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correlations to practiceborehole heat exchangers, from .../Jeff Spitler - Design and... ·...
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2016-09-19 1 Design and optimization of groundwater-filled and grouted borehole heat exchangers, from correlations to practice Jeffrey D. Spitler Oklahoma State University Saqib Javed Chalmers University of Technology Lund University
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Transcript of correlations to practiceborehole heat exchangers, from .../Jeff Spitler - Design and... ·...
20
16
-09
-191
De
sign
an
d o
ptim
izatio
n o
f g
rou
nd
wa
ter-fille
d a
nd
gro
ute
d
bo
reh
ole
he
at e
xcha
ng
ers, fro
m
corre
latio
ns to
pra
ctice
Jeffre
y D
. Sp
itler
Ok
lah
om
a S
tate
Un
iversity
Sa
qib
Jave
d
Ch
alm
ers U
nive
rsity o
f Tech
no
log
y
Lun
d U
nive
rsity
20
16
-09
-192
No
rth A
me
rica
•G
rou
ted
•N
o ca
sing
•S
ha
llow
er
•B
ore
ho
le re
sistan
ce
ap
pro
xima
tely
co
nsta
nt.
Sca
nd
ina
via
•G
rou
nd
-wa
ter fille
d
•C
ase
d fro
m su
rface
to
be
dro
ck.
•“U
sua
lly” sh
ort d
istan
ce
to b
ed
rock
.
•D
ee
pe
r
•B
ore
ho
le re
sistan
ce
varie
s with
an
nu
lus
tem
pe
ratu
re a
nd
he
at
extra
ction
rate
.
0
20
40
60
80
10
0
12
0
14
0
16
0
18
0
20
019
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
Borehole Depth (m)
Av
era
ge
Bo
reh
ole
De
pth
Sw
ed
en
USA
All b
ore
ho
les
Pu
blicly
-bid
pro
jects
(Ave
rag
e #
BH
~1
00
)
Swe
dish
da
ta: F
rom
SG
U, v
ia S
ign
hild
Ge
hlin
of Sve
nsk
t Ge
on
erg
icen
trum
USA
da
ta: F
rom
an
alysis o
f com
me
rcial p
roje
ct da
tab
ase
s, Rya
n C
ard
ao
f Ge
oP
ro,
Inc., S
ou
th D
ako
ta
20
16
-09
-193
Ba
ckg
rou
nd
–G
W-fille
d b
ore
ho
les
•Lu
nd
Un
iversity
-C
lae
sson
& H
ellströ
m(1
98
8)
sho
we
d e
ffects o
f na
tura
l con
vectio
n in
bo
reh
ole
s.
•Lu
nd
–K
jellsso
n&
He
llström
(19
97
) –la
bo
rato
ry m
ea
sure
me
nts
•Lu
leå
Un
iv. Tech
no
log
y –
Ge
hlin
, et a
l. (20
03
) –th
erm
osip
ho
n e
ffect
•Lu
leå
–G
usta
fsson
, et a
l. (20
08
-20
10
) –n
atu
ral
con
vectio
n in
bo
reh
ole
s –sim
ula
tion
an
d
exp
erim
en
t
•S
till no
wa
y to
qu
an
tify e
ffects fo
r de
sign
pu
rpo
ses.
Exp
erim
en
tal fa
cility a
t Ch
alm
ers
-10 -5 0 5
10
15
20
04
89
61
44
19
22
40
28
83
36
38
4
Temperature Change [K]
Tim
e [h
ou
rs]
Te
st 4
Te
st 1
Te
st 5
Te
st 2
Te
st 3
-75
-50
-25 0
25
50
75
10
0
04
89
61
44
19
22
40
28
83
36
38
4
Heat Transfer Rate (W/m)
Tim
e [h
ou
rs]
Te
st 4T
est 1
Te
st 5
Te
st 2
Te
st 3
Se
ries o
f inje
ction
an
d
extra
ction
TR
Ts ove
r 27
mo
nth
s.
