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4. Results
4.3. Sensitivity analysis
4.3.8. Sensitivity to fire event duration
The longer the bulk supply system is subjected to a fire event, the longer the reservoir has to buffer against the reduced net inflow (or increased net outflow). The longer the fire event duration, the greater the possibility of consequent supply failure event occurring. The sensitivity of the supply system to these events needs to be tested in order to gauge the tolerance for variation. The values tested are listed in Table 4.3.10, in line with those tested by Chang & van Zyl (2012).
Table 4.3.10: Fire duration sensitivity values
Parameter Low Value Baseline High Value
Fire event duration
(Poisson mean (hours)) 0.44 0.84 1.62
The values in Table 4.3.10 vary significantly with respect to each other, however when compared to a system that experiences pump failure durations with an average of 48 hours, the duration appears insignificant. The results of the sensitivity analysis are presented in Figure 4.3.8. In line with the observation regarding the fire event durations to be tested, the results appear to be largely unaffected by the change in fire event duration. The same
0.00 0.01 0.10 1.00 10.00 100.00 1,000.00
0.0 2.0 4.0 6.0 8.0 10.0
failure frequency (failures per annum)
Cost ($) Millions
Low (3) Baseline (4.5) High (9)
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reasoning, as for the fire event frequency can be applied. The duration is not significant enough to cause an already largely reliable solution system, at or below design criterion, to fail more frequently, as the size of the components built into the system are resilient to long ,supply (pump failure) interruptions.
Figure 4.3.8: Pareto-optimal front for varying fire event duration 4.3.9. Sensitivity to pipe length
As was demonstrated in section 4.2.2 above, the pipe system cost makes up approximately 45% of the overall system cost. The pipe cost is influenced by the number of pipes, the length of the pipes and pipe diameter and is determined for each pipe from the equation presented below:
πΆπππππ = 480 Γ πΏππππ Γ (π·ππππ)0.935
Where: πΆπππππ = Pipeline capital cost ($)
πΏππππ = Length of pipe (m)
π·ππππ = Diameter of pipe (m)
0.00 0.01 0.10 1.00 10.00 100.00 1,000.00
0.0 2.0 4.0 6.0 8.0 10.0
failure frequency (failures per annum)
Cost ($) Millions
Low (0.44) Baseline (0.84) High (1.62)
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From this equation, as presented previously in 3.6.6, the resultant increase in the cost of the pipeline system as a response to an increase in the pipe length is evident and easily calculated. However what is not as simply determined is the effect that the extra pipe length has on the pump and pipe sizing, and the impact of the sizing of these supply parameters on system configuration and cost. An increase in pipe length means an increase in primary, frictional losses. In order to respond to the pressure and flow reduction, the pump size must be increased, however the increase in flow results in a subsequent increase in frictional losses. This creates evolutionary pressure to increase the pipe diameter, and reduce pump power. The increased supply side cost also creates evolutionary pressure toward reservoir capacity as a more cost effective means of decreasing failure frequency; however increasing reservoir capacity is only effective at reducing failure frequency over a certain range of supply ratios. The lengths to be used in the variation of the pipe system are presented in Table 4.3.11, in line with the values tested by Chang & van Zyl (2012).
Table 4.3.11: Pipe system length sensitivity values
Parameter Low Value Baseline High Value
Pipe System Length (km) 1 10 100
As can be seen in Figure 4.3.9, the difference in cost is highly substantial, with the high value pipe system cost a factor of 100 more than the low value pipe system cost. The total system cost increases at a higher rate in the high value system, owing to the additional cost to overcome frictional losses through increasing pump size. Equally, increasing pipe diameter has a far more substantial cost in a 100 km pipe system compared to a 10 km pipe system..
The observation however should be taken in the relative cost of solutions that meet the design criterion failure frequency.
Chapter 4: Results 141
Figure 4.3.9: Pareto-optimal front for varying pipe length
The shift in balance between system components as the length of the pipe increases provides insight into the cost implication of system component design under varying system constraints. This variation is represented as component size, as a percentage relative to the baseline in Figure 4.3.10. This demonstrates the component sizing of the nearest solution that meets the design criterion. A significant pump power response to increase in length is observed as the reservoir needs to experience a certain supply ratio regardless of pipe length, to attain a certain failure frequency (in this case the design criterion). The increase in pump power is non-linear. This is due, in part, to the non-linear increase in frictional losses and the additional power required in overcoming them. The converse is true for the decrease in pump power for the low value system. The lesser increase in pipe diameter is as a result of the large increase in cost involved in increasing the size of a pipe that is 100 km in length. The reservoir increase is also relatively minor and is likely due to the inefficiency of increasing the reservoir capacity in the design criterion failure frequency zone. What is proposed is that increasing the supply ratio at the design criterion remains an efficient means of decreasing failure frequency for long length pipelines. The distinct lack of multiple pipe systems in the short distance model, that could be expected owing to the reduced cost associated with adding an extra pipe, is likely due to the reduced pipe failure rate (in failures/km/annum), and
0.00 0.01 0.10 1.00 10.00 100.00 1,000.00
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
failure frequency (failures per annum)
Cost ($) Millions
Low (1) Baseline (10) High (100)
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the relative insensitivity to pipe failure frequency and duration, as demonstrated in 4.3.5 and 4.3.6. The result is the complete inefficiency of pipe systems consisting of more than a single pipe.
Figure 4.3.10: Relative Component Sizing for Varying Pipe Length