## 2 Material and Methods
\[Q_{fluid}=Q_{cond}.\frac{1}{1-G/V}=\frac{Q_{H_{3}BO_{3}}}{[H_{3}BO_{3}]}\frac{1}{ 1-G/V} \tag{5}\]  
\[Q_{NCG}=Q_{cond}.\frac{G/V}{1-G/V}=\frac{Q_{H_{3}BO_{3}}}{[H_{3}BO_{3}]}\frac{G/ V}{1-G/V} \tag{6}\]  
The ratio (\(R\)) of the geothermal steam fluid rate and boric acid production rate is finally calculated as follows:  
\[R_{f}=\frac{Q_{fluid}}{Q_{H_{3}BO_{3}}}=\frac{1}{[H_{3}BO_{3}]}\frac{1}{1-G/V} \tag{7}\]  
Furthermore, the analogous ratio \(R_{NCG}\) of NCG emissions to boric acid production is calculated using the following equation:  
\[R_{NCG}=\frac{Q_{NCG}}{Q_{H_{3}BO_{3}}}=\frac{1}{[H_{3}BO_{3}]}\frac{G/V}{1-G /V} \tag{8}\]  
According to the definitions in equations 7 and 8, the \(R_{f}\) and \(R_{NCG}\) are dimensionless expressions representing the amount of steam associated with the production of a given amount of the tracer adopted boric acid (annual production rate in the data Tables 3-5). In Table 2, the first steam characterization data of boric acid and gas content (\(G\)/\(V\)) for different wells from ref. [39] are reported and, from the average of the data, the \(R_{f}\) and \(R_{NCG}\) values are calculated:  
\[R_{f}=1153.2\]  
\[R_{NCG}=82.9\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**STEAM FROM WELLS** & **G/V (\%wt/wt) (a)** & **[H\({}_{3}\)BO\({}_{3}\)] (\%a)** & **[H\({}_{3}\)BO\({}_{3}\)] (mg/L) (a)** \\ \hline \hline Foro forte (del Capanno) & 5.00 & 0.58 & 580 \\ \hline Foro dei Visconti (Piazza Anna) & 5.00 & 0.50 & 500 \\ \hline Foro forte di Piazza Anna & 11.80 & 0.53 & 530 \\ \hline Foro di S.Arturo in Piazza Anna & 10.30 & 0.47 & 470 \\ \hline Foro Venella & 6.70 & 0.52 & 520 \\ \hline Foro del Cancello & 6.00 & 0.16 & 160 \\ \hline Foro dei lagoon & 6.00 & 0.42 & 420 \\ \hline Il\({}^{\circ}\) foro lagoon & 10.50 & 0.65 & 650 \\ \hline Foro dell’ammoniaca & 5.80 & 0.35 & 350 \\ \hline Foro dei tini & 6.00 & 0.48 & 480 \\ \hline Foro del Terrazzo & 6.30 & 0.42 & 420 \\ \hline Foro della turbine & 5.80 & 0.60 & 600 \\ \hline Foro umido, debole, tra i lagoni & 0.82 & 2.80 & 2800 \\ \hline Foro umido di Piazza Anna & 14.60 & 4.60 & 4600 \\ \hline Average & 7.19 & 0.934 & 934 \\ \hline \hline \end{tabular} \({}^{(a)}\) Gas content expressed as a percentage of the total fluid (condensable phase + NCG), \({}^{(b)}\) boric acid concentration as part in each thousand in the condensable phase, \({}^{(c)}\) boric acid concentration as milligrams per liter in the condensable phase.  
\end{table} 
Table 2: Early steam characterization data according to ref. [39]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & **Tuscan** & **Boric Acid** & **Boric Acid** & **Steam** & **NCG Emission** & **Average** & **Average** \\  & **Libbra/y** & **Production** & **Production** & **Calculated** & **Calculated from** & **Scam Flow** & **Steam Flow** \\  & **(Kg/y)** & **(Kg/y)** & **from R\({}_{\text{f}}\) (_ty_)** & **from R\({}_{\text{NG}}\) (_ty_)** & **R\({}_{\text{NG}}\) (_ty_)** & **Rate (_t/h_)** & **Rate (_t/h_)** \\ \hline
1826 & 149,000 & 50,591 & 51 & 58,343 & 4193 & 6.7 & 0.48 \\ \hline
1827 & 66,000 & 22,410 & 22 & 25,843 & 1857 & 3.0 & 0.21 \\ \hline
1828 & 197,000 & 66,889 & 67 & 77,138 & 5544 & 8.8 & 0.63 \\ \hline
1829 & 376,000 & 127,667 & 128 & 147,228 & 10,581 & 16.8 & 1.21 \\ \hline
1830 & 602,000 & 204,403 & 204 & 235,722 & 16,942 & 26.9 & 1.93 \\ \hline
1831 & 789,000 & 267,897 & 268 & 308,944 & 22,204 & 35.3 & 2.53 \\ \hline
1832 & 1,103,000 & 374,513 & 375 & 431,895 & 31,041 & 49.3 & 3.54 \\ \hline
1833 & 1,347,000 & 457,360 & 457 & 527,437 & 37,908 & 60.2 & 4.33 \\ \hline
1834 & 1,725,000 & 585,707 & 586 & 675,448 & 48,545 & 77.1 & 5.54 \\ \hline
1835 & 1,841,000 & 625,093 & 625 & 720,870 & 51,810 & 82.3 & 5.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculated steam flow rates and NCG flow rates from boric acid production data according to ref. [36].