Page 472 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

438 Applied Process Design for Chemical and Petrochemical Plants

the details of the DIERS work noted in the above para- that exist when the gas velocity reaches the speed of
graph and at least comparing the results. Keep in mind sound. At that condition, the actual pressure in the throat
that the problem of two-phase flow under the relieving will not fall below P 1/rc even if a much lower pressure
conditions cannot be ignored. exists downstream (36]. The maximum velocity at outlet
end ( or restriction) in a pipe or nozzle is sonic or critical
Sizing for Gases or Vapors or Liquids for Conventional velocity. This is expressed (9]:
Valves with Constant Backpressure Only

This type of valve may be used when the variations in v, = � kg RT = � kg (144) P 'V (7- 5)
backpressure on the valve discharge connection do not
exceed 10% of the valve set pressure, and provided this where k = ratio of specific heats at constant pressure/ con-
backpressure variation does not adversely affect the set stant volume, cp/c,. see Table 7-5.
pressure. v, = sonic velocity of gas, ft/sec
g = acceleration of gravity, 32 ft/sec/sec
Procedure R = individual gas constant = (MR/M) = 154.4/M
MR = universal gas constant = 1544
1. For a new installation, establish pressure vessel nor- M = mol weight
0
mal maximum operating pressure, and temperature, ::!:_ = upstream absolute temperature, R
and then the safe increment above this for vessel V = specific volume of fluid, cu ft/lb
design conditions and determine the maximum P 1 = P' = upsu·eam pressure, psi abs
allowable working pressure (MAWP) of the new ves- d = pipe inside diameter, in.
sel. (Have qualified fabricator or designer establish W = gas rate, lb/hr
this. See previous discussion of topic.) Z = gas compressibility factor
2. Establish the maximum set pressure for the pressure Pc = Peril = critical pressure, psia
relieving valves as the MAWP, or lower, but never
higher. The critical pressure at a pipe outlet is [33c]:
3. Establish actual relieving pressure (and correspond-
ing temperature) from Figure 7-7A (at 110% of set Peri,= [W/(408d 2)] -(ZT/M) 112 ,psiabs (7-6)
pressure for non-fire and non-explosive conditions).
Explosive conditions may require total separate eval- The velocity v5 will occur at the outlet end or in a
uation of the set pressure ( never above the NIA MP), restricted area [9] when the pressure drop is sufficiently
which should be lower or staged; or, most likely, will high. The condition of temperature, pressure and specif-
not be satisfied by a standard SRV due to the ic volume are those occurring at the point in question.
extreme rapid response needed. Critical pressure will normally be found between 53%
and 60% of the upstream pressure, P', at time of relief
The capacity for flow through the valve is estab- from overpressure, including accumulation pressure in
lished by the conditions of this paragraph. psia. That is, P' represents the actual pressure at which the
relief device is "blowing" or relieving, which is normally
4. For existing vessel and re-evaluation of pressure above the set pressure by the amount of the accumulation
relieving requirements, start with the known MAW'P pressure, (see Figure 7-7A).
for the vessel, recorded on the vessel drawings and Thus, if the downstream or backpressure on the valve
on its ASME certification papers. Then follow step 2 is less than 53%-60% (should be calculated) of the values
and 3 above. of P', note above, critical (sonic) flow will usually exist. If
the downstream pressure is over approximately 50% of
Establish critical flow for gases and vapors the relief pressure, P', the actual critical pressure should
be calculated to determine the proper condition. Calcu-
Critical or sonic flow will usually exist for most ( com- lation of critical pressure (29]:
pressible) gases or vapors discharging through the nozzle
orifice of a pressure relieving valve. The rate of discharge Pc= P1 [2/(k + l)Jk/(k - l) (7-7)
of a gas from a nozzle will increase for a decrease in the
absolute pressure ratio P 2 /P 1 (exit/inlet) until the linear l'c/P1 = re = [2/ (k + 1) Jk/(k - I) (7-8)
velocity in the throat of the nozzle reaches the speed of
sound in the gas at that location. Thus, the critical or For critical flow conditions @13 � 0.2.
sonic velocity or critical pressures are those conditions This equation is conventionally solved by Figure 7-21.