Answering this question is the same as determining the required relieving rate for the system. There is no difference between determining the relieving rate for a rupture disk and a relief valve. They both require a set pressure (burst pressure for rupture disk), an allowable overpressure, an evaluation and calculation of the required relieving rate for each credible scenario and then choosing the flow rate associated with the worst-case scenario.  Determining the controlling relieving rate is a paper in of itself and I will not attempt to get into details here.

How Big?

There are two recognized methods that can be used to answer this question, the Resistance to Flow Method or the Coefficient of Discharge Method.

Resistance to Flow Method

The Resistance to Flow Method analyzes the flow capacity of the relief piping. The analysis takes into account frictional losses of the relief piping and all piping components. Calculations are performed using accepted engineering practices for determining fluid flow through piping systems such as the Bernoulli equation for liquids, the Isothermal or adiabatic flow equations for vapor/gas and DIERS methodology for two-phase flow.

Piping component losses may include nozzle entrances and exits, elbows, tees, reducers, valves and the rupture disk (note that the rupture disk and its holder are considered a unit). Let me emphasize that in this method, the rupture disk is considered to be just another piping component, nothing more, and nothing less. Therefore the rupture disk’s contribution to the over all frictional loss in the piping system needs to be determined. This is accomplished by using “Kr”, which is analogous to the K value of other piping components. Kr is determined experimentally in flow laboratories by the manufacturer for their line of products and is certified per ASME Section VIII, Division 1³. It is a measure of the flow resistance through the rupture disk and accounts for the holder and the bursting characteristics of the disk.

Below is a list of some models of Continental Disc Corporation rupture disks with their certified Kr values⁴.

For comparison, the following is a list of some models of Fike rupture disks with their certified Kr values⁵.

If at the time of sizing the manufacturer and model of the rupture disk are unknown, there are guidelines to help you choose Kr. API RP521² recommends using a K of 1.5. However, ASME Section VIII, Division 1³ states that a Kr of 2.4 shall be used. Which one? Remember that ASME is Code (meaning LAW for the most part) and API is a recommended practice. In addition, as can be seen in the tables above, even ASME may not be as conservative as you may think. Therefore, it is in the engineer’s best interest to determine ahead of time the manufacturer and model of the rupture disk that eventually will be purchased. This can be done without knowing the exact size, as Kr is more manufacturer and model specific than size specific (see above tables). If a number of manufacturers are on the allowable purchase list, then at the very least choose the most likely models you would buy from each manufacturer and use the largest Kr from that list. This will be a significantly better guess than just using guidelines.

Once the piping system is laid out and all the fitting types are known, including the rupture disk, the engineer can proceed with the calculations in the following manner (presented here as a suggestion, there are many ways to do it).

1. Known are the two terminal pressures, these being the relieving pressure (upstream) and the downstream pressure (a knock-out pot, atmosphere, etc.).
   
   
2. Also known are the fluid properties and required relieving rate (the flow the rupture disk needs to pass).
   
   

3. Choose a pipe size. This will be the size to use for all components, including the rupture disk.

4. For vapor/gas or two-phase flow, use one of the accepted calculation methods to determine the maximum flow through the system. The maximum flow through the system is commonly known as critical flow or choked flow. For liquids, use the Bernoulli equation to calculate the flow that will balance the system pressure losses.

5. Per ASME Section VIII, Division 1, multiply this flow by 0.9 to take into account inaccuracies in the system parameters. Compare the adjusted calculated flow to the required relieving rate. If it is greater, then the calculation is basically done. However, the next smaller line size should also be checked to make sure the system is optimized; you want the smallest sized system possible. If the adjusted calculated flow is less than the required relieving rate, the pipe is too small, choose a larger size and repeat the calculations.

Why not just choose a large Kr? Isn’t that more conservative?

Many times, relief is not to atmosphere but to some downstream collection and treatment system, e.g. knockout drums and flares or thermal oxidizers. These are more often than not specified at a time period in the design that predates the actual purchase of the rupture disk. The flow used to size this equipment will be based on the capacity of your relief system as determined above.

If the rupture disk contributes a significant portion of the frictional losses to the system, a fictitiously large Kr might result in an oversized piping system. Sounds all right on the surface but once the actual rupture disk is chosen, the calculation must be repeated with the “real” Kr and this may be a much lower value than originally used. More fluid will flow through the system than previously determined because there will actually be less resistance to flow. The result is that the downstream processing equipment may have been undersized.

The opposite is also true. An initial guess of a fictitiously small Kr might ultimately result in oversized downstream equipment and the excessive expenditure of a significant amount of money.

Atmospheric discharge must also be similarly analyzed because the flow capacity determined after rupture disk selection may have a major impact on the emissions reported for permitting if they were based on the initial value of Kr.

Coefficient of Discharge Method

The second calculational method is the Coefficient of Discharge Method. The rupture disk is treated as a relief valve with the flow area calculated utilizing relief valve formulas and a fixed coefficient of discharge, ‘Kd’, of 0.62. This method does NOT directly take into account piping so there are restrictions in its use. These restrictions are known as the “8 & 5 Rule” which states that in order to use this method to size the rupture disk ALL of the following four conditions MUST be met³:

1. The rupture disk must be installed within 8 pipe diameters of the vessel or other overpressure source.
2. The rupture disk discharge pipe must not exceed 5 pipe diameters.
3. The rupture disk must discharge directly to atmosphere.
4. The inlet and outlet piping is at least the same nominal pipe size as the rupture disk.