ASHRAE Journal - July 2010 - 26

	

Rp =

(11) 	

p , ext

U

Rg =

1 4p k grout

Design Criterion TinHP

Calculation of the Total Length of Borehole L

4

grout

bore

grout

4

bore

( )
U

4

where hconv	is	the	film	convection	coefficient,	 rp,in	and	rp,ext	are	the	inner	and	outer	 radii	of	the	pipe,	 kpipe	is	the	thermal	conductivity	of	the	 pipe	material,	 kgrout	 is	 the	 thermal	 conductivity	 of	 the	grout,	 k	is	the	ground	thermal	conductivity,	 and	 LU is the	center-to-center	distance	between	the	two	pipes	(Figure 3).
Application Cases

Final Calculation of the Total Length of Borehole In the Borefield L

Figure 4: Flowchart of the calculation procedure for boreholes sizing.

Equations	 1	 to	 11	 have	 been	 implemented	in	an	Excel	spreadsheet.	The	calculation	procedure	for	designing	a	single	 borehole	 or	 a	 borefield	 is	 illustrated	 in	 the	flowchart	presented	in	Figure 4.	The	 spreadsheet	can	either	be	used	for	heating	or	cooling	applications	with	proper	 signs	for	ground	loads	(positive	ground	 loads	 correspond	 to	 heat	 rejection	 into	 the	ground).	The	use	of	the	spreadsheet	 will	 be	 illustrated	 using	 two	 examples	 for	a	single	borehole	and	for	a	borefield.	 Results	will	be	compared	with	those	obtained	from	more	sophisticated	software	 tools	and	from	data	found	in	the	literature. As	 shown	 in	 Figure 5,	 there	 are	 four	 major	parts	in	the	spreadsheet:	first	set	of	inputs;	first	set	of	results;	second	set	of	inputs;	 and	final	results	(which	includes	five	sets	 of	 iterations).	The	 iterations	 are	 required	 for	multiple	borehole	configurations	as	Tp	 depends	on	H,	which	is	not	known	a priori.
Single Borehole

The	 first	 application	 is	 for	 a	 single	 borehole	in	a	cooling-dominated	build26	 ASHRAE	Journal	

ing.	The	three	ground	thermal	pulses	are	 12	 kW	 (40,000	 Btu/h),	 6	 kW	 (20,000	 Btu/h)	 and	 1.5	 kW	 (5,000	 Btu/h),	 respectively.	This	 is	 roughly	 equivalent	 to	 a	 2.5-ton	 (8.8	 kW)	 heat	 pump	 that	 rejects	12	kW	into	the	ground	at	peak	 conditions.	 The	 monthly	 and	 yearly	 pulses	 can	 be	 estimated	 using	 hourly	 simulation	results	or	equivalent	full	load	 operating	hours.	 Using	this	last	method,	it	is	estimated	 here	 that	 during	 the	 peak	 month,	 the	 heat	pump	operates	half	the	time,	so	the	 monthly	ground	load	is	6	kW.	Finally,	on	 an	annual	basis,	the	net	amount	of	heat	 rejected	into	the	ground	is	equivalent	to	 a	heat	pump	operating	one-eighth	of	the	 time,	which	corresponds	to	1.5	kW. Then,	 ground	 properties	 and	 fluid	 thermal	capacity	are	entered,	as	well	as	 the	total	mass	flow	rate	per	kW	of	peak	 hourly	 ground	 load.	The	 maximum	 (in	 cooling)	 or	 minimum	 (in	 heating)	 heat	 pump	 inlet	 temperature	 acceptable	 at	 peak	 conditions	 is	 entered	 next.	This	 value,	in	fact,	is	the	design	criterion	for	 sizing	the	borefield. The	 next	 block	 of	 inputs	 concerns	 the	 borehole	 characteristics	 from	 the	 borehole	radius	to	the	internal	film	coefficient.	The	block	for	the	first	set	of	results	
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shows	intermediate	results	on	all	effective	 thermal	resistances,	as	well	as	the	total	 length,	which	is	151.7	m	(498	ft)	in	this	 case.	The	heat	pump	outlet	temperature	 as	well	as	the	average	fluid	temperature	 in	the	borehole	also	are	provided.	They	 are	obtained	through	an	energy	balance	 on	the	borehole.	In	the	case	of	a	single	 borehole,	calculations	stop	here	as	there	 is	no	borehole	thermal	interference. It	is	interesting	to	note	the	impact	of	 a	few	key	parameters.	For	example,	in	 cooling	mode,	if	the	undisturbed	ground	 temperature	is	20°C	(68°F)	(instead	of	 15°C	 [59°F]),	 the	 length	 increases	 to	 185.2	m	(608	ft),	a	22%	increase.	The	 last	two	values	in	the	borehole	characteristics	block,	LU and hconv	have	a	relatively	large	impact	on	the	effective	borehole	resistance	(Rb)	and,	consequently,	 on	 the	 borehole	 length.	 For	 example,	 when	the	distance	between	the	pipes	is	 reduced	to	a	point	where	the	pipes	are	 touching	each	other,	i.e.,	Lu	is	reduced	 from	 0.0511	 to	 0.0334	 m	 (2	 in.	 to	 1.3	 in.),	the	value	of	Rb	increases	from	0.120	 to	by	0.143	m·K/W)	[0.246	°F·ft·h/Btu]	 (an	18%	increase	with	a	corresponding	 increase	of	the	total	length	of	6.5%	from	 151.7	to	161.6	m	[498	ft	to	530	ft]).	For	 turbulent	 flows,	 hconv	 is	 usually	 above	
	 July	 2010

Iterations Until Convergence on L

Designer Choice of the Borefield Parameters B, NB, A

New Input Parameters, Depending on L B/H, In(t10y /ts)

Multiple Boreholes Design (Borefield)

  r  r   ln   + ln   +      r   L           k −k  r   ln  k +k   r − L      2
bore bore

               

Single Borehole Design

ln rp,ext / rp,in 	 2 k pipe

(

)

(10)

Input Parameters Ground Loads: qh, qm, qy Soil Properties Fluid Properties Borehole Characteristics
ASHRAE Journal - July 2010

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