Inverse modeling of the natural state of geothermal reservoirs using adjoint and direct methods

Abstract

The application of the adjoint and direct methods to inverse modeling of the natural state of a convective geothermal system is discussed. The methods have been applied to other subsurface modeling problems, but they have seldom been used in the geothermal context and not at all for high-enthalpy, two-phase systems.There are two important features of the natural state problem that make it an interesting challenge for inverse modeling. The first is that good downhole temperature measurements are typically available from 1 to 2 km deep wells, scattered over a large area of the geothermal system. Secondly, the geological structure of the system controls how the convective plume develops over geological time and thus downhole temperatures can be used to infer the large-scale permeability distribution. This interaction of large-scale, heat induced convection and geological structure determines the size and shape of hot geothermal systems and makes inverse modeling of their natural state particularly useful, no matter what method is used.Another important issue with natural state geothermal modeling is the challenge of the computational task involved. Most previous inverse modeling studies of the natural state of high-enthalpy geothermal reservoirs have used the derivative-based Levenberg-Marquardt method with derivatives of model outputs evaluated by finite differences. This is a very time-consuming process since many lengthy forward simulations of a transient approach to the steady natural state are required. In the present study adjoint and direct methods are used for the efficient evaluation of derivatives and prove to be very effective.A synthetic two-dimensional vertical slice model is used to test the applicability of the adjoint and direct methods. The results show that the methods offer much faster inversions compared to those based on finite differencing.