Engineering, 2013, 5, 202-207
doi:10.4236/eng.2013.51b037 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Copyright © 2013 SciRes. ENG
3D Conceptual Modelling and Direct Utilization
Calculations of the Albanian Geothermal Resources
Nevton Kodhelaj1, Aida Bode2
1Department of Energy Resources, Faculty of Geology and Mining, Polytechnic University, Tirana, Albania
2Department of Natural Resources, Faculty of Geology and Mining, Polytechnic University, Tirana, Albania
Email: nevtonkodheli@yahoo.com, boaal@yahoo.com
Received 2013
ABSTRACT
Balneological use of the Albanian Geothermal springs and waters dates back centuries, but the first modern use started
in 1937. Unfortunately they had not been used for its energetic values yet. The temperature of the water is above 60°C
and the flow above 1 6 l/s, thus direc t utilization is po ssible, in particular for space heati ng. Thre e-dimensional te mpera-
ture field calculations and engineering calculations on a heating system with heat exchangers are presented here. The
results show that the water temperature is expected to be stable and considerably higher temperature is expected through
deep well drilli ng. T he Unive rsit y’s Ca mpus o f Tir ana is c omposed of 29 buildings, which are partially heated through
a coal heater. The installed capacity is 2558kW while the coal consumption is about 920 kg/h. The University’s Ca mpus
of Tirana is one of the most important areas a nd with the hi ghest d ensit y of pop ulatio n in T ira na, so it is the bes t ar ea to
show the heat exchanger efficiency. The economic analyses prove that the bor ehole heat exchangers are more conven-
ient than the coal heating syst ems .
Keywords: Geothermal; Temperature Field; Mode lling ; Radiato rs; Wells; Bo rehole Heat Exchangers
1. Introduction
Albania is a small country of only 28 787 km2 surface
area and around 4 500 000 inhabitants, situated in the
southwest part of the Balkan Peninsula, next to the
boundary of the A fri ca n a nd the Eur o -Asiatic p lates. T his
setting makes the presence of geothermal resources pos-
sible. Surface manifestations of geothermal resources are
found throughout Albania, ranging from the region of
Peshkopia in the northeast, where hot springs with water
temperature of about 43°C and inflow above 14 l/s are
found, through the central part of the country with dif-
ferent sources (including the springs of Llixha-Elbasan)
with temperatures above 66°C, to the Peri-Adriatic de-
pression with a number of wells (drilled for oil and gas
research) producing water with temperatures around
40°C with variable yield s. The thermal waters in Albania
are only used for balneology. This form of use dates back
to early in history, or to the time of the Roman Empire
(i.e. the Sarandaporo’s thermal baths). So far, the geo-
thermal resources have not been utilized for other pur-
poses, such as for their energetic values. Estimated tem-
perature measurements based on different geothermome-
ters indicates that the temperature of the waters in the
formation of the Llixha reservoir may be above 220°C.
The reservoir is believed to be in the depth interval of
4500-5000 m. Tirana’s geothermal heat sources are:
Underground waters of the Tirana quaternary depres-
sion;
Underground waters of the tortonian’s sand stones;
Heat of the peri-superficial quaternary or tortonian
laye rs ;
Limestone’s and dolomites saturated with artesian
waters.
The following is addressed in the material:
The general geological conditions in the areas;
A re view of the theoretical basis of heat transfer;
Finite-volume modeling of the whole geothermal sys-
tem down to 5000 m depth, incorporating both ther-
mal convection and conduction, based on a simple
boundary conceptual model;
House heating calculations;
Borehole heat exchangers calculations;
Economic analyses.
All this aims at demonstrating that the thermal water
flowing from the Llixha springs is usable for direct utili-
zation and the borehole heat exchangers heating systems
are economically feasible, despite their elevated prelimi-
nary cost. This utilization would diversify the energy
resources, mitigate the electricity supply the region, help
improve living conditions for the local community and
protect the environment of the region.
N. KODHELAJ, A. BODE.
Copyright © 2013 SciRes. ENG
203
2. Geological Background of the Llix-
