Smart Proxy Modeling of a Fractured Reservoir Model for Production Optimization: Implementation of Metaheuristic Algorithm and Probabilistic Application

Numerical reservoir simulation has been recognized as one of the most frequently used aids in reservoir management. Despite having high calculability performance, it presents an acute shortcoming, namely the long computational time induced by the complexities of reservoir models. This situation applies aptly in the modeling of fractured reservoirs because these reservoirs are strongly heterogeneous. Therefore, the domains of artificial intelligence and machine learning (ML) were used to alleviate this computational challenge by creating a new class of reservoir modeling, namely smart proxy modeling (SPM). SPM is a ML approach that requires a spatio-temporal database extracted from the numerical simulation to be built. In this study, we demonstrate the procedures of SPM based on a synthetic fractured reservoir model, which is a representation of dual-porosity dual-permeability model. The applied ML technique for SPM is artificial neural network. We then present the application of the smart proxies in production optimization to illustrate its practicality. Apart from applying the backpropagation algorithms, we implemented particle swarm optimization (PSO), which is one of the metaheuristic algorithms, to build the SPM. We also propose an additional procedure in SPM by integrating the probabilistic application to examine the overall performance of the smart proxies. In this work, we inferred that the PSO had a higher chance to improve the reliability of smart proxies with excellent training results and predictive performance compared with the considered backpropagation approaches.

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have to rely on suitable approximation techniques such as the least-squares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wisely selected simulations and to process their output further to obtain a risk-dependent proxy function of the loss. In this paper, we present and analyze various adaptive machine learning approaches that can take over the proxy modeling task. The studied approaches range from ordinary and generalized least-squares regression variants over generalized linear model (GLM) and generalized additive model (GAM) methods to multivariate adaptive regression splines (MARS) and kernel regression routines. We justify the combinability of their regression ingredients in a theoretical discourse. Further, we illustrate the approaches in slightly disguised real-world experiments and perform comprehensive out-of-sample tests.