluid is injected behind a more viscous fluid, small perturbations at the interface amplify rather than dampen. The leading edge of the injected fluid that advances slightly faster encounters lower flow resistance, moves even faster, and eventually fingers ahead of the main front. This viscous fingering phenomenon, first described by Saffman and Taylor in 1958, explains why a low-viscosity water injected into a reservoir containing high-viscosity heavy oil can finger through to producing wells while leaving most of the oil uncontacted. The mobility ratio formalizes this instability: when M exceeds 1.0, the interface is mathematically unstable, and the degree of instability and fingering severity increase as M rises further above 1.0. At M equal to 10, recovery at water breakthrough in a five-spot pattern is typically only 30-40% of the oil in the swept area; at M equal to 0.1, breakthrough recovery approaches 70-80%.

The correct formulation of mobility ratio for a waterflood uses endpoint relative permeabilities: k_rw is evaluated at residual oil saturation (the saturation behind the flood front after all displaceable oil has been swept) and k_ro is evaluated at connate water saturation (the initial condition ahead of the front). This "endpoint" formulation, credited to Craig, gives the mobility ratio that governs the overall stability of the flood. Some texts use an "average" formulation based on relative permeabilities at average saturations within the swept zone, which gives a more conservative (lower) M value and is used for Buckley-Leverett fractional flow analysis rather than sweep efficiency estimation. Engineers must be precise about which formulation applies to the problem at hand.

Fast Facts: Mobility Ratio

Formula: M = (k_rw / mu_w) / (k_ro / mu_o) at endpoint saturations
Units: Dimensionless
Favorable range: M less than or equal to 1.0
Typical waterflood M range: 0.5-5 for light oil; 10-100 for heavy oil
Polymer flood target: Reduce effective water mobility to achieve M approaching 1.0
CO₂ flood M: 10-100+ due to CO₂ viscosity of 0.03-0.08 cP vs. oil at 0.5-5 cP
Steam flood challenge: Steam viscosity below 0.02 cP gives M of 100+ in heavy oil
Craig's reference: "The Reservoir Engineering Aspects of Waterflooding" (1971) remains the standard reference for sweep efficiency vs. M curves

Field Tip:

Before finalizing a waterflood design, calculate M using core-measured endpoint relative permeabilities and measured reservoir fluid viscosities at reservoir temperature. If M exceeds 3, the project economics will likely underperform predictions based on simple volumetric calculations. Consider polymer injection for light-to-medium oil (up to 50 cP) or review pattern geometry to reduce injector-producer distances, which reduces the travel time for fingers to reach producers. For heavy oil above 200 cP, a waterflood with M above 50 is usually not economic without thermal or chemical enhancement regardless of pattern design.

Mobility Ratio in EOR Processes

Polymer flooding directly attacks unfavorable mobility ratio by increasing the effective viscosity of the injected water. Partially hydrolyzed polyacrylamide (HPAA) and xanthan gum polymers dissolved at concentrations of 200-2,000 ppm increase water viscosity from approximately 1 cP to 5-50 cP depending on polymer type, concentration, and shear rate. The polymer also reduces k_rw through a mechanism called resistance factor (RF) and residual resistance factor (RRF), where polymer adsorption on pore surfaces reduces the permeability to water while leaving permeability to oil relatively unaffected. Together, viscosity increase and permeability reduction can reduce M from values of 3-10 down to near 1.0, substantially improving areal sweep and incremental recovery. Large-scale polymer floods in Daqing (China), Saskatchewan (Canada), and offshore Bohai Bay have demonstrated incremental recoveries of 5-12% OOIP attributable specifically to mobility control.

For CO₂ and miscible gas floods, the mobility problem is more severe because gas viscosities are orders of magnitude lower than oil viscosity. Water-alternating-gas (WAG) injection addresses this by periodically switching between CO₂ and water injection slugs. The water slug builds a temporary permeability barrier (high k_rw reduces effective gas mobility) and the alternating pattern reduces the effective gas-to-oil mobility ratio at the field scale. Foam-assisted WAG (FAWAG) goes further by generating foam in the reservoir, where CO₂ is dispersed as bubbles in a surfactant solution, raising the apparent viscosity of the CO₂ phase from 0.05 cP to an effective value of 1-10 cP. The North Sea Snorre and Ekofisk fields have piloted FAWAG with encouraging mobility control results at reservoir conditions.

