reservoir · recovery
Fractional Flow (Single Point)
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Inputs
fraction
fraction
cp
cp
Description
Computes the fractional flow of water at a single saturation point — the fraction of total flowing volume that is water, given relative permeability and viscosity ratios at that point. The single-point building block of Buckley-Leverett displacement theory; the full graphical (Welge tangent) construction across a complete saturation range is not built here.
Variables
| Symbol | Unit | Description |
|---|---|---|
| fw | fraction | Water Fractional Flow |
| krw | fraction | Relative permeability to water at the saturation point of interest, from core relative permeability (SCAL) data. |
| kro | fraction | Relative permeability to oil at the same saturation point, from core relative permeability (SCAL) data. |
| μw | cp | Viscosity of the displacing water phase at reservoir conditions. |
| μo | cp | Viscosity of the displaced oil phase at reservoir conditions. |
Assumptions
- Horizontal flow with capillary pressure and gravity effects neglected — the simplified (not the full gravity/capillary-corrected) fractional flow form
- krw and kro are representative values at the single saturation point being evaluated, not a full relative permeability curve
- Viscosities are evaluated at representative reservoir conditions for each phase
Limitations
- Evaluates fw at one saturation point only — does not sweep across the full Sw range or perform the Welge tangent construction needed to find shock-front saturation or predict breakthrough timing
- Neglects gravity and capillary pressure, which can matter in dipping reservoirs or at low displacement rates
- This platform has no relative-permeability-curve infrastructure yet — krw/kro must be supplied directly rather than read from a kr(Sw) curve
Use Cases
- → Single-point displacement check: Evaluate the water fraction of total flow at a specific saturation of interest (e.g. at the flood-front or at current average reservoir saturation).
- → Mobility ratio cross-check: Pair with the Mobility Ratio calculator (same kro/krw/μo/μw inputs) for a consistent picture of displacement favorability at a given saturation.
- → Foundation for future Buckley-Leverett work: Provide the single-point fractional-flow building block that a future full Buckley-Leverett/Welge implementation (once array-input infrastructure exists) would sweep across the saturation range.
Related Calculations
Region Notes
Permian Basin
Fracture-dominated flow in unconventional benches deviates strongly from the matrix relative-permeability assumptions underlying this formula — apply with caution outside conventional waterflood settings.
Gulf of Mexico
Light-oil Miocene/Pliocene waterfloods with low μo/μw ratios typically show fw rising sharply at moderate Sw, consistent with the region's generally favorable mobility ratios.
North Sea
Brent Group waterfloods commonly evaluate fw at several candidate saturations to bracket expected breakthrough behavior ahead of full simulation studies.
Global
Always pair this single-point result with the full fw(Sw) shape (from lab kr curves) before drawing conclusions about breakthrough timing — a single point cannot reveal the shock-front behavior the full curve shows.
References
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