Rapid, Stochastic Updating of Reservoir Models to Dynamic Data – An Evaluation of P-Field Approach

Continuous dynamic data such as well flowing bottom-hole pressure carry information that characterizes reservoir heterogeneity. A novel approach to analyze continuous monitoring pressure data and to update reservoir models based on incremental information is presented. First, the pressure transient data is analyzed to identify the size and shape of permeability heterogeneity in the presence of fluctuations in rate and pressure. Unlike the complicated pressure or rate deconvolution algorithms presented in the literature, a simple semi-analytical approach is presented here that attempts to reconstruct the bottom hole pressure response after removing the effect of rate fluctuation. Using the reconstructed pressure profile, estimates of the radius to the boundary of the heterogeneous region and the effective average permeability are obtained by applying a simple optimization procedure for fitting the pressure and pressure-derivative plots. <br> Once the configuration of the reservoir heterogeneity in the vicinity of wells has been identified that information is used to condition high-resolution reservoir models. The conditional probability distribution that characterises the uncertainty in permeability value at any location is perturbed using the dynamic pressure response as conditioning information. The gradual deformation of the conditional probability distribution is carried out within a p-field simulation framework. In the p-field approach, permeability values are sampled from the conditional distributions using a correlated field of random numbers (or uniform probability values). This approach retains the computational efficiency of the traditional gradual deformation algorithm, while at the same time is amenable to modelling non-Gaussian permeability fields that exhibit severe discontinuities such as facies/indicator type distributions. Moreover, since the updated conditional distribution is available in the p-field approach, uncertainty assessment is possible by sampling several realizations from the updated distribution. The application of the proposed method is demonstrated on a realistic 3-D example.<br>