Analysis of the performance of the buried pipe grid of a heat pump

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Transactions of the Engineering Institute of Canada, 6, B-17, pp. 1-24,

1964-03-01

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Analysis of the performance of the buried pipe grid of a heat pump

Brown, W. G.; Wilson, A. G.

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S e r

TH1

N2lr2 no. 214 c . 2 BLDG NATIONAL R E S E A R C H COUNCIL CANADA DIVISION O F BUILDING R E S E A R C H ANALYSIS O F T H E P E R F O R M A N C E O F T H E B U R I E D PIPE GRID O F A H E A T P U M P BY

W. G . BROWN AND A. G . WILSON

R E P R I N T E D F R O M

TRANSACTIONS O F T H E ENGINEERING I N S T I T U T E O F CANADA VOL. 6, NO. B-17, D E C E M B E R 1 9 6 3 , P A P E R NO. E I C - 6 3 - M E C H 28

BUILDING RESEARCH

(-z:--',

O F T H E DIVISION O F BUILDING R E S E A R C H P R I C E

5 0

C E N T S _{O T T A W A NRC 7 9 1 8} MARCH 1964

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ANALYSIS OF TIlE PERFORMANCE OF THE BURIED PIPE GRID OF A HEAT PUMP

by

W.G. Brown and A.G. Wilson Both of Building Services Section

Division of Building Research National Research Council

Ottawa

The heat pump as a means of supplying both winter heating and summer cooling has already seen considerable application, principally in the southern United States where summer air-conditioning is particularly desirable and where air-conditioning loads are comparable to winter heat- ing loads. Its success in turn has inevitably aroused interest in its applicability in more northern regions, as in Canada. Since the heat pump is relatively new in practice however, only a moderate amount of performance data are available, pertaining primarily to operation in the South. Furthermore, available data, which consist primarily of over- all performance factors under localized conditions are not always suited to conversion for design under different conditions of operation. This can be understood by considering the primary operating differences between heat pumps in northern and southern climates. In the North the heating season is both longer and more severe, and summer air-conditioning, if provided, is required for a shorter period. Under these conditions the heat pump is less attractive because its capacity for heating decreases with increasing temperature difference between a building and its

external environment, i.e. the heat source. With the heat pump cycle reversed for cooling the capacity wauld then be greater than required. Consequently, in order to evaluate the feasibility of a heat pump under these conditions, when reduced performance is coupled with high install- ation and equipment costs, it is clear that accurate design methods and data must be available.

Natural heat sources in northern climates (air, water or ground) are available only at comparatively low temperatures when winter heating requirements are greatest. Although air is the most accessible source it has two serious disadvantages: its temperature is the lowest of the natural sources, and there is the difficulty of evaporator coil frosting at time of greatest heat demand. Water is not usually available, hence for most potential heat pump installations the ground would serve as the heat source. The only substantial investigation of a heat pump using the ground as a source under Canadian conditions is that of Hooper (1).

Page 2 o f Vol. 6 No. 017

s t u d y of t h e ground h e a t s o u r c e was i n s t i t u t e d i n Ottawa by t h e D i v i s i o n o f B u i l d i n g R e s e a r c h o f t h e N a t i o n a l R e s e a r c h C o u n c i l . The work was c a r r i e d o u t a t a t i m e when t h e r e was l i m i t e d e x p e r i e n c e w i t h h e a t pumps b u t g r e a t i n t e r e s t i n t h e i r p o s s i b i l i t i e s . T h i s p a p e r r e p o r t s a n a n a l y s i s of e x p e r i m e n t a l r e c o r d s o b t a i n e d from a b u r i e d p i p e g r i d o p e r a t e d o v e r a f u l h e a t i n g s e a s o n . The p u r p o s e of t h e a n a l y s i s is t w o - f o l d : 1. t o compare a c t u a l p i p e p e r f o r m a n c e w i t h t h e o r y o v e r a l o n g p e r i o d o f t i m e , t h e r e b y j u d g i n g t h e a p p l i c a b i l i t y o f t h e t h e o r y f o r p r a c t i c a l u s e , 2. t o i n d i c a t e t h e s u i t a b i l i t y o f s i m p l i f i e d d e s i g n methods. THEORY OF THE THERMAL PERFORMANCE OF BURIED PIPES

B e f o r e p r e s e n t i n g t h e e x p e r i m e n t a l r e s u l t s i t w i l l b e u s e f u l f i r s t t o r e v i e w t h e a v a i l a b l e t h e o r y , which i n p r a c t i c e h a s sometimes b e e n

i g n o r e d o r i n c o m p l e t e l y c o n s i d e r e d . The b a s i c t h e o r y , which h a s been a v a i l a b l e f o r many y e a r s , h a s more r e c e n t l y been c l e a r l y p r e s e n t e d b y

I n g e r s o l l , Zobel and I n g e r s o l l ( 2 ) . The summary g i v e n h e r e i s s i m i l a r . For a s i n g l e p i p e w i t h d r a w i n g h e a t a t a c o n s t a n t r a t e and b u r i e d a t g r e a t d e p t h o r o p e r a t e d f o r r e l a t i v e l y s h o r t t i m e s t h e " d e c r e a s e " i n t e m p e r a t u r e below t h e normal u n d i s t u r b e d t e m p e r a t u r e a t a n y r a d i a l d i s t a n c e i n c l u d i n g t h e p i p e s ~ r f a c e ' ~ i s g i v e n by:

w h e r e : & T t h e " d e c r e a s e " i n t e m p e r a t u r e below t h e normal t e m p e r a t u r e a t t h e p o i n t i n q u e s t i o n

Q

t h e h e a t e x t r a c t i o n r a t e p e r u n i t l e n g t h o f p i p e k

=

t h e t h e r m a l c o n d u c t i v i t y of t h e s o i l I t h e l i n e s o u r c e i n t e g r a l ( s e e r e f e r e n c e ( 2 ) f o r t a b u l a t i o n ) r

=

t h e r a d i u s

=

t h e t h e r m a l d i f f u s i v i t y o f t h e s o i l t

.

t h e t i m e from t h e b e g i n n i n g of h e a t w i t h d r a w a l .

-

+C

For v e r y s h o r t t i m e s ( l e s s t h a n a b o u t 1 h o u r f o r most p r a c t i c a l p u r p o s e s ) t h e t h e o r y i s n o t e x a c t .

