Mobility Ratio Definition / Meaning
Mobility ratio is a dimensionless parameter used in reservoir engineering to describe the ease with which one fluid can move through a porous medium compared to another fluid. It is a critical concept in reservoir management and improved oil recovery (IOR) methods, particularly in waterflooding and enhanced oil recovery (EOR) processes. The mobility ratio directly affects the sweeping efficiency of a displacing fluid (such as water or gas) pushing oil toward production wells.
Mathematical Definition
Mobility ratio (M) is defined as the ratio of the mobility of the displacing fluid to the mobility of the displaced fluid. Mobility itself is the ratio of relative permeability to viscosity for a given fluid phase. The standard formula is:
M = (kr,displacing / μdisplacing) / (kr,displaced / μdisplaced)
Where:
- kr,displacing = relative permeability of the displacing fluid (e.g., water) at the relevant saturation
- μdisplacing = viscosity of the displacing fluid (in centipoise, cP)
- kr,displaced = relative permeability of the displaced fluid (e.g., oil) at the relevant saturation
- μdisplaced = viscosity of the displaced fluid (in cP)
Interpretation and Significance
The value of M tells engineers whether the displacement process will be stable or unstable:
- M < 1 (Favorable): The displacing fluid moves slower than the displaced fluid. This promotes a stable, piston-like displacement with high sweep efficiency. Less bypassed oil remains.
- M = 1 (Neutral): The two fluids have equal mobilities. Displacement is neither strongly stable nor unstable.
- M > 1 (Unfavorable): The displacing fluid moves faster than the displaced fluid. This leads to viscous fingering, early breakthrough, and poor sweep efficiency. Significant amounts of oil can be left behind.
Typical Values and Industry Examples
In waterflooding, water has a much lower viscosity than oil in most reservoirs, so M is often greater than 1. The table below shows common scenarios:
| Displacement Process | Typical M Range | Impact on Sweep |
|---|---|---|
| Waterflood (light oil, μo ≈ 1 cP) | 1-3 | Moderate fingering, fair sweep |
| Waterflood (heavy oil, μo > 100 cP) | >10 | Severe fingering, very poor sweep |
| Polymer flood (polymer viscosity ≈ 30 cP) | 0.5-1.0 | Favorable, improved sweep |
| Miscible gas injection (CO2 or hydrocarbon gas) | <1 (often 0.2-0.8) | Favorable, good microscopic displacement |
Role in Reservoir Management and Improved Recovery
Engineers use mobility ratio to design and optimize secondary and tertiary recovery projects. Key applications include:
- Waterflood Design: If M is too high, engineers may reduce injection rates, pattern spacing, or implement infill wells to control fingering.
- Polymer Flooding: Adding polymers to injection water increases its viscosity, lowering M to near or below 1. This is a common improved oil recovery method for reservoirs with unfavorable mobility ratios.
- Foam or gel treatments: These can block high-permeability streaks and reduce the mobility of the displacing fluid.
- WAG (Water-Alternating-Gas) injection: Alternating water and gas slugs helps maintain a favorable M and improve conformance.
Factors Affecting Mobility Ratio
Several reservoir properties influence M:
- Fluid viscosities: Viscous oils yield high M. Heating or diluting oil can reduce viscosity.
- Relative permeability curves: The shape of kr functions at the displacement front affects the effective mobilities.
- Wettability: In oil-wet reservoirs, water relative permeability tends to be lower, which can reduce M somewhat.
- Heterogeneity: Permeability variations (layering, fractures) worsen the effects of unfavorable M by accelerating fingering through high-perm zones.
Usage Example
In a field development plan for a sandstone reservoir with oil viscosity of 50 cP and water viscosity of 0.5 cP, the engineer calculates the mobility ratio at the flood front. Assuming typical relative permeabilities, M comes out to about 6. This indicates an unfavorable displacement. The team decides to implement a polymer flood to increase the injectant viscosity to 15 cP, lowering M to below 1. This significantly improves sweep efficiency and incremental oil recovery.
Practical Considerations
Mobility ratio is not the only factor controlling recovery. Engineers also consider capillary number, gravity segregation, and reservoir geometry. However, M is a first-order screening tool. Many EOR methods aim to reduce M by increasing the viscosity of the displacing fluid or decreasing the viscosity of the displaced oil (e.g., thermal methods). In modern reservoir simulation, mobility ratio is tracked at each grid block to monitor conformance.