Free Online Waterflood Calculator: Buckley-Leverett Fractional Flow

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The S-shaped curve is the fractional flow of water at each saturation, built from Corey relative permeabilities and the viscosity ratio. The dashed Welge tangent drawn from connate water touches the curve at the front saturation: its contact point is the shock front, its slope gives pore volumes injected at breakthrough, and its extension to full water cut gives the average saturation behind the front, which is the oil recovered when water arrives. Raise the oil viscosity and watch the tangent flatten: that is why heavy oil floods break through early.

Waterflood prediction from one elegant construction

Buckley-Leverett theory is the rare piece of reservoir engineering that fits on a napkin and still runs the world: build the fractional flow curve from relative permeability and the water-oil viscosity ratio, draw one tangent line from connate water, and you have the saturation of the advancing water front, the pore volumes injected when it reaches the producer, and the oil recovered at that moment. The tool above does the construction live from Corey-form relative permeability inputs, draws the curve and the Welge tangent, and reports front saturation, breakthrough water cut, breakthrough timing, recovery at breakthrough, and the ultimate movable oil.

Fractional flow curve of water saturation with the Welge tangent line drawn from connate water touching the curve at the front saturation, predicting breakthrough timing and recovery for a waterflood
One curve and one tangent: Buckley-Leverett theory predicts the water front, breakthrough timing, and recovery from relative permeability alone.

This completes the Reservoir Engineering Suite in the bar above: rock volume from material balance, deliverability from the well test, rate from nodal analysis, and now the waterflood that recovers what primary depletion leaves behind.

Why the tangent works

Water injected into oil-bearing rock does not advance as a smooth gradient; it forms a shock front, a sharp jump from connate water to the front saturation. The frontal advance equation says each saturation travels at a speed set by the slope of the fractional flow curve, and the tangent construction finds the one saturation whose speed is consistent with material balance across the jump. Everything after that is reading the geometry: the tangent slope is the reciprocal of pore volumes injected at breakthrough, and extending the tangent to a water cut of one gives the average saturation behind the front, which converts directly to recovered oil.

What the inputs do

  • The viscosity ratio is the headline: raise oil viscosity from 2 to 20 cp and watch breakthrough come dramatically earlier with less oil recovered, the mathematical statement of why heavy oil floods struggle.
  • The Corey exponents shape the curves: higher exponents mean straighter relative permeability crossover and a sharper, more efficient front.
  • Swc and Sor bracket the prize: the ultimate movable fraction is fixed by the endpoints before any flooding begins.
  • Recovery at breakthrough versus ultimate movable shows how much of the flood happens after water arrives, which is the part that costs water handling money.

What this tool is for

Screening flood efficiency before simulation, teaching the most examinable construction in petroleum engineering with live geometry, and sanity-checking simulator output against the analytical answer it must honor in one dimension. Real floods add gravity, heterogeneity, and pattern geometry, which is what reservoir simulation is for; the physics of the front, though, is exactly this page.

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