Identifying Injector-Producer Relationships in Waterflood Using Hybrid Constrained Nonlinear Optimization

Abstract A key barrier to optimal field management, i.e., maximizing oil production and reducing operational cost, is the understanding of underlying structure of the field, which continuously changes over time. Analyzing readily available injection and production data to identify injector-producer relationships (IPRs) offers a convenient way to this understanding. The capacitance-resistive model (CRM) provides an intuitive and straightforward way to characterize IPRs through production and injection rate fluctuations. However, it requires a large number of model parameters. The number of parameters increases quadratically with number of production and injection wells in the reservoir. For fields consisting of hundreds of wells identifying IPRs among the wells is challenging. Moreover, there is no analytical solution for solving the parameter values due to the nonlinear time constant parameters of the CRM and the constraints. This paper presents a new method, a hybrid constrained nonlinear optimization (HCNO), for estimating the optimal parameter values of a nonlinear predictive model. HCNO is optimization-based algorithm such that it estimates the optimal values of the model parameters satisfying the constraints. HCNO separates the connectivity and time constant parameters of CRM then uses two different optimization algorithms. A constrained nonlinear optimization algorithm is applied to estimating the time constant parameters, and subsequently the connectivity parameters are estimated by a constrained linear optimization algorithm with the estimated time constant parameters. The coupled optimization is performed at each iteration, which leads to faster convergence. HCNO is tested on several synthetic oil fields. The result showed that the search time and the prediction error by HCNO were significantly less than those of estimating the parameters as a whole by solely constrained nonlinear optimization. The identification of IPRs by the optimal parameter estimation will help field engineers’ decision making process in optimizing waterflooding.