Applicability of a Solar Adsorption Cooling Machine in Semiarid Regions: Proposal of Supplementary Cooler Using Earth-Water Heat Exchanger

Up to now air conditioning and domestic cooling systems in Algeria mainly operate in the traditional way, which needs an important expenditure of electrical energy. These technologies use CFCs for their operation, most of which deplete the ozone layer. The alternative systems must use safe refrigerants for the environment and have a high performance to reduce CO₂ emissions and therefore reduce the greenhouse effect.

The environmental problems have given a renewed interest to another system (field) called sorption chillers (adsorption and absorption). These alternatives machines become increasingly attractive because the fluids used, in these systems, are benign to the environment whatsoever ammonia, water or alcohols … etc. This technology is particularly attractive for the countries which have a very important solar potential.

This work focus on the possibility of installing a solar adsorption machine in the region of Biskra in the Southeast of Algeria [1]. This type of installations includes a set of thermal systems such as: cooling machine (Chiller), the solar heating system and cooling system (cooling tower, air-cooler…).

The biggest problem objected to the system operating in the semiarid and Saharan regions is how to provide cold water to cool the adsorbers, unlike hot water which we get it easily from solar water heaters. A lot of geometries are suggested to the coolers design in the literature [2-8].

Citherlet et al. [2] analyzed the performances of the solar adsorption chiller in Switzerland, they used a solar adsorption cooling machine (SORTECH ACS08) with a nominal cooling capacity of 8kW. This chiller uses the silica gel/water as working pair, with a finned tubes heat exchanger (dry cooling tower) DCT as a recooler with 287 m² of heat transfer area to cool the cooling water. Results showed that in the case when the ambient air temperature exceeds 34°C, the DCT doesn’t work well.

In the semiarid and Saharan zones, like Biskra (south-east of Algeria), the average ambient temperature can exceed 34°C in all the summer and can reach 35°C in July and August as shown in Fig. 1 [9]. Thus, the DCT efficiency decreases, which make it unable to cool the cooling water to the desired temperature. A hybrid cooling tower can improve the operating limits of the system. However, this makes it more complex, without forgetting the scarcity of water in these regions.

Due to the fact that ground temperature is always lower than air temperature in summer, the solar assisted ground-source cooling system increases system efficiency [10, 11] and makes it a very attractive technology especially in the Saharan regions.

figure_1.png

Figure 1. Evolution of the average monthly ambient temperature in the region of Biskra (2014) [9]

In an attempt to solve this problem; the present paper suggests the exploitation of the shallow geothermal energy by using an earth-water heat exchanger EWHE as a cooler to replace the DCT when the ambient temperature exceeds its operating limits. For that we have designed the appropriate EWHE to the region of Biskra to replace a DCT found in the literature.

3.1 Sizing calculation method

The following assumptions were made in modeling the system: (i) The maximum duration of continuous operation of the EWHE doesn’t exceed few hours just during the peak temperatures (ii) analysis is based on steady state conditions, (iii) the soil around the heat exchanger is homogenous, (iv) soil conductivity is constant, (v) water flow is uniform along the length of the buried pipes (vi) Thermo-physical properties of water are calculated using correlation from literature, and finally (vi) we assumed that the soil properties are isotropic and there is perfect contact between the soil and the pipe.

The calculation model is based on the resolution of the heat equation (Fig. 4):

$m C p(T(x)-T(x+d x))=\frac{(T(x)-T s)}{R_{t h}} d x$(1)

where R_th Rth is the overall thermal resistance between pipe water and surrounding soil of the water soil heat exchanger can be expressed by the relation(2) [15]:

$R_{t h}=R_{w}+R_{t}+R_{s}$(2)

The thermal resistance Rw due to convective heat transfer between water in the pipe and the inner surface of the pipe calculated as:

$R_{w}=\frac{1}{h_{i} P_{i}}$(3)

where

$h_{i}=N u \lambda_{w} / d i$(4)

The Nusselt number for water flow inside a pipe given by Eq. (5)  [16] is a function of Reynolds number $R e$ , and Prandlt number for, $2300<\mathrm{Re}<10^{5}$ and  $1.5<\mathrm{Pr}<500$

$N u=0.012\left(\mathrm{Re}^{0.87}-280\right) \operatorname{Pr}^{0.4}\left[1+\left(\frac{d i}{L}\right)^{0.66}\right]$(5)

The thermal resistance of the tube Rt:

