Waterflood Fractional Flow Analysis

Buckley-Leverett fractional flow analysis for waterflood performance prediction. Computes water fractional flow curve from Corey relative permeability and fluid viscosities, applies the Welge tangent construction to determine breakthrough saturation and oil recovery factor.

Buckley-Leverett theory. The fractional flow equation fw = 1/(1 + (kro/krw)·(μw/μo)) assumes incompressible, immiscible, horizontal displacement with no capillary or gravity effects. The Welge tangent construction accounts for the saturation shock (piston-like displacement front) that forms when the fw curve has an inflection point.

Mobility ratio. M = (Krw_end·μo)/(Krow_end·μw). With default parameters: M = (0.35×5.0)/(1.0×0.5) = 3.5. Values above 1 indicate unfavorable displacement — water fingers through oil, causing early breakthrough and high water cut before significant oil recovery. Typical light oil waterfloods have M = 1–5; heavy oil can exceed M = 50.

Welge tangent resolution. The BT saturation is approximate (±0.05) due to the saturation table step size. For higher resolution, reduce the Sw step or add rows near the expected BT region. The exact BT point satisfies dfw/dSw = fw/(Sw−Swi) simultaneously.

Recovery factors. BT recovery is the oil recovered when water first arrives at the producer — after this, water cut rises rapidly. Ultimate recovery assumes infinite PV injected (economically unrealistic). Practical recovery lies between these bounds, determined by the economic water cut limit (typically fw = 0.95–0.99).

Reference: Buckley, S.E. and Leverett, M.C. (1942). "Mechanism of Fluid Displacement in Sands." Trans. AIME 146: 107–116. Welge, H.J. (1952). "A Simplified Method for Computing Oil Recovery by Gas or Water Drive." Trans. AIME 195: 91–98.

• Reservoir & Fluid Properties (rows 3–10): Corey model endpoints (Swi, Sorw, Krow_Swi, Krw_Sorw), exponents (No, Nw), and fluid viscosities (μo, μw). Default parameters represent a moderately unfavorable waterflood (M ≈ 3.5) in a medium-viscosity oil reservoir.
• Displacement Parameters (rows 12–15): Endpoint mobility ratio M = (Krw_Sorw·μo)/(Krow_Swi·μw) characterizes displacement efficiency — M > 1 is unfavorable (early breakthrough, low recovery), M < 1 is favorable. Mobile oil saturation and ultimate displacement efficiency set the theoretical maximum recovery.
• Fractional Flow Table (rows 17–30): Water saturation sweep from Swi to 1−Sorw in 0.05 steps. Columns: Sw, Krow (from PO.SCAL.Corey.Krow), Krw (from PO.SCAL.Corey.Krw), fw (water cut via LAMBDA), and Welge tangent slope fw/(Sw−Swi). The fw LAMBDA uses the mobility-weighted form (Krw/μw)/(Krw/μw + Krow/μo) to avoid division by zero at endpoints.
• Welge Tangent Analysis (rows 32–39): The Welge construction finds the breakthrough front saturation Sw_f where a straight line from (Swi, 0) is tangent to the fw curve — this occurs at the maximum of the Welge slope column. PV injected at BT = 1/slope. Average Sw behind front from the Welge material balance: Sw_avg = Sw_f + (1−fw_f)/slope. BT and ultimate oil recovery factors expressed as fraction of OOIP.