- The paper demonstrates that incorporating dead-end fractures significantly enhances matrix heat extraction through combined density- and pressure-driven convection.
- The paper uses transient CFD simulations with variable Rayleigh and Péclet numbers to model coupled thermal-hydraulic processes in fracture intersections.
- The paper challenges Darcy's law by showing that shear-driven, oscillatory flows in dead-end geometries require revised upscaling models for geothermal systems.
Heat Transfer Enhancement via Density- and Pressure-Driven Flow at Fracture Dead-Ends
Background and Motivation
Heat transport within fractured geological media is governed by complex, coupled thermal-hydraulic (TH) processes, where the geometry, connectivity, and hydraulic properties of fracture networks critically determine fluid circulation and, consequently, thermal behavior. Fractures are often several orders of magnitude more permeable than their host matrix, making them dominant advective pathways. Previous investigations have characterized heat transport at the scale of individual fractures, emphasizing forced and natural convection, as well as conduction through the rock matrix. However, the role of fracture intersections—specifically T-intersections where one fracture terminates in a dead-end—remains inadequately explored. This limitation is acute given the stronger diffusive transport for heat relative to solute, and the unique boundary conditions encountered in impermeable rock matrices.
Methodology
The study employs transient CFD simulations using OpenFOAM’s chtMultiRegionFoam solver to model coupled flow and heat transport in a domain comprising both fluid (water) and solid (granite). The model features a horizontal main production fracture intersected by a vertical dead-end fracture, embedded within an impermeable matrix. The governing equations implement mass, momentum, and energy conservation with temperature-dependent fluid properties, and conduction-only for the solid phase. Distinct boundary conditions emulate thermal tracer tests by injecting warmer fluid at the inlet. Characteristic nondimensional numbers—Reynolds, Péclet, and Rayleigh—are systematically varied, along with dead-end fracture orientation (via rotation angle θ), to interrogate their effects on TH processes.
Key Findings
Interplay of Natural and Forced Convection
Simulation results demonstrate that when fluid circulation is induced within the dead-end fracture—either by natural convection (buoyancy-driven, associated with temperature-dependent density) or by pressure gradients (forced convection, linked to fracture orientation misalignment)—heat transfer from fluid to matrix is substantially enhanced. This enhancement is quantitative: configurations with both temperature-dependent properties and dead-end fractures consistently show larger surface heat fluxes and lower outlet temperatures relative to setups without dead-end fractures or with constant fluid properties.
At high Rayleigh numbers and larger pressure gradients (i.e., rotated dead-end fractures), forced convection dominates, resulting in robust circulation patterns within the dead-end fracture. This circulation maintains higher fluid temperatures in the fracture, thus increasing the thermal gradient and promoting heat flux into the matrix. At low Rayleigh or Péclet numbers, flow in the dead-end fracture is suppressed, yielding conduction-dominated heat transport.
Influence of System Parameters
- Inlet Velocity and Péclet Number: Increased inlet velocity yields rapid outlet temperature increases (shorter residence time) but diminishes heat flux due to reduced interaction time with the matrix. At low velocities and thermal Péclet numbers, advective transport plays a minor role and natural convection turns inefficient, resulting in nearly all heat loss occurring via conduction.
- Thermal Conductivity of Matrix: Higher matrix thermal conductivity (lower solid-phase Péclet number) facilitates more efficient heat extraction from the fluid, increasing the magnitude of matrix heat flux.
- Rayleigh Number: Larger Rayleigh numbers, achieved by increasing the inlet temperature difference, sustain stronger natural convection in the dead-end fracture, boosting heat transfer to the matrix. Outlet temperature reductions are nonlinear with respect to inlet temperature, evidencing the emergent TH coupling.
- Pressure Gradient Along Fracture Intersection: Rotation-induced pressure gradients drive circulation even in the absence of temperature-dependent density, and superimposed buoyant and forced convection mechanisms at non-orthogonal intersections result in asymmetric, oscillatory flow structures which further enhance heat transport.
Structural Implications for Fracture Networks
Analysis of stochastic DFN models for field sites shows that dead-end fractures can represent a significant proportion of fracture surface area (up to 20% or more). Even in sparsely fractured networks, dead-end features are prevalent and thus potentially exert substantial influence on reservoir-scale heat exchange.
Theoretical Implications
The study challenges the applicability of Darcy’s law for predicting flow and heat transfer at fracture intersections—since Darcy's law cannot capture shear-driven circulation inherent to dead-end geometries. Navier–Stokes-based modeling is required to resolve these mechanisms. Consequently, upscaled DFN models employing a Darcy framework must incorporate effective parameters that reflect the contribution of natural and forced convection in dead-end fractures. The enhancement mechanism identified here necessitates revised interface laws or parameterization for accurate upscaling, particularly in the context of geothermal reservoir modeling and thermal tracer interpretation.
Practical Applications and Future Directions
The findings indicate that dead-end fractures, through density- and pressure-driven circulation, can substantially enhance matrix heat extraction in fractured geothermal reservoirs and must be explicitly considered in modeling and operational strategies. The parametric results—formulated in terms of nondimensional numbers—are transferrable to a range of scales, facilitating input into field-scale simulation frameworks and yielding improved predictions for thermal recovery, tracer testing, and reservoir management.
Future research should address the effects of surface roughness and spatial aperture variability on localized convection and heat transfer, as well as their impacts on network-scale TH processes. The integration of these mechanisms into DFN modeling frameworks and the development of new predictive upscaling laws remain critical.
Conclusion
This work provides a comprehensive numerical investigation into the mechanisms of heat transfer at fracture intersections with dead-ends, demonstrating that density- and pressure-driven circulation within dead-end fractures significantly amplifies heat exchange with the rock matrix. The results have direct relevance for the interpretation of thermal tests, design of geothermal systems, and upscaling in network models, and emphasize the need for advanced modeling frameworks that capture these coupled TH phenomena. The limitation of Darcy-based models in dead-end geometries is underscored, motivating future developments in modeling approaches.