ASHRAE Journal - July 2010 - 27

1000	W/(m2·K)	[176	Btu/h·ft2·°F]	while	 for	laminar	flows	it	is	generally	below	 100	 W/(m2·K)	 [17.6	 Btu/h·ft2·°F].	 In	 the	present	case,	everything	else	being	 equal,	a	laminar	flow	with	hconv	=	100	 W/(m2·K)	[17.6	Btu/h·ft2·°F]	would	lead	 to	a	required	borehole	length	of	174.5	 m	(573	ft). Finally,	 the	 proposed	 approach	 was	 checked	 against	 the	 DST	 model, 12	 which	is	often	considered	as	a	reference	 software	tool	for	simulating	ground	heat	 exchangers.	In	this	test,	the	DST	model	 is	 run	 with	 three	 consecutive	 constant	 ground	 load	 pulses	 of	 10	 years,	 one	 month,	and	six	hours	using	the	data	given	 in	the	first	set	of	inputs.	Results	from	the	 DST	model	give	a	total	length	of	150	m	 (492	ft),	which	is	in	good	agreement	with	 the	 value	 of	 151.7	 m	 (498	 ft)	 obtained	 with	the	proposed	approach.	
Multiple Boreholes

1st SET OF INPUTS Ground loads peak hourly ground load monthly ground load yearly average ground load Ground properties thermal conductivity thermal diffusivity Undisturbed ground temperature Fluid properties thermal heat capacity total mass flow rate per kW of peak hourly ground load max/min heat pump inlet temperature Borehole characteristics borehole radius pipe inner radius pipe outer radius grout thermal conductivity pipe thermal conductivity center-to-center distance between pipes internal convection coefficient

UNITS qh qm qy k α Tg Cp m fls TinHP rbore rpin rpext kgrout kpipe LU hconv W W W W.m K 2 -1 m .day °C
-1 -1

Single borehole 12000 6000 1500 2 0.086 15 4200 0.050 40.2 0.060 0.0137 0.0167 1.50 0.42 0.0511 1000

Multiple boreholes -392250 -100000 -1762 2.25 0.068 12.41 4000 0.074 4.44 0.054 0.0137 0.0167 1.73 0.45 0.0471 1000

J.kg-1.K-1 -1 -1 kg.s .kW °C m m m W.m -1.K-1 W.m .K
-1 -1

m W.m -2.K-1

1st SET OF RESULTS Calculation of the effective borehole thermal resistance convective resistance Rconv pipe resistance Rp grout resistance Rg effective borehole thermal resistance Rb Calculation of the effective ground thermal resistances short term (6 hours pulse) R6h medium term (1 month pulse) R1m long term (10 years pulse) R10y Total length calculation assuming no borehole thermal interference heat pump outlet temperature ToutHP average fluid temperature in the borehole Tm total length L 2nd SET OF INPUTS Borefield characteristics

m.K.W -1 m.K.W -1 m.K.W m.K.W m.K.W
-1 -1

0.012 0.076 0.076 0.120 0.114 0.180 0.191 45.0 42.6 151.7

0.012 0.071 0.060 0.102 0.101 0.160 0.170 1.1 2.8 9899.3

-1

m.K.W -1 m.K.W -1 °C °C m

In	this	second	example,	the	data	are	 provided	by	Shonder,	et	al.14	They	are	 relative	to	a	school	and	have	been	used	 to	 compare	 five	 different	 design	 programs	against	each	other.	This	heating	 application	uses	a	12	×	10	borefield	with	 6.1	m	(20	ft)	spacing	between	boreholes.	 Much	of	the	data	in	the	first	set	of	inputs	 is	 extracted	 from	 the	 comparison	 study14	 except	 for	 the	 center-to-center	 distance	between	pipes	that	is	assumed	 to	be	equal	to	0.0471	m	(1.85	in).	This	 corresponds	 to	 a	 case	 where	 the	 distance	between	the	pipes	is	the	same	as	 the	distance	between	the	pipes	and	the	 borehole	wall.	After	analyzing	test	data	 achieved	on	various	boreholes	Remund	 13	 recommended	 this	 spacing	 for	 such	 calculations.	 For	multiple	boreholes,	the	procedure	 is	a	little	more	complicated	than	for	single	 boreholes	 due	 to	 the	 presence	 of	 Tp	 in	 Equation	 1.	This	 temperature	 penalty	 depends	 on	 the	 borehole	 depth,	 which	 is	 the	 unknown	 a priori.	An	 iterative	 procedure	 is	 required.	 The	 following	 three-step	procedure	is	recommended	to	 properly	account	for	Tp.	 First,	calculations	should	be	performed	 by	 assuming	 that	 Tp	 is	 zero	 as	 for	 a	 single	borehole.	This	will	lead	to	an	approximate	value	of	the	total	length	of	the	
July	2010	

distance between boreholes number of boreholes borefield aspect ratio

B NB A

m -

6.1 120 1.2

FINAL RESULTS Total length calculation (with Tp) 1st iteration

distance-depth ratio logarithm of dimensionless time temperature penalty total borefield length

B/H ln(t10y/ts) Tp L B/H ln(t10y/ts) Tp L B/H ln(t10y/ts) Tp L B/H ln(t10y/ts) Tp L B/H ln(t10y/ts) Tp L L H

°C m °C m °C m °C m °C m m m

0.074 -1.120 -0.240 10151.5 0.072 -1.170 -0.238 10149.7 0.072 -1.170 -0.238 10149.7 0.072 -1.170 -0.238 10149.7 0.072 -1.170 -0.238 10149.7 10149.7 84.6

2nd iteration

distance-depth ratio logarithm of dimensionless time temperature penalty total borefield length distance-depth ratio logarithm of dimensionless time temperature penalty total borefield length distance-depth ratio logarithm of dimensionless time temperature penalty total borefield length distance-depth ratio logarithm of dimensionless time temperature penalty total borefield length total borefield length borehole depth

3rd iteration

4th iteration

5th iteration

Final results

Figure 5: Spreadsheet for designing vertical geothermal boreholes—examples of results.

borefield.	In	the	present	example,	the	approximate	length	is	9899	m	(32,470	ft). Based	 on	 this	 approximate	 value,	 the	 designer	enters	the	second	set	of	inputs,	

i.e.,	B	(distance	between	the	boreholes),	 NB	(number	of	boreholes)	and	A	(aspect	 ratio	of	the	borefield).	Depending	on	the	 available	 ground	 area	 and	 the	 ground	
ASHRAE	Journal	 27
ASHRAE Journal - July 2010

Table of Contents for the Digital Edition of ASHRAE Journal - July 2010
