Annealing Techniques Applied to Reservoir Modeling and the Integration of Geological and Engineering (well Test) Data

Stochastic reservoir models must honor as much input data as possible to be reliable numerical models of the reservoir under study. Traditional simulation algorithms are unable to honor either complex geological/morphological patterns or engineering data from well tests. The technique developed in this dissertation may be used to incorporate such information into stochastic reservoir models. This dissertation develops the application of the optimization methods known as simulated annealing, to stochastic simulation. The essential feature of the method is the formulation of stochastic imaging as an optimization problem with some specified objective function. The additional information to be matched by the stochastic images is built into the objective function. Complex geological patterns and effective properties inferred from well tests may be incorporated into stochastic reservoir models with relatively modest computational effort. Complex geological patterns or spatial features require multivariate spatial statistics (n > 2) in addition to conventional bivariate (n = 2) statistics. By considering selected multivariate spatial statistics it is possible to impose such geological patterns on stochastic images. The effective permeability inferred from a well test constrains the possible spatial distribution of elementary grid block permeability values near the well bore. Once again, it is possible to impose this well test information through an understanding and heuristic quantification of the averaging process near the well bore.