ASHRAE Journal - December 2023 - 30

FEATURE
FIGURE 5 Site energy use at older Texas GSHP schools and U.S. average school
EUIs.6
School (Years of Operation)
Mason ES (24)
Faubion ES (24)
Cedar Park MS (23)
Cedar Park HS (23)
Steiner Ranch ES (22)
Leander MS (22)
Giddens ES (22)
45
40
35
30
25
20
CBECS EUIs for Schools: 83.1 kBtu/ft2 (2003), 68.5 kBtu/ft2 (2012), 62.7 kBtu/ft2 (2018)
formation initial temperature was 55°F (13°C), or 15°F
(8°C) lower than those in the warm climate systems
shown in Figures 4 and 5.
The resulting cooling mode COPs were 2.17 and 2.56,
but do not include the significant contribution of fan
power. The combined power of the system cooling pumps
is 0.46 hp/ton (95 Wpump/kWhp), while the recommended
value for GSHPs is 0.075 hp/ton (16 Wpump/kWhp).9 The
combined effects of the large amount of auxiliary power
(fans and pumps), small bore separation distance and
supplemental heat likely contributed to overheating the
ground loops in a short period.
Complexity and Uncertainty of Modeling GHX Performance
Heat transfer mechanisms in moist soil and rock
formations are exceedingly complex. GHX performance
calculations that assume formations behave as a solid by
using heat conduction models alone will be inadequate.
In the case of vertical GHXs, the uncertainty is
compounded by the limited porosity and
moisture content that can be obtained
from deep formations. A primary source
of uncertainty is the influence of phase
change (evaporation, freezing) induced
by temperature change resulting from
the addition or removal of heat.
Farouki10 states: " In unsaturated
soils, increased temperature at certain
locations causes the water to evaporate,
absorb a latent heat of vaporization of
586 cal/g @ 20°C (1055 Btu/lb @ 68°F).
Consequently, the local vapor pressure
increases and the water vapor diffuses
through the interconnected regions to
regions of lower vapor pressure, the
120°F
100°F
80°F
60°F
40°F
20°F
108
101
73
A
30
ASHRAE JOURNAL ashrae.org D ECEMBER 2 0 2 3
diffusion coefficient depending on the temperature. It
may condense then at such location giving up its latent
heat. By this process, and because of the high latent heat
of evaporation of water, a significant amount of heat
may be transferred. "
Figure 7 plots the results of the changes in thermal
conductivity of a moist porous soil while drying (heat
rejection) and wetting (heat absorption). There is
a significantly higher conductivity when the soil is
drying (cooling mode) compared to wetting (heating
mode). The decline of moisture from 8.2% to 7.4% is
equivalent to a reduction of 1.0 lb (0.45 kg) in a 130 lb/ft3
(2080 kg/m3) soil. The resulting evaporative cooling
would be 1,060 Btu (1120 kJ), which is equivalent to a
40°F (22°C) change in 130 lb/ft3 (2080 kg/m3) dry soil
with a specific heat of 0.2 Btu/lb·°F (0.84 kJ/kg·°C).
However, continued drying would lower formation
conductivity, and water migration would be critical to
maintain effective heat transfer and mitigate long-term
temperature rise.
As the temperature falls below the freeze point of
water, phase change is available to somewhat mitigate
temperature decline. However, the latent heat of
water solidification is only 14% of the latent heat of
evaporation. The temperature at which ice forms
is dependent on soil type with complete freezing
occurring near 32°F (0°C) in course soils and down
to -40°F (-40°C) in fine soils.10 The apparent thermal
conductivity of the frozen ice/soil will likely be lower
than the wet soil and further impact the heat rate as
the frozen cylinder around the GHX grows. These
FIGURE 6 Average monthly GHX temperatures in mixed climate district system.8
Avg Ground Loop
Supply Temp
108
102
103
99
COP=2.17
(AHU Fan Power Not Included)
64
54
36
34
25
S
O
N
D
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21
The original hot water system remained in operation. This would limit the removal of heat
from the ground loop resulting in overheating.
F
M
A
M
J
J
96
96
Avg Ground Loop
Return Temp
COP = 2.56
(AHU Fan Power Not Included)
93
90
90
86
89
85
Winter Loop Temps
37
91
89
92
90
107
98
66
54
100
92
71
95
91
73
Avg Outdoor
Air Temp
kBtu/ft2·yr
2010
2011
2012
2013
2014
2015
2016
1017
2018
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ASHRAE Journal - December 2023

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