Centrifugal Estimation of Capillary Pressure-Saturation Relationship at a Physical Point.

Capillary pressure-saturation functions, θ(ψ), are often derived from measurements assuming that capillary pressure and saturation are uniform throughout the sample volume. Because of the nature of the boundary conditions this assumption is often debatable. Several researchers have proposed techniques to account for gradients in capillary pressure and saturation through the definition of a point θ(ψ) function. It is argued that once this point θ(ψ) relationship has been found, effective properties can be readily calculated assuming the sample is homogeneous.
The increased body force acceleration in a centrifuge speeds up the equilibration of the capillary pressure profile during drainage or imbibition experiments. By increasing centripetal acceleration in a stepwise fashion, each step lasting a prolonged period of time, a number of average capillary pressure and saturation pairs can be collected for a sample. In this study we use the one-dimensional integral method to determine the parameter values of the Brooks and Corey (BC) capillary pressure-saturation model for a physical point. The BC model is numerically integrated over the length of the sample: for each grid point the capillary pressure is simulated and, using the BC model, point saturation values are established. The calculated average saturation is then compared to the measured average saturation and, using an iterative least-square minimization technique, the parameters of the BC model (pore-size distribution index, λ, residual moisture content, θ_r, and air-entry value, ψ_b) are optimized.
The integral method was applied to capillary pressure saturation data obtained from multi-RPM centrifuge experiments on Berea Sandstone cores and unconsolidated coarse-grained Hanford samples. As expected, the average θ(ψ) function shows curvature close to ψ_b, while the point θ(ψ) function does not. Furthermore, the pore size distribution index, λ, is smaller for the average θ(ψ) function indicating an apparent wider pore size range than would be expected at a physical point.