Grid-Based Inversion Methods for Spatial Feature Identification and Parameter Estimation from Pressure Transient Tests

Abstract

Abstract We present and compare three different grid-based inversion methods for estimation of formation parameters and spatial geological feature identification based on pressure transient test (PTT) data from multiple-well locations. The first and second methods employ efficient adjoint schemes to determine the gradient of the objective functions resulting in the most likely set of reservoir parameters and an ensemble of updated realizations of the parameters, respectively. The second method is based on the Langevin equation. The third method uses ensemble Kalman filtering (EnKF) for data assimilation, in which the outcome is an ensemble of updated parameter realizations. These three methods use a grid-independent prior model (in view of the limited prior knowledge of the system expected to be available), described by as few parameters as possible, and consider a non-uniform grid with the highest resolution near the wells. With these methods, the existence of and location of many sub- seismic features such as strong spatial permeability variations, faults, fractures and pinch outs may be determined using exploration and production data. Such features may not be known a priori, particularly in the exploration of heterogeneous carbonate reservoirs. We examine each method considering the degree of prior information required, the computational overhead and the applicability to the reservoir characterization workflow. Our results indicate that the first method provides a good history match to the observed PTT data and is suited for the early exploration phase of the reservoir. However, the parameters must be convolved with the smaller scale data to produce multiple realizations away from the implausibly smooth most-likely solution. The observed PTT data lies within the ensemble of predicted pressures in the EnKF and Langevin-based methods which are both applicable to probabilistic workflows where uncertainty is treated rigorously. However, EnKF seems to be computationally more efficient than the Langevin approach.