Use of solution error models in history matching

Uncertainty in reservoir models can be quantified by generating large numbers of history-matched models, and using those models to forecast ranges of hydrocarbons produced. The need to run large numbers of simulations inevitably drives the engineer to compromises in either the physics represented in the reservoir model, or in the resolution of the simulations run. These compromises will often introduce biases in the simulations, and the unknown reservoir parameters are estimated using the biased simulations, which can lead to biases in the parameter estimates. Solution error models can be used to correct for the effects of the biases. Solution error models work by building a statistical model for the differences between fine and coarse simulations (or between full physics and reduced physics simulations) using data from simulations at a limited number of locations in parameter space. The statistical model then produces estimates of the error elsewhere in parameter space; these estimates are used to correct the effects of the coarse model biases. In this work, we apply a solution error model to material balance calculations. Material balance is frequently used in reservoir engineering to estimate the initial oil in place. However such models are very simple, treating the reservoir as a tank and allowing instantaneous equilibration of fluids within the tank. The results of material balance simulations will therefore not be consistent with multi-cell reservoir simulations. We use a model based on Teal South Reservoir in the Gulf of Mexico to demonstrate how an error model can correct a material balance model to the accuracy of a reservoir simulation.