Bayesian reservoir simulation

Reservoir reserve can be estimated from different methods, i.e. analogy, volumetric, decline curve analysis, material balance and reservoir simulation. This technique may use two methods of calculation: deterministic or stochastic. Deterministic method uses a single value for each parameter, stochastic method uses a probability model for each parameter and a simulation is used to generate the reserve distribution. Reservoir simulation applies the techniques of modeling to the analysis of the behavior of petroleum reservoir system, and refers to the hydrodynamics of flow within the reservoir. The basic of reservoir model consists of the partial differential equations which governs the flow of all fluid in the reservoir. The simulator cannot be used to predict the performance of a reservoir unless the parameter built into it describe the flow of the reservoir system. The process of modifying the existing model parameter until a reasonable match is made with the observations is called history matching, i.e., parameter estimation in reservoir models. An approach based on Bayesian methodology was proposed, where the reservoir model and parameters were updated sequentially in time, using information contained in observations from production wells. This paper addresses the issue Bayesian sequential estimation in reservoir simulation for history matching. The method consist of two steps, i.e. forecast (prior) and update (posterior). The forecast is computed using the model solution (reservoir simulation) to predict the state from time t - 1 to t. In the update step, the state forecast is updated by considering the mismatch between measurements and predictions. A single phase flow modeling is discussed . Simulation study for simple radial reservoir model shows that the Bayesian methodology can be used to history match the rese