Relief valves protect pressure vessels and other equipment from being subjected to pressures that exceed their design limits.
In this scenario, a bellows pressure relief (PR) valve needs to be sized in line with the mass flow rate for a gas pipeline with natural gas under critical flow conditions, i.e., when total superimposed pressure plus built-up back pressure is equal to or less than the critical flow pressure. An Engineer, a PE and mechanical engineering consultant in Florida, turned to Knovel.
Calculating the Flow Rate
The Engineer starts by searching ‘pr valve and gas and sizing’.
(Click the search box image to execute the search and follow along)
An equation for the flow rate is found in the title Pressure Safety Design Practices for Refinery and Chemical Operations, on p. 182 of Section 8.5.2 Sizing for Vapor – Critical Flow:
* For the purposes of this example, natural gas is assumed to be pure methane.
He knows the inlet parameters for the valve are P
1 and that the orifice is diameter (D
1). They are 3000 psia, 150ºF and 1 in (25.40 mm), respectively. A can be calculated as π x D
12/4. However, he still needs to determine M and.
To make this determination, he needs to find the molecular weight of methane. He uses Data Search starting with the Search query (material or substance name = methane) and (molecular weight EXISTS)
This search retrieves a number of highly relevant references, among them Knovel Critical Tables . He opens an interactive table called Physical Constants and Thermodynamics of Phase Transitions (highlighted):
The table contains 137 hits for methane and its derivatives. To hone in on methane, he uses the Filter, matching on the Entire Cell:
and finds the molecular weight of methane to be equal 16.04:
(click to view details)
His next step is to find and calculate the compressibility factor of Methane.
The compressibility factor, = z, is found by performing a search on ‘compressibility factor’
The compressibility factor can be calculated using Brill-Beggs equations below:
However, he chooses to work with the data right away by using the interactive Excel spreadsheet on p. 23 instead. He opens this interactive spreadsheet by clicking within the blue frame of the PDF page:
(click to work with the interactive spreadsheet)
After inserting the given pressure and temperature values, the compressibility factor is calculated to be 0.8329.
His last step is to calculate the Mass Flow Rate for natural gas. The mass flow rate of natural gas is calculated using equation 4 as follows:
The flow rate was calculated using Mathcad 14 but can be calculated using Excel or a scientific calculator. Note that the symbol for specific heat ratio was changed from K to g (K stands for degrees Kelvin in Mathcad) and that for compressibility factor -
from to z. The Ф-parameter was introduced into equation 4 to allowing him to readily change the inlet flow parameters (pressure, temperature and orifice area).
The Engineer was able to find a practical solution for pressure relief valve sizing based on the calculated flow rate. He is now free to choose a manufacturer from a potential list of suppliers of bellows-type pressure relief valves at his disposal.