Modeling of Relative Permeability Hysteresis Using Limited Experimental Data and Physically Constrained ANN

We developed a relative permeability (k_r) model using an artificial neural network (ANN) that can simultaneously fit one or more drainage and imbibition experimental scans while also predicting relative permeability and residual saturations for other scans. The ANN model uses saturation and phase connectivity and is constrained to giving continuous and physical values for any hysteresis path. The new model can estimate continuous k_r values even when saturations move outside residual saturation limits owing to vaporization or solubilization. To demonstrate the approach, we fit one measured drainage and imbibition k_r curve from gas–water experimental data to develop contours of k_r in saturation-connectivity space. Relative permeability is then predicted as paths, described by simple functions, are traversed. The results show that residual saturations vary automatically as small k_r values are encountered and increase with increasing initial saturation without the use of Land’s model. The ANN model simultaneously fits all experimental data, unlike current empirical Corey or hysteresis models. Once tuned, the ANN model accurately predicts other measured hysteresis scans not used in tuning.