Differential sensitivity analysis and multi-variant simulation of formation pressure and temperature in heterogeneous media

Abstract

Methodology of differential sensitivity analysis and sensitivity-based aggregate simulation for formation pressure, temperature and fluid flow is developed here. It is aimed at estimation of variations of formation pressure, temperature and velocity field for fluid flow due to variations in the properties of the medium and fluids in the pores. It includes the use of the so-called “sensitivity functions” defined as partial derivatives of the formation pressure and temperature with respect to parameters of the rock and fluids in the pores. It is shown that the sensitivity functions are defined by the same system of equations as formation pressure and temperature fields with the right-hand side of the equations dependent on the type of sensitivity function.There are several important applications of the differential sensitivity analysis and sensitivity functions:(1)Sensitivity functions allow to estimate, under certain conditions, the magnitude of variation of formation pressure and temperature fields1(2)Using sensitivity function-based technique, it is possible to partially decouple the system of equations for formation pressure and temperature fields under conditions of slow variations of temperature or pressure in time.(3)Differential sensitivity analysis may serve as a basis for calculation of multiple versions (aggregate simulation) of formation pressure and temperature fields due to various changes in the parameters of the medium and pore fluids.