Application of PSO and MOPSO to Gas Injection Analysis
Authors: Kato Yoshitake , Okano Hirofumi , Takahashi Satoru 
Published: May 2016

Abstract
History matching of the numerical model was conducted in a heterogeneous sandstone reservoir where the hydrocarbon gas injection inter-well test was implemented to confirm the injectivity and the incremental oil effect prior to the expansion to full field operation.
To decrease the degree of the misfit between simulated and measured values, some of the model parameters were calibrated using one of the stochastic sampling algorithms, Particle Swarm Optimization (PSO). However, it was difficult to lead all the misfit components of a pair of production wells to a good matching quality simultaneously. These two wells observed gas-breakthrough, but they seemed to show the trade-off of matching accuracy between one component and the others.
In order to overcome the difficulty in the conventional single-objective optimization method above, PSO with the principle of multi-objective optimization, MOPSO, was applied. Multi-objective optimization algorithms are useful to find many "pareto solutions", which represent the models that are not inferior in every set of objective functions to any other models. Therefore, engineers can compare multiple history-matched models in "pareto solutions". The aim of this study is to demonstrate the MOPSO method for history matching of a reservoir model of the real field.
MOPSO helped us find a lot of good models as the "pareto solutions", including ones whose GOR matching accuracy of a well were improved dramatically, which had been difficult with single-objective PSO. The key was which objective functions should be grouped into a set or which should be handled individually. Also, the analysis of each model in the "pareto solutions" provided the understanding about the relationship between matching accuracy of individual wells and the model parameters.
Throughout this study, MOPSO was found an effective methodology especially for difficult history matching problems. Multi-objective optimization algorithms have the high potential for the application to various types of optimization studies including the selection of reservoir development scenarios.

1. Introduction
A variety of optimization algorithms have been applied to automated history matching of numerical models of reservoirs for parameter sampling in order to make that process more easily and more efficiently. Input values to parameters should be sampled to find global optimum position in the parameter space quickly by avoiding the convergence to local optimum areas. This paper introduces an application case of one of the algorithms for stochastic sampling, Particular Swarm Optimization (PSO) algorithm (e.g., Mohammed et al, 2009; Okano, 2013).
About the PSO algorithm, some studies have been reported in petroleum industry. For example, Mohamed et al. (2009) investigated the efficiency of three stochastic sampling algorithms, Hamiltonian Monte Carlo (HMC) algorithm, PSO algorithm and the Neighbourhood Algorithm (NA), and found that PSO tended to concentrate sampling more in the low misfit regions and it was able to obtain a good history match in fewer iterations than NA for the example case although the behavior of these algorithms were likely to depend on the algorithm parameter setting.