Guidelines for Pressure Relief Design

18   Relief Device Scenario Capacity Calculations
A relief system is designed to handle the emergency condition arising from a specific series of events (“scenarios”). Thus, the first step is to define the “worst credible case” scenario for design.  The discussion and check list of Section 2.3 is useful for that purpose.

The vent load and size will depend on the assigned value of the relieving pressure.  In the absence of chemical reaction, the relief system size will be smaller for higher relieving pressures.

Set point specification must be low enough so that the device is fully open at relieving pressure.  Typical over-pressure allowances for full opening are as follows.

Device                                                  Pressure to Open, % of Set

Rupture Disc                                       100

Pilot Operated Valve                       100

Safety (“POP”) Valve                        110

ASME Sec I                                          103

ASME Sec VIII                                    110

Conservation Vents                        150-200

API 2000 Sizing (None-ASME Coded Vessels)
For API Standard 2000 Tanks (Full vacuum to 15 psig design pressure) When determining the possible causes of overpressure or vacuum in a tank,  sizing is based on either SCFH Air or NCMH Air, consider the following :

A.   Inbreathing from liquid movement out of the tank

i.      Vip = 8.02 Vpc , when

1.        Vip = inbreathing rate  (SCFH) and

2.        Vpc = liquid discharge (gpm)

B.  Out-breathing from movement of liquid into the tank

i.      Vop = 8.02*Vpf, where

1.        Vop  out-breathing rate (SCFH Air),

2.        Vfp max fill rate(gpm)

ii.      Vop =16.04*Vpr, if fluid is volatile

C.  Inbreathing from thermal effects

i.      VIT = 3.08*C Vtk0.7*Ri  where

1.         VIT  max thermal flowrate cooling (SCMH Air),

2.        C = depends on storage factors.

3.        Vtk tank volume(ft3),

4.        Ri (insulation factor)

D.   Out-breathing from thermal effects

i.      VOT = 1.51* Y*Vtk0.9* Ri , whre

1.        VoT  is max thermal flowrate heating(SCFH Air),

2.        Y (factor for latitude),

3.        Ri (insulation factor)

E.  Fire case

i.      Q = 3.091 * (Q * F /L)*(T/M) where

1.        q -  required flow capacity for fire SCFH air

2.        Q  - heat input from fire  (use table 4 API 2000 sec. 3.3.3.3)

3.        F - Environmental factor  (see API 2000 Sec 3.3.3.3. table 3)

4.        L - Latent Heat of vaporization of stored liquid at relieving conditions

5.        T  - absolute temperature degree Rankine

6.        M - Molecular weight of vapor

ASME Section VIII Coded Vessels Capacity Sizing

A.  Heat input from fire Exposure   (Based on NFPA which has been adopted by OSHA)

Wetted Perimeter Factor (horizontal tanks)

The wetted perimeter factor (Fwp) is one (1) for vertical tanks and when the vessel content is a gas.  The wetted                      perimeter factor is used for liquid filled tanks that are mounted horizontally.  The wetted perimeter factor is used to              determine the percent of the total area of the tank that will actually contain the liquid, wetted perimeter, due to it being        mounted horizontally.  This is another means of reducing the maximum possible heat absorbed by the vessel hence the          fluid for horizontally mounted tanks.  Here, the logic is, if the vessel is 100% full then the liquid will create a wetted                perimeter around the total inside surface of the vessel. If on the other hand, the vessel is only 50% full then the liquid            will wet only 50% of the total inside surface area of the vessel.  This wetted perimeter factor is based on a formula that        calculates the wetted surface area of the tank based on the percent fullness of the vessel.  See Table 2.  For spherically        or other type designed tanks, the wetted perimeter factor must be calculated differently and by the user.

% Volume                                                                      Weted Perimeter Factor(Fwp)

0                                                                                                             0

5                                                                                                             0.20

10                                                                                                           0.25

20                                                                                                           0.34

30                                                                                                           0.40

40                                                                                                           0.45

50                                                                                                           0.50

60                                                                                                           0.55

70                                                                                                           0.60

80                                                                                                           0.66

90                                                                                                           0.74

100                                                                                                          1.00

Must also include any piping below 30 feet from grade that is connected to the vessel.

A designer may also choose to use API 520/521 heat input due to Fire exposure:

Q = 34,500A 0.82   if no fire fighting procedures are in place

Q = 21,000A0.82  if fire fighting procedures are in place

A = Area exposed to fire includes any piping ( ft2)

The heat input from fire can be reduced based on certain environmental factors.

Q EFFECTIVE = QFire (Kp)

i.  Bare vessel                                                                                           1

ii.  Approved insulation                                                                          0.3

iii.  Approved Water Spray                                                                     0.3

iv.  Approved insulation and Water Spray Drainage                     0.15

v.   Earth Covered Storage                                                                    0.03

vi.   Underground Storage                                                                      0

Once the heat input has been determined the relief capacity is calculated by dividing the heat input by the heat of vaporization of the fluid inside the tank.  Add any heat input from process to the Fire heat input to determine total heat input.

Capacity (W) lbs./hr. =  (Q fire + Q process)/Hvap

A fire heat input value of 20,000 Btu/hr./ft2 of total area is recommended for portable tanks in use inside the fences, with no credit factors to be applied.

