Numerical Experience with an Ensemble-Based Method for Constrained Waterfooding Optimization

Juan Alberto Rojas Tueros¹; Bernardo Horowitz¹; Ramiro Brito Willmersdorf¹

¹ Universidade Federal de Pernambuco

doi:10.20906/CPS/CILAMCE2015-0498

Resumo

An implementation of an ensemble-based method for constrained waterflooding optimization is presented. Net present value (NVP) is maximized subject to constraints on total production and injection rates. Tuning of algorithm parameters is discussed. An ensemble-based method is implemented for waterflooding optimization. The objective function is maximized using the sequential quadratic programming algorithm. Control variables are the flow rates of the wells. An approximate gradient is computed based on the covariance matrix of control vectors of ensemble realizations as well as the cross-covariance of the corresponding NVP values obtained through simulations of the realizations. The simulations are performed in parallel. The realizations contained in the ensemble are perturbations of previous controls during the optimization process. Filters were developed to enforce feasibility of realizations with respect to problem constraints. The proposed methodology was applied to a reservoir model with 12 wells and 6 control cycles. The optimization problem is subject to constraints on total production and injection rates. We conducted an extensive parametric study the assess influence of the various algorithmic parameters. Ensemble size is one of the major parameters studied since it is essential to use small number of realizations in the ensembles. Completion controls are a priori assumed to be temporally correlated. Spherical and Gaussian correlation functions were tested. Controls perturbation sizes varied from 5% to 15%. Also studied was the imposition or not of feasibility on the realizations. It was found that results obtained using an ensemble size of 5.5% of the total number of controls was only 3.4% lower than that obtained with an ensemble twice as large. The Gaussian correlation function works better for small ensembles, with or without the imposition of feasibility, while the spherical function has a better performance for larger ensembles with feasibility imposed on the realizations. This work through par

Palavras-chave: Waterflooding optimization; Ensemble-based methods; Constrained optimization