En i onmen al and Clima e Technologies
2021, ol. 25, no. 1, pp. 479–490
h ps://doi.o g/10.2478/ uec -2021-0035
h ps://con en .sciendo.com
479
©2021 Viole a Madan, Ingo Weidlich.
This is an open access a icle licensed unde he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/
licenses/by/4.0).
In es iga ion on Rela i e Hea Losses and Gains o
Hea ing and Cooling Ne wo ks
Viole a MADAN1*, Ingo WEIDLICH2
1, 2 Ha enCi y Uni e si y, Henning-Vosche au-Pla z 1, Hambu g, 20457, Ge many
Abs ac – The in eg a ion o dis ic hea ing (DH) and cooling (DC) in he sus ainable ene gy
sys em o he u u e equi es a signi ican educ ion in ope a ing empe a u es. Supply
empe a u es below 70 °C a e equi ed o new 4 h Gene a ion DH. Main bene i s a e he use
o low exe gy hea sou ces and he educ ion o hea losses. The educ ion o hea losses is
achie ed by educing he d i ing empe a u e di e ence be ween he medium pipe and he
g ound. The dec ease o he e u n empe a u e le el is limi ed by he consume beha iou
and he g ound empe a u e le el. As a consequence, he educ ion o he supply empe a u e
is accompanied by a educ ion o he maximum ansmi able hea low. Fo ene gy e iciency
and economic easons, he ela i e hea losses a e he e o e an impo an design alue o DH
ne wo ks. The s udy p oposes an app oach o es ima e he ela i e hea losses by using s eady-
s a e hea loss models and analyses he alues o di e en DH gene a ions. In pa icula , due
o he ising o he nea -su ace soil empe a u e, he ela i e cold losses a e also s udied.
Keywo ds – Cold losses; dis ic cooling; dis ic hea ing; hea losses
Nomencla u e
A C oss-sec ional a ea m²
cp Hea capaci y J/(kgK)
D Hal o he dis ance be ween he pipe axes m
di, do Inne and ou e insula ion diame e m
h Hea loss ac o –
T Tempe a u e K
Q

