We propose a workflow to reduce initial uncertainty of the reservoir model by incorporating production data. Advanced statistical methods such as sensitivity analysis, Gaussian process response surfaces, sequential experimental design and gradual deformation are combined to produce a very cost effective approach to production data assimilation. In previous works, response surface and experimental design methods have been proven quite effective for uncertainty propagation workflows; however they were only able to deal with continuous and discrete parameters. By using the gradual deformation method we are able to include stochastic parameters such as permeability and porosity, thus avoiding previous limitations. The advantages of using advanced non-parametric response surface methods are highlighted both in obtaining accurate global sensitivity indices and also to apply a full probabilistic inversion approach. Note that both methods generally require several thousands of model runs and are therefore unpractical without using response surface methods. Statistical diagnostics are used to validate the response surface models and adaptive sequential design strategies are proposed to improve their accuracy.
The workflow is applied to production data assimilation of a Brazilian oil field. In a first phase the production history mismatch is analyzed to understand the general behavior of the model as well as to select the uncertain parameters mostly responsible for this mismatch. To perform this phase experimental design and sensitivity analysis techniques are used. In a second phase another objective function is built using only data that seem to be possibly matched using the current model and set of parameters. The new objective function is used in a probabilistic inversion loop to obtain posterior distribution of parameters and to reduce the forecasting uncertainty. The results of the study can then be directly used to obtain reliable probabilistic forecasts. Moreover, posterior distributions of parameters can be utilized to reduce uncertainty ranges in a subsequent study with the updated geological model.