Hybrid Mathematical Modelling of Three-Phase Flow in Porous Media: Application to Water-Alternating-Gas Injection

Abstract Machine learning algorithms are extensively used to reduce the complexity of applied problems in various fields, including energy. Accurate prediction of the performance of water alternating gas (WAG) as an enhanced oil recovery (EOR) process is of great importance in the optimal management of the hydrocarbon resources. In the current work, a hybrid mathematical model is proposed for the near-immiscible WAG process. We use data-driven sub-models, including least square support vector machine (LSSVM) and adaptive neuro-fuzzy inference system (ANFIS) in series with an empirical model (EM) and a first principle model (FPM) to study three-phase flow in porous media. The LSSVM and ANFIS sub-models predict the two-phase water-oil, gas-oil, and gas-water relative permeabilities. The outputs from these models are supplied to the empirical models (EMs) to estimate the three-phase relative permeabilities for oil, gas, and water phases. The model developed using LSSVM shows a better prediction performance in estimating the relative permeabilities, compared to that using ANFIS. The relative importance parameter analysis shows that for the LSSVM sub-model, water saturation is the most influencing input parameter for the gas-water and oil-water systems while for the gas-oil system, gas saturation is the most important input parameter. Using the models proposed in this work, some hybrid models are developed to forecast the ultimate recovery factor (RF) in the testing phase. The predicted ultimate RF values are 92.0%, 91.6%, and 82.9% for the correlation-based EM-FPM, LSSVM-EM-FPM, and ANFIS-EM-FPM hybrid models, respectively, in comparison to the measured ultimate RF value of 93.6% after three cycles of water- and gas-injection. Among the proposed hybrid models, the LSSVM-EM-FPM model significantly removes the non-linearity of the two-phase relative permeabilities. In general, the LSSVM-EM-FPM hybrid model possess the same level of accuracy as that of the EM-FPM hybrid model, but with significantly less model complexity and non-linearity. Thus, the LSSVM-EM-FPM hybrid model can be used in demanding applications such as optimization and control of this oil recovery process, leading to a better resource management.