## 3 Analyzed Model
In case of BF overpressure, only the valves related to the selected circuit open;
* Valves of selected circuit start opening when the BF pressure remains over the threshold for 2 s and takes 3 s to open completely (similarly the valves closure);
* The valves are surfaces simulated as:
* walls when closed;
* suitable time-dependent porous-jump during their opening/closure;
* interiors when completely opened;
* The correlation between pressure losses of valves and their opening degree has been calculated apart with suitable simulations and adopted in the model to define the time-dependent porous-jump;
* The boundary conditions (Figure 6) are:
* adiabatic walls;
* outlet pressure to the network \(p\) = 0 mmWC gauge;
* inlet mass-flow: operating conditions are 100 kNm\({}^{3}\)/h and 100 \({}^{\circ}\)C as normal field values. To simulate overpressure events inlet temperature is suddenly increased;
* The model uses the symmetry of the system in order to reduce the number of computational cells. With these assumptions, monitoring the pressure wave along the circuit is possible. For this purpose, some surfaces, acting as pressure measure, are located in the most significant points, as shown in Figure 4.  
The events that generate the overpressure, such as slip and channeling phenomena, are simulated with instantaneous variation of the mouth temperature: This means a different actual volume of gas with a consequent higher pressure on top. At the initial instant, the gas temperature goes from 100 \({}^{\circ}\)C (normal operation) to a higher value and the pressure increases, starting from the normal value of 700 mmWC, with 100 kNm\({}^{3}\)/h of BF gas flow rate. Three different scenarios for top gas temperature are analyzed:  
* 174 \({}^{\circ}\)C (low severity grade);
* 240 \({}^{\circ}\)C (medium severity grade);
* 342 \({}^{\circ}\)C (high severity grade). Out of simplicity, the simulated events are persistent, i.e., they are not exhausted in time as in reality. This means that the valves continue to open and close. It is observed that cyclones, due to their high losses of pressure, prevent the reduction of the BF overpressure. In order to clean the gas as much as possible, a circuit that partially bypasses only the cyclones is an effective solution. Among all scenarios analyzed, the three more relevant circuits are reported (Figures 7 and 8):  
* The first circuit (C1) simulates the original conditions (all the tapping point valves are closed): bleeder valve B1 set to open at BF top pressure equal to 950 mmWC; in case the pressure continues to rise, at 1050 mmWC, bleeder valve B2 opens, too (any B2 opening is not simulated but only foreseen);
* The second circuit (C2) partially bypasses the cyclones and transfers the gas to the reserve scrubber through a new DN800 emergency pipeline. In this case, the spare scrubber is intercepted, flushed with nitrogen and maintained at 50 mmWC under normal conditions. The opening of tapping point valves (V2 and V4) and clean relief valve (B3) is simultaneous and set at the BF top pressure equal to 850 mmWC. If the pressure continues to rise, bleeder valve 1 and bleeder valve 2 open at a BF top pressure equal to 1050 mmWC (any B1 and B2 opening is not simulated but only foreseen);* The third circuit (C3) partially bypasses the cyclones and transfers the gas to the reserve scrubber through the existing common DN2800 pipeline. In this case, the backup scrubber is always connected to the upstream circuit. The opening of tapping valves (V2 and V3) and clean relief valve (B3) is simultaneous and set at the BF top pressure equal to 850 mmWC. If the pressure continues to rise, bleeder valve 1 and bleeder valve 2 open at BF top pressure equal to 1050 mmWC (any B1 and B2 opening is not simulated but only foreseen). Figure 6: Detail of surfaces acting as porous jump (septum): (**a**) upstream circuit; (**b**) downstream circuit. Pressure values refer to normal operating conditions.