PSI - Issue 19

Aaron Stenta et al. / Procedia Structural Integrity 19 (2019) 27–40 Author name / Structural Integrity Procedia 00 (2019) 000–000

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appears on a coke drum is low-cycle fatigue cracking that results from the very extreme temperature cycling of the drum as it rapidly heats up and cools down. This leads to very high thermal stresses with a correspondingly low number of expected Mean Cycles to Crack Initiation . The rate at which cracks appear increases with the number of cycles that the drum is subjected to. Since damage only accumulates during each cycle, the age of the drum can be expressed for the most part in terms of the Total Number of Operating Cycles . When fatigue cracks appear, they are typically found and repaired at the next scheduled shutdown, and so there is not normally any Unscheduled Downtime . This may not be the case later in life as the cracking and bulging become more severe. From a revenue perspective, it is more beneficial to shorten the coke Drum Cycle time so that more coke can be produced and sold over the same period of time. Based on the amount of product that is produced, a certain amount of revenue is acquired per cycle. For the base example here, it is assumed that one cycle leads to a representative revenue of about $620,000 USD. However, running shorter cycles leads to a more rapid rate of fatigue damage accumulation due to the higher thermal stress ranges. This reduces the permissible number of fatigue cycles and shortens the expected life of the drum. The question is, what should the cycle time be in order to maximize the expected annual return (total revenue minus total costs divided by lifetime) over the lifetime of the drum? This question is answered by using the decision network to maximize the expected utility over all possible combinations of decisions. As fatigue cracks appear, they have to be repaired at some cost. This repair cost is assumed to be about $225,000 USD per crack for this illustrative and simplified example. The rate at which cracks appear is assumed to be an increasing function of the number of cycles so that more cracks appear as the drum ages. The average number of cycles until crack initiation is assumed to be about 2,400 cycles for a 24 hour cycle time. This average number of cycles is assumed to decrease as the cycle time decreases according to some relationship that was previously defined in Panzarella (2016), but this could be replaced with any suitable fatigue model. After some number of cycles, the accumulated repair costs outweigh the benefit obtained by continued operation of this drum, and the drum is replaced by a new drum at some additional cost (the installation cost is assumed to be about $26,000,000 USD here). This is taken into account in the network by adding in the cost of installation. At the end of the recommended run time, it is assumed that this lifecycle is repeated, considering any adjustment that might be required as costs and revenues change over time.

Fig. 4. Coke Drum Low-Cycle Fatigue Bayesian Decision Network.