I am trying to make a pressure relief valve calculation in Excel for determining the minimum required area of discharge to get a desired mass flow rate. I am using the ACHIE relief valve sizing article and the example in it to validate my calculations. However, when I convert the metric units to imperial units, the formulas to not calculate the correct discharge area. Based on the example problem in the article, my discharge area should be 0.167 sq.ft, but my Excel sheet is calculating ~0.64 sq.ft. I could really use a fresh pair of eyes on this one. below is a table of the orginial metric values, my conversion factors, and the new imperial value. As well as a link to the ACHIE pressure relief valve sizing article, see pg 75 (pg 8 of the pdf) for the example problem.
I suspect my error is either with the C value or maybe my pressure conversion.
Article: https://www.aiche.org/sites/default/files/cep/20131068_r.pdf
Table:
I suspect my error is either with the C value or maybe my pressure conversion.
Article: https://www.aiche.org/sites/default/files/cep/20131068_r.pdf
Table:
Variables | Metric Values | Metric Units | Conversion Factors | Imperial Values | Imperial Units |
W | 50 | kg/s | 2.205 | 110.23 | lb/s |
P_MAWP | 8 | barg | 2088.54 | 16,708.32 | lbf/ft^2 |
Built-up Backpressure | 10% | unfired pressure vessels | 10% | % | |
P_backpressure | 0.7 | barg | 2088.54 | 1,461.98 | lbf/ft^2 |
T | 473 | K | 391.73 | deg F | |
P_set | 7 | barg | 2088.54 | 14,619.78 | lbf/ft^2 |
MW | 100 | kg/kmol | 1 | 100 | lb/lbmol |
Y | 1.3 | 1.3 | |||
z | 1 | 1 | |||
P_max | 8.8 | barg | 2088.54 | 18,379.15 | lbf/ft^2 |
P_atm | 1.013 | bar | 2088.54 | 2,115.69 | lbf/ft^2 |
P_1 | 9.813 | bara | 2088.54 | 20,494.84 | lbf/ft^2 |
Pb% (figure 7) | 17.5% | % | 17.5% | % | |
Kb (figure 7) | 1 | 1 | |||
Kd | 0.975 | 0.975 | |||
C | 7.32E-03 | sqrt(kg kmol-K)/N-s | 0.16646 | 1.70E-02 | sqrt(lb-lbmol-F)/lbf-s |
gc | 1 | unitless | 1 | ||
A | 1.55E-02 | m^2 | 10.7584 | 0.64323 | ft^2 |
Rg | 8314 | Pa-m^3/kmol-K | 0.18587 | 1545.347 | sqrt(lb-lbmol-F)/lbf-s |