## 3 Results and Discussion
### Economic Tool to Evaluate the Advantages of Regeneration  
The volume of chemical regeneration agent of 37 wt.% HCl \((V_{HCl,37\%})\) consumed at industrial scale and its respective chemical regeneration cost \((P_{r})\) can be calculated based on Equations (9) and (10), respectively:  
\[V_{HCl,37\%}=\frac{Q_{HCl,\ exp}\cdot t_{op}}{m_{GAC,\ exp}}\cdot m_{GAC}\cdot \frac{7.4\ wt.\%}{\delta} \tag{9}\]  
\[P_{r}=V_{HCl,37\%}\cdot P_{HCl} \tag{10}\]  
where:  
\(Q_{HCl,\ exp}\): experimental flow of HCl, \(1\times 10^{-4}\) L/min at laboratory conditions. \(t_{op}\): operation time for chemical regeneration equilibrium determined by the breakthrough curve, 249 min (Figure 3a). \(m_{GAC,\ exp}\): experimental mass of powder AC in the experimental column, 8.16 g  
\(m_{GAC}\): mass of GAC in the fixed-bed industrial filter, \(1\times 10^{6}\) g  
\(\delta\): HCl purity, 37 wt.%  
\(P_{HCl}\): Bulk HCl price, (in $/L).  
The bulk HCl price is USD 196 for 250 kg of 37 wt.% HCl [49]; therefore, the price of HCl per volume unit can be estimated according to Equations (11) and (12):  
\[V_{HCl,\ 37 wt.\%}=\frac{m_{HCl,\ 37 wt.\%}}{\rho_{HCl,\ 37 wt.\%}} \tag{11}\]  
\[P_{HCl}(\$/L)=\frac{\$196}{V_{HCl,\ 37 wt.\%}} \tag{12}\]  
where:  
\(\rho_{HCl,\ 37 wt.\%}\): density of HCl 37 wt.%; 1.19 kg/L.  
\(m_{HCl,\ 37 wt.\%}\): mass of HCl 37 wt.%; in kg.  
\(V_{HCl,\ 37 wt.\%}\): volume of HCl 37 wt.%; in L.  
Finally, \(P_{HCl}=0.9330\)USD/L (=USD 196. 1.19 kg/L)/250 kg  
Applying Equation (9);  
\[V_{HCl,\ 37\%}=\frac{0.1\cdot 10^{-3}\cdot 249}{8.16}\cdot 10^{6}\cdot \frac{7.4}{37}=610\ L/ton\]  
Figure 3: (a) Breakthrough curve for 7.4 wt.% HCl during dynamic regeneration of GAC-Exh using RSSCT experiments; (b) derivative function of the breakthrough curve. \(\frac{dy}{dx}=\frac{d\left(\frac{\langle x(t^{+})\rangle}{\langle x(t^{+}) \rangle}\right)}{d\delta}\).  
Then from Equation (10)  
\(P_{r}=0.9330\ \$/L\)-610 \(L/ton=569.4\) USD/ton of GAC regenerated. On the other hand, the initial cost of purchasing the amount of virgin GAC (\(P_{o}\)) can be calculated by Equation (13):  
\[P_{o}=m_{GAC}.P_{v} \tag{13}\]  
where  
\(P_{v}\): GAC-Virgin purchasing cost, USD/ton. The current total purchasing cost of the GAC-Virgin for power plants is 6270 USD/ton, including shipping and transportation costs [49]. In order to analyse the economic benefits by applying the chemical regeneration strategy in the power plant for scenario one compared with scenario two, the ratio \(\left(\frac{C_{r,1}}{C_{w,2}}\right)\) (Equation (14)) was used as parameter for the economical assessment, and it can be applied as follows:  
\[0<\left(\frac{C_{r,1}}{C_{w,2}}\right)\leq 1\ \text{Economically feasible}:\ \text{the closer to zero, \ the higher is the profit.} \tag{14}\]  
\[\left(\frac{C_{r,1}}{C_{w,2}}\right)=1\ \text{Breakout.} \tag{15}\]  
\[\left(\frac{C_{r,1}}{C_{w,2}}\right)>1\ \text{Economically not feasible.} \tag{16}\]  
where:  
\(C_{r,1}\): cost of the GAC management with regeneration strategy in scenario one (in USD/year)  
\(C_{w,2}\): cost of the GAC management in scenario two without regeneration and replacing filter by new batch of GAC-Virgin when exhaustion occurs (in \(\$/year\))  
In scenario two, GAC-Exh from the filter is replaced with virgin material at a purchasing cost \(P_{0}\), which in turn will be exhausted after a specific saturation time \(t_{sv}\), for a number of \"n\" exhaustion/replacement cycles. Then, \(C_{w,2}\) can be calculated according to Equation (17):  
\[C_{w,2}=\frac{P_{o_{1}}+P_{o_{2}}+\dots P_{o_{n}}}{t_{sv_{1}}+t_{sv_{2}}+ \dots t_{sv_{n}}} \tag{17}\]  
\(P_{o_{n}}\): Purchasing cost of GAC-Virgin for replacement of the GAC-Exh in an exploitation cycle \"n\" (in \(\$\)). \(t_{sv_{n}}\): Saturation or exhaustion time for GAC-Virgin of an exploitation cycle \"n\" (in years).