Page 3 of Vol. 6 No. B17

When t h e p i p e i s b u r i e d h o r i z o n t a l l y a t f i n i t e d e p t h t h e "image" method must b e u s e d t o o b t a i n t h e c o r r e c t t h e o r e t i c a l t e m p e r a t u r e "decrease". T h i s method c o n s i s t o f i m a g i n i n g a s e c o n d p i p e w i t h n e g a t i v e Q' a t a d i s t a n c e above t h e ' k q u i v a l e n t l ' ground s u r f a c e e q u a l t o t h e d e p t h of t h e r e a l p i p e below t h i s s u r f a c e a s i l l u s t r a t e d i n Fig. 1. F o r p r a c t i c a l p u r p o s e s t h e l v e q u i v a l e n t m s u r f a c e l i e s a t a h e i g h t of y

-

k / h above t h e a c t u a l ground l e v e l . (Here h is t h e c o e f f i c i e n t of h e a t t r a n s f e r between t h e ground s u r f a c e a n d t h e s u r r o u n d i n g a i r . ) The t h e o r e t i c a l t e m p e r a t u r e " d e c r e a s e " a t t h e r e a l p i p e s u r f a c e o r a t a p o i n t i n t h e g r o u n d i s t h e n g i v e n by t h e sum of t h e l'decreases'' d u e t o t h e r e a l and v i r t u a l p i p e s a t t h e i r r e s p e c t i v e d i s t a n c e s r and r ' from t h e p o i n t i n q u e s t i o n .

Summarized i n e q u a t i o n form t h i s becomes:

For l o n g t e r m o r s t e a d y - s t a t e o p e r a t i o n e q u a t i o n ( 2 ) r e d u c e s t o :

When two o r more r e a l p i p e s a r e i n p r o x i m i t y , t h e i r t e m p e r a t u r e

" d e c r e a s e " e f f e c t s a t a g i v e n p o i n t a r e o b t a i n e d by a d d i n g t h e e f f e c t s f o r t h e i n d i v i d u a l p i p e s . The t i m e v a l u e i n s e r t e d i n t h e e q u a t i o n s i s a l w a y s t h a t f r o m t h e b e g i n n i n g o f o p e r a t i o n o f t h e i n d i v i d u a l p i p e s . The above c o n s i d e r a t i o n s a p p l y o n l y t o w i t h d r a w a l o f h e a t a t c o n s t a n t r a t e . When h e a t i s withdrawn i n t e r m i t t e n t l y o r when t h e r a t e i s n o t c o n s t a n t t h e t h e o r e t i c a l t e m p e r a t u r e " d e c r e a s e w is found by s u m a a t i o n o f p a r t i a l e f f e c t s a s g i v e n by e q u a t i o n (2). The m a t h e m a t i c a l method assumes a s e r i e s o f p u l s e s d u r i n g w h i c h h e a t i s e x t r a c t e d a t c o n s t a n t r a t e . For e a c h p u l s e , e q u a t i o n ( 2 ) i s u s e d a s t h o u g h h e a t e x t r a c t i o n w e r e c o n t i n u o u s and t h e n f o l l o w e d a t t h e end of t h e p u l s e p e r i o d by a s e c o n d c o n t i n u o u s i n t e r v a l w i t h e q u a l b u t n e g a t i v e h e a t e x t r a c t i o n . F o r a s i n g l e p u l s e of d u r a t i o n t l t h e n e t t h e o r e t i c a l t e m p e r a t u r e " d e c r e a s e " a t t i m e t from t h e b e g i n n i n g o f t h e p u l s e i s g i v e n by:

Page

4

of Vol.

6

No. B17

The

above equations are mathematically sound but have not had extensive practical verification, particularly for long operating periods. The factors tending to limit applicability are:

1. inherent non-uniform soil properties,

2. non-uniform soil properties due to vertical m~isture distribution,

3.

temperature induced moisture migration,

4.

moisture freezing effects.

Of these f,ctors the last can almost certainly be eliminated for

practical purposes. Ingersoll, Zobel, and Ingersoll (2) point out that freezing e f ~ e c t s are invariably small. The other factors would be expected to depend on soil type as well as local precipitation and watershed.

EXPERIMENTAL

-

EQUIPMENT AND PROCEDURE The Heat Pump

The heat pump used in conjunction with the investigation of the buried pipe grid consisted of 3 Brown-8overi compressors of 2+ hp each which could be connected in parallel. The refrigerant (Freon 12) was circulated through 3 heat exchangers, (evaporators), where heat was extracted from the secondary refrigerant of the ground pipes. The condenser consisted of a forced-air Freon heat exchanger.

The Ground Grid

The ground pipe grid, (Fig. 2) consisted of 5 parallel loops of 1-in.

copper pipe, (1.125 in. O.D.) approximately 189 feet long, on 5-ft. centres and buried

6

ft deep. The l o ~ p s were connected to common supply and

return headers and, by means of shut-off valves, could be used in any parallel combination. All pipes connecting the grid and the headers were insulated to reduce heat transfer between supply and return refrigerant. The liquid circulated in the pipes was calcium chloride brine having specific gravity 1.21 and specific heat 0.71. The original

Page

5

of Vol.

6

No. B17 soil at the grid site was mainly sand, thus sand was used to backfill the

54-

by 100-ft excavation to give the best possible soil uniformity. The completed excavation with the pipes in place prior to backfilling is shown in Fig.

3.

About 200 thermocouples, (20-gauge copper-constantan with neoprene insulation and a waterproof cover), were installed to measure pipe surface, brine, and surrounding ground temperatures. Pipe surface thermocouples were soldered in place at the middle of each supply and return run and also at 15-ft intervals along the middle loop, (loop

C).

Ground thermocouples, supported hy waoden sticks, were installed vert-

ically and horizontally, I/$, 112, 1 and 2 ft from the centre-line at the middle of each pipe run. Additional ground thermocouples were

installed at the same location at depths of 1,

3

and about

9

ft below the ground surface, bedrock was encountered at about

9

ft). Thermocouples were also installed at horizontal distances of

4

and

6

ft beyond the

outermost pipes, and were used to determine the normal ground temperatures during the tests.

Measurements

Ground and pipe-surface temperatures were measured on a self-balancing potentiometer indicator, (sensitivity

0.1'~).

Brine flow rates,

(6

to 20 gal/min) were measured with a calibrated volumetric displace- ment meter. Heat extraction rates were calculated from the temperature increasesalong the pipe and the brine flow rates. Differential pressures across 5/8-in. orifices in each pipe loop were equalized to ensure

identical brine flow rates. In conjunction with operation of the pipe grid, several samples of soil were analyzed for density, moisture content and grain-size distribution.

Scope of Tests and Analysis of Data

The records of the experimental investigation sere obtained in two stages:

(1) Preliminary tests

A

short-term test of 3-daysf duration -was made using pipe loop

C

in the summer prior to the main heating season tests. In the analysis, the results were used to study the operating characteristics of the pipe loop and to determine the effective thermal conductivity and diffusivity of the ground.

