The parameters that govern fluid flow through heterogeneous reservoirs are numerous and uncertain. Even when it is possible to visualize all the parameters together, the complex and nonlinear interaction between them makes it difficult to predict the dynamic reservoir responses to production. A flow simulator may be used to evaluate the responses and make reservoir management decisions, but normally only one deterministic set of parameters is considered, and no uncertainty is associated with the responses or taken into account for the decisions.
This paper introduces the concept of a "quality map," which is a 2D representation of the reservoir responses and their uncertainties. The quality concept may be applied to compare reservoirs, to rank stochastic realizations, and to incorporate reservoir characterization uncertainty into decision making (such as choosing well locations) with fewer full-field simulation runs.
The data points necessary to generate the quality map are obtained by running a flow simulator with a single vertical well completed in all the layers and varying the location of the well in each run to have good coverage of the entire horizontal grid. The quality of the horizontal cell in which the well is located is the cumulative oil production after a long production time.
The geological model uncertainty is captured by generating multiple stochastic realizations and building a quality map for each realization. The quality maps of all the realizations provide a distribution of quality values for each cell of the map grid. A mean quality map can be obtained by taking the expected value for each cell, and a map of quality uncertainty can be obtained by taking the standard deviation of the distribution for each cell.
If a loss function is specified, an L-optimal quality map can be generated by retaining, for each cell, the quality value that minimizes the expected loss. This map allows us to locate wells accounting for the geological uncertainty as well as for the risk profile of the decision maker.
The methodology for building the quality map is presented in detail, and the applications of the map are demonstrated with 50 realistic reservoir models.