In preferentially oil‐wet porous media, laboratory waterflooding experiments are prone to capillary end effects. The wetting phase (oil) will tend to accumulate at the outlet where the capillary pressure is zero and leave a highly remaining-oil saturation at steady state (defined by a stable pressure drop and a zero oil‐production rate) compared to the residual‐oil saturation. Andersen et al. (2017c) derived analytical solutions describing how the capillary pressure and relative permeability of water (the injected phase) could be determined on the basis of pressure drop and average saturation at steady states obtained at different water‐injection rates. Plotting these values against inverse rate reveals linear trends at high rates, with slopes and intercepts that directly quantify the saturation functions in the range of negative capillary pressures. The method is similar to the Gupta and Maloney (2016) intercept theory but quantifies entire functions rather than a single point and provides the trends also at low rates, thus using all the information.
Our aim is to demonstrate how pressure drop and oil production at steady state for different water‐injection rates can be used to derive relative permeability and capillary pressure from waterflooding. This is done in three ways. First, synthetic transient waterflooding tests are generated (using a core‐scale simulator), applying the same saturation‐function correlations as assumed in the analytical solution. Then, more‐general correlations are assumed when generating the synthetic data. This is to test the robustness of the analytical solution in producing functions similar to the “true” ones. Finally, we perform a waterflooding experiment in the laboratory on a high‐permeability (3 darcies) Bentheimer sandstone core, altered to an oil‐wet state. Forced imbibition was started at a rate of 0.4 pore volumes (PV) per day, which was increased stepwise after approaching a steady state. Twelve rates were applied, differing overall by a factor of ≈1,000 to yield states governed by capillary forces and advective forces. The results were interpreted using both full history matching of the transient data and matching of the steady‐state data with the analytical solution.
The experimental procedure and model demonstrate that only water relative permeability and capillary pressure determine the steady state during waterflooding, and hence can be estimated accurately. The analytical solution could simultaneously match the trends and magnitude of a steady‐state pressure drop and production with injection rate to give an estimation of the saturation functions. The estimated saturation functions from the analytical solution agreed well with the estimates from full history matching.