Estimation of well test parameters using global optimization techniques

Well test analysis is used to estimate relevant well and reservoir parameters such as permeability, skin factor, wellbore storage coefficient and external reservoir radius. The analysis has shifted from traditional type-curve matching to the use of nonlinear regression. The problem with this method is that nonlinear regression is a local search algorithm that yields locally-optimal estimates of the unknown well and reservoir parameters. Such local estimates are often found in the vicinity of the initial guess. Global optimization techniques have the ability to jump over local optimal points in their search for the best solution in the problem space. Thus, these algorithms have a higher probability of finding the global optimum values of the unknown parameters, albeit, there is no guarantee that such values would be found. In this work, we study the use of some recently-developed global optimization techniques to estimate well test parameters such as average reservoir permeability (k), skin factor (s), wellbore storage coefficient (C), drainage radius (re), etc. Three global optimization algorithms; covariance matrix adaptation evolution strategy (CMA-ES), differential evolution (DE) and particle swarm optimization (PSO); were used to estimate several well test parameters in homogeneous, radial-composite and naturally-fractured reservoirs. The performances of these algorithms were compared to that of the Levenberg-Marquardt (LM) algorithm. Comparison was done in terms of effectiveness and reliability. Results show that DE has the best performance while the LM has the worst performance in estimating the parameters of the models considered.