( 2 ) Operation during the heating season

From October to Mqy the ground grid pipe loops were used in various combinations with varied heat extraction rates. The method of analysis

Page 6 of Vol. 6 No. B17

of the data for this period consisted of comparing observed pipe surface temperatures at various times with theoretical calculations using the ground properties determined from the preliminary tests.

RESULTS AND DISCUSSION (1) Preliminary Tests

Pipe Surface Temperatures

-

From the point of view of heat pump design the only temperature of importance in connection with the buried pipes is that of the brine. Calculation showed that at the brine flow rates used in the tests the temperature difference between the brine and pipe surface would be a negligible 0.05OF, hence these temperatures were assumed equal. Figure 4 gives pipe surface temperatures measured during

the 3-day preliminary test.

Heat Extraction Rates and Determination of Soil Thermal Properties

-

During the preliminary test some difficulty in the temperature measurement occurred with the result that recordings were made only to the nearest 0.5'~. Under this condition the heat extraction rate could not be

accurately determined directly since the temperature rise of the brine in

0

traversing the pipe loop was of the order of only 2 F. With the help of ground temperature measurements about the pipe, however, coupled with moisture content and density measurements of the soil, the heat extract-

ion rates as well as the effective thermal conductivity a ~ ~ d diffusivity of the soil could be fairly accurately established.

The relationship between

k

and is:

where

p

is the soil density, and C the soil specific heat. P

Kersten (3) shows that the specific heat can be determined from:

where

M

is the percentage moisture content and C is the specific heat of the dry soil, (0.16 to 0.17 ~ t u / l b

-

OF). With the average dry density of 102 lb/cu ft and average moisture content of 12.4 per cent, and with C

=

0.165 the relationship between

k

and becomes

k = 3 0 m .

Since the heat extraction rate was not constant during the test it was necessary to use the procedure represented by equation (4), thereby divid-

ing the test period into short intervals with constant heat exchange in each interval. For the short duration of the test it was not necessary to

P a g e 7 o f Vol. 6 NO. B17 c o n s i d e r t h e e f f e c t o f t h e o f t h e p i p e n o r o f t h e p r o x i m i t y o f s u p p l y and r e t u r n p i p e s . I n t h e a n a l y s i s v a r i o u s v a l u e s o f k w e r e asumed a n d t h e p i p e s u r f a c e t e m p e r a t u r e w e r e u s e d t o d e t e r m i n e t h e Q W s . T h e t h e o r e t i c a l t e m p e r a t u r e decrease^'^ a t 0.25, 0.5 a n d 1.0 f t r a d i i w e r e t h e n c a l c u l a t e d and c o n p a r e d w i t h t h e measured v a l u e s . Normal t e m p e r a t u r e s w e r e assumed t o r e m a i n c o n s t a n t t h r o u g h o u t t h e t e s t p e r i o d a n d e q u a l t o t h e t e m p e r a t u r e s 0 2 j u s t p r i o r t o t h e t e s t . The v a l u e o f k 0.9 B t u / h r - F - f t , ( Q(

=

0.03 f t / h r ) w i t h t h e h e a t e x t r a c t i o n r a t e d i s t r i b u t i o n i n F i g . 5 g a v e t h e b e s t a g r e e - ment b e t w e e n t h e a c t u a l a n d t h e o r e t i c a l t e m p e r a t u r e " d e c r e a s e s " a t t h e v a r i o u s r a d i i ( F i g . 6 ) . A l t h o u g h t h e d i r e c t l y measured h e a t e x t r a c t i o n r a t e s w e r e v e r y i n a c c u r a t e t h e i r v a l u e s w e r e i n o v e r - a l l a g r e e m e n t w i t h t h o s e o f F i g . 5 , from which i t w i l l b e n o t i c e d t h a t h e a t e x t r a c t i o n r a t e s i n c r e a s e d d u r i n g t h e f i r s t few h o u r s warm-up p e r i o d and t h e n d e c r e a s e d g r a d u a l l y f o r t h e r e m a i n d e r o f t h e t e s t . T h i s c o n t i n u a l d e c r e a s e was d u e t o t h e method of o p e r a t i o n o f t h e p r i m a r y r e f r i g e r a t i o n s y s t e m , ( c o n s t a n t s u p e r h e a t i n which h e a t e x t r a c t i o n d e c r e a s e s a s t h e e v a p o r a t o r o r h e a t e x c h a n g e r t e m p e r a t u r e d e c r e a s e s ) . Any o t h e r p r a c t i c a l method o f o p e r a t i o n , e.g. c o n s t a n t e v a p o r a t o r p r e s s u r e , w o u l d a l s o show t h i s t r e n d . T h e r e was some m i n o r u n c e r t a i n t y a b o u t a l c u l a t e d v a l u e s o f h e a t f l o w , c o n d u c t i v i t y a n 3 d i f f u s i v i t y d u e t o p o s s i b l e e r r o r s i n t h e r m o c o u p l e p o s i t i o n i n g , ( a b o u t 1 / 4 i n . ) . I n a d d i t i o n , some t e m p e r a t u r e e r r o r was a p p a r e n t , p r e s u m a b l y d u e t o s w i t c h i n g e r r o r s o r i m p e r f e c t g r o u n d i n g o f e q u i p m e n t , ( s e e 1 . 0 - f t r a d i u s a t b e g i n n i n g of t e s t i n F i g . 6 ) . The 0 v a l u e o f t h e r m a l c o n d u c t i v i t y o f 0.9 ~ t u / h r - F - f t , however, a g r e e s w e l l w i t h t h e a c c e p t e d v a l u e o f 1 . 0 B t u / h r - O ~ - f t f o r s a n d y s o i l h a v i n g a m o i s t - u r e c o n t e n t o f a b o u t 1 0 p e r c e n t ( 3 ) . The a s s u m p t i o n of c o n s t a n t d i f f u s - i v i t y i s s u p p o r t e d by r e s u l t s of P e n r o d ( 4 ) , who r e p o r t s t e s t s u s i n g a h e a t pump t o d e t e r m i n e t h e t h e r m a l d i f f u s i v i t y o f a c l a y - t y p e s o i l . H i s r e s u l t s f o r s e v e r a l d a y s o p e r a t i o n showed a c o n s t a n t d i f f u s i v i t y up t o a t l e a s t 1.5 f t f r o m a b u r i e d p i p e . E f f e c t o f S o i l F r e e z i n g a n d M o i s t u r e M i g r a t i o n