20
16
-09
-194
Re
sults
0
0.0
2
0.0
4
0.0
6
0.0
8
0.1
0.1
2
02
04
06
08
0
Effective Borehole Resistance
(K/(W/m))
Ab
solu
te h
ea
t flux (W
/m)
1°C
-3°C
12
°C-1
4°C
16
°C-2
0°C
20
°C-2
4°C
Co
mp
ariso
n to
Gro
ute
d B
ore
ho
les
0.0
0
0.0
2
0.0
4
0.0
6
0.0
8
0.1
0
0.1
2
0.1
4
0.0
00
.02
0.0
40
.06
0.0
80
.10
0.1
20
.14
Eff. BH Resistance - Grouted (K/(W/m))
Eff. B
H R
esistan
ce -
GW
-filled
(K/(W
/m))
Std. B
en
ton
ite G
rou
tT
EG
, k=1
.73
TE
G,k=
2.7
7
20
16
-09
-195
Co
rrela
tion
s
()
25
.0
*1
4.
0ann
ann
Ra
Nu
=
()
25
.0
*30
.0
po
po
Ra
Nu
=
()
25
.0
*20
.0
BH
WB
HW
Ra
Nu
=
6E
3.1
7E
0.4
*>
>a
nn
Ra
6E
8.1
7E1
.4
*>
>p
oR
a
5E
4.5
7.9
E2
*>
>B
HW
Ra
For th
e re
sistan
ce a
cross th
e a
nn
ulu
s:
For re
sistan
ce a
t the
ou
ter p
ipe
wa
ll:
For re
sistan
ce a
t the
bo
reh
ole
wa
ll:
An
nu
lus co
rrela
tion
0 5 10 15 20 25 30 350.0E+01.0E+7
2.0E+73.0E+7
4.0E+75.0E+7
Nusselt number
Rayleigh Num
ber
20
16
-09
-196
Oth
er B
ore
ho
les a
t Ch
alm
ers
0.0
0
0.0
1
0.0
2
0.0
3
0.0
4
0.0
5
0.0
6
0.0
7
0.0
8
0.0
9
0.1
0
0.1
1
0.1
2
0.1
3
0.1
4
0.1
5
0.0
00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
00
.11
0.1
20
.13
0.1
40
.15
Rb* (model), K/(W/m)
Rb
* (e
xpe
rime
nta
l), K/(W
/m)
UT
UH
F
Lab
ora
tory
me
asu
rem
en
ts (3
m h
igh
test b
ore
ho
le)
0.0
0
0.0
2
0.0
4
0.0
6
0.0
8
0.1
0
0.1
2
0.1
4
01
02
03
04
05
0
Borehole resistance (K/(W/m))
Me
an
Flu
id T
em
pe
ratu
re (°C
)
50
W/m
75
W/m
10
0 W
/m
K&
H 5
0 W
/m
K&
H 7
5 W
/m
K&
H 1
00
W/m
20
16
-09
-197
No
rwe
gia
n B
ore
ho
les
0.0
0
0.0
1
0.0
2
0.0
3
0.0
4
0.0
5
0.0
6
0.0
7
0.0
8
0.0
9
0.1
0
0.1
1
0.1
2
0.1
3
0.1
4
0.1
5
0.0
00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
00
.11
0.1
20
.13
0.1
40
.15
Rb* (model), K/(W/m)
Rb
* (e
xpe
rime
nta
l), K/(W
/m)
UT
UH
F
Sw
ed
ish B
ore
ho
les
0.0
0
0.0
5
0.1
0
0.1
5
0.2
0
0.2
5
0.3
0
0.3
5
0.0
00
.05
0.1
00
.15
0.2
00
.25
0.3
00
.35
Rb* (model), K/(W/m)
Rb
* (e
xpe
rime
nta
l), K/(W
/m)
UT
UH
F
20
16
-09
-198
Ap
plica
tion
: Se
nsitiv
ity to
An
nu
lus Te
mp
era
ture
0.0
0
0.0
2
0.0
4
0.0
6
0.0
8
0.1
0
0.1
2
05
10
15
20
25
Rb, Rb* (K/(W/m))
An
nu
lus T
em
pe
ratu
re (°C
)
Rb
Rb
*
He
at re
jectio
n ra
te ke
pt a
t 35
W/m
Ap
plica
tion
: Se
nsitiv
ity to
He
at R
eje
ction
Ra
te
0.0
0
0.0
2
0.0
4
0.0
6
0.0
8
0.1
0
0.1
2
01
02
03
04
05
06
07
08
0
Rb, Rb* (K/(W/m))
He
at re
jectio
n ra
te (W
/m)
Rb
Rb
*
An
nu
lus te
mp
era
ture
kep
t at 8
.9°C
20
16
-09
-199
Co
nclu
sion
s –G
W-fille
d B
ore
ho
les
•C
orre
latio
ns fo
r na
tura
l con
vectio
n in
bo
reh
ole
s w
ith sin
gle
U-tu
be
s give
rea
son
ab
le p
erfo
rma
nce
.
