Answer Happy

Q2. Case Study: Building a reliable system PLC Flame Pro CV. PRV ES ty Alarm MV. Tank Figure 1. Tank system diagram The flammable liquid is drawn from a process source and pumped into a sealed tank. The height of tank is 10 meters. A typical level control system including a level sensor (LS-1), a control valve (CV-1) and a programmable logic controller (PLC-1) is installed to maintain the tank level below 8 meters. One manual valve (MV-1) is also installed to enable to liquid out of the tank to other equipment. In the normal operation situation, this valve is 30 percent open. The tank is contained in an environment with the possibility of sparks such as electricity spark. The site engineer worries that if the tank becomes full, it will rupture and become a potential explosion hazard. For this reason, a pressure relief valve (PRV) is installed to relieve the liquid pressure. An alarm system is also installed for the safety reason. If the level control system fails and the level of the liquid in the tank reach to 8.5 meters, then the alarm will be triggered to notify the operator. The operator can fully open the manual valve (MV-1) and manually release the liquid from the tank. The operator can also shut down the pump to stop the liquid going into the tank. Assume this operator has only about 10 minutes to response the alarm. The site engineer worries about this situation and hopes to increase the reliability of this system (decrease the failure probability). Furthermore, the site engineer wants to decrease the possibility of potential explosion hazard. Below is the reliability data table he can use for the analysis. It is assumed that power supply for all the components always work.
Component Failure mode Failure probability Level sensor LS-1 Fail to operate 1E-6 Level sensor Spurious operation (shift in calibration) 3E-5 Control valve CV-1 Fail to operate 4E-5 Programmable logic Fail to operate 3E-5 controller PLC-1 Pump P Fail to run 3E-5 Pressure relief valve PRV Fail to open 1E-5 Pressure relief valve PRV Spurious operation 2E-6 Manual valve MV-1 Failure to remain open 4E-6 Safety alarm Fail to run 2E-4 Tank Structure failure 3E-9 (All the data in this table are referred from the book "Loss Prevention in the Process Industries" by Frank P. Lees (1986) Malfunction of the system Control system mafunction Spuro operation Foto operate PLC-1 Falto oporte CV. Suure Fallon Pump Spurious operation PRV Falt rema open MV1 Tak JE-5 3E-5 4E-5 BE- 2E-6 4E-6 BE Figure 2. Fault tree for the reliability analysis of the system
a) What is the reliability of the top event (malfunction of the system)? b) What is the reliability of the top event if one redundant pump had been added? c) What is the reliability of the top event if two redundant pumps had been added? d) What is the reliability of the top event if a redundant Control Valve is added? e) What is the reliability of the top event if two redundant Control Valves are added? f) Please discuss if the reliability of the top event was improved or not? g) If we did the modifications as per the following figure, what is the reliability of the top event for the following system? PLC-2 PLC-1 Flammable liquid CV-2 c. 1 PRV $1 Safety Alarm Pump 8.5 meters LS-1 LS-2 MV.1 Tank Figure 6. Tank system diagram after installing an automatic emergency shutdown system