UC San Diego
UC San Diego Previously Published Works
Title
Role of Nonequilibrium Water Vapor Diffusion in Thermal Energy Storage Systems in the
Vadose Zone
Permalink
https://escholarship.org/uc/item/2h13q3gf
Journal
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING, 144(7)
ISSN
1090-0241
Authors
Baser, T
Dong, Y
Moradi, AM
et al.
Publication Date
2018
DOI
10.1061/(ASCE)GT.1943-5606.0001910
Peer reviewed
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University of California
1
ROLE OF NONEQUILIBRIUM WATER VAPOR DIFFUSION IN GEOTHERMAL
1
ENERGY STORAGE SYSTEMS IN THE VADOSE ZONE
2
by T. Başer, Ph.D., S.M.ASCE
1
, Y. Dong, Ph.D., A.M.ASCE
2
, A.M. Moradi, Ph.D.
3
,
3
N. Lu, Ph.D., F.ASCE
4
, K. Smits, Ph.D.
5
, S. Ge, Ph.D.
6
, D. Tartakovsky, Ph.D.
7
,
4
and J.S. McCartney, Ph.D., P.E., M.ASCE
8
5
Abstract: Although siting of geothermal energy storage systems in the vadose zone may be
6
beneficial due to the low heat losses associated with the low thermal conductivity of unsaturated
7
soils, water phase change and vapor diffusion in soils surrounding geothermal heat exchangers
8
may play important roles in both the heat injection and retention processes that are not considered
9
in established design models for these systems. This study incorporates recently-developed
10
coupled thermo-hydraulic constitutive relationships for unsaturated soils into a coupled heat
11
transfer and water flow model that considers time-dependent, nonequilibrium water phase change
12
and enhanced vapor diffusion to study the behavior of geothermal energy storage systems in the
13
vadose zone. After calibration of key parameters using a tank-scale heating test on compacted silt,
14
the ground response during 90 days of heat injection from a vertical geothermal heat exchanger
15
1
Research Associate, University of Alberta, Dept. of Civil and Environmental Engineering, 9211 - 116 Street NW
Edmonton, Alberta, Canada T6G 1H9. tugce@ualberta.ca.
2
Associate Professor, State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and
Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, P.R. China. ydong@whrsm.ac.cn.
3
Research Associate, Center for Experimental Study of Subsurface Environmental Processes (CESEP), Colorado
School of Mines, Dept. of Civil and Environmental Engineering, 1500 Illinois St., Golden, CO 80401.
amoradig@mines.edu.
4
Professor, Colorado School of Mines, Dept. of Civil and Environmental Engineering, 1500 Illinois St., Golden, CO
80401. ninglu@mines.edu.
5
Assistant Professor, Center for Experimental Study of Subsurface Environmental Processes (CESEP), Colorado
School of Mines, Dept. of Civil and Environmental Engineering, 1500 Illinois St., Golden, CO 80401.
ksmits@mines.edu.
6
Professor, University of Colorado Boulder, Dept. of Geosciences. Boulder, CO 80309-0399.
Shemin.Ge@colorado.edu.
7
Professor, Stanford University, Dept. of Energy Resources Engineering, 367 Panama St., Stanford, CA 94305.
tartakovsky@stanford.edu.
8
Associate Professor, University of California San Diego, Dept. of Structural Engineering. 9500 Gilman Dr., La Jolla,
CA 92093-0085, mccartney@ucsd.edu.
Manuscript Click here to download Manuscript 2018-01-13 - Baser et al -
JGGE Manuscript.docx
2
followed by 90 days of ambient cooling was investigated. Significant decreases in degree of
16
saturation and thermal conductivity of the ground surrounding the vertical geothermal heat
17
exchanger were observed during the heat injection period that were not recovered during the
18
cooling period. This effect can lead to a greater amount of heat retained in the ground beyond that
19
estimated in conduction-based design models.
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INTRODUCTION
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An important challenge facing society is the storage of energy collected from renewable
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sources. One such application is the storage of heat collected from solar thermal panels in the
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subsurface so that it can be harvested later (Claesson and Hellström 1981; Nordell and Hellström
24
2000; Chapuis and Bernier 2009). A practical mode of heat injection into the subsurface involves
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circulation of a heated carrier fluid through a closely-spaced array of closed-loop geothermal heat
26
exchangers in boreholes to reach ground temperatures ranging from 35 to 80 °C (Sibbitt et al.