•G
ives “co
nse
rvative
” pre
dictio
n o
f resista
nce
for d
esig
n
pu
rpo
ses.
•Im
ple
me
nte
d in
GLH
EP
RO
.
•E
ffect o
f he
igh
t on
scalin
g?
•A
vera
ge
un
certa
inty, a
nn
ulu
s Nu
sselt
#: ±
29
%
•B
ette
r con
trolle
d e
xpe
rime
nts: n
ice, b
ut e
xpe
nsive
.
•C
orre
latio
ns fo
r do
ub
le U
-tub
es, co
-axia
l he
at
exch
an
ge
rs are
ne
ed
ed
.
Gro
ute
d B
ore
ho
les
•M
an
y sim
plifie
d m
eth
od
s for p
red
icting
bo
reh
ole
th
erm
al re
sistan
ce. (Fe
w fo
r inte
rna
l the
rma
l re
sistan
ce.)
•M
ultip
ole
alg
orith
m –
Lun
d U
nive
rsity (1
98
7); la
ter
refin
em
en
t Cla
esso
na
nd
He
llström
(20
11
)•
2-d
ime
nsio
na
l con
du
ction
he
at tra
nsfe
r calcu
latio
n
•V
aria
ble
-ord
er: 1
0th
ord
er g
ives a
ccura
cy to
8 sig
nifica
nt
dig
its
•V
erifie
d a
ga
inst d
eta
iled
nu
me
rical m
od
els
•D
ifficult to
imp
lem
en
t
•H
en
ce, sim
ple
r me
tho
ds a
re d
esira
ble
20
16
-09
-19
10
Pa
ram
etric S
tud
y: 2
16
Ca
ses
Pa
ram
ete
rLe
ve
lsN
um
be
r of
lev
els
θθθ θ2
–T
he
ratio
of
the
bo
reh
ole
rad
ius
too
ute
rp
ipe
rad
ius.
Sin
cep
ipe
ou
ter
dia
me
ter
isa
lwa
ys
fixed
at
32
mm
,b
ore
ho
led
iam
ete
rsa
re9
6m
m,
19
2m
m,
an
d2
88
mm
.
