Using Least Square Support Vector Machines to Approximate Single Phase Flow

Abstract

Abstract Data driven modelling has earned more and more attention in oil and gas industry, but most of these models have been applied to make decision or estimate correlation between properties. This paper proposed an approach to simulate the reservoir without reservoir simulation process. The complete reservoir model consists of partial differential equations, boundary and initial conditions, expresses the information of the reservoir behaves. The Least Square Support Vector Machines (LS-SVM) is applied to train the flow model with the feed of the partial differential equations, whereas the initial and boundary conditions as act as constraints of an optimization problem. Only the kernel of the support vector machines is used to demonstrate the flow model without explicitly computing the feature mapping function. Specific modification is required to deal with Neumann boundary conditions since the derivatives of the kernel function do not necessarily satisfy the Mercer theorem. Artificial Neural Network (ANN) is presented to modify LS-SVM formulation to Single phase flow problem. With the advent of artificial intelligence and data science the method becomes particularly interesting due to the expected essential gains in the execution speed.