Analytical model for convection-conduction heat transfer during water injection in fractured geothermal reservoirs with variable rock matrix block size

The purpose of management in geothermal reservoirs is to economically enhance the energy recovery. This paper describes a model to analyze the process of cold water injection into a fully penetrating well with a number of n equally spaced horizontal fractures in a fractured geothermal reservoir. Previous models basically focused on the numerical and semi-analytical methods or a combination of two. Here, an analytical model is presented in which the effects of thermal convection and conduction are investigated. This solution has the ability to account the following phenomena: convection transport in fractures and conduction from the matrix block to the fracture. Specified assumptions are made which allow the model to be formulated as two coupled one-dimensional partial differential equations, one for the fracture and one for the matrix block in the direction perpendicular to the fracture. The convection-conduction heat transfer between fracture and matrix is not affected by the matrix block size distribution in dual porosity models. In the present study, a heat transfer model is introduced for a radial system with matrix block size distribution to assess the heat transfer shape factor known as a matrix-fracture exchange coefficient. The results delineated that heat transfer is strongly dependable on matrix block size distribution during the early time region. To calculate the total amount of heat extracted from a geothermal reservoir, two methods were defined and also a conceptual definition for the thermal recovery efficiency was presented. Finally, the proposed model was validated by comparing the results of the analytical solution with a pre-defined numerical method in the literature.