Hea low a e W
q Leng h ela ed hea low W/m
ν Flow eloci y m/s
λg, λi Hea conduc i i y o he g ound and insula ion W/(mK)
H Bu ial dep h m
R The mal Resis ance mK/W
1. INTRODUCTION
Dis ic hea ing (DH) and dis ic cooling (DC) can mainly con ibu e o a sus ainable
ene gy sys em based on enewable ene gy p oduc ion. The empo al and local uncoupling o
*Co esponding au ho .
E-mail add ess: iole a.madan@hcu-hambu g.de
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he demand and supply a e ad an ageous o he in eg a ion o enewable ene gy sou ces and
he sec o coupling app oach [1]. O he bene i s a e he signi ican imp o emen o he ene gy
e iciency o high popula ion densi y a eas and mo e lexible exchange o he ene gy sou ce.
The de elopmen o DH ex ends o e ou gene a ions and includes he op imiza ion o
ma e ials, hea sou ces, pipe design and ope a ing condi ions. Dec easing o he ope a ing
empe a u e is one o he main objec i es o newe DH gene a ions, as a lowe empe a u e
le el a ou s he in eg a ion o low empe a u e hea sou ces and he educ ion o hea losses.
Lund e al. de ine a supply empe a u e le el below 100 °C o he 3 d and 30–70 °C o he
4 h Gene a ion DH [1].
The hea losses and gains a e he main in luencing pa ame e s o design and e iciency o
a DH o DC sys em. I is a majo in e es o minimize he hea losses (and gains in case o
DC) o ene gy sa ings and economic easons. Addi ional app oaches o dec ease hea losses
a e he imp o emen o he pipe insula ion and he applica ion o win o iple pipes [2].
Howe e , lowe ope a ion empe a u es p omise he highe impac compa ed o ma e ial
changes in he pipe sys ems.
Fo he de e mina ion o s eady–s a e hea losses, analy ic solu ions [3] and explici
solu ions o speci ic geome ies a e a ailable [4], [5]. The explici solu ion o Wallen én is
implemen ed in DIN EN 13941–1, which ep esen s he s a e o he a o he hea loss
calcula ion in dis ic hea ing [6]. Wallen én p oposes an explici solu ion o one o wo
insula ed pipes and win pipes in he g ound by applying he mul ipole me hod [5]. K isgaa d
and Had ig in oduce a co ec ed dep h o he pipe axis o conside he hea ans e
coe icien a he g ound su ace [4]. This assump ion is also adap ed in DIN EN 13941–1
[6]. The model o K isgaa d and Had ig has been e alua ed by Oppel e al. o DH and DC
alica ion. In [7] a maximum de ia ion o 2.0–2.7 % o DH and 3.8–6.2 % o DC was
epo ed o he K isgaa d/Had ig model compa ed o simula ions wi h he ini e olume
me hod in he case o wo insula ed single pipes.
Bøhm e iewed di e en me hods o he calcula ion o s eady–s a e hea losses and
obse ed he undis u bed empe a u e o he g ound as a c i ical alue o he exis ing s eady–
s a e models. In his s udy, he did expe imen s and FEM simula ions o ind he loca ion o an
undis u bed g ound empe a u e ha can be applied in he s eady-s a e heo y o achie e
accep able accu acy. He ound he loca ion o his empe a u e app oxima ely a he op o
he casing o p einsula ed pipes [8]. Howe e , o he esea che s showed a measu able
inc ease o he empe a u e nea o DH pipes in he ield [9], [10]. Ano he ac o is he change
in he nea –su ace empe a u e ield due o clima e change, u baniza ion and he mal
exposu e o he soil. Henning and Limbe g ound a g ound empe a u e ise o mo e han 4 K
in u ban egions compa ed o u al egions in Be lin [11].
Rega ding low empe a u e DH, wo e ec s ha e o be conside ed: The dec ease o he
supply (and e u n) empe a u e on he one hand and he dec ease o empe a u e g adien
be ween he e u n and supply pipe on he o he hand. The educ ion o he supply empe a u e
le el goes along wi h a signi ican educ ion o he absolu e hea losses o he sys em. The
dec ease o empe a u e g adien be ween he supply and e u n pipe educes he ans e ed
hea ene gy o he consume . This loss o pe o mance could be compensa ed by he end o
low ene gy buildings [1]. S a egies o supply exis ing buildings wi h empe a u es below
70 °C a e desc ibed in [12]. In his con ex he ela i e hea losses may be he main design
alue o new DH gene a ions.
The ela i e hea losses a e usually calcula ed depending on he annual hea consump ion
[13] o by a de ailed modelling o he speci ic ne wo k [14], [15]. I no measu emen s o he
consump ion da a a e a ailable, he es ima ion o he annual demand o space hea ing and
domes ic ho wa e is p one o e o s [13], [14]. The s udy p oposes an app oach o es ima e
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ela i e hea losses and gains by applying s eady–s a e hea loss models. The calcula ion
me hod can easily be adap ed by he ne wo k ope a o o ge a i s imp ession o he ne wo k
e iciency and capaci y equi ed o he hea p oduc ion. In he ollowing s udy, he ela i e
hea losses a e calcula ed wi h he p oposed me hod and he esul s a e compa ed o di e en
gene a ions DH ne wo ks and DC. Hea ing and cooling ne wo ks in Hambu g and
