Simultaneous inversion of permeability, skin and boundary from pressure transient test data in three-dimensional single well reservoir model

This study presents a novel approach for simultaneous inversion of the key reservoir parameters like horizontal permeability, vertical permeability, skin, and boundary distances for spatial distribution across the grid cells in a 3D single well reservoir model (SWRM). These parameters are first estimated from the standard pressure transient analysis of well test pressure and rate data, which also act as a priori for the inverse problem. A field-worthy layer cake geological model is prepared based on the prior information obtained from pressure transient analysis, followed by a sequential flow simulation of field well test operation. The simulation results provide the model pressure versus rate data as the synthetic data for this study. A cost function is defined incorporating the well test pressure data and model pressure data, which would determine the convergence. The inversion process is to optimize the spatial distribution of reservoir parameters to minimize the difference between the measured pressure transient data and the modelled one, which is obtained from the multiphase fluid flow simulator that solves the implicit black-oil fluid-flow diffusivity equations at every step. A Gauss-Newton (GN) inversion scheme is used for the inversion. The reliability of inversion results depends on the accuracy of priori reservoir parameters fed to the solver, which can be refined if required through uncertainty parameter optimization (UPO). This approach helps to obtain a faster and reliable update of reservoir parameters in a layer cake homogeneous geomodel, hereby introducing the required heterogeneity. This increases the confidence and reliability of a geomodel, which is further used for various production prediction strategies.