Reservoir uncertainty description via petrophysical inversion of seismic data

Hydrocarbon reservoir characterization commonly combines seismic, petrophysical, and well-log information in a variety of procedures. As an inference problem, this combination can be formulated in a unified inverse framework, reducing the bias of nonlinear relationships among intermediate variables and providing a comprehensive calculation of uncertainties at final estimates of the medium parameters. In addition, the unified formulation leads to the joint estimation of reservoir and medium elastic properties as well as related parameters of interests. This problem is formulated from a set of continuous variables that commonly characterizes the reservoir (total porosity, shale volume fraction, and water saturation), which can be related to the medium mechanical properties with a petrophysical model calibrated to the specific setting of the reservoir and target stratum. The joint model property configuration is related to the observed seismic data via Zoeppritz incidence-angle-dependent reflectivity and convolution with a source wavelet for each CDP gather. Data and calibrated information are combined in a posterior probability density of the model parameters that is evaluated with a sampling approach, using a Markov-chain Monte Carlo algorithm. From a large number of realizations, one can calculate expected values and full marginal probability distributions for reservoir properties and elastic properties. The method is illustrated with the estimation of reservoir parameters at a gas reservoir presenting a Class 2 AVA response, with focus on the estimation of water saturation. The calculated saturation probability distributions show coherent results with the known saturation at various well locations.