27
2012; Başer et al. 2016a; McCartney et al. 2017). Unsaturated soils in the vadose zone are ideal
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thermal energy storage media because low heat losses can be expected due to the low thermal
29
conductivity of unsaturated soils (McCartney et al. 2013). The mode of heat transfer during
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injection of heat into unsaturated soils is complex as it may be coupled with thermally-induced
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water flow in either liquid or vapor forms along with latent heat transfer associated with phase
32
change. However, most design models for geothermal heat storage systems focus on ground
33
temperature changes during heating and do not consider coupled heat transfer and water transport
34
(Claesson and Hellström 1981; Eskilson 1987). Although some recent studies on geothermal
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energy storage systems highlighted the importance of considering coupled heat transfer and water
36
flow in their performance evaluation (Catolico et al. 2016; Moradi et al. 2016), the impact of water
37
vapor diffusion and phase change in unsaturated soils during heat injection on the heat retention
38
3
during a subsequent ambient cooling phase is an important topic that has not been investigated.
39
This paper presents simulations of the response of a low-permeability, low activity,
40
incompressible, unsaturated silt layer surrounding a single geothermal heat exchanger to
41
understand the impacts of considering water vapor diffusion and water phase change on the
42
transient heat injection and retention processes. Comparison of the simulation results from the
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coupled heat transfer and water flow model with a simpler heat transfer model without water vapor
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diffusion or phase change permits an evaluation of the importance of these heat transfer
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mechanisms in simulating geothermal energy storage systems in the vadose zone.
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BACKGROUND
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Most models of heat transfer from geothermal heat exchangers employ analytical solutions to
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the heat equation assuming conduction is the primary mechanism of heat transfer, using constant
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thermal properties that do not consider the effects of changes in degree of saturation expected
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during heat transfer in unsaturated soils (e.g., Kavanaugh 1985; Eskilson 1987). Analytical
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solutions have been developed for geothermal heat exchanger geometries including the infinite
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line source (Ingersoll and Plass 1948; Beier et al. 2014), finite line source (Acuña et al. 2012;
53
Lamarche and Beauchamp 2007), hollow cylinder source (Ingersoll et al. 1954; Gehlin 2002),
54
finite plate source (Ciriello et al. 2015), and one- and two-dimensional solid cylinder sources (Tarn
55
and Wang 2004). Although numerical simulations of geothermal heat exchangers have also been
56
performed, most have also considered conduction as the primary mechanism of heat transfer
57
(Ozudogru et al. 2015; Welsch et al. 2015; Başer et al. 2016a). While these conduction-based
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analytical models and numerical simulations may be practical for the design of geothermal heat
59
exchangers in dry or saturated low permeability soils, they may not be practical for design of those
60
in unsaturated soils due to the potential for convective heat transfer associated with thermally-
61
4
induced liquid water or water vapor flow, which may result in irreversible changes in behavior
62
during cyclic heat injection and extraction (or ambient cooling). Further, the thermal properties of
63
unsaturated soils are highly dependent on the degree of saturation, even when conduction is
64
assumed to be the primary mode of heat transfer (e.g., Farouki 1981; Côté and Konrad 2005; Smits
65
et al. 2013; Lu and Dong 2015). Conduction-only models may also not be practical for use in
66
saturated soils with high permeability due to the potential for thermally-induced convection of
67
water from buoyancy effects (Catolico et al. 2016).
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Because the properties of water in liquid and gas forms are dependent on temperature, heat
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transfer in the unsaturated soils in the vadose zone leads to thermally induced water flow through
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soil. Specifically, temperature dependency of the density of liquid water
w
(Hillel 1980), dynamic
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viscosity of liquid water
w
(Lide 2001), surface tension of soil water (Saito et al. 2006), relative
72
humidity at equilibrium R
h,eq
(Philip and de Vries 1957), saturated vapor concentration in the gas
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phase c
v,sat
(Campbell 1985), vapor diffusion coefficient in air D
v
(Campbell 1985), and the latent
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heat of water vaporization L
w
(Monteith and Unworth 1990) may lead to thermally-induced water
75
flow through unsaturated soils. The movement of water in soil caused by thermal and hydraulic
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gradients and the associated impacts on heat transfer have been studied experimentally for more
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than 100 years (Bouyoucos 1915; Lewis 1937; Smith 1943; Gurr et al. 1952; Baladi et al. 1981;
78
Shah et al. 1983; Ewen 1988; Gens et al. 1998, 2007, 2009; Cleall et al. 2011; Smits et al. 2011;
79
Moradi et al. 2015, 2016; Başer et al. 2016b). Some general observations from these studies are:
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(1) heat transfer occurs in unsaturated porous media by conduction, convection in both liquid and
81
gas phases, and latent heat transfer associated with water phase change; (2) water movement due
82
to a temperature gradient is controlled by both vaporization/condensation processes as well as
83
development of suction gradients caused by changes in water properties with temperature (i.e.,
84
