Using Karhunen–Loéve decomposition and artificial neural network to model miscible fluid displacement in porous media

Abstract

In this paper, we describe an approach to model fluid displacements in porous media that combines two powerful techniques, namely Karhunen–Loéve (KL) decomposition and artificial neural networks (ANNs). The KL decomposition, for data compression and feature identification, is used to extract coherent structures or eigenfunctions using fluid concentration maps obtained from fine-mesh numerical simulations of miscible fluid displacements of oil by solvent in a two-dimensional vertical cross-section. Twenty KL eigenfunctions that capture 98.8% of the total energy are extracted. Corresponding data coefficients are constructed by projecting the fluid concentration maps of the numerical simulations onto the KL eigenfunctions. Processing these data coefficients through an ANN is found to be a powerful tool in predicting the fluid displacements of the fine-mesh numerical simulations without actually performing these simulations.