can be calculated from Equation 6, and a new T i+1 calculated from Equation 5 can be used to verify the assumed T i+1 . For this depressurisation example of LNG feed gas, however, excluding the (Z i / Z i+1 ) term does not show a noticeable impact on the resulting temperature profile: is gas constant. With an assumed T i+1, Z i+1 can be calculated from Eq. 6, and a new T i+1 calculated from Eq.5 can be used to verify the assumed T i+1. For this depressurization example of LNG feed gas, however, excluding the ( Z i / Z i+1 ) term does not show noticeable impact on the
results are shown in Figure 4, but the P profile results are not shown. In this second LNG feed gas example, P and T profiles from the simulator using PR result in maximum absolute differences of 5.2% and 2.6% (in ºR), respectively, compared to the profiles from using SRK in the same sim - ulator. At least for the LNG feed gas examples, different property packages in the simulator do not result in identical temperature profiles. Additionally, Z s calculated from these two packages show up to 3.2% difference, as shown in Figure 5 . As the commonly used PR and SRK packages in the sim - ulator do not result in the same or entirely consistent sets of Z s over the range of depressurisation, the time-dependent P and T profiles generated from the program vary depend - ent upon the specific depressurisation cases and selected property package. The T profile generated by the simulator for adiabatic depressurisation typically does not seem to account for the kinetic energy term or D v 2 /2g c . At high (or sonic) veloci- ties of the discharge gas stream during depressurisation, a change in kinetic energy ( D v 2 /2g c ) may further decrease the exhaust temperature, which may need to be considered when specifying the minimum metal design temperature requirement. Non-adiabatic depressurisation Depressurisation of a segment exposed to fire involves heat input to the fluid inside and follows a non-adiabatic path. Literature,² including API empirical correlations, presents methods for calculating heat transfer from fire to the fluid inside a segment. The spreadsheet model can be expanded to include non-adiabatic depressurisation by adding a net heat input rate q to the gas inside the segment. However, quick or instantaneous heat transfer is assumed to simplify the non-adiabatic spreadsheet model, and the necessary heat transfer rate correlations are excluded. For comparison purposes, the same assumption is used for running the fire case depressurisation feature of the simulator. Temperatures ( T ) of the gas in the depressurised seg- ment (constant volume) with q (BTU/sec) heat input can be 3 of 6
resulting temperature profile. T i+1 / T i = (P i / P i+1 ) ((1-n)/n) ( Z
Eq. 5
i / Z i+1 )
(Eq 5)
(Eq 6)
Equations 1 to 6 can be used to generate transient adi- abatic gas phase depressurisation profiles of P , m , and T using a spreadsheet model. The results calculated for the LNG feed gas example are compared with depressurisation profiles generated from a simulator using the PR package. Figures 2 , 3 , and 4 plot the time-dependent P i , m i , and T i from the two methods, and the results for this LNG feed gas agree reasonably well with an absolute per cent error of about 1%. In Figure 4 comparing time-dependent T i , the absolute per cent errors between results from the simulator and this model reduce from 3% maximum (in °R) to 0.2% when PV Work Term Contribution (PVWTC) in the commercial pro - gram is increased from 93% to 100%. Moreover, relative to the initial entropy at the starting time, the simulator shows depressurised gas entropy does not exactly stay constant even at 100% PVWTC but increases by about 2.0% after 15 minutes of depressuring time. In this example, at 93% PVWTC, the entropy at 15 minutes is about 2.5% higher than the initial entropy. As Equation 4 is based on an isen- tropic path, transient profiles from the spreadsheet will likely show larger deviations when compared to those from the simulator at smaller percentages of PVWTC term, which is reportedly the isentropic efficiency of the work done on the surrounding by the expanding fluid. To further check the depressurisation profiles from the same commercial simulator but different versions or prop- erty packages, P and T profiles from the simulator using PR and SRK (Soave Redlich Kwong) separately are gen - erated for another LNG feed gas example with composi- tion slightly different from the previous example. T profile
100
0.905
0.9
Simulator PR
Model 1st case Simulator PR 1st case 93% PVWT Simulator PR 1st case 100% PVWT Simulator SRK
50
0.895
0.89
0
0.885
0.88
-50
0.875
0.87
Simulator Z - PR Simulator Z - SRK
-100
0.865
0.855 0.86
-150
0
200
400
600
800
0
200
400
600
800
Time, seconds
Time, seconds
Figure 4 Comparison of temperature profiles
Figure 5 Comparison of Z profiles
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