**3.1 Experimental techniques**

In view of continuous monitoring of gases emanated from the hot spring Agni Kunda at the spring site of Bakreswar, a field laboratory was established. In this

*Quantitative Approximation of Geothermal Potential of Bakreswar Geothermal Area… DOI: http://dx.doi.org/10.5772/intechopen.96367*

#### **Figure 4.**

*Schematic diagram of the experimental set-up installed at Bakreswar (modified after [19]).*

regard, a giant inverted SS funnel was placed under hot water at Agni Kunda at a position where gas out flux was significantly high, to trap hot spring gases which were comprised of He, Ar, O2, N2, CH4, CO2, 222Rn, etc. A portable and programmable μ-GC (micro-gas chromatograph) CP 490 (make Agilent, Netherland) comprised of a μ-thermal conductivity detector, was utilized to detect the relative concentration of different gases present in the spring gas. Here, ultra-pure (>99.998 vol%) H2 gas was utilized as the carrier gas for running the equipment. The entire measurement was carried out in-round-the clock (24 7) measurement fashion for a continuous five-year (1st August 2005 to 31st July 2010). The back-up power supply was maintained to keep a stable and continuous power supply in case of a power failure. The schematic diagram of the experimental set-up is illustrated in **Figure 4**. Further details of the above-mentioned experimental procedure are already described by [19]. Here, the average value of the He concentration (vol%) of 5 years of continuous measurement was adopted in our study. Moreover, the flow rate of the emanated gases from the spring vent was measured by means of collecting the spring gases in a gas container (5 litres) from the main channel of the incoming gas line. The gas collection procedure was kept running up to a certain time until its pressure makes equilibrium with the pressure (1.58 atm) at the spring vent underwater. This type of measurement was done once every month for a continuous five years, and the average value of those was considered as the final value of the gas flow rate under consideration. The ambient temperature of the study area was monitored for the same interval at the time of measurement of gas flow rates.

#### **3.2 Analytical techniques**

To move towards the desired direction for calculation, the following steps were adopted.

The volume of He gas (*VHe*) emanating from the spring per second was estimated as

$$V\_{He} = F \times \mathcal{C}\_{He} \tag{4}$$

Where *F*= average flow rate of He gas emanation (recorded); *CHe*= relative concentration of He in the gas mixture, which was expelled through the spring vent (recorded). The no. of moles of He gas emanated per unit second from the hot spring was calculated using the real gas equation as stated below:

$$(V - nb)\left(P + \frac{n^2 a}{V^2}\right) = nRT\tag{5}$$

$$\text{i.e., } \frac{ab}{V^2} n^3 - \frac{a}{V} n^2 + (bP + RT)n - PV = 0 \tag{6}$$

Where *V* (i.e.,*VHe*) = volume of the He gas at temperature T and pressure P; R = universal gas constant = 0.0821 litre atm/ mole K; *n*= number of mole (to be calculated); 'a' and 'b' are real gas constants and for He, a = 0.03457 atm litre<sup>2</sup> / mole<sup>2</sup> ; b = 0.02370 litre/mole [43]. Solving the Eq. (6) and considering the real root for 'n', the corresponding total number of He atom (*NHe*) was calculated by

$$N\_{He} = n \times N\_A \tag{7}$$

Here, *NA*= Avogadro's number = 6*:*<sup>022140857</sup> � <sup>10</sup><sup>23</sup> [44]. The relative contribution of the individual isotope in the generation of He atoms was calculated according to their relative abundance in the natural resources because the total number of He atom is produced via the radioactive decay series of 238U, 235U, and 232Th. Here, the same was not applicable to the 40 K series as it disintegrates through only β emission. Therefore, for production of He atoms,

$$\begin{aligned} & \text{The relative contribution of Uranium } (C\_U) \\ &= \frac{\text{conc. of Uranium } (\mathbf{U})}{\text{total conc. of Uranium } (\mathbf{U}) \text{ & } \text{Priorium } (\mathbf{Th})} \end{aligned} \tag{8}$$

$$\begin{aligned} & \text{The relative contribution of Thorium } (C\_{Th}) \\ &= \frac{\text{conc. of Thorium } (\mathbf{Th})}{\text{total conc. of Uranium } (\mathbf{U}) \text{ & } \text{Thorium } (\mathbf{Th})} \end{aligned} \tag{9}$$

