Modeling heat transfer in complex heterogeneous fractured system is key for geothermal energy applications. Discrete fracture network (DFN) modeling is the ideal framework to reproduce the advective part of the transport, which is determined by the fracture connectivity and heterogeneity. This approach in general sacrifices the representation of the rock matrix, disregarding both its diffusive heat exchange with the fractures and the effects of its thermo-mechanical deformation on the fracture aperture. Here we propose a new semi-analytic formulation that can be implemented in a DFN simulator with particle tracking approach. The contribution of the rock matrix in terms of diffusive heat exchange and thermal contraction/expansion is analytically evaluated, which respectively impact the advective heat transfer and the fracture aperture variation. The methodology enables investigating the reservoir behavior and optimizing the geothermal performance while keeping the computational effort within reasonable values. This allows exploring the uncertainty in cases when the characterization is poor, which is the spirit of the DFN modeling.


Deep geothermal energy represents a powerful and clean energy prospect, with the potential to generate huge and virtually unlimited energy (Giardini, 2009). Geothermal plants generally involve hot reservoirs located in the crystalline basement, characterized by a very low permeability of the rock mass and a complex system of preexisting natural fractures. A characterization of the rock and fracture properties is in general difficult, which increases the uncertainty on the performance. Thus, numerical modeling is key to forecast the performance of geothermal energy applications under a number of scenarios.

Modeling heat transfer in complex heterogeneous fractured systems is challenging. The flow through the fracture network controls the heat advective transport, while the diffusive thermal exchange with the host rock controls the geothermal performance (Bruel, 2002). The two processes occur on very different length and time scales, which complicates their numerical simulation especially in the case of a large reservoir domain with thousands of fractures. The complexity is further increased when thermal deformations are taken into account. Host rock cooling provokes thermal contraction which tends to increase the fracture aperture. This may result in the variation of the advective transport, slowing down or speeding up the heat production, or opening new fast flow paths that may shortcut the geothermal doublet. Quantifying these processes is crucial for the optimization of heat extraction.

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