-

The p r e d o m i n a n c e o f l a r g e p a r t i c l e s i n t h e s o i l g r a i n - s i z e d i s t r i b u t i o n i n d i c a t e d t h a t a l m o s t a l l t h e m o i s t u r e p r e s e n t would h a v e b e e n f r o z e n a t 3 2 O ~ . P u b l i s h e d d a t a ( 3 ) show t h a t a t t h e m o i s t u r e c o n t e n t s p r e s e n t i n t h e t e s t f r e e z i n g w o u l d n o t c h a n g e t h e s o i l t h e r m a l p r o p e r t i e s a p p r e c i a b l y . F u r t h e r m o r e , u s i n g a v a i l a b l e t h e o r y ( 2 ) , t h e e r r o r d u e t o n e g l e c t o f t h e l a t e n t h e a t d u r i n g f r e e z i n g was f o u n d t o b e a n e g l i g i b l e 0 . 2 ~ ~ f o r any c o n t i n u o u s t e s t . M o i s t u r e m i g r a t i o n i n d u c e d by t e m p e r a t u r e g r a d i e n t s may o r may n o t h a v e c o n t r i b u t e d t o t h e h e a t e x t r a c t i o n . S i n c e t h e mechanism i s n o t y e t f u l l y u n d e r s t o o d ( 5 ) , a c c u r a t e e s t i m a t e s o f i t s e f f e c t c a n n o t b e made. I n g e n e r a l , however, w i t h m o i s t u r e m i g r a t i o n p r e s e n t t h e h e a t e x t r a c t i o n r a t e s would b e e x p e c t e d t o b e h i g h e r t h a n w i t h o u t m i g r a t i o n d u e t o i n c r e a s e d t h e r m a l c o n d u c t i v i t y o f t h e s o i l n e a r t h e p i p e a n d p o s s i b l y t o

Page 8 of Vol. 6 No. B17

t h e l a t e n t h e a t of c o n d e n s a t i o n of t h e m i g r a t i n g m o i s t u r e . An i n c r e a s e d t h e r m a l c o n d u c t i v i t y n e a r t h e p i p e would t e n d t o c a u s e g r e a t e r d i s c r e p a n c y between t h e t h e o r e t i c a l and measured c u r v e s f o r t h e 0.5 a n d 1 f t r a d i i o f F i g . 6 , w h e r e a s t h e t r a n s f e r of l a t e n t h e a t would t e n d t o r e d u c e t h e d i s c r e p a n c y . U n f o r t u n a t e l y no d e f i n i t e c o n c l u s i o n s can b e drawn a b o u t t h e e f f e c t s o f t h e m o i s t u r e m i g r a t i o n d u e t o t h e i n a c c u r a c y of t h e

measurements. The r e s u l t s of t h e a n a l y s i s i n d i c a t e , however, t h a t s i m p l e c o n d u c t i o n t h e o r y a s s u m i n g c o n s t a n t t h e r m a l c o n d u c t i v i t y a n d d i f f u s i v i t y a g r e e s w e l l w i t h t h e r e s u l t s of measurements.

( 2 ) O p e r a t i o n During t h e H e a t i n g S e a s o n

P r o c e d u r e and Measurements

-

From O c t o b e r t o May t h e p i p e l o o p s were u s e d a r b i t r a r i l y i n v a r i o u s ~ a r a l l e l a r r a n g e m e n t s . For t h e f i r s t 2% weeks i n O c t o b e r p i p e C was used a l o n e f o r 7 h o u r s e a c h d a y , ( e x c e p t i n g weekends). From November t o A p r i l o p e r a t i o n was c o n t i n u o u s f o r a b o u t 100 h o u r s each week. B e g i n n i n g w i t h l o o p C , p r o g r e s s i v e l y more p i p e l o o p s w e r e added t o t h e s y s t e m d u r i n g t h i s p e r i o d . During A p r i l a n d May s h o r t

t e s t s , ( 3 t o 30 h o u r s ) w e r e made u s i n g t h e i n d i v i d u a l p i p e l o o p s . The number o f c o m p r e s s o r s i n u s e was a l s o v a r i e d . During t h i s p e r i o d t e m p e r a t u r e s w e r e measured t w i c e d a i l y w i t h a p r e c i s i o n o f O . l ° F .

A n a l y s i s

-

S i n c e t h e h e a t pump was o p e r a t e d a r b i t r a r i l y , t h e r e s u l t s would b e of l i m i t e d d i r e c t u s e f o r p r a c t i c a l d e s i g n p u r p o s e s . The r e s u l t s o f t h e p r e l i m i n a r y t e s t , however, i n d i c a t e d t h a t t h e o r e t i c a l c a l c u l a t i o n s b a s e d s i m p l y o n h e a t c o n d u c t i o n t h e o r y might b e e x p e c t e d t o a g r e e f a i r l y w e l l w i t h o b s e r v e d d a t a . I f t h i s c o u l d b e e s t a b l i s h e d t h e d e s i g n p r o c e d u r e f o r b u r i e d p i p e s c o u l d be g i v e n a mo:.e r i g i d b a s i s . I n t h i s r e p o r t , t h e n , t e s t r e s u l t s a r e d i s c u s s e d o n l y i n t h e i r r e l a t i o n t o t h e o r y . H e a t e x t r a c t i o n r a t e s were d e t e r m i n e d w i t h t h e h e l p of t h e f o l l o w i n g e q u a t i o n s : where: w = b r i n e flow r a t e , I b p e r h r , C

=

s p e c i f i c h e a t of t h e b r i n e , ( 0 . 7 1 ~ t u / l b - O F ) P

A

_{T ' t e m p e r a t u r e r i s e a l o n g t h e p i p e , ( O F )} L

=

p i p e l e n g t h between t e m p e r a t u r e m e a s u r i n g s t a t i o n s . Average h e a t e x t r a c t i o n r a t e s and o p e r a t i n g t i m e s f o r t h e f u l l h e a t i n g s e a s o n a r e g i v e n i n T a b l e I. The t h e o r e t i c a l p i p e g r i d was assumed t o o p e r a t e w i t h t h e same h e a t e x t r a c t i o n r a t e s a n 3 t h e same t i m e p e r i o d s a s t h e a c t u a l p i p e g r i d . The p i p e s u r f a c e t e m p e r a t u r e s a t v a r i o u s t i m e s d u r i n g t h e h e a t i n g s e a s o n c o u l d t h e n b e c a l c u l a t e d u s i n g t h e t h e o r y and t h e g r o u n d t h e r m a l p r o p e r t i e s as d e t e r m i n e d from t h e p r e l i m i n a r y t e s t . S i n c e a g r e a t

Page 9 of Vol. 6 No. B 1 7

number o f o p e r a t i n g p e r i o d s had t o be c o n s i d e r e d t h e h e a t e x t r a c t i o n r a t e d u r i n g e a c h p e r i o d was assumed c o n s t a n t and e q u a l t o t h e a v e r a g e o b s e r v e d h e a t e x t r a c t i o n r a t e .