su oundings ha e been selec ed o c ea e ealis ic bounda y condi ions o he calcula ions.
2. METHODOLOGY
In he ollowing, he da abase, he hea loss models and he model pa ame e s applied o
he calcula ions will be desc ibed.
2.1. Da abase
Hambu g’s DH ne wo k and se e al o he local hea ing ne wo ks a e co e ing abou a
qua e o he hea ing demand o he ci y. The he mal egis e o Hambu g p o ides an
o e iew o he hea ing ne wo ks and ope a o s [16]. Fo he in es iga ion o he hea losses,
di e en hea ne wo ks a e selec ed ha mee he empe a u e equi emen s o he second,
hi d and ou h DH gene a ions [1]. Hambu g’s DH ne wo k p o ides a supply empe a u e
o 133 °C o he s anda d ou e empe a u e o −12 °C o Hambu g acco ding o he na ional
annex o DIN EN 12831 [17]. Due o his high empe a u e le el, Hambu g’s DH ne wo k is
classi ied as 2nd Gene a ion DH. To ep esen he 4 h Gene a ion DH (TS < 70 °C), he supply
and e u n empe a u es o a new esiden ial a ea ‘Waisengä en’ in Schwe in, a ci y in
no he n Ge many, ha e been selec ed o he s udy. The new esiden ial buildings in he a ea
o ‘Waisengä en’ is ope a ed by S ad we ke Schwe in GmbH, he public u ili y p o ide o
Schwe in [18]. The ene gy concep o he new buildings combines geo he mal hea supply
wi h home s a ions o egula e he domes ic ho wa e empe a u e [19].
The empe a u es o he dis ic and local hea ing ne wo ks selec ed o his s udy a e aken
om he o icial echnical connec ion condi ions o he ne wo k ope a o s [18], [20]–[22] and
a e summa ized in Table 1. The e u n empe a u es in he o icial echnical connec ion
condi ions a e maximum e u n empe a u es allowed by he ope a o s. Fo he ollowing
in es iga ion, a win e and summe case a e conside ed o in es iga e he ela i e hea losses
and gains o he sys ems.
TABLE 1. SELECTED HEATING AND COOLING NETWORKS
Sys em ope a o
Supply/ e u n
empe a u e win e case
(−12 °C)
Supply and e u n
empe a u e summe case
(20 °C)
Dis ic Hea ing
Gene a ion acco ding o
Lund e al. [1]
Wä me Hambu g GmbH 133/60 °C 90/20 °C 2nd
Innogy SE 100/55 °C 69/20 °C 3 d
HanseWe k Na u GmbH 80/45 °C 70/45 °C 3 d
S ad we ke Schwe in GmbH 56/35 °C 56/35 °C 4 h
Wä me Hambu g GmbH
(Cooling ne wo k) 8/15 °C 6/12 °C –
A highe accu acy o de e mina ion o hea losses and gains can be ob ained by knowing
he g ound empe a u e p o ile [23]. The e o e, his o ical wea he da a o Hambu g lis ed in
DIN 4710:2003–01 [24] has been applied in he s eady s a e hea loss models p esen ed in
sec ion 2.2. The g ound empe a u es in Janua y and July a e ep esen a i e o he win e
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and summe case. Fo he sake o a classi ica ion he esul ing empe a u e p o iles o
Hambu g we e d awn oge he wi h gene alized cu es acco ding o Dahlem in Fig. 1.
I is impo an o poin ou ha he wea he da a summa ized in DIN 4710:2003–01 [24] is
he a e age empe a u e o he yea s 1961–1990. Cu en wea he da a om he Ge man
Wea he Se ice (Deu sche We e diens ) [25] sugges s ha he g ound empe a u es sligh ly
inc eased in he las decades and he ambien empe a u e can ise up o 35 °C du ing he
summe season.
Fig. 1. G ound empe a u e p o iles o he ci y o Hambu g compa ed wi h cu es acco ding o Dahlem wi hou g ound
wa e [23], [24].
2.2. Model o S eady-S a e Hea Loss
Dis ic hea ing ne wo ks usually consis o wo insula ed symme ical bu ied pipes wi h a
ci cula c oss–sec ion as shown in Fig. 2. Fo he calcula ion o he s eady–s a e hea losses,
pu e hea conduc ion is usually assumed, while con ec ion, mois u e anspo and phase
changes a e neglec ed. O he assump ions a e homogeneous ma e ial p ope ies and no
he mal esis ances o he medium pipe and casing [10]. Radial hea conduc ion h ough he
insula ion o he g ound and be ween he pipes is he p ocess desc ibed by he mos s eady–
s a e hea loss models o DH applica ion. In he ollowing, he e m ‘hea loss’ e e s o he
leng h- ela ed hea loss in W/m i no o he wise speci ied in he ex .
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Fig. 2. Geome y o wo insula ed pipes in he g ound.
Wallen én desc ibes he hea loss o each DH pipe as a supe posi ion o symme ical and
an i–symme ical hea losses e e ing o he mul ipole me hod [3]. Thus, he hea losses o
he supply and e u n pipe can be calcula ed acco ding o Eq. (1) and Eq. (2).
,,
s sym s a s
qq q= +
(1)
,,
sym a
qq q= −
(2)
The symme ical and an i–symme ical hea losses (3) and (4) can be calcula ed by applying
he empe a u es Tsym and Ta de ined in Eq. (5) and Eq. (6).
( )2
sym sym g g sym
q TT h= − ⋅ πλ ⋅
(3)
2
a a ga
qT h= ⋅ πλ ⋅
(4)
2
s
sym
TT
T+
=
(5)
2
s
a
TT
T−
=
(6)
The i s –o de mul ipole o mula o calcula e he ecip ocal o he hea loss ac o o he
symme ical p oblem is de ined in Eq. (7). The o mula o he an i–symme ical hea loss
ac o is gi en in [5]. The dimensionless he mal esis ance pa ame e β is de ined in Eq. (8).
22 2
00 0
222
1
2
0
4416( )
4
ln ln 1 1
14
sym
o
dd d
D H DH
HH
hdD d
D
−

