Exact Solution of Heat Transport Equation for a Heterogeneous Geothermal Reservoir

Sayantan Ganguly
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Sayantan Ganguly: Environmental Hydrogeology Group, Department of Earth Sciences, Utrecht University, Princetonlaan 8A, 3584 CB Utrecht, The Netherlands

Energies, 2018, vol. 11, issue 11, 1-19

Abstract: An exact integral solution for transient temperature distribution, due to injection-production, in a heterogeneous porous confined geothermal reservoir, is presented in this paper. The heat transport processes taken into account are advection, longitudinal conduction and conduction to the confining rock layers due to the vertical temperature gradient. A quasi 2D heat transport equation in a semi-infinite porous media is solved using the Laplace transform. The internal heterogeneity of the geothermal reservoir is expressed by spatial variation of the flow velocity and the effective thermal conductivity of the medium. The model results predict the transient temperature distribution and thermal-front movement in a geothermal reservoir and the confining rocks. Another transient solution is also derived, assuming that longitudinal conduction in the geothermal aquifer is negligible. Steady-state solutions are presented, which determine the maximum penetration of the cold water thermal front into the geothermal aquifer.

Keywords: geothermal reservoirs; heat transport in porous media; thermal front; analytical modeling; Laplace transform; closed form solution (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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