The method of c a l c u l a t i n g p i p e s u r f a c e t e m p e r a t u r e s was t h a t o f e q u a t i o n ( 4 ) , t h e c o n t r i b u t i o n t o any p a r t i c u l a r p i p e s u r f a c e t e m p e r a t u r e " d e c r e a s e " due t o a l l o t h e r p i p e s a t t h e i r r e s p e c t i v e d i s t a n c e s b e i n g i n c l u d e d .

E x a c t d i s t a n c e s o f t h e p i p e s from on2 a n o t h e r a r e g i v e n i n Fig. 7. I n p r a c t i c e t h e d i f f e r e n c e between t h e a c t u a l ground s u r f a c e e l e v a t i o n a n d t h e * ' e q u i v a l e n t N e l e v a t i o n c a n b e e x p e c t e d t o b e s m a l l when l i t t l e o r no snow c o v e r i s p r e s e n t , > ? h e n c e t h e " i m a g i n a r y " p i p e s w e r e assumed t o l i e 6 f t , ( e q u a l t o t h e d e p t h of b u r y ) a b o v e t h e a c t u a l ground s u r f a c e . The d i s t a n c e s o f t h e s e "imaginary" o r v i r t u a l p i p e s from s u p p l y p i p e C s a r e t h e n a s shown i n Fig. 7. S i n c e c o n s t a n t h e a t e x t r a c t i o n r a t e s were assumed d u r i n g e a c h o p e r a t i n g p e r i o d i t was n e c e s s a r y t o assume t h e r m a l p r o p e r t i e s s l i g h t l y d i f f e r e n t from t h o s e d e t e r m i n e d i n t h e p r e l i m i n a r y t e s t i n o r d e r t o c a l c u l a t e t h e t e m p e r a t u r e " d e c r e a s e s * ' more a c c u r a t e l y . From t h e p r e l i m i n a r y t e s t i t

was found t h a t t h e b e s t agreement between measured and c a l c u l a t e d temper- a t u r e s was o b t a i n e d w i t h k n 1 . 0 ~ t u / h r - O ~ - f t and

=

0.04 f t 2 / h r when

a c o n s t a n t h e a t e x t r a c t i o n r a t e , e q u a l t o t h e a v e r a g e o v e r t h e t e s t

p e r i o d , was assumed. C o n s e q u e n t l y t h e s e v a l u e s were used i n t h e a n a l y s i s o f t h e h e a t i n g s e a s o n r e c o r d s .

Although t h e above method i s a p p r o x i m a t e , d e t a i l e d c a l c u l a t i o n s were made t o d e t e r m i n e t h e agreement between o b s e r v e d and c a l c u l a t e d t e m p e r a t u r e s a t s e v e r a l t i m e s d u r i n g t h e h e a t i n g s e a s o n . An example of t h e c a l c u l a t i o n p r o c e d u r e i s g i v e n i n t h e Appendix. I t w i l l be n o t e d t h a t a l t h o u g h t h e i n d i v i d u a l c o n t r i b u t i o n s o f a l l p i p e s e x c e p t t h e one under c o n s i d e r a t i o n , and of a l l p e r i o d s e x c e p t t h e l a s t a r e s m a l l , n e v e r t h e l e s s t h e i r t o t a l e f f e c t i s c o n s i d e r a b l e . I n t h e s e c a l c u l a t i o n s t h e d e r i v a t i v e of e q u a t i o n ( 1 ) w i t h r e s p e c t t o t i m e was used t o o b t a i n b e t t e r c o m p u t a t i o n a c c u r a c y f o r t i m e s g r e a t e r t h a n 2000 h o u r s .

The r e s u l t i n g d i f f e r e n t i a l form o f t h e d e r i v a t i v e becomes:

n 4 ( T) ~

=

'

a t

exp -r

_,

4 T k t m 4 t m where, A ( A T ) i s t h e c o n t r i b u t i o n t o t e m p e r a t u r e " d e c r e a s e " c a u s e d by h e a t e x t r a c t i o n a t r a t e

Q'

f o r t h e t i m e p e r i o d A t , and tm i s t h e mean t i m e from t h e p e r i o d i n q u e s t i o n , ( i n t h e Appendix, A ( 4 T ) i s w r i t t e n s i m p l y 4 T).

When t h e snow c o v e r i s a p p r e c i a b l e i t s c o n d u c t a n c e must b e i n c l u d e d i n a d e t e r m i n a t i o n of t h e t w e q u i v a l e n t w e l e v a t i o n .

P a g e l o of Vol. 6 No. 61 7

Observed and c a l c u l a t e d t e m p e r a t u r e s and t e m p e r a t u r e " d e c r e a s e s " f o r t h e v a r i o u s p i p e s of t h e p i p e g r i d a t t h e end of s e v e r a l o p e r a t i n g p e r i o d s

d u r i n g t h e h e a t i n g s e a s o n ( T a b l e 1 1 ) , were i n good agreement f o r e s s e n t i a l l y t h e w h o l e h e a t i n g s e a s o n . I n d e t e r m i n i n g t h e a c t u a l t e m p e r a t u r e s t h e

t o t a l " d e c r e a s e " was s u b t r a c t e d from t h e normal t e m p e r a t u r e s a s measured beyond p i p e s A and E. I n c a s e s i t was a l s o n e c e s s a r y t o a p p l y a s m a l l c o r r e c t i o n t o t h e s e t e m p e r a t u r e s d u e t o t h e e f f e c t s of n e a r b y p i p e s . I n g e n e r a l , t h e c a l c u l a t e d t e m p e r a t u r e s were s l i g h t l y lower t h a n o b s e r v e d v a l u e s , i n d i c a t i n g t h a t a ground p i p e g r i d d e s i g n e d on a t h e o r e t i c a l b a s i s would p r o b a b l y be somewhat o v e r s i z e d . The maximum d i f f e r e n c e n o t e d b e t w e e n o b s e r v e d and c a l c u l a t e d t e m p e r a t u r e s of

OF,

( p i p e A , Mar. 22) was

p r o b a b l y d u e i n p a r t t o c a l c u l a t i o n e r r o r s c a u s e d by t h e u n c e r t a i n t y o f t h e measured h e a t e x t r a c t i o n t e r m s . S i n c e e q u a t i o n (1) shows t h a t h e a t f l o w i s d i r e c t l y p r o p o r t i o n a l t o t e m p e r a t u r e "decrease", t h e amount o f o v e r - d e s i g n which would r e s u l t from t h e o r e t i c a l c a l c u l a t i o n s c a n b e e s t i m a t e d d i r e c t l y from t h e o b s e r v e d and t h e o r e t i c a l t e m p e r a t u r e " d e c r e a s e s " . The r e s u l t s f o r p i p e C , which was most c a r e f u l l y i n s t r u m e n t e d , would i n d i c a t e a p r o b a b l e o v e r d e s i g n of 10 t o 20 p e r c e n t .