$R_{t}=\frac{\ln \left(r_{e} / r_{i}\right)}{2 \pi \lambda_{t} L}$(6)

figure_4.png

Figure 4. Thermal balance of a pipe elementary segment

The thermal resistance Rs of the soil annulus is given by the Eq. (7)

$R_{s}=\frac{\ln \left(r_{s} / r_{e}\right)}{2 \pi \lambda_{s} L}$(7)

Several works in the literature have considered the appropriate thickness of the soil annulus. As a conclusion to all of these researches, the soil thickness is varying with the duration of operation of the heat exchanger. In this paper, the duration of operation of the WEHE doesn’t exceed few hours. For that, the thickness of the soil annulus was taken as being equal to the radius of the pipe (r_s=2r_i). [17-19]

After dividing the Eq.(1) on dx this equation can be written as following :

$-m C p \frac{d T}{d x}=\frac{(T(x)-T s)}{R_{t h}}$(8)

Then  

$T(x)=A \exp \left(\frac{-x}{m C p R_{t h}}\right)+\mathrm{B}$(9)

We can determine the constants A, B if we take into account boundary conditions:

- For $=>\infty$  , $T(x)=T_{s}==>B=T_{s}$ ;

- For $x=0$ , $T(x)=T_{0}==>A=T_{0}-T_{s}$

$T(x)=\left(T_{0}-T_{s}\right) \exp \left(\frac{-x}{m C p R_{t h}}\right)+T_{s}$(10)

Also we can write the eq. (10) as:

$T(x)=\left(T_{0}-T_{s}\right) \exp \left(\frac{-x}{\rho C p S v R_{t h}}\right)+T_{s}$(11)

Pressure drop in the heat exchanger is equal to the sum of the linear, singular and pressure losses between the inlet and outlet of the exchanger [20].

$\Delta P_{t}=\Delta P_{l i n}+\Delta P_{\sin }+\Delta P_{i o}$(12)

Where the linear pressure losses are calculated as [21]:

$\Delta P_{l i n}=\Lambda \rho_{w} L \frac{v_{w}^{2}}{2 \mathrm{d}}$(13)

The calculation of the loss ratio of load $\Lambda$  depends on the nature of the flow, laminar or turbulent [20].

For $2100<\mathrm{Re}<10^{5}$ , the BLASUIS formula is used

$\Lambda=0.3164 \mathrm{Re}^{-0.25}$(14)

The singular pressure loss is defined by

$\Delta P_{\mathrm{sin}}=\xi \rho_{w} \frac{v_{w}^{2}}{2}$(15)

Pressure losses due to the inlet and outlet of the heat exchanger are calculated as following [20]:

$\Delta P_{i o}=\frac{3}{4} \rho_{w} v_{w}^{2}$(16)

3.2 Model validation

In this paper we have validated the calculation code with the experimental data obtained by Moummi et al. [12], in the University of Biskra. The authors used an earth-air heat exchanger, using the same (geometric and climatic) data. The specific parameters and characteristics of the heat exchanger tested by Moummi et al. [12] are given in Table 2.

In order to validate the calculation method, we have provided a simple comparison between the results from this study and the literature in Fig. 5. The comparison results show that a good agreement had been found between the air temperatures calculated in this study with the ones reported in the literature. The code reflects the real phenomenon with a maximum field error of (1°C), which can be relied upon to design the water-earth heat exchanger (WEHE).

In this work, we are interested in the applicability of the solar adsorption air refreshment system in the region of Biskra and the water cooling system was investigated. Previous work in the literature used a finned tubes heat exchanger (dry cooling tower DCT) in the SACM and showed that when the ambient air temperature exceeds 34 °C, the heat transfer area needed of the heat exchangers increases enormously.

In this paper we have proposed a supplementary water cooling system to the chiller based on shallow geothermal energy by using an earth-water heat exchanger (EWHE). The proposed EWHE operates just during the peak ambient temperatures to avoid the dysfunctioning of the DCT. Through the modeling work of the EWHE, we have designed WEHE in Biskra. Results are very encouraging and show that the geothermal solution is effective; with a very low cost.

Continuous use of the EWHE causes the saturation of the soil because of the low thermal diffusivity of this last, where the soil temperature in the immediate vicinity of the heat exchanger increases which causes the decrease of its efficiency. For that, another study to know the influence of the EWHE on the soil and the influence of soil on the EWHE as a function of time is required to ensure continuous water cooling. This study will allow us to define how many exchanger must be used, distance between the tubes and also between the geothermal heat exchangers in the case of the abolition of the use of the DCT completely.