Combined Natural State and History Matching Using the Adjoint or Direct Sensitivity Method

Abstract

Gradient based inversion of high-enthalpy geothermal reservoir models is a demanding task even for just a handful of model parameters. Moreover, as more parameters are included the inverse process becomes slower and parameter uniqueness is a concern. These issues can, nevertheless, be lessened by using appropriate mathematical tools to obtain geologically sound and well calibrated models within a reasonable amount of time.
For highly parameterized models, parameter reasonableness can be imposed by choosing an appropriate regularization scheme for the inversion. Furthermore, the derivatives of model outputs needed for gradient based inversion can be found accurately and at a low computational cost using either the adjoint or direct sensitivity methods. Using a synthetic vertical slice model, we demonstrate these methods for the inverse problem of simultaneously matching downhole natural state temperatures along with history matching of production pressure and enthalpy data. The adjoint and direct methods were found to be reliable and computationally faster than the finite differencing approaches predominantly used in geothermal modelling.