3, 6
, 93
Sh
an
ksp
acin
gco
nfig
ura
tion
;co
rresp
on
ds
toP
au
l’s
(19
96
)A
,B
,C
con
figu
ratio
ns
Clo
se, M
od
era
te, W
ide
For θ
2=
3, θ
1 =
0.3
33
, 0.5
55
, 0.6
67
For θ
2 =
6, θ
1 =
0.1
67
, 0.3
89
, 0.8
33
For θ
2 =
9, θ
1 =
0.1
11
,0.3
70
,0.8
89
3
λλλ λ–
the
gro
un
dth
erm
al
con
du
ctivity
(W/m
-K)
1, 2
, 3, 4
4
λλλ λg
–th
eg
rou
nd
the
rma
lco
nd
uctiv
ity(W
/m-K
)0
.6, 1
.2, 1
.8, 2
.4, 3
.0, 3
.66
Sa
mp
le R
esu
lts (λ=
3)
0.0
0
0.1
0
0.2
0
0.3
0
0.4
0
0.5
0
0.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
Rg [m-K/W]
λg
[W/m
-K] S
ho
nd
er &
Be
ck (20
00
)K
av
an
au
gh
(19
85
)G
u &
O'N
ea
l (19
98
)P
au
l (19
96
)S
ha
rqa
wy
et a
l. (20
09
)B
au
er e
t al. (2
01
1)
Liao
et a
l. (20
12
)A
bd
Ela
tty et a
l. (20
12
)0
th-o
rde
r Mu
ltipo
le1
st-ord
er M
ultip
ole
Mu
ltipo
le (2
01
1)
20
16
-09
-19
11
Sa
mp
le R
esu
lts (λ=
3)
0.0
0
0.1
0
0.2
0
0.3
0
0.4
0
0.5
0
0.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
Rg [m-K/W]
λg
[W/m
-K]
Sho
nd
er &
Be
ck (20
00
)K
avanau
gh (1
98
5)
Gu
& O
'Ne
al (19
98
)P
aul (1
99
6)
Sha
rqa
wy e
t al. (2
00
9)
Bau
er e
t al. (20
11
)Lia
o e
t al. (2
01
2)
Ab
d E
latty et a
l. (20
12
)0
th-o
rde
r Mu
ltipo
le1
st-ord
er M
ultip
ole
Mu
ltipo
le (2
01
1)
Sa
mp
le R
esu
lts (λ=
3)
0.0
0
0.1
0
0.2
0
0.3
0
0.4
0
0.5
0
0.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
Rg [m-K/W]
λg
[W/m
-K]
Sh
on
de
r & B
eck (2
00
0)
Ka
va
na
ug
h (1
98
5)
Gu
& O
'Ne
al (1
99
8)
Pa
ul (1
99
6)
Sh
arq
aw
y e
t al. (2
00
9)
Ba
ue
r et a
l. (20
11
)Lia
o e
t al. (2
01
2)
Ab
d E
latty
et a
l. (20
12
)0
th-o
rde
r Mu
ltipo
le1
st-ord
er M
ultip
ole
Mu
ltipo
le (2
01
1)
20
16
-09
-19
12
Be
st me
tho
ds
Gro
ut T
herm
al
Co
nd
uctiv
ity (λ
g )
Lo
w
(0.6
– 1
.2 W
/m-K
)
− S
harq
awy et al. (2
009
)
− F
irst-ord
er M
ultip
ole
− F
irst-ord
er M
ultip
ole
− F
irst-ord
er Mu
ltipo
le
Med
ium
(1.2
– 2
.4 W
/m-K
)
− S
ho
nd
er & B
eck (2
00
0)
− K
avan
aug
h. (1
98
5)
− G
u &
O'N
eal (199
8)
− L
iao et al. (2
012
)
− Z
eroth
-ord
er Multip
ole
− F
irst-ord
er M
ultip
ole
− Z
eroth
-ord
er Mu
ltipo
le
− F
irst-ord
er M
ultip
ole
− L
iao et al. (2
012
)
− F
irst-ord
er M
ultip
ole
Hig
h
(2.4
– 3
.6 W
/m-K
)
− S
ho
nd
er & B
eck (200
0)
− K
ava
na
ugh
(198
5)
− G
u &
O'N
eal (1
998
)
− L
iao
et al. (2
01
2)
− Z
eroth
-ord
er Mu
ltipo
le
− F
irst-ord
er Mu
ltipo
le
− Z
eroth
-ord
er Multip
ole
− F
irst-ord
er M
ultip
ole
− L
iao
et al. (2
012
)
− F
irst-ord
er M
ultip
ole
•M
etho
ds
here
have
mea
nab
solu
tep
ercen
tage
error
low
erth
an
3%
and
maxim
um
ab
solu
te
percen
tage
error
lessth
an1
0%
.
•Italics
ind
icatem
axim
um
abso
lute
percen
tage
error
low
erth
an5
%.