  
++

  

 ⋅+
  
 

= +β+ + −
 

 +β 
  +
−β 
(7)
ln
go
ii
d
d
λ
β= 
λ
(8)
Wallen én quan i ies he ela i e e o s o he calcula ed hea losses as less han 0.5 %,
when he i s o de o mulae a e used [5]. Fo he ollowing analysis, he Wallen én and
Tg, λg

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K isgaa d/Had ig model a e applied o calcula e he sys em hea losses. The wo models
di e in he calcula ion o he he mal soil esis ance and in he alue o he g ound
empe a u e. The co ec ed bu ied dep h implemen ed by K isgaa d and Had ig o conside
he hea ans e coe icien a he soil su ace is de ined in Eq. (9). Fo a de ailed desc ip ion
o he K isgaa d/Had ig model e e o [4].
*
0.0685
g
HH= + ⋅λ
(9)
The g ound empe a u e applied o he hea loss calcula ions is a key di e ence be ween
he Wallen én and K isgaa d/Had ig model. Wallen én p oposes he empe a u e on he
g ound su ace, while K isgaa d and Had ig apply he empe a u e a he g ound le el o he
pipe axis a ins alla ion dep h. To in es iga e he in luence o he g ound empe a u e on
calcula ed hea losses, he esul s ob ained by using he o iginal models a e p esen ed among
he esul s in sec ion 3. Bøhm in es iga ed he loca ion o an undis u bed g ound empe a u e
o s eady–s a e hea loss calcula ion o achie e accu a e esul s. The undis u bed g ound
empe a u e posi ion o p einsula ed pipes ound by Bøhm co esponds o he g ound
empe a u e a he op o he casing and is applied in his s udy. Fo his pu pose, he unc ion
equa ion o he ci y o Hambu g de i ed using he wea he da a in DIN 4710:2003–01 is
applied [24].
To calcula e he ela i e hea losses, he sum o he leng h ela ed hea losses (1) and (2) is
di ided by he maximum amoun o hea anspo ed in he ne wo k acco ding o he basic
equa ion o he modynamics (10). The ele an c oss–sec ional a ea A is he c oss–sec ional
a ea o he wa e pipe. Due o he s a iona y condi ion, only he ull load case is conside ed.
Acco ding o he AGFW (Ge man Dis ic Hea ing Associa ion), he s eady–s a e condi ion
is only applicable o ne wo k leng hs below 10 km [26].
()
p s
Q A c T T=ρ⋅ ⋅ ⋅ ⋅ −

(10)
The esul ing pa ame e p oposed in his s udy o es ima e ela i e hea losses is a
pe cen age hea loss pe me e o pipe leng h acco ding o Eq. (11). The co esponding uni
is %/m.

