Proceedings of the 34 ARA Congress “Scientific Research – Security – Sustainable Development Connections”
AN APPROXIMATE METHOD FOR RAPID ESTIMATION OF THE INTERFERENCE OF VERTICAL HEAT EXCHANGERS IN A NEAR SURFACE GEOTHERMAL INSTALATION Ioan David, Mircea Visescu, Camelia Stefănescu, Daiana Baliga Faculty of Hydrotechnical Engineering Timisoara, George Enescu Street 1/A Timisoara
[email protected] Abstract. The near surface natural energy reservoir of the earth can be exploited to heating and cooling using ground source heat pump (GSHP) systems. There are two main categories of GSHP systems, the open and the closed-loop system. The open system use groundwater to supply water to the heat pump directly from a production well. The closed-loop system utilizes horizontal or vertically arranged gound heat exchanger in which flows a working fluid (e.g water with antifreeze agent). Such GSHP systems can change the temperature distribution in the ground in an area close to it, or even remote from the system. In the paper an rapid estimation methode of the modified temperature field in the ground by a closed GSHP system using analytical assessment methods will be proposed. The proposed method, which takes into account the interference among vertical heat exchangers, may be regarded as a useful and practical tool for planning of such systems because especially it refers to the impact on the ground temperature and indirectly on the own performance of the system
Geothermal energy sources in the depth (2000-4000 m) to which mainly refers the above data, there was a significant increase in the use of shallow geotermiei up to 100m: the near surface natural energy reservoir of the earth which can be exploited to heating and cooling using ground source heat pump (GSHP) systems [2]. The main objective of the paper is to develop a method for quick calculation of the temperature field in the area of the vertical heat exchangers for near surface geothermal installations. The method allows a rapid evaluation and analysis of the dependence of mutual influence (interference) among the vertical heat exchangers of the system. The knowledge of the temperature field further enables both statements about the impact on the environment as well as on their own performance of the system
1. Introduction According to World Energy Council (WEC), 36.4% of global primary energy is based on using oil. The trend of increasing global demand for oil in addition with risk factors such as political instability in various regions of the world, terrorist attacks, limited production capacity and default business with oil speculation, etc.. All this leads to rising oil prices increasingly difficult to control. In this context the general need to increase the share of alternative energy sources including geothermal energy have an important place. The geothermal energy has become a strategic goal of Europe and the whole World. Besides economic issues, increasing the share of alternative energy sources contributes significantly to reducing releases of carbon dioxide also it contributes to reducing environmental pollution. To highlight the growth trend of using geothermal energy it is sufficient to mention that in the last decade the direct use of this technology increased by 43% , wich shows enormous potential. In this context Figure 1 illustrate the total installed capacity of energy from geothermal resources on the continents [1].
2. Heating/cooling systems using surface geothermal sources The Heating / cooling Systems which use the surface geothemal energy extract the thermal energy from underground at a depth of up to 100m. The near surface geothermal energy resource exploitation is based on the fact that the ground temperature can be considered after a depth of about 3 - 5 m practically constant equal to the yearly average air temperature. This natural energy reservoir of the earth can be exploited to heating and cooling using ground source heat pump (GSHP) systems. There are two main categories of GSHP systems, the open and the closed-loop system. The open system use groundwater to supply water to the heat pump directly from a production well. The heated /cooled water from the heat pump after the thermal energy transfer is returned in the underground by injection wells. The closed-loop system utilizes horizontal or vertically arranged gound heat changer in which flows a working fluid (e.g water with antifreeze agent).
Fig. 1. Installed capacity for electricity generation and direct use of geothermal energy on the continent [1].
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In the paper we consider closed-loop heating / cooling system with vertical heat exchangers sketched in Figure 2.
