Asymptotic analysis of vertical geothermal boreholes in the limit of slowly varyng heat injection rates

Hermanns Navarro, Miguel and Perez Perez, Jose Miguel (2014). Asymptotic analysis of vertical geothermal boreholes in the limit of slowly varyng heat injection rates. "SIAM Journal of Applied Mathematics", v. 74 (n. 1); pp. 60-82. ISSN 0036-1399. https://doi.org/10.1137/130930170.

Description

Title: Asymptotic analysis of vertical geothermal boreholes in the limit of slowly varyng heat injection rates
Author/s:
  • Hermanns Navarro, Miguel
  • Perez Perez, Jose Miguel
Item Type: Article
Título de Revista/Publicación: SIAM Journal of Applied Mathematics
Date: 2014
ISSN: 0036-1399
Volume: 74
Subjects:
Freetext Keywords: Geothermal heat exchangers, geothermal boreholes, borehole thermal resistances,heat equation, asymptotic matching, intermediate scale
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Mecánica de Fluidos y Propulsión Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Theoretical models for the thermal response of vertical geothermal boreholes often assume that the characteristic time of variation of the heat injection rate is much larger than the characteristic diffusion time across the borehole. In this case, heat transfer inside the borehole and in its immediate surroundings is quasi-steady in the first approximation, while unsteady effects enter only in the far field. Previous studies have exploited this disparity of time scales, incorporating approximate matching conditions to couple the near-borehole region with the outer unsteady temperatura field. In the present work matched asymptotic expansion techniques are used to analyze the heat transfer problem, delivering a rigorous derivation of the true matching condition between the two regions and of the correct definition of the network of thermal resistances that represents the quasi-steady solution near the borehole. Additionally, an apparent temperature due to the unsteady far field is identified that needs to be taken into account by the near-borehole region for the correct computation of the heat injection rate. This temperature differs from the usual mean borehole temperature employed in the literatura.

More information

Item ID: 35921
DC Identifier: http://oa.upm.es/35921/
OAI Identifier: oai:oa.upm.es:35921
DOI: 10.1137/130930170
Official URL: http://epubs.siam.org/doi/abs/10.1137/130930170
Deposited by: Memoria Investigacion
Deposited on: 14 Oct 2015 07:32
Last Modified: 14 Oct 2015 14:46
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