Capillary Number Definition / Meaning
The Capillary Number (often denoted as Nc or Ca) is a dimensionless quantity used in reservoir engineering to describe the relative importance of viscous forces compared to capillary forces acting on a fluid within a porous medium. It is a critical parameter in Reservoir Management & Improved Recovery because it directly influences how much oil can be displaced from the pore spaces of a reservoir rock.
Definition and Formula
The Capillary Number is defined by the ratio:
Nc = (μ × v) / (σ × cos θ)
Where:
- μ = viscosity of the displacing fluid (e.g., water or injected chemical) [Pa·s or cP]
- v = Darcy velocity (superficial velocity) of the displacing fluid [m/s]
- σ = interfacial tension between the displacing fluid and the oil [N/m]
- θ = contact angle between the fluid interface and the rock surface (a measure of wettability)
In simpler terms, Nc = (viscous forces) / (capillary forces). A high Capillary Number means viscous forces dominate, while a low number means capillary forces are more important.
Role in Oil Recovery
During waterflooding or enhanced oil recovery (EOR) processes, oil is trapped in pores by capillary forces. The Capillary Number helps predict how much of that trapped oil can be mobilized. At low Nc values (typically below 10-5), capillary forces hold oil droplets in place, leading to high residual oil saturation. As Nc increases, the viscous drag from the flowing fluid becomes strong enough to overcome capillary pinning, and more oil is displaced. This relationship is often shown in a capillary desaturation curve, which plots residual oil saturation versus Capillary Number.
Practical Applications in Reservoir Management
Engineers use the Capillary Number to design and optimize recovery methods. The goal is to increase Nc to a level where residual oil is significantly reduced. Common strategies include:
- Increasing injection rate (v): Pumping water or gas faster raises the viscous force. However, this may cause early breakthrough or fracturing.
- Reducing interfacial tension (σ): Adding surfactants (surfactant flooding) can lower σ by several orders of magnitude, dramatically boosting Nc.
- Increasing displacing fluid viscosity (μ): Polymer flooding thickens the water, improving the viscous-to-capillary force ratio and also improving sweep efficiency.
The table below shows typical Capillary Number ranges for different recovery processes:
| Recovery Process | Typical Nc Range | Effect on Residual Oil |
|---|---|---|
| Waterflooding (conventional) | 10-6 to 10-5 | High residual oil (30-50% OOIP) |
| Polymer flooding | 10-5 to 10-4 | Moderate reduction |
| Surfactant flooding | 10-3 to 10-2 | Very low residual oil (5-15% OOIP) |
| Low-salinity waterflood | 10-6 to 10-5 (but wettability change) | Moderate reduction via altered contact angle |
Usage Example
In a surfactant flood design, engineers target a Capillary Number above 10-3 to mobilize residual oil. For instance, if the reservoir has an interfacial tension of 30 mN/m and the injection velocity is 1 ft/day, a surfactant that reduces σ to 0.01 mN/m would increase Nc from about 10-6 to 3×10-3, enabling recovery of an additional 20% of the original oil in place.
Key Takeaways
- The Capillary Number is a fundamental scaling parameter for displacement efficiency in porous media.
- Low Nc means capillary trapping dominates; high Nc means viscous forces can flush out trapped oil.
- EOR methods like surfactant and polymer flooding are designed to increase Nc by reducing interfacial tension or increasing viscosity.
- Understanding Nc helps reservoir engineers select the most cost-effective recovery technique for a given field.
By monitoring and manipulating the Capillary Number, operators can significantly improve oil recovery from mature fields, making it a cornerstone concept in modern reservoir management.