## 3 Methodology
### Techno-Economic Analysis (TEA)  
The levelized cost of M-TES (LCM) in ($/MWh) can be estimated as [34,35]:  
\[LCM=\left(CC+\left(\frac{TC}{year}\times SLT\right)\right)\div(TH\times SLT\ ) \tag{1}\]  
where \(CC\) is the capital cost, \(TC\) is total transportation cost per year, \(SLT\) is the system lifetime, and \(TH\) is the total heat provided by the system over one year. To simplify the cost calculations, carbon tax and interest accumulation were ignored. The total heat from M-TES (TH) in one year (MWh/year) can be calculated as:  
\[TH=\ ESD\ \times\ TW\ \times\ N\times\ \ \eta\ \times\ ODPY \tag{2}\]  
where \(ESD\) is energy storage density, \(TW\) is Total material weight, \(N\) is the number of trips per day, \(\eta\) is M-TES system efficiency, and \(ODPY\) is the number of operating days per year, respectively. The total GHG emitted from the system in one year, GHG Transportation in (tCO\({}_{2}\)e/year), will be:  
\[\text{GHG}_{\text{Transportation}}=2\ \text{D}\ \times\ \text{N}\ \times\ \text{ODPY}\ \times\ \text{CO}_{2\text{e}}\ \text{factor} \tag{3}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{4}{c}{**Truck Mode**} \\ \hline  & **RNG Truck** & **EV Truck** & **Diesel Truck** \\ \hline System capital cost estimate CAD\$ & 470,000 & 570,000 & 400,000 \\ Fuel price (CAD\$/L diesel equivalent) & 0.47 * & 0.32 & 1.4 \\ Other transportation cost (OTC), e.g., & & & \\ insurance + maintenance + driver rate & 1.4 & 1.4 & 1.4 \\ (CAD\$/km) [32,33] & & & \\ \hline \hline \end{tabular}  
* discounted price from British Columbia for low-carbon fuel standards (LCFS) trucks.  
\end{table} 
Table 4: The summary of truck modes and associated costs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Surrey DEN Target GHG Intensity** & **0.07 tCO\({}_{2}\)e/MWh** \\ \hline Natural gas boiler efficiency, \(\eta_{\text{ING}}\) & 95\% \\ M-TES system efficiency, \(\eta_{\text{TA-TES}}\) & 90\% \\ \hline Natural gas fuel GHG intensity, GHG\({}_{\text{NG}}\) & 180 kgCO\({}_{2}\)e/MWh \\ \hline Constant heat supply from a vertical & 1100 MWh \\ geothermal exchange system attached to DEN & \\ \hline Emission factors and transportation & From [30,31] \\ methodologies and guides & \\ \hline System level energy storage density of M-TES & (0.1 MJ/kg–2 MJ/kg) \\ \hline M-TES system lifetime & 12 years \\ \hline Tank size/trip & 10,000 kg \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The assumptions used in the analysis. where D is the distance between IWH and DEN. The transportation cost factor (TCF) in ($/km) can be calculated as:  
\[\text{TCF}=\text{OTC}+(\eta_{\text{Fuel}}\times\text{FP}) \tag{4}\]  
where OTC is other transportation costs (insurance, maintenance, and driver rate) in $ per kilometer, \(\eta_{\text{Fuel}}\) is the fuel efficiency in liters per 100 km, and FP is the fuel price in dollar per liter, respectively. The total transportation cost, \(TC\), in $/year, will be:  
\[TC=2D\times N\times ODPY\times TCF \tag{5}\]  
where the transportation cost (TC) is in $ CAD dollar, \(D\) is the distance between IWH and DEN, \(N\) is number of trips per day, \(ODPY\) is the number of operating days per year, \(TCF\) is the transportation cost factor [32, 33]. The GHG\({}_{\text{Avoided}}\) is the avoided GHG, when using M-TES instead of natural gas (NG) boilers in tCO\({}_{\text{2e}}\)/year. Thus, we have to find out how much a natural gas boiler going to emit GHG when producing the same amount of heat that M-TES is bringing in, this is the first part of the equation. Then, the GHG that is emitted due to M-TES is subtracted and can be calculated as:  
\[\text{GHG}_{\text{Avoided}}=((\text{TH}_{\text{M-TES}}\,\text{X}\,\eta_{\text{NG }})\,\text{X}\,(\text{GHG}_{\text{NG}}))-\text{GHG}_{\text{Transportation}} \tag{6}\]  
where THM-TES is the total heat from M-TES in one year (MWh/year), \(\eta_{\text{NG}}\) is the efficiency of the boilers, and GHG\({}_{\text{NG}}\) is the GHG intensity when using NG boilers.