•Italics
+B
old
ind
icatem
axim
um
abso
lute
error
smaller
than
1%
.
Imp
licatio
ns fo
r De
sign
•1
st-ord
er m
ultip
ole
exp
ressio
ns g
ive e
xcelle
nt
accu
racy
ove
r en
tire ra
ng
e.
(MA
PE
=0
.2%
, Ma
x. AP
E=
2%
)
•N
oth
ing
else
com
es clo
se.
•E
asy
to im
ple
me
nt, e
.g.:
�� =�2�� ,
� = ����� ,� = ���� =
12�� � ,�= �� −�
�� +� ,�=2��� ��
�� = 14��� �+ln�
2�� 1−�� �� −� 1− 4��� �
1−�� �
1+�1−� +� 1+
16��� �1−�� �
20
16
-09
-19
13
Imp
licatio
ns fo
r De
sign
•S
imila
r stud
y fo
r inte
rna
l the
rma
l resista
nce
.
•M
AP
E=
0.2
%, M
ax. A
PE
< 6
%
•S
till ea
sy to
imp
lem
en
t.
�� =1��� �+ln
1+�� �� 1−�� � −
� 1−�� �+4��� 1+�1−� (1−�� �� −� 1−�� �+8��� � (1+�� �!
Gro
ut R
esista
nce
•A
ffecte
d b
y:
•P
ipe
resista
nce
•G
rou
nd
the
rma
l con
du
ctivity
0.0
0
0.0
5
0.1
0
0.1
5
0.2
0
0th-order
Multipole
1st-order
Multipole
Multipole
method
0th-order
Multipole
1st-order
Multipole
Multipole
method
Tu
rbu
len
t (Rp
=0
.05
)Lam
inar (R
p=
0.1
85
)
Rg [m-K/W]
-1 0 1 2 3 4 5 6
-18
0-9
00
90
18
0
Temperature Rise [K]
ψ
ψ ψ
ψ [D
eg
ree
s]
Bo
reh
ole
wa
ll − Tu
rbu
len
t B
ore
ho
le w
all −
Lam
ina
r P
ipe
1 −
Turb
ule
nt
Pip
e 1
− La
min
ar
20
16
-09
-19
14
Se
nsitiv
ity to
Gro
un
d C
on
du
ctivity
0.0
0
0.0
5
0.1
0
0.1
5
0.2
0
0.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
Rg [(m-K)/W]
λg
[W/(m
-K)]
λ = 1
W/(m
-K)
λ = 4
W/(m
-K)
θ₂ =
9
θ₂ =
3
Qu
estio
ns?
20
16
-09
-19
15
Re
fere
nce
sS
pitler, J.D
. and
S. Jav
ed. 2
01
6. C
alcu
latio
n o
f bo
reho
le therm
al resista
nce. In
S.J.
Rees A
dvan
ces in g
rou
nd
-sou
rce heat p
um
p sy
stems. L
on
do
n: W
oo
dh
eadP
ub
lishin
g.
Sp
itler, J.D., S
. Javed
and
R. K
alskin
Ram
stad. 2
01
6. N
atu
ral co
nvectio
n in
gro
un
dw
ater-filled
bo
reho
les used
as g
rou
nd
hea
t excha
ng
ers.Ap
plied
En
ergy.
16
4:3
52
-36
5.
Sp
itler, J.D., R
. Gru
nd
man
nan
d S
. Javed
. 20
16
. Ca
lcula
tion
To
ol fo
r Effective
Bo
reho
le Th
erma
l Resista
nce. 1
2th
RE
HV
A W
orld
Co
ngress –
Clim
a2
01
6. A
albo
rg,
Den
mark
. May
22
-25
.
Javed
, S. an
d J.D
. Sp
itler. 20
16
. Accu
racy o
f Bo
reho
le Th
erma
l Resista
nce
Ca
lcula
tion
Meth
od
s for G
rou
ted S
ing
le U-tu
be G
rou
nd
Hea
t Exch
an
gers. S
ub
mitted
for P
ub
lication
.
