Hysteresis of transport properties like relative permeability (Kr) can lead to computational problems and inaccuracies for various applications including CO2 sequestration and chemical enhanced oil recovery (EOR). Computational problems in multiphase numerical simulation include phase labeling issues and path dependencies that can create discontinuities. To mitigate hysteresis, modeling Kr as a state function that honors changes in physical parameters like wettability is a promising solution. In this research, we apply the state function concept to develop a physics-informed data-driven approach for predicting Kr in the space of its state parameters.

We extend the development of the relative permeability equation-of-state (kr-EoS) to create a predictive physics-based model using Artificial Neural Networks (ANN). We predict kr as a function of phase saturation (S) and phase connectivity (χ^), as well as the specific Sχ^ path taken during the displacement, while maintaining other state parameters constant such as wettability, pore structure, and capillary number. We use numerical data generated from pore-network simulations (PNM) to test the predictive capability of the EoS. Physical limits within Sχ^ space are used to constrain the model and improve its predictability outside of the region of measured data.

We find that the predicted relative permeabilities result in a smooth and physically consistent estimate. Our results show that ANN can more accurately estimate kr surface compared to using a high-order polynomial response surface. With only a limited amount of drainage and imbibition data with an initial phase saturation greater than 0.7, we provide a good prediction of kr from ANN for all other initial conditions, over the entire Sχ^ space. Finally, we show that we can predict the specific path taken in the Sχ^ space along with the corresponding kr for any initial condition and flow direction, which makes the approach practical when phase connectivity information is not available. This research demonstrates the first application of a physics-informed data-driven approach for prediction of relative permeability using ANN.

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