A Functional Data Analysis Approach to Surrogate Modelling in Reservoir and Geomechanics

Abstract

Generally computational costs of reservoir and geomechanical models can be particularly high, making uncertainty evaluation and risk assessment difficult to perform. To overcome this problem, several approximation methodologies based on surrogate modelling have been developed and are commonly adopted. On the other side, Functional Data Analysis is a well-established technique in statistics but its application in reservoir uncertainty evaluation is less common. We present here a functional data analysis technique for reservoir and geomechanical models. The proposed approach, combines surrogate modelling and Functional Data Analysis to build, for a definite set of input values in the uncertainty space, a functional interpolation whose objects are functions representing the output variables in a full range of times or in a given time-space domain of interest. The methodology is particularly suited for geomechanical uncertainty assessment where the output variables are characterized by a relatively smooth behaviour and the computational cost for a direct Monte Carlo approach is very high. The methodology is first illustrated with a geomechanical uncertainty characterization problem and then through a real reservoir application. In low-dimensional uncertainty characterization studies, the proposed method makes possible to perform reliable time-space dependent risk assessment with a very limited computational cost.