DISCUSSION

The d e t a i l e d a n a l y s i s of t h e r e s u l t s o f summertime p r e l i m i n a r y t e s t s was s u f f i c i e n t t o d e t e r m i n e n o t o n l y t h e e f f e c t i v e t h e r m a l p r o p e r t i e s of t h e g r o u n d , b u t a l s o t h e h e a t e x t r a c t i o n r a t e s and t h e i r v a r i a t i o n w i t h t i m e . Although h e a t e x t r a c t i o n r a t e s d u r i n g t h e t e s t w e r e n o t a c c u r a t e l y measured, n e v e r t h e l e s s t h e g e n e r a l agreement between o b s e r v e d and c a l c u l a t e d ternper- a t u r e s i n t h e s u r r o u n d i n g ground i n d i c a t e d t h a t c o n d u c t i o n t h e o r y i g n o r i n g f r e e z i n g and m o i s t u r e m i g r a t i o n e f f e c t s i s a p p l i c a b l e .

With t h e h e l p of t h e r e s u l t s from t h e summertime t e s t , i t was t h e n f o u n d p o s s i b l e t o c a l c u l a t e p i p e s u r f a c e t e m p e r a t u r e s w i t h e n c o u r a g i n g a c c u r a c y f o r a n y t i m e d u r i n g t h e h e a t i n g s e a s o n . The d e g r e e o f a g r e e m e n t between t h e measured and o b s e r v e d t e m p e r a t u r e s o f f e r f u r t h e r e v i d e n c e t h a t s i m p l e c o n d u c t i o n t h e o r y c a n be used. It i s n o t t o b e e x p e c t e d t h a t a l l t y p e s of s o i l woxld y i e l d s u c h encourag- i n g r e s u l t s a s t h e above. I n t h e p r e s e n t i n s t a n c e t h e m o i s t u r e c o n t e n t of t h e ground remained r e l a t i v e l y c o n s t a n t b o t h w i t h d e p t h and t h r o u g h o u t t h e y e a r , t h e r e b y p r e s e r v i n g c o n s t a n t t h e r m a l p r o p e r t i e s . I n some s o i l s , however, l a r g e m o i s t u r e c o n t e n t g r a d i e n t s may be p r e s e n t c a u s i n g v a r i a t i o n s

i n t h e t h e r m a l p r o p e r t i e s a s r e p o r t e d by Hooper ( 1 ) . - . I n a d d i t i o n , m o i s t u r e c o n t e n t s have b e e n o b s e r v e d t o v a r y t h r o u g h o u t t h e y e a r ( 6 ) .

A p p l i c a t i o n t o D e s i g n

The a n a l y s i s h a s shown t h a t f o r o n e i n s t a l l a t i o n a t l e a s t , t h e o r y and a c t u a l p e r f o r m a n c e of a b u r i e d p i p e g r i d w e r e i n good a g r e e m e n t . C o n s e q u e n t l y i t would b e e x p e c t e d t h a t a p i p e g r i d c o u l d b e f a i r l y a c c u r a t e l y d e s i g n e d i n some c a s e s w i t h o u t r e l y i n g on e m p i r i c a l methods. O b v i o u s l y s u c h a method would have t o i g n o r e somewhat t h e c y c l i c n a t u r e o f

Page 1 1 of Vol. 6 No. B17 h e a t demand which would v a r y b o t h d a i l y and t h r o u g h o u t t h e y e a r . To a v o i d t h e s e d i f f i c u l t i e s e q u a t i o n ( 3 ) i n t h e f o l l o w i n g form i s sometimes used f o r d e s i g n p u r p o s e s : w h e r e _Ts i s t h e t e m p e r a t u r e " d e c r e a s e " a t t h e p i p e s u r f a c e u n d e r s t e a d y s t a t e c o n d i t i o n s , S i s t h e d e p t h of b u r y of t h e p i p e , R i s t h e p i p e r a d i u s , and o t h e r symbols a r e a s p r e v i o u s l y d e f i n e d . E q u a t i o n ( 9 ) i s o n l y a p p l i c a b l e when h e a t e x t r a c t i o n i s c o n t i n u o u s d u r i n g t h e h e a t i n g s e a s o n : f o r example, when a u x i l i a r y h e a t i n g i s u s e d t o s u p p l y a p e r c e n t a g e of t h e r e q u i r e d h e a t d u r i n g p e r i o d s of peak demand. T h i s i s t h e t y p e of o p e r a t i o n t e s t e d and d e s c r i b e d by Hooper ( 1 ) .

For i n s t a l l a t i o n s i n which t h e h e a t pump s u p p l i e s a l l , o r n e a r l y a l l , of t h e r e q u i r e d h e a t , however, o p e r a t i o n would n o t b e c o n t i n u o u s and e q u a t i o n ( 9 ) u s i n g t h e peak demand v a l u e f o r

Q'

would a l w a y s r e s u l t i n c o z s i i i e r a b l e o v e r d e s i g n . T h i s i s s o b e c a u s e t h e a b i l i t y of a h e a t pump u s i n g a b u r i e d p i p e t o s u p p l y h e a t d e p e n d s on i t s p r i o r h i s t o r y of o p e r a t i o n

-

u n l i k e o t h e r methods of s u p p l y i n g h e a t . It w i l l be a p p r e c i a t e d t h a t t h i s p a r t o f t h e d e s i g n would b e g u i d e d i n p r a c t i c e by t h e r e l a t i v e c o s t s of t h e h e a t pump i n s t a l l a t i o n and a u x i l i a r y e q u i p m e n t , a s w e l l a s by good judgment

i n e s t i m a t i n g n o t o n l y t h e maximum h e a t demand and i t s d u r a t i o n , b u t a l s o a r e a l i s t i c h e a t demand h i s t o r y p r i o r t o t h e maximum.

The e q u a t i o n s g i v e n i n t h i s p a p e r c a n b e used t o e s t i m a t e t h e s u i t a b i l i t y of v a r i o u s p i p e s i z e s , p i p e s p a c i n g and d e p t h of bury. To c o m p l e t e t h e d e s i g n , t h e t h e r m a l p r o p e r t i e s of t h e ground, a s w e l l a s t h e normal g r o u n d t e m p e r a t u r e s must be known. These l a t t e r would n o t be g e n e r a l l y a v a i l a b l e , b u t methods a r e a v a i l a b l e f o r e s t i m a t i n g them ( 2 ) .

