Prediction of Reservoir Variables Based on Seismic Data and Well Observations - Lien Eide, Alfhild; Omre, Henning; Ursin, Bjørn (Journal of the American Statistical Association, 2002)
Offshore petroleum reservoirs are usually explored by acquisition of vast amounts of seismic reflection data and observations along a small number of wells drilled through the reservoirs. The seismic data are indirect measurements of reservoir characteristics and have good spatial coverage but low precision. The well observations are sparse but precise. Information from these sources of data are integrated to characterize the reservoir variables of interest-reservoir porosity in the current study. Critical parameters in the acquisition procedure are unknown and are simultaneously estimated. This process, termed seismic inversion, constitutes a spatial, multivariate, ill-posed inverse problem. The problem is cast in a Bayesian framework with a focus on sampling from the posterior model. High dimensionality, nonlinear components, and unknown parameters in the likelihood model, along with a complex design of the conditioning data, complicate the problem. A fast sequential sampling algorithm containing several parts subject to analytical evaluation is developed under relatively weak, realistic assumptions. Samples of spatial reservoir porosity characteristics can be used to predict and assess uncertainty in the petroleum volume contained in the reservoir. Moreover, porosity is highly correlated with permeability, which represents the fluid flow characteristics. Porosity and permeability are the critical factors in determining and optimizing the future production from petroleum reservoirs. The study is based on data from the Troll field in the North Sea.