# Multi-Hop Routing Protocols for Oil Pipeline Leak Detection Systems
## 3 System Architecture, Scenarios of Multi-Hop LoRa, and Results
### Flat Topology Calculations
#### 3.1.2 The Energy Consumption of LoRa Nodes Calculations  
In Figures 4 and 5, we calculate the energy consumption per node for one day. We consider energy consumption only for the send and receive modes. We select 200 m as the distance between sensors based on the previous traffic calculations. From [47], we used the same value of the current for send and receive mode. The energy value in joules was calculated; for sending mode, it is 0.323 joule, and for receiving mode, it is 0.218 joule. To calculate the energy consumption for a single node, we use Equation (2), where N is the sequence number of the sensor in the communication, E\({}_{Rm}\) is the energy for receiving mode, E\({}_{Sm}\) is the energy needed to send the packets, and P\({}_{s}\) is the packet size. \[\text{E}=[(\text{N}-1)\;\text{E}_{Rm}+\text{N}\;\text{E}_{Sm}]\;\text{P}_{s} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Scenario 1**} & \multicolumn{6}{c}{**Scenario 2**} & \multicolumn{6}{c}{**Scenario 3**} \\ \hline Pipeline length & \multicolumn{10}{c}{10 km} \\ \hline Communication Scenarios & \multicolumn{6}{c}{Hop-by-hop} & \multicolumn{6}{c}{The third neighbor} & \multicolumn{6}{c}{The ninth neighbor} \\ \hline Distances (m) & 10 & 50 & 100 & 150 & 200 & 500 & 10 & 50 & 100 & 150 & 200 & 500 & 10 & 50 & 100 & 1500 & 200 & 500 \\ Devices & 1000 & 200 & 100 & 67 & 50 & 20 & 1000 & 200 & 100 & 67 & 50 & 20 & 1000 & 200 & 100 & 67 & 50 & 20 \\ No. Hops & 1000 & 200 & 100 & 67 & 50 & 20 & 340 & 68 & 34 & 23 & 17 & 7 & 100 & 20 & 10 & 7 & 5 & 2 \\ \hline \multicolumn{10}{c}{Packets} & \multicolumn{10}{c}{1 byte/ 255 bytes} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Multi-Hop Communication Scenarios’ Parameters. Figure 3: The number of bytes/days at different sensor distances (packet size is 255 bytes). Each sensor sends one byte every 3 h. As an example, node 2 in the first scenario will send the two packets (packet of node 1 and its packet) and receive one packet, so it consumes around 1 joule per day. Table 5 shows energy assumptions. In Figure 4, the energy consumption per node is presented. The node IDs (1, 10, and 40) are shown in the x-axis where the distance between sensors is 200 m. The nodes which cooperate for the communication in the three scenarios are selected. The amount of energy consumed per node is shown in Figure 5. The x-axis shows the node's IDs, on the other hand the values of the y-axis are presented in logarithmic-scale. We calculate the energy consumption to show the difference between the three communication scenarios. We first determine the number of received and transmitted packets for each node included in the communication, then apply Equation (1) to find the nodes' energy consumptions. Device 1 consumes around 0.2 joules in all three scenarios, depicted in Figure 5. Device 40 consumes around 440 joules in the first scenario whereas it consumes around 10 joules in scenario 3,  
Figure 4: Energy consumption for nodes 1, 10, and 40—when distance is 200 m.  
Figure 5: Energy consumption for the 50 devices—where the distance is 200 m. \begin{table}
\begin{tabular}{c c} \hline \hline
98 mA & Drawing current of send mode \\
66 mA & Drawing current of receive mode \\
1 packet each 3 h & Packets \\
1-day & Total assumed duration \\
50 Node & Number of Nodes \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Energy consumption specifications. which are shown in Figure 5. Less energy consumption is observed in scenario 3 due to the smaller number of hops. Moreover, to show the communication scenarios' effect on energy consumption, we applied Equation (2) on the 50 nodes and calculate the total energy per day in the three scenarios. For example, in scenario 1, the devices consume around 11,674 joules, whereas in the third scenario the devices consume 148 joules.