Thermal-Hydro-Mechanical-Compositional analysis is crucial for addressing challenges like wellbore stability, land subsidence, and induced seismicity in the geo-energy applications. Numerical simulations of coupled thermo-poromechanical processes provide a general-purpose tool for evaluating these phenomena across laboratory and field scales. However, efficient integration of the coupled equations for fluid mass, energy and momentum poses multiple numerical and implementation difficulties, such as combining different numerical methods on staggered grids and associated limitations on admissible grids. This paper introduces a novel fully-implicit Finite Volume Method (FVM) for modeling thermal compositional flow in thermo-poroelastic rocks. The scheme employs gradient-based, coupled multi-point approximations of fluid mass, momentum and heat fluxes.

The novelty of the scheme lies in its integration of temperature as a parameter in the flux approximation process. The scheme supports a wide range of cell topologies, arbitrary heterogeneity and anisotropy as well as various boundary conditions, while respecting local flux balance under temperature gradients. Overall, the scheme represents a unified FVM-based approach for the integration of all conservation laws relevant to geo-energy applications on a cell-centered collocated grid. Additionally, the implemented two-stage block-partitioned preconditioning strategy enables the efficient solution of obtained linear systems.

The framework, implemented in the open-source Delft Advanced Research Terra Simulator (open-DARTS), leverages the Operator-Based Linearization (OBL) technique for flexibility in compositional fluid properties. Rigorous validation demonstrates the framework’s capabilities in capturing advanced phenomena, including thermal expansion, thermo-poroelastic effect and compositional flow with phase transitions. The performance of preconditioning strategy is assessed using the mechanical extension of the SPE10 benchmark model.

This study presents a method to address the significant uncertainties in subsurface modeling that impact the efficiency of energy transition applications such as geothermal energy extraction and CO₂ geological sequetsration. The approach combines a physics-based geomechanical proxy model with an ensemble smoother with multiple data assimilation (ES-MDA), aimed at enhancing uncertainty quantification through the integration of vertical displacement measurements from fluid production and injection. The data from wells is limited in spatial coverage, while these measurements offer extensive spatial information, improving the understanding of subsurface behavior by reflecting changes in reservoir pressure and temperature. The open-DARTS simulator for fluid flow and a geomechanical proxy are used to perform data assimilation with ES-MDA. By generating an ensemble of model realizations with varied permeability, calculating vertical displacements at the surface, and applying ES-MDA, we effectively identify the probability distribution of the vertical displacement of the model conditioned to observed subsidence data. Entropy is used as a statistical measure to quantify the reduction of uncertainty of subsurface models based on observations. Our approach was tested on a 2D conceptual and 3D realistic datasets, demonstrating its capability to provide data assimilation. This workflow represents an advancement in subsurface modeling, supporting informed decision-making in geothermal energy production and CO₂ sequestration by offering an improved alternative for data assimilation and enhancing tools for uncertainty quantification.

The open Delft Advanced Research Terra Simulator (open-DARTS) framework is an open-source reservoir simulation software. The open-DARTS focused on energy transition applications, such as geothermal energy production and carbon sequestration. It enables the modeling of compositional thermal flow, coupled with a geomechanical solver based on the Finite Volume discretization and adjoints method for inverse modeling. The open-DARTS supports different grid types (structured, corner-point geometry, and unstructured), discrete fracture networks, contact mechanics, and various thermal-chemical interactions. The recently proposed generic nonlinear formulation supports the most general nonlinear PDEs designed for various energy transition applications. The open-DARTS has been implemented in C++ and Python to optimize hardware utilization while ensuring flexibility. The most computationally expensive part is written in C++ and compiled into libraries, which are subsequently exposed to Python using pybind11. This allows the extension and overriding of C++ functions by user-defined Python code. For example, using only a Python interface, one can adjust a timestep strategy, nonlinear solver, or properties output. Besides, the Python interface of open-DARTS provides straightforward coupling with other Python-based numerical modeling packages, including the meshing, file storage, caching, and visualization modules. The open-DARTS core uses the advantages of C++ language, such as efficient low-level memory management, object-oriented programming, compile-time polymorphism, and parallelization with OpenMP. One of the advantages of open-DARTS is the Operator-Based Linearization (OBL) technique, which can resolve challenges associated with complex physics and reduce the computation time, especially for ensemble-based simulations. We would also like to share our experience on the project, repository, and the development workflow configuration using gitlab.com, including the build system (cmake), handling merge requests, automated testing in CI/CD pipelines, documentation management (gitlab.io), wiki utilization, and release publishing. Additionally, Python’s integration into open-DARTS offers the advantage of straightforward installation via PyPI and simplifies defining requirements for users who prefer to avoid compiling code from source files.

The role of Thermal-Hydro-Mechanical-Compositional analysis in the development of geo-energy resources has been amplified in recent years. As an example, challenges such as wellbore stability, land subsidence and induced seismicity highlight the necessity for comprehensive geomechanical evaluations which are then coupled with thermo-hydrodynamical processes within the reservoir. Numerical simulations of the coupled thermo-poromechanical processes provide a general-purpose tool capable of performing these evaluations at both continuum laboratory and field scales. However, efficient integration of the coupled system of fluid mass, energy and momentum conservation equations poses multiple numerical and implementation difficulties, such as combining different numerical methods on staggered grids and associated limitations on admissible grids. This paper introduces a new fully-implicit scheme of the Finite Volume Method (FVM) for modeling thermal compositional flow in thermo-poroelastic rocks. The scheme uses the gradient-based variant of coupled multi-point approximations of fluid mass, momentum, heat convection and conduction fluxes, which are derived from their respective local balances. The novelty of the scheme is that it incorporates temperature into the approximation of these fluxes. Consequently, the approximation of displacement gradients depends on temperatures, while the approximation of temperature itself is derived from the balance of heat conduction fluxes. At the same time, we utilize a single-point upstream weighting for the temperature-dependent terms in heat convection fluxes. The resulting scheme respects the local balance of fluxes in the presence of temperature gradients. Besides, it also supports star-shaped and various boundary conditions. Overall, the scheme represents a unified FVM-based approach for the integration of all conservation laws relevant to geo-energy applications on a cell-centered collocated grid. Furthermore, the implemented two-stage block-partitioned preconditioning strategy enables the efficient solution of obtained linear systems. The proposed modeling framework has been implemented in an open-source Delft Advanced Research Terra Simulator (DARTS). Moreover, the flexibility regarding compositional fluid properties is reinforced by the Operator-Based Linearization (OBL) technique incorporated into DARTS. The proposed modeling framework has undergone rigorous validation in convergence study, and comparisons against established analytical and numerical solutions. The framework covers advanced physical phenomena including thermal expansion and contraction, porosity dependent on pressure, temperature and strain, and multiphase flow with phase changes and chemical alterations. The framework capabilities and the performance of the preconditioning strategy have been assessed in the mechanical extension of the 10th SPE Comparative study (SPE10) model.