The general equation of heat transfer by conduction is known as:
∂T v pw + − α ⋅∇ ⋅ (∇T ) = 0 ∂t R
(1)
In this equation R is the retardation factor defined as
R= 1+
1 − n ( ρC )s n ( ρC )w
(2)
α denote the thermal diffusivity of the ground (m /s) 2
λ α =( )M ρC
Fig. 2Heat exchangers for heating / cooling arranged vertically in the soil [6] The heating / cooling systems of this type requires less space compared to horizontal heat exchangers, therefore it can be used in tight spaces where the installation space for the exchangers is small. The performance of the installation depends basically on the temperature difference between heat source wich is the natural ground outside of the boreholes and the heating system with the refrigerant which is recycled through the heat pump. Sampling earth heat leads to changes in initial temperature T 0 from the outer wall of the borehole where the temperature will be namely T B , T B < T 0 in case of heating systems, and T B > T 0 in case of cooling systems. The temperature changes are propagated in time and leads to changes in an area more or less extended around probes. This change reached even 6 - 80C and can have a negative influence on the system performance due to interference effects between the heat exchanger boreholes. The average temperature change in a more or less extended area of the GSHP system can move through transported by groundwater and so can arise a form of heat pollution. This can even lead among others to conflicts of legal nature of the owners of adjacent parcels that are or are to be achieved with heat exchanger arrangements. This new problem is mentioned in the recently specialized literature [6]. Therefore the existence of a rapid calculation method for evaluating changing temperature in underground looked as environment impact actually. In the paper are proposed quick methods for calculating the temperature field based on approximated analytical solutions which presents advantage of rapid analysis of the influence of different geometrical and physical parameters of the system in interaction with the underground environment where the heat exchanger boreholes of a GSHP system are located. In this phase of work will be taken into account closed-loop systems only. 3. Mathematical modelling of temperature field outside of vertical heat exchangers. For description of mathematical modelling is considered a GSHP system with vertical boreholes presented in Fig. 2 (i.e. closed-loop system for heating and / or cooling)
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(3)
Indices s and w refers to soil, water and M is for the ground medium (water + soil) The significance of the other notations: ρ = density [kg/m3] C = heat capacity [Jkg-1K-1] λ = thermal conductivity [Wm-1K-1] n = ground medium porosity [-] T = temperature [K] t = time[s;h] V pw = pore velocity [m/s] Characteristic parameter of ground (λ, ρ, C, α) are calculated taking into account both constituent components: solid (s) and fluid (fluid is usually water i.e. w). So for example for a parameter φ (e.g. λ, ρ, C, α) we have:
φ=n×φ w + (1-n ) ×φs
(4)
In a first stage is taken into account the equation (1) when the underground current is missing (V pw =0).
y B
ρBM
M
rM
Fig. 3 Calculation scheme for a single borehole B To obtain the fundamental solution corresponding to a borehole located in the point S(x B ,y B ) we consider the following initial and boundary conditions: – the initial temperature of the ground in an arbitrary point M having coordinates (x, y) is (5) T(M,t=o) = T 0 – the temperature on the exterior mantle of the borehole
Proceedings of the 34 ARA Congress “Scientific Research – Security – Sustainable Development Connections” T(B, t) = T B
(6) Two equation can be rewritten in a more suitable form, which shows the interference of the boreholes clearly. For this purpose is considered one of the boreholes as reference borehole e.g. B i and a interference coefficient μ will be introduced defined by the equation:
It also will notice that from ground extracted heat flow Q per unit length of the borehole can be expressed as:
lim 2π r λM
x ,y → Bw
∂T = −Q ∂r
(7)
n
Where with B w is notated the outside wall of the borehole. The fundamental solution for equation (1) taking into account the initial and bondary condition (4,5 and 6) for a heat exchanger borehole B are:
T( M ,t ) = To
(8)
(- and+ correspond the heating and cooling respectively). E(u) is the exponential integral
E= i (u )
i
E( uBi Bi )
du
∫exp ( −u ) u
= T( M , t) To
(16)
(9)
u denote the argument defined as:
ρ BM 2 4α t
Q E ( uBiM ) (1 + µ Bi ∑ ) 4πλ (17)
This equation allow calculation of the temperature at a arbitrary point M of the ground at time t, representing the effect of cooling / heating generated by the n heat exchanger boreholes of the GSHP system located in the point B i . The obtined analytical solution (17) with the introduced approximations (11-12) is a simple explicit mathematical equation which allows contrary to other methods in the literature a quick analysis of the influence of different geometrical and geothermal parameters on the temperature distribution. In technical applications usually are used systems with 2, 4, 9 or more equidistant placed heat exchanger boreholes arranged in a network. To calculate the temperature distribution is sufficient to consider a representative system consisting of 4 boreholes (B i , i=1, 2, 3, 4) Fig. 4.
u
uBM =
E( uB j Bi )
So the equation (15) can be written in the following form:
Q E ( uBM ) 4πλ ∞
µB ∑ =
∑
=j 1, j ≠ ì
(10)
In the literature the integral is given in form of tables or graphs. To facilitate making quick calculations we suggest the following approximations with errors below 5%:
E (u ) = ln(0.6 u −1 ) (11) for u