Endpoint mobility ratio - the formulation using k_rw at S_or and k_ro at S_wc, the standard for sweep efficiency analysis; distinguished from the average mobility ratio used in fractional flow calculations.
Favorable mobility ratio - M less than or equal to 1.0; displacing fluid is at least as viscous as displaced fluid, producing stable fronts and high sweep efficiency.
Unfavorable mobility ratio - M greater than 1.0; displacing fluid is less viscous and more mobile than displaced fluid, producing viscous fingering and poor sweep.
Viscous fingering - the physical instability that manifests when M is unfavorable; fingers of injected fluid penetrate ahead of the main flood front, causing early breakthrough and leaving bypassed oil.

Frequently Asked Questions About Mobility Ratio

How is mobility ratio measured for a specific reservoir?

Mobility ratio is calculated rather than directly measured, using inputs from laboratory core analysis and fluid property measurements. Endpoint relative permeabilities are measured by steady-state or unsteady-state flooding experiments on preserved core plugs at reservoir temperature and net confining stress. Oil viscosity is measured by pressure-volume-temperature (PVT) analysis of recombined reservoir fluid samples at reservoir temperature and pressure. Water viscosity at reservoir temperature is calculated from correlations or measured directly. Engineers then apply the M formula using these laboratory-derived values. Uncertainty in k_rw and k_ro measurements (typically plus or minus 10-20%) translates directly into uncertainty in M, which is why flood performance predictions carry ranges rather than single-point values.

Does mobility ratio change during a waterflood?

Yes, because the relevant relative permeabilities are evaluated at local saturation conditions, which evolve as the flood progresses. At early time, ahead of the flood front, oil is at connate water saturation and k_ro is at its endpoint value, giving the "classical" M. Behind the front, both oil and water are flowing at intermediate saturations, and local mobility ratios differ from the endpoint value. The Buckley-Leverett fractional flow framework accounts for this by tracking saturation profiles rather than assuming a sharp front. Additionally, if a polymer flood transitions from a polymer slug to a chase water stage, the local mobility ratio at the polymer bank-chase water interface is different from the polymer bank-oil interface and must be calculated separately to assess slug integrity.

Why does steam flooding have an extremely unfavorable mobility ratio?

Steam viscosity at reservoir conditions is approximately 0.01-0.02 cP, far lower than even light crude oil at 0.5-2 cP and orders of magnitude lower than the heavy oils and bitumens that steam flooding targets. A bitumen reservoir with oil viscosity of 10,000 cP at original temperature may have a steam-to-oil mobility ratio exceeding 10,000, which would be catastrophically unfavorable without thermal effects. The practical saving grace is that steam dramatically heats the reservoir in the steam zone, reducing heavy oil viscosity by 3-5 orders of magnitude as temperature rises from 15 to 200 degrees Celsius. The effective mobility ratio in the steam zone is therefore evaluated not at original oil viscosity but at steam-zone temperature viscosity, which may be only 5-20 cP. Gravity drainage in steam-assisted gravity drainage (SAGD) also helps by providing a gravity-driven flow mechanism that is less sensitive to mobility ratio than a horizontal displacement process.

Why Mobility Ratio Matters in Oil and Gas

Mobility ratio is the foundational concept explaining why secondary and tertiary recovery methods succeed or fail. A waterflood that is economic for a 1 cP light oil reservoir may recover only a fraction of the oil from a 50 cP medium-heavy oil reservoir because the mobility ratio shifts from 0.5 to 25 with the same injected water. The global industry has recovered trillions of barrels of oil from secondary recovery programs, and the incremental opportunity from managing mobility ratio through polymer, surfactant, or gas mobility control EOR is substantial. For reservoir engineers, calculating and reporting mobility ratio for any flood design is not optional: it is the first and most important number that investors, regulatory agencies, and technical reviewers examine when evaluating the credibility of recovery factor projections and EOR project economics.