100%
s
qq
q
Q
+
= ⋅

(11)
2.3. Model Pa ame e s
The calcula ion pa ame e s a e selec ed acco ding o ypical ope a ing condi ions o DH
ne wo ks. Key pa ame e s a e summa ized in Table 2. The s eel pipe dimension o DN 200
can be applied o dis ic hea ing and cooling; he dimensions o he pipe and insula ion
comply wi h he s anda ds DIN EN 253 and DIN EN 17415–1 [27], [28].
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TABLE 2. CALCULATION PARAMETERS
Pa ame e Symbol Value
Hea conduc i i y o he g ound λg 1.2 W/(mK)
Hea conduc i i y o he insula ion λi 0.027 W/(mK)
C oss-sec ional a ea A 0.0346 m²
Hea capaci y o wa e cp 4190 J/(kgK)
Inne insula ion diame e di 0.219 m
Ou e insula ion diame e do 0.315 m
Dis ance be ween he pipe axes 2D 0.565 m
Bu ied dep h H 0.9575 m
Flow eloci y ν 1 m/s
3. RESULTS
Fo he ne wo ks lis ed in Table 1 he absolu e hea losses and gains calcula ed wi h he
Wallen én and K isgaa d/Had ig model a e isualized in Fig. 3 and Fig. 4, each o win e
and summe case. The esul s p esen ed in Fig. 2 and Fig. 3 a e ob ained by applying he
g ound empe a u es p oposed by he o iginal au ho s o isualize he in luence o he selec ed
g ound empe a u e on he hea losses. Fo he Wallen én model, a g ound su ace empe a u e
o 0.8 °C (win e ) and 18.5 °C (summe ) and o he K isgaa d/Had ig model 4.6 °C (win e )
and 14.9 °C (summe ) a e applied [24].
Fig. 3. Calcula ed hea losses – win e case.
0
10
20
30
40
50
60
70
80
0
10
20
30
40
50
60
70
80
133/60 100/55 80/45 56/35 8/15
Del a |supply- e u n|, K
Hea losses and cold gains, W/m
Ne wo k supply/ e u n empe a u e, °C
Win e
Wallen en model K isgaa d/Had ig model del aT supply- e u n
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Fig. 4. Calcula ed hea and cold losses – summe case.
Fig. 5. Calcula ed ela i e hea losses – win e case.
The esul ing hea losses ob ained wi h he Wallen én and K isgaa d/Had ig model show a
cons an de ia ion o abou 3 W/m. The ela i e de ia ion be ween he calcula ed hea losses
inc eases wi h dec easing empe a u e g adien be ween he wa e pipe and g ound
empe a u e. The ela i e de ia ion has a ange o 4–12 % o he DH and eaches he
maximum alue o 38 % o DC. The ela i e de ia ion be ween he wo models is less han
0.5 % i he same alue is applied o he g ound empe a u e.
-20
0
20
40
60
80
-10
-5
0
5
10
15
20
25
30
35
40
90/20 69/20 70/45 56/35 6/12
Del a |supply- e u n|, K
Hea -and cold losses, W/m
Ne wo k supply/ e u n empe a u e, °C
Summe
Wallen en model K isgaa d/Had ig model del aT supply- e u n
0
10
20
30
40
50
60
70
80
0
0.2
0.4
0.6
0.8
1
1.2
133/60 100/55 80/45 56/35 8/15
Del a |supply- e u n|, K
Rela i e hea losses and cold gains, %/km
Ne wo k supply/ e u n empe a u e, °C
Win e
el. hea losses el. cold gains del a T supply- e u n
a
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The Wallen én model wi h he undis u bed g ound empe a u e p oposed by Bøhm is
applied o de e mine he ela i e hea losses. The g ound le el o he op o he pipe casing
co esponds o a dep h o 0.8 m. The undis u bed g ound empe a u e esul s in 4 °C o he
win e case and 15.5 °C o he summe case. The esul ing ela i e hea losses pe kilome e
pipe leng h a e p esen ed in Fig. 5 and Fig. 6.
Fig. 6. Calcula ed ela i e hea - and cold losses – summe case.
4. DISCUSSION
In he p e ious sec ion he esul s ob ained by he Wallen én and K isgaa d/Had ig model
o s eady–s a e hea losses o di e en hea ing and one cooling ne wo k ha e been p esen ed
in Fig. 3 and Fig. 4. A cons an de ia ion o abou 3 W/m occu s be ween he esul s due o
di e en g ound empe a u es implemen ed in he o iginal models. As he hea losses a e
cons an ly dec easing wi h dec easing empe a u e g adien be ween he medium pipe and
g ound empe a u e, he ela i e de ia ion o he hea losses ises up o 38 % o he DC case.
These esul s o he di e en s eady–s a e models o low empe a u e DH and DC show he
signi icance o an accu a e selec ion o he undis u bed g ound empe a u e o hese
applica ions. In his con ex , an op imized g ound empe a u e posi ion o he 4 h Gene a ion
DH and o DC should be u he in es iga ed. The o e all end o dec easing hea losses o
newe DH gene a ions due o he dec ease o he d i ing empe a u e g adien be ween he
pipe and he g ound is con i med in he esul s o he win e and summe case. The ou line s
o he 90/20 °C and 69/20 °C ne wo ks in he summe can be explained by he lowe e u n
empe a u e o 20 °C compa ed o he o he in es iga ed hea ing ne wo ks.
In his wo k, he pe cen age hea loss pe me e o pipe leng h is p oposed as a pa ame e
o es ima e he ela i e hea losses and gains o a sys em. In Fig. 5 and Fig. 6 he ela i e hea
losses a e p esen ed o a win e and summe case.
In he win e case, he ela i e hea losses o he in es iga ed hea ing ne wo ks inc ease,
while he empe a u e le el is dec easing. As he absolu e hea losses dec ease as shown in
Fig. 3, he in luence o he slope o he anspo ed hea lux 𝑄𝑄󰇗 causes he ising end. Fo
0
20
40
60
80
100
0
0.2
0.4
0.6
0.8
1
90/20 69/20 70/45 56/35 6/12
Del aT |supply- e u n|, K
Rela i e hea -and cold losses, %/km
Ne wo k supply/ e u n empe a u e, °C
Summe
el. hea losses el. cold losses del aT supply- e u n