A geothermal open loop system consisting of one production well and several injection wells is considered. The production well serves to raise hot water from a geothermal underground reservoir, which can be used for building heating or for other purposes. As a result, the water is cooled and then pumped through injection wells back into the geothermal reservoir. The cooled water begins to be filtered in the reservoir in the direction of the production well. A mathematical model describing the distribution of a cold water front in such a system is presented. A software package has been developed that makes it possible to evaluate the efficiency of the location of injection wells in a geothermal reservoir in order to increase the operating time of such a system, since the operation of the geothermal system life is over as soon as the cold water front reaches the production well.

Topics
Geothermal energy, Mathematical modeling
1.
F.
 
Kreith
 and
D. Y.
 
Goswami
,
Heat Pumps, Energy Management and Conservation Handbook
(
CRC Press
,
USA
,
2008
).
Google Scholar
 
2.
N. A.
 
Vaganova
 and
M. Y.
 
Filimonov
, “Simulation and numerical investigation of temperature fields in an open geothermal system,” in
Finite Difference Methods, Theory and Applications
, Lecture Notes in Computer Science 9045, edited by
Dimov
,
Farago
, and
L.
 
Vulkov
 (
Springer Verlag
,
Germany
,
2015
), pp.
393
–
399
.
Google Scholar
Crossref
Search ADS
 
3.
N. A.
 
Vaganova
 and
M. Y.
 
Filimonov
, “Simulation of optimal exploitation of an open geotermal loop,” in
All-Russian Conference with the School for Young Scientists Thermophysics and Physical Hydrodynamics 2016, TPH 2016, Journal of Physics: Conference Series
, Vol.
754
(
Institute of Physics Publishing
,
United Kingdom
,
2016
) p.
112004
.
Google Scholar
 
4.
N. A.
 
Vaganova
 and
M. Y.
 
Filimonov
, “Refinement of model of an open geothermal system,” in
Applications of Mathematics in Engineering and Economics (AMEE’16), AIP Conference Proceedings
 
1789
, edited by
V.
 
Pasheva
,
N.
 
Popivanov
, and
G.
 
Venkov
 (
American Institute of Physics Publising
,
Melville, NY
,
2016
) p.
020020
.
Google Scholar
 
5.
N. A.
 
Vaganova
 and
M. Y.
 
Filimonov
, “
A general model of an open geothermal system
,” in
5th International Conference on Science and Engineering in Mathematics, Chemistry and Physics 2017, ScieTech 2017
,
Journal of Physics: Conference Series
, Vol.
820
(
Institute of Physics Publishing
,
United Kingdom
,
2017
) p.
012010
.
Google Scholar
Crossref
Search ADS
 
6.
M. Y.
 
Filimonov
 and
N. A.
 
Vaganova
, “
Simulation of optimal operation of a multiple wells open geothermal system
,” in
3rd All-Russian Scientific Conference Thermophysics and Physical Hydrodynamics with the School for Young Scientists, TPH 2018
,
Journal of Physics: Conference Series
, vol.
1128
(
Institute of Physics Publishing
,
United Kingdom
,
2018
) p.
012139
.
Google Scholar
Crossref
Search ADS
 
7.
N. A.
 
Vaganova
, “
Computer simulation of operation of an open geothermal system consisting of multiple wells
,” in
44th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2018, AIP Conference Proceedings 2048
, edited by
V.
 
Pasheva
,
N.
 
Popivanov
, and
G.
 
Venkov
 (
American Institute of Physics Publising
,
Melville, NY
,
2018
) p.
030011
.
Google Scholar
Crossref
Search ADS
 
8.
P. Y.
 
Polubarinova-Cochina
,
Theory of ground water movement
(
Princeton University Press
,
Princeton, NJ
,
1962
).
Google Scholar
 
9.
I.
 
Rubinstein
 and
L.
 
Rubinstein
, “Cauchy problem for heat-conduction equation,” in
Partial Differential Equations in Classical Mathematical Physics
(
Cambridge University Press
,
1994
), pp.
296
–
324
.
Google Scholar
Crossref
Search ADS
 
10.
V. N.
 
Nikolaevskij
, “Mechanics of porous and fractured media,” in
Series in Theoretical and Applied Mechanics: Volume 8
(
World Scientific
,
1990
), pp.
324
–
382
.
Google Scholar
 
11.
A. A.
 
Samarsky
 and
P. N.
 
Vabishchevich
,
Computational Heat Transfer, Volume 2, The Finite Difference Methodology
(
Wiley
,
NY
,
1977
).
Google Scholar
 
12.
N.
 
Vaganova
, “
Mathematical model of testing of pipeline integrity by thermal fields
,” in
40th International Conference of Applications of Mathematics in Engineering and Economics
,
AIP Conference Proceedings
 
1631
, edited by
G.
 
Venkov
 and
V.
 
Pasheva
 (
American Institute of Physics
,
Melville, NY
,
2014
), pp.
37
–
41
.
Google Scholar
Crossref
Search ADS
 
13.
M. L.
 
Brun
,
V.
 
Hamm
, et al., “Hydraulic and thermal impact modelling at the scale of the geothermal heating doublet in the paris basin, france,” in
Proceedings of Thirty-Sixth Workshop on Geothermal Reservoir Engineering
(
Stanford University, Stanford
,
California
,
2011
), pp.
SGP-TR-191
.
Google Scholar
 
This content is only available via PDF.
© 2019 Author(s).
2019
Author(s)