Prediction of Capillary Pressure and Relative Permeability Curves using Conventional Pore-scale Displacements and Artificial Neural Networks

Abstract

Traditional network models use simplified pore geometries to simulate multiphase flow using semi-analytical correlation-based approaches. In this work, we aim at improving these models by (I) extending the numerical methodologies to account for pore geometries with convex polygon cross sections and (II) utilizing Artificial Neural Networks (ANN) to predict flow-related properties. Specifically, we simulate fluid displacement sequences during a drainage process in bundles of capillary tubes with randomly generated convex polygon cross-sections. In the beginning, we assume that capillary tubes are fully saturated with water and that they are strongly water-wet. Then, oil is injected to displace water during the primary drainage process. The model calculates threshold capillary pressures for all randomly generated geometries using Mayer-Stowe-Princen (MS-P) method and the minimization of Helmholtz free energy for every pore-scale displacement event. Knowing pore fluid occupancies, we calculate saturations, phase conductances, and two-phase capillary pressure and relative permeability curves. These parameters are then used as input to train an ANN. ANN theories and related applications have been significantly promoted due to the fast increasing performance of computer hardware and inheratively complicated nature of some research areas. Various Artificial Intelligence (AI) applications have been developed specifically for the oil and gas industry such as AI assisted history matching, oil field production and development predictions, and reservoir characterization. The objective of this study is to develop an ANN training and predicting workflow that can be integrated with the conventional pore network modeling techniques. This hybrid model is computationally much faster which is beneficial for large-scale simulations in 3D. It could also be used to improve prediction of flow-related properties in similar rock types. Specifically, we are interested in the training of ANNs to predict threshold capillary pressures and multi-phase flowrates as a function of cross-sectional shapes and wettabilities given for each capillary tube of the bundle. To do so, we have generated multi-phase flow properties for two large datasets consisting of 40,000 and 60,000 capillary tubes each. The predictive capability of the ANN is gauged by performing some quality control steps including blind test validations. We present the results primarily by demonstrating the calculated errors and deviations for any randomly generated bundles of capillary tubes from the aforementioned dataset. We show that generating high-quality training dataset is critical to improving model’s predictive capabilities for a wide range of pore geometries, e.g., shape factors and elongations. Additionally, we demonstrate that feature selection and preprocessing of the input data could significantly impact ANN’s predictions. We analyze a wide range of structures for the ANN models. The Multi-layer perceptron (MLP) Neural Network with three hidden layers is adequate for dealing with the complexity and non-linearity of most of our studied cases. This model is approximately an order of magnitude faster than conventional direct calculations using a personal desktop computer with four cores CPU. Such improvement in the speed of calculations becomes extremely important when dealing with larger models, adding more dimensionality, and/or introducing pore connectivity in 3D.