Chain-stopping event

We will consider the MWD in two simple cases. The first is when chain transfer is sufficiently rapid to ensure that all other chain-stopping events can be ignored. In such a situation, whereas the compartmentalized nature of the reaction may affect the rate of initiation of new chains, it will not affect the lifetime distributions of the chains once they are formed. The MWD may then be found from the bulk formulas, provided only that the average number of free radicals per particle, is known. Such an approach has been used by Friis et al. (1974) to calculate the MWD evolved in a vinyl acetate emukion polymerization. These authors included in addition the mechanisms of terminal bond polymerization and of transfer to polymer (both of which cause broadening). The formulas required for the in corporation of these mechanisms could be taken from bulk theory. 

In these systems (Section I,C,l,a) Gerrens (1959) recognized that if combination is the only chain-stopping event, then the number-average molecular weight (MJ is inversely proportional to the entry rate coefficient ... 

In a pseudo-bulk system, the MMD is more complicated. Assuming that the distribution of radical lengths from Equations (5.42) and (5.43) is known, the number MMD is obtained from the total rate of chain-stopping events ... 

The instantaneous MMD can be found from a knowledge of the rate coefficients for chain-stopping events, which are transfer (to monomer, polymer and chain-transfer agent) and termination, and for chain growth, which is propagation. In addition, since in a zero-one system entry into a particle which already contains a growing chain results (by definition) in instantaneous termination, entry is also a chain-stopping event in a zero-one system. 

The measured average molecular weights, eg, obtained from molecular weight distributions, of macromolecules generated by free radical polymerization processes are often lower than those predicted by accounting for initiation, propagation, and termination processes. This experimental observation can be attributed to chain stopping events via chain transfer reactions (163,164). The transfer reaction can be described via equations 22 and 23. 

Firstly, we assume that termination is solely by disproportionation and that the propagation probability factor is equal for each chain length. The probability for the occurrence of a polymer chain—hence its distribution function—with the length P is given by the probability of P - 1 propagation steps and the probability of one chain-stopping event (termination or transfer). 

It should be noted that the propagation step must be highly favoured over chain stopping events to produce polymer with a significant chain length and the value of a must be near to one. Hence, eqn (1.63) shows that for a chain-length distribution of a polymer produced in a steady-state experiment, where chain stopping events are termination by disproportionation or transfer, the dispersity becomes nearly 2. 

The radicals Rx and R2- may now undergo reactions to give final products which regenerate these same radicals but ultimately they combine with each other to stop the chain of events. The combination reactions would be... 

Whilst it is quickly possible to get bogged down in mathematical detail, the takeaway message is to ensure that in the estimation of likelihood one looks at the probability of actual harm occurring. Stopping elsewhere along the hazard-to-harm path is fraught with difficulty as the estimated likelihood will depend on exactly which event constitutes harm in the eyes of the assessor. Similarly, by looking at the end-to-end chain of events the presence or absence of controls can be factored in to the likelihood estimation. 

Sometimes the initiating event is selected (the backward chaining stops) because it represents a type of event that is familiar and thus acceptable as an explanation for the accident or it is a deviation from a standard [166]. In other cases, the initiating event or root cause is chosen because it is the first event in the backward chain for which it is felt that something can be done for correction. ... 

The accident report on a friendly fire shootdown of a U.S. Army helicopter over the Iraqi no-fly zone in 1994, for example, describes the chain of events leading to the shootdown. Included in these events is the fact that the helicopter pilots did not change to the radio frequency required in the no-fly zone when they entered it (they stayed on the enroute frequency). Stopping at this event in the chain (which the official report does), it appears that the helicopter pilots were partially at fault for the loss by not following radio procedures. An independent account of the accident [159], however, notes that the U.S. commander of the operation had made... 

But the selection of a stopping point and the specific operator action to label as the root cause—and operator actions are almost always selected as root causes—is not the real problem here. The problem is the oversimplification implicit in using a chain of events to understand why this accident occurred. Given the design and operating conditions of the plant, an accident was waiting to happen ... 

Where does all this leave us There are two possible reasons for conducting an accident investigation (1) to assign blame for the accident and (2) to understand why it happened so that future accidents can be prevented. When the goal is to assign blame, the backward chain of events considered often stops when someone or something appropriate to blame is found, such as the baggage handler in the... 

Virtually all incidents involve some sort of human error. Either a person initiated a train of events or failed to respond correctly as events started to go awry. Indeed, it is almost certain that some type of human error will be involved in incidents because usually the operator being, in Trevor Kletz phrase, the last man on the bus had an opportunity to stop the chain of events. If he or she fails to do so, this does not mean that he is to blame—after all there were probably many other mistakes made by supervisors, managers, engineers, and designers. 

Although this type of error is indeed an error, it is important to recognize that the person who failed to stop the chain of events is probably not the person who initiated or propagated that chain of events. He or she was merely the last man on the bus. ... 

Under normal plant operating conditions, heat release is determined by the cyclo-hexanol/cyclohexanone mix flow, which is instrument-controlled in order to keep the correct mix-to-nitiic acid ratio. By cutting off the KA oil feed, the reaction stops and heat release ceases. In most industrial reactors, the water cooling system inside the reactor is regulated by the temperature of the reaction mix. Redimdant alarms and emergency stops are installed to automatically cut off the flow of the cyclo-hexanol/cyclohexanone mix in case of a malfunction. Some of the conditions and chains of events that could lead to potentially dangerous situations include ... 

While the term detection function is commonly understood, the term control function has several different interpretations. ISO 13702 defines control as the limitation of the extent and/or duration of a hazardous event. In this paper we further specify the term and state that control means to reduce the likelihood that a critical deviation will develop into a major accident once it occurs, i.e. to stop the unwanted chain of events when critical deviation occurs. 

Establishing detection and control safety barriers to stop the unwanted chain of events before it develops into a major accident. 

An operational barrier can be seen as a determined specific action that shall be carried out in the case of critical deviation to prevent or to stop the development of an unwanted chain of events. A manual shutdown valve is often treated as a technical barrier element however, it will not perform the barrier function unless somebody activates it on demand. This action is an operational barrier element. 

Strong markov process For a diffusion process, the Markov property can be extended to a sequence of random times known as the strong Markov property and can be expressed as follows let r , n = 1,2,... be an increasing sequence of stopping times for the process X(t ), n > 0, and suppose X T) = x the Markov chain X Tn+i), X Tn+i), , Xj+n behaves as if the process had started anew at X Tn) = Xn, and is independent of the Markov chain of events X(ri),..., X T -i). It should be noticed that a Markov process does not necessarily obey the strong Markov property because of subtle links between the random times. The converse is however true. 

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