A new approach combining Karhunen-Loéve decomposition and artificial neural network for estimating tight gas sand permeability

The Karhunen-Loéve (KL) decomposition, known for its wide applications in scientific problems for data compression, noise filtering, and feature identification, is used to determine an intrinsic coordinate system, or eigenfunctions, that best represents a data set. Projections of the data set onto these eigenfunctions reduces the data set to a set of data coefficients. Processing the data coefficients of the most energetic eigenfunctions through an artificial neural network (ANN) is found to enhance capturing the hidden complex relationships among the data variables. pproach is demonstrated using tight gas sand data to estimate permeability from effective porosity, mean pore size, and mineralogical data. For an arbitrary neural network architecture, combination of KL decomposition and ANN is found to be superior over ANN alone. This combination of two powerful multivariate analysis tools not only correctly estimates the permeability but also eliminates iterative procedures needed for optimizing the neural network topology.