Comparison of Stochastic Sampling Algorithms for Uncertainty Quantification

Abstract

Summary History matching and uncertainty quantification are two important research topics in reservoir simulation currently. In the Bayesian approach, we start with prior information about a reservoir (e.g., from analog outcrop data) and update our reservoir models with observations (e.g., from production data or time-lapse seismic). The goal of this activity is often to generate multiple models that match the history and use the models to quantify uncertainties in predictions of reservoir performance. A critical aspect of generating multiple history-matched models is the sampling algorithm used to generate the models. Algorithms that have been studied include gradient methods, genetic algorithms, and the ensemble Kalman filter (EnKF). This paper investigates the efficiency of three stochastic sampling algorithms: Hamiltonian Monte Carlo (HMC) algorithm, Particle Swarm Optimization (PSO) algorithm, and the Neighbourhood Algorithm (NA). HMC is a Markov chain Monte Carlo (MCMC) technique that uses Hamiltonian dynamics to achieve larger jumps than are possible with other MCMC techniques. PSO is a swarm intelligence algorithm that uses similar dynamics to HMC to guide the search but incorporates acceleration and damping parameters to provide rapid convergence to possible multiple minima. NA is a sampling technique that uses the properties of Voronoi cells in high dimensions to achieve multiple history-matched models. The algorithms are compared by generating multiple history- matched reservoir models and comparing the Bayesian credible intervals (p10-p50-p90) produced by each algorithm. We show that all the algorithms are able to find equivalent match qualities for this example but that some algorithms are able to find good fitting models quickly, whereas others are able to find a more diverse set of models in parameter space. The effects of the different sampling of model parameter space are compared in terms of the p10-p50-p90 uncertainty envelopes in forecast oil rate. These results show that algorithms based on Hamiltonian dynamics and swarm intelligence concepts have the potential to be effective tools in uncertainty quantification in the oil industry.