Modelling temperature dynamics of the SAGD process in an oil reservoir by the discovery of parametric partial differential equations

Abstract

AbstractMany chemical and industrial processes are complex, and the dynamics of such processes cannot be explained using a partial differential equation (PDE) or a system of PDEs with constant coefficients. Parametric PDEs, that is, PDEs with their coefficients varying across time or space, are utilized for this purpose. The non‐availability of data at all spatial locations and partially available process knowledge add to the complexity of modelling such processes. This paper proposes a framework to discover parametric PDEs using data‐driven and hybrid modelling approaches with the temperature dynamics of steam‐assisted gravity drainage (SAGD) process in an oil reservoir as the system under study. We utilize an ensemble of 200 realizations of the temperature dynamics generated using the variogram for the PDE discovery. Permeability, which is one of the oil reservoir's petrophysical properties, is used to develop the hybrid models. We infer that utilizing partial process knowledge aids in improving the model's accuracy.