ASHRAE Journal - December 2021 - 35

TECHNICAL FEATURE
can be found in GHXSizing as well as in Ahmadfard and
Bernier.2
Table 4 shows the input parameters and results when
the bore fi eld is rectangular and the monthly method
(L3) is used. The monthly average ground loads are
determined by averaging all hourly loads during
that month. The monthly peak ground loads are the
maximum hourly loads in a given month, and they are
assumed here to last six hours. As shown in cell C69 in
Table 4, the calculated borehole length is 125.9 m (413 ft)
for the rectangular confi guration.
Figure 5a shows the evolution of the solution and
indicates that convergence is obtained after 15 iterations.
Figure 5b illustrates the evolutions of the maximum
and minimum inlet fl uid temperatures for the
fi nal borehole length (125.9 m [413 ft]). It can be seen
that the heat pump inlet fl uid temperature reaches its
maximum design value of 38°C (100.4°F) during July
of the twentieth year. As for the minimum inlet fl uid
temperature, a value of 9°C (48.2°F), which is much
higher than the minimum design fl uid temperature
of 0°C (32°F), is reached during the fi rst year of
operation.
It can be shown that the pentagonal shape leads to
a shorter length of 106.2 m (348 ft) per borehole. This
is because there is less borehole thermal interaction
as the average distance between boreholes is greater
than for the rectangular shape. The length difference
observed between the rectangular and pentagonal
shapes is in line with the conclusions of a recent study
by Spitler, et al.,20 who have shown that when compared
to regularly spaced confi gurations, irregular
bore fi eld geometries can signifi cantly reduce the total
drilling length of a bore fi eld while yielding the same
performance.
Table 5 examines variations on this sizing problem
for the rectangular geometry. Increasing the number
of segments to 12 for the determination of g-functions
decreases the length to 122.6 m (402 ft) for the rectangular
confi guration, a reduction of 2.6%. In addition, if
short-term effects (i.e., borehole thermal capacity) are
considered, the borehole length is reduced to 118.1 m
(388 ft), a reduction of 6.2% from the base case. The
hourly method leads to a borehole length of 123.7 m
(406 ft).
It is also interesting to compare these results to
those obtained with L2 methods (assuming a peak
FIGURE 4 Geometries used in the third sizing problem (8 m corresponds to 26.2 ft).
Building
Building
8 m
8 m
FIGURE 5 (A) Evolution of the borehole length during the solution process and
(B) fluid temperature evolution for the L3 (monthly) sizing model.
A.
450
400
350
300
250
200
150
100
50
1
B.
39
34
29
24
19
14
9
2 4 6 8 10 12 14 16 18 20
Year
Tin,hp,min (°C)
Tin,hp,max (°C)
duration of 6 hours). As shown in Table 5, the modifi
ed ASHRAE equation and the alternative ASHRAE
equation give borehole lengths of 128.7 m (422 ft)
and 125.5 m (412 ft), respectively, close to the results
obtained with the higher-level methods. Finally, it
is to be noted that this problem was solved using
two commercially available software tools, which
D E C E M B E R 2 0 2 1 ashrae.o rg ASHRAE JOURNAL
35
6
Iteration Number
11
16
8 m
Inlet Fluid Temperature (°C)
Boreholes Length (m)
https://www.ashrae.org/
ASHRAE Journal - December 2021

Table of Contents for the Digital Edition of ASHRAE Journal - December 2021
