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Mathematical and Numerical Modelling of Process-Structure Interaction in Fractured Geothermal Systems

Periodic Reporting for period 2 - MaPSI (Mathematical and Numerical Modelling of Process-Structure Interaction in Fractured Geothermal Systems)

Reporting period: 2023-02-01 to 2024-07-31

In the development and production of high-temperature geothermal resources, large induced gradients in pressure and temperature during injection operations result in complex, coupled dynamics. This includes boiling of geothermal fluids and deformation of the fractured rock. The interaction of coupled processes with changes in formation structure related to deformation and propagation of fractures is currently not well understood. This provides a core motivation as well as challenging test cases for the mathematical and numerical developments in the MaPSI project. The MaPSI project has been funded by the ERC to establish mathematical models and simulation technology that assess subsurface process-structure interaction in geothermal systems during hydraulic and thermal stimulation.

The project aims to develop pioneering mathematical and numerical models that simulate multiphase flow and phase-change in thermo-poroelastic media with deforming and propagating fractures. Through this approach, MaPSI seeks to advance expertise in development and production of high-temperature geothermal systems, knowledge is crucial to promote sustainable resource exploitation.

MaPSI has as its main objective to provide mathematical models and simulation technology required to assess subsurface process-structure interaction in the context of hydraulic and thermal stimulation in development and production of high-temperature geothermal resources.

This will be achieved by a highly novel and timely research programme which will:
- Combine new techniques with recently developed methodology to develop unprecedented mathematical and numerical approaches to enable modelling of multiphase flow and phase-change in thermo-poroelastic media with fractures that may slip, deform and propagate;
- Advance competences in the main scientific fields involved; and
- Improve understanding of coupled processes in development and production of high-temperature geothermal systems towards sustainable exploitation of the resource.

The project will provide new mathematical and numerical models along with open-source software that have capabilities in modelling of coupled process-structure interaction in fractured porous media that greatly exceed those of existing platforms. Specific case-studies will assess process-structure interactions for development and production operations in high-temperature geothermal systems, providing timely contributions to further developments of these resources.
In geothermal systems, networks of fractures provide main fluid pathways. Hydraulic stimulation of fractured geothermal reservoirs can increase the possibility of geothermal fluid to flow through the formation by causing sliding and dilation of preexisting fractures as well as fracture propagation. This represents a complex coupled process-structure interaction, where the fractured structure of the formation both dominates coupled fluid flow and rock deformation and conversely is altered because of these processes. A main result achieved in the project so far is a novel hydro-mechanical simulation model for hydraulic stimulation of fractured porous rock, where slip, dilation and propagation of fractures result as a consequence of fluid injection.

Fundamental progress has also been made in the simulation of thermal multi-phase flow in high-temperature geothermal systems. For the phase equilibrium problem, we have developed a formulation that enables simultaneous determination of phase stability and splits for a wide range of subsurface conditions. The developed methodology provides a modular way to include and couple the local fluid phase equilibrium within compositional multi-phase flow simulations. Currently, the methodology is being verified against benchmarks from the literature.

Substantial work has also been performed on novel mathematical models for deformable fractured media, numerical solution strategies, and necessary software improvements in the open-source framework PorePy, much of which is central to prepare for the next phase of the project.
The project has made significant progress towards its main objective. Novel results have been published on computational models of process-structure interaction in the context of hydraulic stimulation of geothermal reservoirs, and in parallel, the project has developed new mathematical models and simulation technology required to simulate multi-phase flow in high-temperature geothermal reservoirs. Hence, by combining these developments, the project’s ambitious goal of assessing process-structure interaction in the context of high-temperature geothermal resources should be within reach, although significant progress needs to be made, also in terms of the development of advanced solution techniques, software implementation and code optimization.
Propagation of fractures and pressure (MPa) during fluid injection (Dang et al., 2022).