CONCLUSION

On t h e b a s i s of t h e a n a l y s i s of t e s t r e s u l t s from a b u r i e d p i p e g r i d i t

was p o s s i b l e t o show t h a t a c t u a l p e r f o r m a n c e was i n g e n e r a l agreement w i t h t h e o r e t i c a l c a l c u l a t i o n s . Although a d d i t i o n a l f a c t o r s , s u c h a s v a r i a b l e t h e r m a l p r o p e r t i e s , would be e x p e c t e d i n some p r o b l e m s , n e v e r t h e l e s s t h e p r e s e n t t e s t s i n d i c a t e t h a t s a t i s f a c t o r y d e s i g n of b u r i e d p i p e s and p i p e g r i d s c a n b e a c h i e v e d i n many i n s t a n c e s t h r o u g h t h e u s e of c o n d u c t i o n t h e o r y . The f i n d i n g s r e p o r t e d h e r e a p p l y t o a n y b u r i e d p i p e s w h e t h e r b e i n g h e a t e d o r c o o l e d , f o r example t o p i p e s l e a d i n g from a d i s t r i c t h e a t i n g system. The o n l y d i f f e r e n c e i n t h e t h e o r y f o r s u c h a c o n d i t i o n i s t h a t h e a t i s

b e i n g l o s t from t h e p i p e and t e m p e r a t u r e " i n c r e a s e s 1 ' i n s t e a d o f " d e c r e a s e s n o c c u r .

Page 12 of Vol. 6 No. B17

The heat pump work was initiated in 1949 under the direction of

Mr. R.F. Legget, Director of the Division of Building Research, National

Research Council. A Heat Pump Committee was formed at an early stage

to bring together the limited Canadian experience in this field and to

assist in the guidance of the work. The design and installation of the

heat pump equipment was the responsibility of Mr. A.D. Kent. Emphasis was

placed on different aspects of the work as an understanding of the problem

was developed and those involved in the project at various times included

B.M. Hardy, W.G. Colborne, P. Thibault, and J.S. Keeler. The contributions

of the above are gratefully acknowledged. This is a contribution from the

Division of Building Research, National Research Council, and is published

with the approval of the Director of the Division.

REFERENCES

1.

Hooper, F.C., AIL

experimental sesident

ial heat pump. Canadian Journal

of Technology, Vol. 30, p. 180-197, 1952.

2.

Ingersoll, L.R., O.J. Zobel and A.C. Ingersoll. Heat conduction,

Revised edition, University of Wisconsin Press, 1954.

3.

Kersten, M.S., Thermal properties of soils, p. 161, Highway Research

Bosrd, Special Report No.

2,

Frost action in soils. National

Academy of Sciences, U.S. 1952.

4.

Penrod, E.B., Thermal diffusivity of a soil by the use of a heat pump.

Journal Applied Physics, Vol. 21, p. 425, 1950.

5. Kuzmak, J.M. and P.J. Sereda, The mechanism by which water moves

through a porous material subjected to a temperature gradient.

Soil Science, Vol. 84, p. 291, 1957.

6. Smith, G.S., Intermittent ground grids for heat pumps. Transactions

A.S.H.A.E.,

1956.

APPENDIX I

CdLCUIATED COBTRIBUTIOB OF PIPE LOOP C TO COOLING OF ITS SUPPLY PIPE C s FOR FEB. 2

Date t Q 1 Pipe C s ~ i p e ~ s '

!

Pipe C~ P i p e CR'

( s e e a l s o Hours t o B . t . ~ . / h r - f t

.

r = 0.0469 f t r = 12.00 f t r = 5.25 f t r = 13.09 f t

Table I) Feb. 2, f o r pipe C I I A T

2:15 pm ( s e e Table I )

&

( O F )

Bet t o t a l contribution o f c o i l C = 17.B7°P Bet t o t a l contribution of c o i l D = 0.9jeF B e t t o t a l c o n t r l b a t i a n of c o i l B = 1.5j°F

TADLE

I

HEAT EXTilACTION FROM !CHIME

GROUND

LOOPS

h t e Oct. 2 3 4 5 6 1 0 11 1 2 1 3 1 6 1 7 18 19-20 23-26 26-27

!

30-3 Mov. 6-10 J 3 - 1 7 20-22 22-24 2 7 r l Dec. 4-8 11-15 18-22 27-29 Jan. 2 2-5 8-12 15-19 22-26 29-2 Feb. 5-9 12-16 19-23 26-2 Mar. 5-9 12-16 19-22 27-30 A p r

.

2-6 9-13 16-17 1 7 17-18 18 l e - 1 9 1 9 19-20 2 0 20-21 21 23-27 3 0 lriajr 1 2 3 4 10-11 14 1 5 1 6 1 7 18 P i p e l o o p s i n u s e C C C C C C C C C (31 D C , D C1 D C , D C , D C , D C , D C , D C , 9 C , D C , D

c ,

3 C , D C , D C , D C , D B , C , D B , C , D B, C 1 D B , C , D, E B , C , D1 E B , C , D , E B , C, D, E B , C , D , E A , B , C , D , E A , B , C , D , E A , B , C , D , E A , B , C , D, E A , B , C , D , E A , B , C , D, E A , B , C , D , E A , B , C , D, E A , B , C , D , E A A , B , C , D , E B A , B , C , D , E C A , B , C , D, E D A , B , C , D, E E A, B, C , D , E A A A A A A, B, C , D , E A A A A A O p c r a t i n g S t a r t 9:30 Aii 9:OO Ah5 9:oo MI 8:55 AM 9:15 AD 9:05 AM 8:48 AM 8:52 Aiil 9:15 AN 9:14 AM 9:06 Ai'J 9:lO Aii 9:15 flti 9:50 Alf 3:lO E d 8:57Nti 9:30AX 2:40 PLi 9:43 flil 1 : 5 5 PPii 9:05 AM 9:32N$l 10:55AIM 10:00 AN 9:30 fil 9:35 Nv! 11:30 Ah1 9:05 AX 10:20 AN 10:OO Aii 10:15 AN 12:45 PhI 9:41 AM 1 : 3 3 PFI 10:22 AM 9:15 AliI 9:00 AX 10:OO Alii 10:20 Aid 10:15AR 10:OOAlJ 10:30 N8 5:30 &I 4:53 PM 8:45 Nii 4:%0 PI6 8:45 f l L 4 : 3 0 P%i 8:45 MI 4 :30 PId 8:JQ AM 10:15 MU 1:30 F3J 12:30 Pi1 12:JO PivI 1 2 :30 12:30 WI 9:15 AN 8:30 Ah1 12:30 P i d 1 2 :45 PlJ 1 2 : j 0 pifi 1 2 :30

