Summary Pressure transient analysis (PTA) is a well-established tool for reservoir characterization based on analytical or semi-analytical solutions. It helps quantify large-scale reservoir properties like permeability, boundaries, and compartmentalization through the analysis of data collected during pressure tests, such as drillstem tests (DSTs). However, traditional PTA methods struggle with noisy data, quantification of model parameter uncertainties, and the nonuniqueness inherent in inverse problems, which are poorly handled by prevalent gradient-based optimization methods used for parameter estimation in commercial software. Bayesian data assimilation techniques, such as the ensemble smoother with multiple data assimilation (ES-MDA), can address these limitations. We applied ES-MDA for the probabilistic parameter estimation of an analytical model based on the method of images, a common technique for analyzing DSTs in channel sand reservoirs. Using synthetic and field data sets, we achieved the following: (i) automated history matching of the pressure history, (ii) estimation of the posterior conditional distribution (and the uncertainty range) of permeability, skin, boundary distances, channel width, and initial pressure, which facilitates integration into geological models compared with the conventional use of single-point estimates, (iii) definition of a geometric locus of parameter combinations honoring the observed pressure history, thus addressing the nonuniqueness of the inverse problem, and (iv) processing of the entire pressure history (flowing and shut-in periods) to estimate the distribution of model parameters without relying on the standard use of log-log or semilog analyses of well shut-ins, which are susceptible to wellbore effects.
Kubota et al. (Sun,) studied this question.