ha-Elbasan and Tirana Region
2.1. The Geological Structure of Llixha Region
The Llixha region is situated southwest of Elbasan. The
region is well known for its thermal springs, appreciated
since ancient times for their curative properties. The re-
gion und er stud y is sout h of Shku mbini ri ver valle y. The
surface relief increases rapidly up to intermediate eleva-
tion (300 - 500 m). In the western part of the region, a
system of hills declines gradually in the Cërriku field.
The region has a rich hydro system of small streams and
many underground water-systems. The flow rate for the
under ground waters varies fro m 100 -20 0 l/h in Tha në up
to 5000 l/h in Tregan. This is an inhabited area, with
small villages clustered around the thermal waters no
more than 2-3 km from each other [2,6]. The region lies
between two tectonic regions; the transversal
Vlorë-Elbasan-Dib ër and t he lo ngit ud inal Leskovi k-Drini
river ba y. In the c onte xt o f Alb ania n tect onic s, t he re gio n
represents the western part of the Kruja tectonic zone.
The orientation of these structures is SW-NE as is the
rest of the Albanides structure [1,6]. The lowest part of
the formation is composed of thinner flysch units inter-
calated by clays and sandstone, while the upper part is
composed of thicker flysch with conglomerates. The
Llixha syncline represents a depressed structure with
eastern asymmetry filled in the central part with terygen,
flysch and molasses deposits. The eastern part is distin-
guished by an easterly drop. The tectonics put the upper
deposits in contact with the lower flysch Oligocene for-
mation and has made the surface intrusion of the Eastern
anticline calcareous formations possible; it is regional
and includes the Western anticline chain of the Kruja
tectonic zone (Hyseni and Milo, 2000). The Llixha sys-
tem comprises a reservoir which feeds the southern part
of the Shkumbini River. he main hydrological characte-
ristic of the region is the presence of several hot springs.
The te mper at ur e of t he ho t sp r ing s var ies, r ange s from 50
to 68°C wh ile flo w rates var y from one spring to a nother,
without any seasonal characteristics.
2.2. The Geological Structure of Tirana Region
Tirana aquifer is related with the syncline deposits of
Tirana, whose morphology represent a depression of 10 -
12 km of width and 70-80 km of length. Wells yield in
the region varies between 7-10 l/s, while for the Torto-
nians molasses the wells yield is about 3-4 l/s.
3. Heat transfer Theory
3.1. The Differential Equation for Heat Transfer
This equation is a mathematical expression of the first
law of thermodynamics, the energy preservation low.
The heat increase of an elementary volume
V is equal
with the thermal energy which crosses the surface S. A
solid medium is considered, which is not generating any
energy (so the energy is only flowing through a surface
S). The temperature T at a point P (x, y, z) will be a con-
tinuous function of the position and time. For a homo-
genous solid medium, in which the thermal volume heat
capacity is independent of temperature, the equation is [2,
3]:
222
2
222
1TTT T
Tat
xyx
∂∂∂ ∂
∇=+ +=
∂∂∂
(1)
3.2. The Basics Hypo the si s
In order to solve the thermal diffusion equation let’s as-
sume that the formation temperature is function of the
position (x, y, z) and time (t) [3]. In additions initial and
boundary conditions must be specified. A specific mo-
ment of time is chosen as the origin of the time coordi-
nate. At that time the tempera ture distribution is:
( )
,,,0)(,,
(, ,,0)(, ,)
Txyztf xyz
orTrzt frz
θθ
= =
= =
(2)
The radials symmetric case of a flowing wellbore is
considered, as an example. After a certain production
time the well is shut do wn. To determine the temperature
distrib ution in the we llbore during t he shutd own time, the
end of production is considered as the origin of the time
coordinate. In this case the temperature f(r, z) must be
known, i.e. the initial conditions. To specify the temper-
ature field of a medium the boundary conditions must
also be known beforehand. Different kinds of boundary
conditions can be specified:
Surface temperature is known. It can be constant or
function of po sitio n and time, T = f(x, y, z, t)
The amount of energy flowing through the surface is
known:
( )
,,,
s
T
q xyztn
λ
= −
thederivationperpendiculartothesurface
n

