Sammendrag
Over the last decades several EOR methods have emerged, and corresponding models have been developed and implemented in increasingly more complex simulation tools. In this paper we present methodology and mathematical tools for optimizing and quantifying the value of EOR strategies, such as polymer, smart water or CO2. The developed methodology is demonstrated for polymer injection on medium to highly heterogeneous synthetic reservoir models with different complexity. The purpose of the work is to improve the understanding of the actual benefit of EOR methods, and to provide methodology that quickly allows users to find optimal production strategies that maximize the net present value (NPV).
In this work, the control variables for the optimization problem are polymer concentration and water injection rates for each injecting well, and oil production rates or bottom hole pressures for the producing wells, over the exploration period. Each control variable is constrained with given production limitations. To account for the uncertainty in the reservoir model, an ensemble of geological realizations is considered, and a robust ensemble-based approximate gradient method (EnOpt) is utilized. The gradient is approximated using a sample of control vectors, drawn from a Gaussian multivariate distribution with known mean and covariance. The covariance matrix is defined so that the control variables of the same well is correlated in time. The mean is updated using a preconditioned gradient ascent method with backtracking until an optimum is found.
The presented method is tested on three different synthetic reservoirs: a 2D five-spot field pattern with grid dimension 50×50×1, a 3D field provided by Equinor (the Reek field with dimension 40×64×14), and a 3D field provided by TNO (the OLYMPUS field with dimension 118×118×16). The first two fields have three phases (water, gas, and oil) and the third field has two phases (water and oil). For each case we find the optimal well controls for polymer flooding and then compared with convectional optimized continuous water flooding. The reservoir fluid flow is simulated using the Open Porous Media (OPM) simulator. However, it is worth noting that the optimization method is independent of the reservoir simulator used. Important findings of this study are the feasible control strategies for
polymer EOR methods leading to an increased NPV, and comparison of the economic values for optimized polymer and traditional water flooding for the examples considered.
Vis fullstendig beskrivelse