Calculate Relative Permeability from Capillary Pressure
Estimate effective saturation, water relative permeability, and oil relative permeability using a Brooks-Corey capillary pressure framework and Corey-type flow exponents.
Input Parameters
Calculated Output
Model assumptions: drainage-style Brooks-Corey Pc curve with Corey relative permeability exponents. Validate against laboratory coreflood and centrifuge or MICP data before field decisions.
How to Calculate Relative Permeability from Capillary Pressure: A Practical Expert Guide
Relative permeability and capillary pressure are tightly coupled functions that describe multiphase flow in porous media. Engineers often measure one set of curves in the laboratory and need to infer or calibrate the other for simulation workflows. If you need to calculate relative permeability from capillary pressure, the most common approach is to use a physically reasonable capillary pressure model to estimate effective saturation, then map effective saturation to phase relative permeability with a constitutive model such as Corey or Brooks-Corey style correlations.
In practical reservoir workflows, this conversion is useful in waterflood planning, enhanced oil recovery screening, CO2 storage studies, and any simulation project where capillary pressure data availability is better than full two-phase relative permeability coreflood data. The calculator above follows that logic and gives you a transparent, editable implementation that can be used for sensitivity studies.
Why capillary pressure can be used to estimate relative permeability
Capillary pressure, usually written as Pc = Pnon-wetting – Pwetting, encodes pore-throat size distribution and wettability effects. Relative permeability controls how easily each phase moves at a given saturation. Because both properties are saturation dependent and rooted in pore geometry, you can use capillary pressure to estimate saturation state, then infer flow capacity through a relative permeability function. This is not a universal one-step physics law, but it is a standard engineering closure method.
- Capillary pressure gives a path from pressure measurements to saturation.
- Effective saturation normalizes the usable saturation interval between residual endpoints.
- Corey-style functions convert effective saturation into kr curves for wetting and non-wetting phases.
- Endpoint values and exponents are tuned to match rock type and laboratory data.
Core equations used in the calculator
The workflow implemented above is:
- Convert Pc and entry pressure Pe into a consistent unit system.
- Compute effective water saturation Se from a Brooks-Corey capillary relation:
Se = 1 when Pc < Pe, else Se = (Pe / Pc)lambda, clipped to [0,1]. - Compute water saturation:
Sw = Swr + Se(1 – Swr – Sor). - Compute relative permeability:
Krw = Krw0 Senw,
Kro = Kro0 (1 – Se)no. - Compute Leverett J-function for scaling checks:
J = Pc sqrt(k / phi) / (sigma cos(theta)), with consistent SI units.
This structure is intentionally practical. It combines a capillary pressure to saturation mapping with a relative permeability model that can be calibrated to lab endpoints.
Typical ranges and representative statistics for screening
The following values are representative ranges often used for first-pass screening before detailed core calibration. They are not replacements for measured special core analysis, but they are useful for structured uncertainty studies.
| Rock System | Porosity Phi | Permeability k (mD) | Entry Pressure Pe (kPa) | Swr | Sor | Typical Lambda |
|---|---|---|---|---|---|---|
| Conventional Sandstone | 0.18 to 0.30 | 50 to 1000 | 5 to 60 | 0.15 to 0.30 | 0.15 to 0.30 | 1.8 to 3.5 |
| Carbonate (mixed pore system) | 0.08 to 0.22 | 1 to 300 | 20 to 200 | 0.20 to 0.40 | 0.10 to 0.25 | 1.2 to 2.5 |
| Tight Sand / Siltstone | 0.05 to 0.14 | 0.001 to 1 | 200 to 4000 | 0.25 to 0.50 | 0.05 to 0.20 | 0.6 to 1.6 |
Another useful view is sensitivity to capillary pressure for a fixed parameter set. In many conventional water-wet systems, as Pc rises from near-entry values to higher pressures, effective saturation decreases rapidly, Krw drops strongly, and Kro increases as the non-wetting phase gains connected flow pathways.
| Pc (kPa) | Se | Sw (for Swr=0.22, Sor=0.18) | Krw (Krw0=0.35, nw=3) | Kro (Kro0=0.90, no=2) |
|---|---|---|---|---|
| 40 | 1.00 | 0.82 | 0.35 | 0.00 |
| 100 | 0.40 | 0.46 | 0.02 | 0.32 |
| 250 | 0.16 | 0.32 | 0.00 to 0.01 | 0.64 |
| 500 | 0.08 | 0.27 | Near 0 | 0.76 |
Step by step interpretation workflow
- Start with high-confidence Pc and saturation endpoints. Errors in Swr and Sor can dominate the entire kr estimate.
- Choose a model form that matches displacement history. Drainage and imbibition can produce different curves and hysteresis loops.
- Fit lambda and entry pressure to capillary data first. This anchors Se behavior physically.
- Fit Krw0, Kro0, nw, and no to available flow data. If flow data are limited, use rock analogs and run uncertainty envelopes.
- Check consistency with J-function scaling. If J changes dramatically across analog samples, you may be mixing different pore systems or wettability classes.
- Validate in dynamic simulation. History matching of pressure and water cut is a necessary final check.
Common pitfalls when deriving relative permeability from Pc
- Assuming one curve applies to all facies in stratified reservoirs.
- Ignoring wettability alteration, especially after chemical or low salinity processes.
- Using entry pressure from a different fluid pair without interfacial tension correction.
- Not honoring hysteresis between drainage and imbibition paths.
- Treating Corey exponents as fixed constants instead of calibration parameters.
- Failing to convert units consistently for J-function calculations.
How to use this calculator in advanced workflows
For robust modeling, run this calculator in batch mode logic: pick low, base, and high cases for Pe, lambda, Swr, Sor, and endpoint relative permeability values. Generate curve families, then pass them to a reservoir simulator as separate rock types or uncertainty realizations. If coreflood data become available later, recalibrate exponents and endpoints while preserving capillary consistency.
In CO2 storage and hydrocarbon recovery projects, this approach helps align static rock characterization with dynamic flow behavior. Capillary pressure often captures fine-scale pore throat controls that strongly influence relative permeability shape. If two samples share similar absolute permeability but different entry pressure distributions, they can exhibit very different mobility behavior under multiphase flow.
Reference data and technical context
For supporting background on porosity and permeability concepts and subsurface flow context, consult these sources:
- USGS Water Science School: Porosity and Permeability
- U.S. Department of Energy: Carbon Capture, Utilization, and Storage
- Stanford University research context on capillary pressure and relative permeability
Final engineering guidance
Calculating relative permeability from capillary pressure is best treated as a disciplined integration exercise, not a blind formula conversion. Use capillary pressure to establish saturation state and pore-structure behavior, use Corey-style flow equations to estimate mobility, and then calibrate continuously against laboratory and field response. The highest quality models combine this method with petrophysical facies control, wettability interpretation, and dynamic history matching. If you apply those steps carefully, the Pc to kr conversion becomes a reliable bridge between core-scale physics and reservoir-scale forecasting.