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Multiphase flows through reservoir rocks are a universal and complexphenomenon. Relative permeability is one of the primary determinants inreservoir performance calculations. Accurate estimation of the relativepermeability is crucial for reservoir management and future production. In thispaper, we propose inferring relative permeability curves from sparse saturationdata with an ensemble Kalman method. We represent these curves through a seriesof positive increments of relative permeability at specified saturation values,which guarantees monotonicity within, and boundedness between, 0 and 1. Theproposed method is validated by the inference performances in two syntheticbenchmarks designed by SPE and a field-scale model developed by Equinor thatincludes certain real-field features. The results indicate that the relativepermeability curves can be accurately estimated within the saturation intervalshaving available observations and appropriately extrapolated to the remainingsaturations by virtue of the embedded constraints. The predicted well responsesare comparable to the ground truths, even though they are not included as theobservation. The study demonstrates the feasibility of using ensemble Kalmanmethod to infer relative permeability curves from saturation data, which canaid in the predictions of multiphase flow and reservoir production.

Inference of relative permeability curves in reservoir rocks with ensemble Kalman method