The basement of the study area is predominantly composed of granite gneiss belonging to the Precambrian Chotanagpur Gneissic Complex [26, 30]. Here the relative contribution of U and Th were evaluated according to their (average) content in granite type rock material, i.e., 238U [or 235U] content as 4.80 ppm and 232Th content as 21.50 ppm were considered [10, 45]. Moreover, natural Uranium is an admixture of 238U (99.28%) and 235U (0.71%) [10]. Therefore, for production of He atoms by radioactive decay,

$$\text{The relative contribution of } ^{238}\text{U } (\text{C}\_{U-238}) = \frac{99.28}{100} \times \text{C}\_{\text{U}} \tag{10}$$

$$\text{The relative contribution of}^{235}\text{U } (\text{C}\_{U-235}) = \frac{\text{0.71}}{100} \times \text{C}\_{\text{U}} \tag{11}$$

*Quantitative Approximation of Geothermal Potential of Bakreswar Geothermal Area… DOI: http://dx.doi.org/10.5772/intechopen.96367*

The no. of the He atoms generated (in a unit second) due to the decay of radio nuclei 232Th, 238U and 235U are respectively *CTh*�<sup>232</sup> � *NHe*, *CU*�<sup>238</sup> � *NHe* and *CU*�<sup>235</sup> � *NHe*. According to Eq. (1) to Eq. (3), it is reflected that 6 He atoms and 42.6 MeV/atom heat energy, 8 He atoms and 51.7 MeV/atom heat energy and 7 He atoms and 46.4 MeV/atom heat energy from the decay of 232Th, 238U and 235U are releasing respectively. Therefore, the energy release (per unit second) from 232Th, 238U, and 235U decay can be evaluated respectively by

$$E\_{Th-232} = \frac{42.6}{6} \times C\_{Th-232} \times N\_{He} \tag{12}$$

$$E\_{U-238} = \frac{51.6}{8} \times C\_{U-238} \times N\_{He} \tag{13}$$

$$E\_{U-235} = \frac{4\text{€}.4}{7} \times \text{C}\_{U-235} \times N\_{He} \tag{14}$$

And the total energy generated due to the decay of all these three radioelements were

$$E\_{R(Total)} = E\_{Th-232} + E\_{U-238} + E\_{U-235} \tag{15}$$

An important issue to discuss is that the loss of generated heat energy may be considered to be negligible here as capping of the impermeable and insulating bedrock over the geothermal system prevents the heat transfer by means of conduction and convection [30, 41, 42]. Therefore, the heat energy would be stored inside the geothermal system, which may be subjected to break its dynamical stability after the accumulation of enough energy within it. However, that does not happen as excess heat is drained to the surface, along with the transfer of geothermal fluid through the spring vent [30, 42]. Moreover, here only radiogenic heat is accounted for, and the contribution of energy belonging to primordial heat sources is not included. However, [46] documented that heat from radioactive decay was contributed about half of Earth's total heat flux, and the rest was accounted for from the primordial heat source of the Earth. Considering the similar concept, we can also assume that the primordial heat source also would contribute as much as heat energy generated by radioactive decay of radio-nuclei at the reservoir of the study area.

Therefore, the heat generated by the primordial source,

$$E\_{P(Total)} = E\_{R(Total)} \tag{16}$$

Therefore, total energy contributed from the radiogenic and primordial source is

$$E\_{Total} = E\_{P(Total)} + E\_{R(Total)}\tag{17}$$

Moreover, If the geothermal gradient *<sup>d</sup><sup>θ</sup> dx* is considered to be constant at least up to the depth of the reservoir (x) then the depth (x) of the reservoir could be calculated from the below stated linear relationship.

$$
\theta\_r = \left(\frac{d\theta}{d\mathbf{x}}\right)\mathbf{x} + \theta\_a \tag{18}
$$

Where, *θ<sup>r</sup>* = reservoir temperature of the geothermal system; *θ<sup>a</sup>* = average ambient temperature at the study area.
