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

Abbasi, Mahdi; Khazali, Nastaran; Sharifi, Mohammad

doi:10.1016/j.geothermics.2017.04.002

Cited by 35 publications

(14 citation statements)

References 56 publications

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“…For thermal perturbations in fractured reservoirs, analytical solutions have been developed by exploiting the analogy between fractures and aquifers and between matrix blocks and aquitards for single (or parallel) fractures and semi-infinite (or finite) slab-like matrix blocks (Abbasi et al, 2017;Ascencio et al, 2014;Bodvarsson, 1969;Bodvarsson & Tsang, 1982;Jung & Pruess, 2012;Kocabas, 2005). This configuration of nonoverlapping parallel fractures and matrix blocks is oversimplified because it neglects the complex networks of natural fractures and the multitude of matrix blocks with different shapes and sizes.…”

Section: Introductionmentioning

confidence: 99%

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

Zhou

Oldenburg

Rutqvist

2019

Water Resources Research

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Numerous analytical solutions have been developed for modeling thermal perturbations to underground formations caused by deep-well injection of fluids. Each solution has been derived for a specific boundary value problem and a simplified flow network with one set of parallel fractures. In this paper, new generalized solutions G * (x, s) are developed using (existing) global transfer functions G * 0 x; s ð Þand a new memory function g * (s), where x and s are the space and Laplace variable. The memory function represents the solutions of conductive heat exchange between fractures and matrix blocks and between fractured aquifers and unfractured aquitards. The memory function is developed to account for multirate exchange induced by different shapes, sizes, properties, and volumetric fractions of matrix blocks bounded by multiple sets of orthogonal fractures with different spacing. The global transfer functions represent the fundamental solutions to convective, convective-conductive, and convective-dispersive heat transport in fractures (or aquifers) without exchange and are available for various (1-D linear, 1-D radial, 2-D dipole, and single-well injection-withdrawal) flow fields. The new solutions with exchange are developed using G *, thereby greatly simplifying solution development in a novel way, where ϑ and B * (s) are a fracture-matrix scaling factor and the boundary condition function. The new solutions are applied to several example problems, showing that heat transport in fractured aquifers is significantly impacted by (1) thermal dispersion in fractures that is rarely considered, (2) multirate heat exchange with a wide range of size and anisotropy of rectangular matrix blocks, and (3) heat exchange between aquifers and aquitards.

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Section: Introductionmentioning

confidence: 99%

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

Zhou

Oldenburg

Rutqvist

2019

Water Resources Research

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“…The following interpolations for any element m are used: (16) where the subscript m denotes the element m, T f m is the vector of nodal temperature, q f hm is the vector of the nodal heat transfer rate, and N is the vector of interpolation functions.…”

Section: Numerical Calculationmentioning

confidence: 99%

“…For water flow and heat transfer in a reservoir with multiple fractures, Abbasi et al [16] considered parallel infinite line-shaped fractures at equal spacing and presented its analytical solution. Wu et al [17] took into account equidistant, parallel, infinite disc-shaped fractures and derived its Laplace transform semi-analytical solution.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Analytical Method for Three-Dimensional Heat Transfer in Multi-Fracture Enhanced Geothermal Systems

Liu

Xiang

2019

Energies

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Multiple fractures have been proposed for improving the heat extracted from an enhanced geothermal system (EGS). For calculating the production temperature of a multi-fracture EGS, previous analytical or semi-analytical methods have all been based on an infinite scale of fractures and one-dimensional conduction in the rock matrix. Here, a temporal semi-analytical method is presented in which finite-scale fractures and three-dimensional conduction in the rock matrix are both considered. Firstly, the developed model was validated by comparing it with the analytical solution, which only considers one-dimensional conduction in the rock matrix. Then, the temporal semi-analytical method was used to predict the production temperature in order to investigate the effects of fracture spacing and fracture number on the response of an EGS with a constant total injection rate. The results demonstrate that enlarging the spacing between fractures and increasing the number of fractures can both improve the heat extraction; however, the latter approach is much more effective than the former. In addition, the temporal semi-analytical method is applicable for optimizing the design of an EGS with multiple fractures located equidistantly or non-equidistantly.

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“…Many researchers have also performed numerical simulations on the seepage and heat transfer process of fractured rocks, and studied the thermal-hydraulic coupling mechanism and parameter sensitivity (Cui et al 2016;Jiang et al 2018;Bauer et al 2019;Han et al 2020). Some numerical studies have shown that the heat transfer during the seepage and heat transfer process of the rock fracture system plays an important role (Ewing and Wang 2001;Abbasi et al 2017).…”

Section: Introductionmentioning

confidence: 99%

A fully coupled seepage–heat transfer model including a dynamic heat transfer coefficient in fractured rock sample with a single fissure

Zhang

Wang

Yang

et al. 2021

Geomatics, Natural Hazards and Risk

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Conventional seepage-heat transfer models in simulating the heat transfer between fluid and rock in fractures mainly involve one-way coupling and do not consider the influence of temperature on the seepage. Moreover, it is an enormous challenge to define parameters of the explicit heat transfer between the rock and fluid. In order to resolve these shortcomings, a two-way fully coupled model of the seepage-heat transfer in the fractured rock was established in the present study. Based on the original geometric structure of the experimental device, combined with the actual engineering scale, the local dynamic heat transfer coefficient of the fractured rock was established, which is related to the fracture aperture, flow velocity and thermal parameters. Then, the proposed model was verified through the experiment and excellent agreement was achieved in this regard. It was found that the dynamic heat transfer coefficient changes the temperature distribution of fluid and rock in the original static heat transfer coefficient fracture system. The proposed model simplifies the parameters required for the calculation of the heat transfer coefficient. These parameters are related to characteristic variables, such as velocity and rock temperature, and can be simply obtained from standard laboratory tests.

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

Cited by 35 publications

References 56 publications

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

A Semi-Analytical Method for Three-Dimensional Heat Transfer in Multi-Fracture Enhanced Geothermal Systems

A fully coupled seepage–heat transfer model including a dynamic heat transfer coefficient in fractured rock sample with a single fissure

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