Conditioning geostatistical models to three-dimensional, three-phase flow production data by automatic history matching.

摘要

This work describes the development of a general automatic history matching procedure to generate maximum a posteriori (MAP) estimates and realizations of reservoir model parameters by conditioning to three-dimensional three phase production data. The algorithm is based on fully implicit, three-dimensional, three-phase, variable bubble point black oil flow equations. We are able to estimate gridblock permeability (both horizontal and vertical) and porosity, well skin factor, and three-phase relative permeability curves by conditioning a geostatistical model to multiphase flow production data. Several types of model parameters can be estimated simultaneously. The observed data can be pressure, gas-oil ratio, water-oil ratio, and any combination of these three types of data. An adjoint system of equations for computing the sensitivity coefficients of three-dimensional, three-phase flow production data has been developed and implemented. Using the adjoint solution, we are able to compute the sensitivity of pressure, gas-oil ratio, water-oil ratio to the gridblock permeability and porosity, well skin factor and parameters used to define power law relative permeability curves. By comparison of results with the finite-difference method, we show that the sensitivity coefficients generated by the adjoint method are highly accurate. The advantage of the adjoint method is that the number of linear system solutions is independent of the number of model parameters so this method can be used for large simulation models. We show that the adjoint equation can be directly constructed from the Jacobian matrices computed in a fully implicit reservoir simulator. This approach can handle the problems with large number of model parameters and highly compressible reservoirs. The Levenberg-Marquardt method is applied to minimize the objective functions. The Levenberg-Marquardt method is more robust than regular Gauss-Newton method. Our results indicate that conditioning to more types of data improves the estimates of model parameters and results in a greater reduction in uncertainty. Gas-oil ratio data tend more useful than water-oil ratio data in resolving reservoir model parameters.