Critical review of the local thermal equilibrium assumption in heterogeneous porous media: Dependence on permeability and porosity contrasts

Increasing demand for green energy sparked a renewed interest in extracting geothermal energy resources. An accurate description of the temperature field and related heat extraction potential remains a challenge and is critical for successful geothermal energy exploitation. Typically, two main approaches are used when modeling heat exchange and transport in geothermal reservoirs. The standard approach assumes immediate local thermal equilibrium between solid and fluid phases (LTE), while another approach considers heat transport separately for fluid and solid (LTNE). Both are then coupled through a heat exchange term. In these simple and common models, the host system is described as a heterogeneous porous media in which regions of higher fracture density are represented implicitly by areas of higher permeability within the porous media. In this work, we investigate both, LTE and LTNE, approaches and how they are affected by fluid and host rock characteristic properties. We especially focus on the influence of hydraulic heterogeneity in the porous material on the temperature difference between both approaches. We compare LTE and LTNE heat transfer models in a simple, two dimensional model with a layer of different hydraulic parameters embedded in a host rock, and study in detail the role of heterogeneous distributions of permeability and porosity. This simple geometrical model allows us to gain insights into the complex interaction between the different heat transfer models and fluid flow. Porosity and permeability contrast determine separate regimes in which the LTE assumption is lower or upper bound of outflow temperature. Using these results, we compare LTE and LTNE models in a synthetic field case with a complex heterogeneous porous media with large permeability contrast. We show that both models can diverge up to 7% in local fluid temperature, while the LTNE model is the lower bound if high permeability regions are also assumed to have a higher porosity.