This paper introduces an analytical model analyzing the effect of groundwater flow on heat transfer in an infinite conductive-convective porous domain representing shallow geothermal systems with arbitrarily configured cylindrical heat sources. The model is formulated based on the moving source concept and solved based on the spectral analysis method and the superposition principle. Compared to models based on the Green's function and the Laplace transform, the proposed spectral model has a simpler formulation, computationally efficient and easy to implement in computer codes. It can handle random time-dependent thermal loads and any arbitrarily configured grid distribution. The verification and numerical examples demonstrate the computational capabilities of the model, and show how the groundwater flow can play an important role in the thermal interaction between heat sources. They also feature how to make use of the direction of groundwater flow to avoid undesirable thermal interaction between neighboring installations, rapid depletion of energy sources and unfair mining of geothermal energy.

This paper introduces a spectral model for a moving cylindrical heat source in an infinite conductive-convective domain. This physical process occurs in many engineering and technological applications including heat conduction-convection in ground source heat pump systems, where the borehole heat exchangers likely go through layers with groundwater flow. The governing heat equation is solved for Dirichlet and Neumann boundary conditions using the fast Fourier transform for the time domain, and the Fourier series for the spatial domain. A closed form solution based on the modified Bessel functions is obtained for the Dirichlet boundary condition and an integral form for the Neumann boundary condition. Limiting cases of the moving cylindrical heat source to represent a moving line heat source are also derived. Compared to solutions based on the Green's function and the Laplace transform, the spectral model has a simpler form, applicable to complicated time-variant input signals, valid for a wide range of physical parameters and easy to implement in computer codes. The model is verified against the existing infinite line heat source model and a finite element model.

This paper introduces a thermo-hydro-mechanical finite element model for energy piles subjected to cyclic thermal loading. We address four particular features pertaining to the physics of energy piles: three-dimensionality, embedded heat exchangers, soil constitutive modeling and pile–soil interface. The model is designed to capture the strong coupling between all important physical and thermomechanical processes occurring in a concrete pile embedding U-tubes heat exchangers and surrounded by a saturated soil mass. It encompasses solid and fluid compressibility, fluid and heat flow, thermoplastic deformation of soil, buoyancy, phase change, volume change, pore expansion, melting point depression, cryogenic suction and permeability reduction due to ice formation. The model is distinct from existing energy pile models in at least two features: (1) it can simulate the detailed convection-conduction heat flow in the heat exchanger and the associated unsymmetrical thermal interactions with concrete and soil mass; and (2) it can simulate cyclic freezing and thawing in the system and the associated changes in physical and mechanical properties of the soil mass that likely lead to thermoplasticity and deterioration of pile shaft resistance. The performance of the model is demonstrated through a numerical experiment addressing all its features.

This paper introduces a thermo-hydro-mechanical computational model for freezing and thawing in porous media domains, with focus on freezing and thawing in soil. The model is formulated based on the averaging theory and discretized using a mixed discretization scheme, where the standard and extended finite element methods are simultaneously employed. It is capable of capturing the strong coupling between all important phenomena and processes occurring during relatively high freezing-thawing rates in porous media. Solid and fluid compressibility, buoyancy, phase change, thermomechanical behavior, water volume change, pores expansion, cryogenic suction, melting point depression and water migration to the freezing zone are all considered in the model. The cryogenic suction, in particular, is central to the occurrence of many of these phenomena and processes, and thus treated as a primary state variable, and discretized using the partition of unity method to make sure that it can be captured accurately. The paper presents detailed formulation of the governing equations and the numerical discretization. Verification and numerical examples are given to demonstrate the accuracy and computational capability of the model in describing the behavior of a soil mass subjected to boundary conditions resembling those occurring in the vicinity of an energy pile. The numerical examples show that the model is effectively mesh-independent and can simulate all important phenomena using relatively coarse meshes.

In this paper, we introduce a fully coupled thermo-hydrodynamic-mechanical computational model for multiphase flow in a deformable porous solid, exhibiting crack propagation due to fluid dynamics, with focus on CO₂ geosequestration. The geometry is described by a matrix domain, a fracture domain, and a matrix-fracture domain. The fluid flow in the matrix domain is governed by Darcy's law and that in the crack is governed by the Navier-Stokes equations. At the matrix-fracture domain, the fluid flow is governed by a leakage term derived from Darcy's law. Upon crack propagation, the conservation of mass and energy of the crack fluid is constrained by the isentropic process. We utilize the representative elementary volume-averaging theory to formulate the mathematical model of the porous matrix, and the drift flux model to formulate the fluid dynamics in the fracture. The numerical solution is conducted using a mixed finite element discretization scheme. The standard Galerkin finite element method is utilized to discretize the diffusive dominant field equations, and the extended finite element method is utilized to discretize the crack propagation, and the fluid leakage at the boundaries between layers of different physical properties. A numerical example is given to demonstrate the computational capability of the model. It shows that the model, despite the relatively large number of degrees of freedom of different physical nature per node, is computationally efficient, and geometry and effectively mesh independent.

This paper introduces a multidomain-staggered technique for coupling multiphase flow in a porous medium, dominated by the Darcy laminar flow, with multiphase flow in a wellbore, dominated by the Navier Stokes viscous, compressible flow. The Darcy flow in the porous medium is formulated using the averaging theory, and the Navier Stokes flow in the wellbore is formulated using the drift-flux model. The governing equations are discretized using a mixed discretization finite element scheme, in which the partition of unity finite element method, the level set method and the standard Galerkin finite element method are combined in an integrated numerical scheme. A multidomain technique is utilized to uncouple the physical system into two subdomains, coupled back by enforcing flow constraints at their interaction boundaries. The resulting system of equations is solved using an iterative staggered technique and a multiple time-stepping scheme. This combination between the multidomain technique and the staggered-multiple time-stepping technique enables the use of different mathematical and numerical formulations for the two subdomains, and facilitates the implementation of a standard finite element computer code. The proposed model is tailored to simulate sequestered CO₂ leakage through heterogeneous geological formation layers and abandoned wellbores. A numerical example describing different leakage scenarios is given to demonstrate the computational capability of the model. The numerical results are compared to those obtained from a commercial simulator.