Forward and Adjoint Modeling of Coupled Fluid Flow, Heat Transport, and Deformation in Geothermal Reservoirs

Geothermal reservoirs are governed by tightly coupled interactions between fluid flow, heat transport, and deformation of the host rock, posing significant challenges for numerical modeling and inversion. Capturing these processes is essential for understanding reservoir evolution, permeability development, and fluid circulation in high‐enthalpy systems. We present a forward and inverse modeling framework designed to simulate fluid migration in deforming, porous media under geothermal conditions.

The framework is implemented in the Julia programming language, exploiting its high performance and native support for automatic differentiation (AD). Forward simulations are solved on a staggered-grid, using an implicit finite-difference discretization where the jacobian matrix is assembled using AD and accelerated by automatic sparsity pattern detection. The model solves Darcy flow coupled to incompressible Stokes deformation and includes visco-elasto-viscoplastic rheology with both shear and tensile yielding, enabling the simulation of fracture-like permeability enhancement driven by thermo-mechanical stresses.

AD enables efficient adjoint-based sensitivity analysis, substantially reducing the computational cost of parameter estimation compared to traditional approaches. The resulting gradients provide the foundation for gradient-based optimization and adjoint inversions of geothermal reservoir properties. We demonstrate the capabilities of the framework through representative numerical experiments relevant to geothermal systems, illustrating its ability to capture the coupled thermal, hydraulic, and mechanical processes that control reservoir dynamics.