mn

I time Hours o f o p a r a t i o n 7 2 7.2 7 2 7 . 1 7 . 1 7.6 7.5 7.4 7.3 7 . 1 7.2 7.0 31.5 77.7 25.5 103.7 102.8 98.1 52.2 50.8 103.5 103.0 101.7 100.6 54.8 1 . 9 77.2 103.4 102.2 102.8 100.0 99.8 102.8 99.0 102.4 96.5 103.0 78.5 78.2 102.3 102.5 25.0 7.4 15.9 7 8 16.3 7.9 1 6 . 3 7.8 16.0 9.5 102.3 3.0 3.0 3.0 3.0 3.0 30.7 7.5 3 3 3 .O 3.3 3.3 Heat Loop A 2 8 28 26 24 25 9 10 1 0 4 28 6 7 6 6 6 2 2 22 30 3 0 2 9 18 3 1 2 6 44 4 6 47 ( B t u / h r / f t Loop B 24 30 3 1 21 23 23 18 1 7 2 1 22 21 2 1 2 1 8 8 8 3 7 2 4 6 5 5 5 22 e x t r a c t i o n of Loop C 38 4 3 4 4 44 40 4 2 42 46 50 40 37 56 55 48 39 39 17 20 21 24 22 21 20 2 1 1 9 18 24 27 20 20 2 1 1 5 17 1 7 17 17 1 6 1 6 6 7 7 5 5 5 17 3 4 3 1 6 r a t e s p i p e ) Loop D 38 39 56 55 44 39 39 18 2 1 21 26 22 2 1 20 22 22 18 24 26 18 1 9 2 1 1 7 1 7 1 4 1 6 1 4 1 5 1 5 7 8 8 5 6 5 5 20 4 4 1 7 Loop E 28 28 28 23 20 22 23 22 2 1 2 1 7 8 8 6 7 6 5 5 1 7 4 1 9

TABLE

I1 ( A )

OBSERVED

AND CALCULATED PIPE SURFACE TEXPERATURES

TABLE

I1

( B )

Date

Nov.

3

Dec.

8

J a n .

5

J a n .

19

Fyb. 2

Mar.

22

OBSERVED

AmD

CALCULATED PIPE SURFACE TEI~EXATURE

1 f ~ ~ ~ ~ ~ ~ ~ ~ ~ v

Time

4

:40

4

:32

4

:40

4 :30

2

:15

4:30

Temperature i n

d e g r e e s

P

Date

Nov. 3

Dec.

8

J a n .

5

J a n . 1 9

.

Peb.

2

U r . 2 2

Time

4

:40

4:32

4:40

4:30

2

:I5

4:30

Temperature

i n

d e g r e e s

F

s u

P P ~ Y

p i p e

A

s u p p l y

P i Pe

C

Obs.

25

SU P P ~ Y

P i Pe

B

Obs,

21

26

22

24

24

24

C a l c .

1 9

Obs.

24

24

s u p p l y

P i Pe

C

S U P P ~ Y

P i p e

D

s u p p l y

P i

Pe

A

C a l c .

22

27

23

23

2 1

23

C a l c .

2 1

20

s u p p l y

P i p e

D

I

Obs.

31

18

20

17

1 6

1 5

Obs.

31

18

1 6

15

S ~ P P ~ Y

Pi

Pe

B

Obs.

1 4

Obs.

2 1

27

24

25

Re

t u r n

P i p e

E

C a l c .

30

18

1 9

18

20

17

C a l c .

31

1.9

20

1 6

Obs.

1 6

1 5

Calc.

20

Calc.

- - - - .

2 1

27

20

24

Obs.

2 5

26

Calc.

20

20

R e t u r n

P i p e

E

Calc,

'

1 9

22

Obs.

1 6

1 4

' ~ a l c .

2 1

18

ANALYSIS OF THE PERFORMANCE OF THE B U R I E D PIPE G R I D OF A HEAT PUMP

by

W.G. Brown and A.G. W i l s o n

FIGVRX CAPTIONS

-

1. D i s t a n c e s i n v o l v e d i n a p p l i c a t i o n of t h e "image" method t o d e t e r m i n e t e a p e r a t u r s s a b o u t a b u r i e d p i p e . 2 . Layout of t h e ground p i p e g r i d .

-

L o c a t i o n of t h e t h e r m o c o u p l e s u p p o r t s

-

Loop C p i p , ? s u r f a c e t h e r m o c o u p l e s a t o e

-

M o i s t u r e c o n t e n t and d e n s i t y d e t e r m i n a t i o n s t a t i o n s .

3 . E x c a v a t i o n f o r t h e ground p i p e g r i d s h o s i n g p i p e l o o p s and thermo- c o u p l e s u p p o r t s .

4. P i p e l o o p C s u r f a c e t e m p e r a t u r e s i n p r e l i m i n a r y symmer t e s t s ( a v e r a g e f o r s u p p l y and r e t u r n p i p e s ) .

5. Heat e x t r a c t i o n r a t e s from p i p e C i n p r e l i m i n a r y summer t e s t c a l c u l a t e d u s i n g measured t e m p e r a t u r e d a t a .

6. T e m p e r a t u r e " d e c r e a s e " a t v a r i o u s r a d i i a b o u t p i p e l o o p C f o r summer p r r l i m i r ~ a r y te s t .

- - -

Average measured v a l u e s f o r s u p p l y and r e t u r n p i p z s .

0

-

C a l c u l a t e d v a l u e s , w i t h k

=

0.9 ~ t u / h r - F - f t and M

=

0.03 f t 2 / h r . 7 . D i s t a n c e s of r e a l and v i r t u a l p i p e s from s u p p l y p i p e C

,

S ( f o r u s e i n c a l c u l a t i o n of C s u r f a c e t e m p e r a t u r e s ) . S

VIRTUAL PlPE

I

"EQUIVALENT" SURFACE

_{- - - + - - - -}

ti-

LAYOUT

OF

TRE

GROUi;lD PIP% GRID.

I

-

LOCATION

OF

TIiiRI.TOCOUPLE SUPPORTS

o

-

LOOP C P I P 3 SURFACT 'EERI~lOCOTJPLTS

@

TO

@

-

EIOISTUR3 COlmI\TT

d1D

DTlTSITY DETER-

MIi'lATIOB STATIO7TS.

+.)_(.I

A V A T I

33

?3fY

GlsirLY3D

PIPL

Gfi

ID

B

0 I-I

HOURS FROM START OF TEST

'I!ElIP$RATUR:3 "DZCRFASS" AT V.4RIOUS RllDII AZ9UT

P I E LOOP C PO3 SUICF<R PRSLI:~IIT,IRY T3ST

- - -

AVER,lGE !:lEASURlD V.~TIUE'S FOR SUPPLY Al'lD

?,ZTITRI! PIPYB

.

-

C.rJXIJL.2T";D VALES, ':IITII W . 9 ETU/~KR- 9 - F T A X D ~ 4 . 0 3 F!C2 //FIR.