Adjoint equations for three-dimensional, three-phase flow problems are developed and implemented to calculate the sensitivity of production data to permeability fields and well skin factors. Typically, the development of adjoint equations is rather tedious, but the formulation given here makes the development and numerical solution of adjoint equations straightforward. The procedure for calculating sensitivity coefficients is coupled with a fully-implicit finite-difference simulator to develop an automatic history matching procedure. Even if one does not wish to fully automate history matching, sensitivity coefficients are useful for understanding the physics that control three-dimensional multiphase flow and the influence of local reservoir properties on production data. Procedures to estimate the value of particular types of data (pressure, producing gas-oil ratio and water-oil ratio) for reducing the uncertainty in estimates of reservoir properties are applied and discussed.

You can access this article if you purchase or spend a download.