## 2 Preliminaries
### Safety Barriers
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Principle** & **Classification** & **Description** & **Examples** & **References** \\ \hline \multirow{8}{*}{Barrier types and characteristics} & \(\bullet\) & Passive barriers & \(\bullet\) & Barriers operate continuously without any external actions. & \(\bullet\) & corrosion prevention systems, walls \\  & \(\bullet\) & Activated barriers & \(\bullet\) & External action is required to activate the barriers. & \(\bullet\) & water deluge systems, smoke alarms \\  & \(\bullet\) & Human actions & \(\bullet\) & Rely on the knowledge of the operator to activate barriers. & \(\bullet\) & rules, guidelines, safety principles \\  & \(\bullet\) & Symbolic barriers & \(\bullet\) & Barriers that rely on symbolic indications or warnings to communicate information or provide guidance. & \(\bullet\) & warning boards \\ \hline \multirow{8}{*}{Barrier properties and implementation method} & \(\bullet\) & Passive barriers & \(\bullet\) & Barriers operate continuously without any external actions. & \(\bullet\) & Surface-controlled subsurface safety \\  & \(\bullet\) & Active barriers & \(\bullet\) & External action is required to activate the barriers. & \(\bullet\) & casing, tubing, well packer \\  & \(\bullet\) & Conditional barriers & \(\bullet\) & Barriers that are either not always in place or not always capable of functioning as barriers. & \(\bullet\) & stabbing valve \\  & \(\bullet\) & Operational barriers & \(\bullet\) & Barriers that function while the operation is carried out. & \(\bullet\) & drilling mud \\ \hline \multirow{8}{*}{Barrier elements} & \(\bullet\) & Physical barriers & \(\bullet\) & Barriers consist of physical or mechanical elements. & \(\bullet\) & pressure relief devices, water deluge systems, firewalls \\  & \(\bullet\) & Non-physical barriers & \(\bullet\) & Barriers consist of non-physical elements. & \(\bullet\) & safety training, inspection \\ \hline \multirow{8}{*}{Barrier elements (entropy divided in the category of non-physical barriers)} & \(\bullet\) & Physical and an action from being carried out or an event from taking place. & \(\bullet\) & firewall, heat resistant coating, pressure relief devices \\  & \(\bullet\) & Functional barriers & \(\bullet\) & Rely on systematic or functional means to prevent or mitigate the occurrence or spread of hazards. & \(\bullet\) & physical lock, interlock \\  & \(\bullet\) & Symbolic barriers & \(\bullet\) & Barriers that rely on symbolic indications or warnings to communicate information or provide guidance. & \(\bullet\) & warning boards \\  & \(\bullet\) & Incorporeal barriers & \(\bullet\) & Through non-physical means to raise the risk awareness among individuals to prevent or reduce hazards. & \(\bullet\) & rules for actions, safety guidelines \\ \hline \multirow{8}{*}{Barrier movement characteristics} & \(\bullet\) & Static barriers & \(\bullet\) & Barriers are available for a long time. & \(\bullet\) & well packer \\  & \(\bullet\) & Dynamic barriers & \(\bullet\) & Barriers vary over time. & \(\bullet\) & stabbing valves \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._The classification adopted in this study is based on barrier functions. Hence, SBs are classified into preventive and protective barriers (see Figure 1). The former, involving barriers between causes and the critical event, can reduce the occurrence probabilities of hazard events, while the latter, encompassing the barriers between the critical event and outcomes, can mitigate the consequence severity of the hazard events. Generally speaking, a catastrophic accident starts with one or some initiating events, which proceed in a certain sequence of events and evolve gradually until the accident finally occurs or aborts. SBs play a crucial role in this process. If SBs are effective and reliable, they can largely mitigate and avoid hazardous events, thus giving the system a strong protective effect, and conversely, they cannot slow down the progress of the accident.