=


(3)
Linear surface heat flow. In such a case the amount
of energy transmitted through a given surface is
proportional with the temperature difference be-
twee n the surfaces and the surr oundi ngs:
( )
0ss
q TT
α
= −
(4)
The connecting surface between two media with con-
ductivity
λ
1 and
λ
2, respectively. If T1 and T2 are the
temperatures of the media, then:
N. KODHELAJ, A. BODE.
Copyright © 2013 SciRes. ENG
204
(5)
3.3. The Unstable Temperature Field
Before starting investment in a geothermal project, the
stability of the temperature field involved, in space and
time, needs to be confirmed as well as the projects over-
all sustainability. The methods that can be used to answer
such questions are numerous, but here we will apply the
finite element method (Osmani, 1997). Considering the
differential equation:
( )
,, 0
xyz
TTT
kkk
x xyyz z
T
qxyzct

∂∂ ∂∂ ∂∂
 
++

 
∂∂∂∂∂ ∂
 

+ −=
(6)
The funct ional of this equatio n is (Osmani, 1997) :
2
22
222
vr
y
xz
XX X
k
kk
TTT
dxdydz
xyz
T
q cdxdydz
t
= +


∂∂∂
 
=+ +

 
∂∂∂
 




+−


∫∫∫
∫∫∫
(7)
To integrate the Equation (7) let’s assume the time in-
terval (t, t+Δt) through into dT/dt = C (Ti temperature
values i n the nodes I = 1, 4).
{ }
( )
( )
1
2
1234
3
4
;1, 4
1;
6
,,
vr
ii i
iii ii
XX
Xwhere i
TT T
T
T
T NNNNT
T
Nx y zabxcydz
=+=
∂∂∂



