Problem $1$: Consider the flash distillation problem discussed as part of Workbook $1.$ The liquid and vapor under consideration are flammable. A high level of liquid in the vessel may result in over$-$pressurization of the vessel. Basic process control is implemented to the process that measures the level and manipulates the outlet flow valve to maintain the level. A high$-$pressure alarm is also implemented to alert the operator to take appropriate action. In case the operator fails to respond, a pressure relief valve is installed to release the materials in the vessel to the atmosphere and thus to prevent the failure of the vessel. The management specifies the safety target level as 'probability of release to the atmosphere to be not greater than ${10}^{-4}$ per year'. The release to the atmosphere can cause serious permanent injury to one or more persons and can result in the death of one person as well as causing temporary damage to the environment. The vessel is not isolated, and plant personnel are always exposed to the possible accident scenario. There are no other measures in place to avoid or minimize exposure of plant personnel. The frequency of the occurrence of release can be considered low.

Draw an event tree to determine whether the existing safety systems meet the safety requirement of 'probability of release to the atmosphere to be not greater than ${10}^{-4}$ per year'.

Use the risk matrix method to determine the SIL requirement for the flash distillation process.

Draw an event tree with an additional SIS with SIL obtained using the risk matrix method to determine whether the modified process will meet the safety requirement.

Comment on whether a dike will be helpful to meet the safety requirement.

Identify the SIS and the corresponding SIF you will implement to prevent over$-$ pressurization of the vessel.

Additional information

From a fault tree analysis, the probability of over$-$pressurization of the vessel was determined as $0\mathrm{.}1.$

The Failure rate of the alarm system, operator and the safety relief valve are ${10}^{-2},{10}^{-1},$ and ${10}^{-1},$ respectively.

The MTTF of valves and pressure transmitters are $50$ years.

You can assume a test interval of $2$ years.

Figure $1$: Preliminary design of a flash distillation column.