Determining Identifiable Parameterizations for Large-scale Physical Models in Reservoir Engineering

Abstract

In this paper identifiable parameterizations are determined for models of flow in porous media as applied in the field of petroleum reservoir engineering. Starting from a large-scale, physics-based model parameterization with an extensive parameter space, the best identifiable reduced dimensional parameterization is constructed. This is achieved through the development of an analytical expression for the (finite-time) information matrix of the problem. It is shown that the information matrix can be expressed in terms of controllability and observability properties of the model and the sensitivity of the state space matrices w.r.t. the parameter vector. A reduced dimensional subspace is then obtained after a singular value decomposition of the information matrix, leading to the use of basis functions (spatial patterns) in the original parameter space. The approach is applied to two reservoir models: a siso model with 49 parameters and a mimo model with 441 parameters.