=



=+++
(8)
=
+
+
=
=
∫∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
ΩΩΩΩ
ΩΩΩΩ
ΩΩΩΩ
ΩΩΩΩ
0
0
0
0
1
1
1
1
4
Q
t
T
t
T
t
T
t
T
dxdydzNdxdydzNNdxdydzNNdxdydzNN
dxdydzNNdxdydzNdxdydzNNdxdydzNN
dxdydzNNdxdydzNNdxdydzNdxdydzNN
dxdydzNNdxdydzNNdxdydzNNdxdydzN
T
T
T
T
ddddddd
ddddddd
ddddddd
ddddddd
36
k
ccccccc
ccccccc
ccccccc
ccccccc
36
k
bbbbbbb
bbbbbbb
bbbbbbb
bbbbbbb
36
k
T
X
T
X
T
X
T
X
T
X
4
3
2
1
2
4
342414
43
2
3
2313
4232
2
2
12
413121
2
1
4
3
2
1
2
4
342414
4
3
2
3
2313
4332
2
2
12
413121
2
1
z
2
4
342414
43
2
3
2313
4332
2
2
12
413121
2
1
y
2
4
342414
43
2
3
2313
4332
2
2
12
413121
2
1
x
4
3
2
1
i
(9)
Using the numerical transformations the Equation (6)
is transfor med as follows:
( )
0
T
HT PFt
t
+−=
(10)
H
ddddddd
ddddddd
ddddddd
ddddddd
36
k
ccccccc
ccccccc
ccccccc
ccccccc
36
k
bbbbbbb
bbbbbbb
bbbbbbb
bbbbbbb
36
k
2
4342414
43
2
32313
4332
2
212
413121
2
1
z
2
4342414
43
2
32313
4332
2
212
413121
2
1
y
2
4342414
43
2
32313
4332
2
212
413121
2
1
x
=
+
+
P
dxdydzNdxdydzNNdxdydzNNdxdydzNN
dxdydzNNdxdydzNdxdydzNNdxdydzNN
dxdydzNNdxdydzNNdxdydzNdxdydzNN
dxdydzNNdxdydzNNdxdydzNNdxdydzN
2
4
342414
43
2
3
2313
4232
2
2
12
413121
2
1
=
∫∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
ΩΩΩΩ
ΩΩΩΩ
ΩΩΩΩ
ΩΩΩΩ
F
4
Q=
4. District Heating System Using the
Geothermal Water
In general the geothermal water for districts heating sys-
tems is taken directly from low temperature reservoirs.
Anothe r way is t he use the geothe rmal wate r throug h the
heat exchangers to heat up the fresh water. The hot water
can be stored in tanks if appropriate. This water than is
transmitted to the buildings and can be used for heating
and tap water. Heat flo w to t he buildin gs is co ntrolled b y
the mass flow. In the following are given the basics cal-
culations for the geothermal district heating. The main
elements of the geothermal district heating are the radia-
tors and also this use is affected by the water thermal
energy, building heat loss, pipe heat loss and building
energy storage.
4.1. Boreho le Heat Ex cha n gers
The equation for rate of heat transfer from the fluid in the
heat exchange r to the earth mas s is [5 , 7]:
N. KODHELAJ, A. BODE.
Copyright © 2013 SciRes. ENG
205
120
*;
2
tan tan
2
;
2
sp
QUT
L
USoilresis cePiperesis ce
RR
TT
TT
π
π
= ∆
=+
=+
+
∆= −
(11)
4.2. Results of Simple Ho t Sprin g M od e ll in g
A finite volume model was set up for a crustal volume
with an area of 10 x 10 km and 5 km thickness to model
the te mpe ratur e, de nsit y and fl uid velocity d istribution i n
the Llixha region. Here it is assumed that the medium is
homogeneous and isotropic and that kx = ky = kz = 2
W/m°K [8 ]. We al so know that Q = 20 l/s (corresponding
to mi = Q/6 = 3.3 l/s or 3.224 kg/s for each of the hot
springs), cp =4180 J/kg°C [2]. The temperature at depth
in the formation is set at 221°C while the te mperature of
the water at the surface is in the range 60-65°C. The
temperature gradient of the surroundings is assumed
12°C/km. The modeling software FLUENT is use to solve
the problem, it provides calculation results for tempera-
ture, density and velocity for the volume modeled. In the
model water flo ws with a velo city of 1.2 5*10-7 m/s [8,9].
The results for temperature are shown in the Figure 1.
The gri d
The temperature magnitud e
The density magnitude
The velocity magnitude
The veloci ty vect ors
Figure 1. Modeling results.
N. KODHELAJ, A. BODE.
Copyright © 2013 SciRes. ENG
206
4.3. Calculation for the Radiators and BHE
In these calculations, it was assumed that the supply
temperature of the water is 60°C, the reference tempera-
ture 65°C, the ground temperature 6°C. The calculations
were done for 4 different scenarios: The indoor tempera-
ture is assumed to change at the range of 18-20°C, the
outdoor temperature in the range of -10 to -4 °C, the re-
turn water temperature in the range of 33-40°C, the ref-
erence inflow in the range of 3.93-7 kg/s, the reference
system inflow 18-24 kg/s. Based on these data, the rela-
tive heating of the radiators was calculated as 0.83-0.92,
the relative heating of the building as 0.87-0.88, and the
transmissivity coefficient τ=0.94. To be within these pa-
rameters, it i s sufficient that the supply water temperature
be 60°C, and the inflow of the system 16-27 kg/s. Thus
the parameters for the Llixha thermal springs satisfy all
these d e mand s, Fi gure 2. Acc or ding to the mea suremen t s,
the earth temperature in 100 m depth in Tirana is T0=18°
C. The fluid exit temperature is 3.5°C lower than the
fluid entry temperature. For these parameters the heat
exchangers, for the installed capacity of 100 kW results
that is sufficient the drilling process of 15 wells 100 m
depth each. The economic analyses (profit-expenditure)
of three systems: Wa ter-Water geothermal pumps, Earth-
Water geothermal pump and the existing coal heater are
presented in Figure 3. So it can clearly see that the max-
imal profit is for the Water-Water system than for the
Earth-Water and finally for the coal heater. The payback
period for the geothermal heating pumps varies from 2.8
up to 10.75 years.
18 18.4 18.8 19.2 19.620
Indoor temperature (°C)
20
30
40
50
60
Water temperature (°C)
water supply temperature
return watre temperature
Figure 2. Llixha geothermal springs calculations.
1 2 3 4 5 6 7 8 910 11
Time (years)
-500000
-400000
-300000
-200000
-100000
0
100000
200000
Cumulative difference (€)
Coal heater
Water-Water pump
Earth-Water pump
Figure 3 . Economic analysis of the BHE.
5. Conclusions
The water temperature is expected to be stable in
the future;
The geothermal water from the Llixha hot springs
fulfills all requirements for district heating’s in the
region;
Considerably higher temperature expected through
further well drilling;
Albanian geothermal regime allows different scale
borehole heat exchangers applications;
Demographic and geological features of the stu-
dent’s city allow, and furthermore are feasible the
borehole heat exchanger’s utilization;
Use of the geothermal waters in Albania is eco-
nomically feasible and can mitigate the economic
problem, improve the living standards of the com-
munities and diversify the energy reso urces.
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[6] Hyseni, A., and Melo, V., 2000: The geodynamics of
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Nomencla ture
[H] Matrix of conductivity of the thermal field;
[P] Matrix of instabili ty of the the rmal field;
[F] Source vector;
Q Rate of heat exchanger (BTU/hr or W) for the whole heat exchanger length;
L length of heat exchanger (m);
U conductance rate for heat transfer from the circulating fluid to the earth
(BTU/hr/°F or W/°C/m) for the operating conditions;
ΔT differe nce in fluid temperature;
T0 earth temperature (°F or °C);
T1 fluid entry temperature (°F or °C);
T2 fluid exit tempera ture (°F or °C) .