Portable or mobile equipment that goes in and out of the plant will usually come under codes (Department of Transportation, State Fire Marshal, etc.

B.    Broken Internal Tube of Heat Exchanger

Valid scenario if high pressure side greater than 1.5 low pressure side.

F = 40d2 sqrt((ρ (P1 - P2))

F= emergency vent rate into protected system lbs./min.

d= tube diameter i.d. of tube inches

P1= source pressure of fluid flowing through break, psig

P2= relieving pressure, psig. Use set pressure or set plus accumulation, whichever gives worst-case (check for                                   sonic flow)

ρ = density of flowing fluid, lb/ft3 (for gas use upstream value)

This equation gives a conservative design allowance for the liquid or gas emergency input flows.  Actual flows should be somewhat less. The heat content and mixing effects of this flow are considered later in the calculation of required system capacity.

C.    Ambient Temperature Changes
Devices are quite small even for low pressure tanks.

Heat input Rate

Q = MCpr

Q = emergency heat input rate, Btu/min

M = inventory of system (lbs.)

C  = specific heat of contents, Btu/lb./oF (should use constant volume values but constant pressure good                                            enough for liquids)

rt = rate of ambient temperature change, oF/min

The rate of ambient temperature change is the maximum expected value at the particular equipment location.  Large equipment will actually pick up heat at a lower rate than this allowance.

D.     Thermal Venting Requirements
i.       Inbreathing and out breathing can be determine directly from the API recommendations.

E.     Full-Open Control Valve
For the Full Open Control valve failure, the designer can use vendor flow programs to determine the maximum                          flowrate based on upstream and relieving pressure.  In the absence of a vendor flow program the designer can                          estimate the flow based on the equation below.

F = 1.05Cv sqrt (ρ (P1 - P2))

F= flow coefficient of valve, gpm/psi

if not known then use: Cv = 19d2

d= the seat opening diameter in inches

P1= pressure upstream of control valve

P2 = relieving pressure, psig. Use set pressure or set plus accumulation, whichever gives worst-case                                                      (check for sonic flow)

ρ = density of flowing fluid, lb/ft3 (for gas use upstream value)

If P2 is less than ½ P1,  and the fluid is a gas, the flow will be sonic in the valve.  If the flow is sonic use P2 = 1/2 P1  Manufactures specification for the maximum flow capacity of devices should be obtained in the absence of other data or standards.

F.    Over-Pumping
The emergency flow due to imbalance of in vs out flows is simply the difference between the flows under the                           proposed emergency condition.  The flow of the “unpumped” stream is usually assumed to be blocked.  Thus, the                       emergency flow becomes the maximum flow of the pump (or compressor) at the relieving pressure of the system.  The           value of flow is determined from manufactures literature for that particular item or equipment.

Most of the equations being presented here are for single-phase venting entering the relief nozzle.  However, the                    equations are still valid if the stream undergoes some phase change after it leaves the protected equipment (after it has        entered the relief system).  Vapor venting should be checked to see if they are high enough to cause liquid “boil over”.            If so, the two-phase vent rate is used.  Consult a process safety specialist for assistance with multi-phase flow in the            vent.

G.    Excess Inflow or Outflow

W = (F*ρw / ρF)

Where W= minimum relief flow rate lbs./min

F = Emergency load on system as determined from above scenarios lbs. /min

ρw= density of stream entering the relief system, lb/ft3

ρF= density of the stream entering (or leaving) the protected system (tank etc.)

The value of ρw can change during the emergency.  For example, a top vent from a partially-full tank will see a gas stream first during uncontrolled addition of liquid.  However, the vent steam will change to all-liquid if enough material is available to fill the tank.  The design is based on the worst-case condition.

For vacuum relief, the “F” stream is the fluid flowing from the vessel. The “W” stream is the air or gas flowing in through the breaker.

H.     Thermal Expansion
If the rate of temperature change has not been determined, calculate it from the emergency energy input:

r  = Q / MCp

rt = rate of temperature change oF/min

Q = emergency heat input rate,  Btu/min

M = inventory of system (lbs.)

C = specific heat of contents, Btu/lb./oF (should use constant volume values but constant pressure good                                             enough for liquids)

Next, determine the expansion coefficient:

For ideal gas:

β = 10.73 (z) / Mw ( P + 14.7)

β = coefficient of expansion, ft3/lb-oF

P = relieving pressure, psig (set pressure or maximum accumulated pressure, depending on which gives the                                         largest relief flow)

Z = compressibility factor:  use value of 1.0 for ideal gas

Mw = Molecular weight

For liquids, β can be found from the densities at two temperatures within the emergency range:

β  = ( 1 / ρ2 -1/ ρ1) / ( t2 - t1)

where, ρ = densities of flowing fluid within relieving range

t = temperaeture of fluid at selected pressures

Finally, the relief flow rate is calculated from:

W = ρ β Mrt

W = relief flow rate, lbs. / min.

ρ = fluid density at relieving conditions, lb/ft3

For gases,    ρ = [ Mw(P + 14.7)] [ 10.7 (z) ) t = 460)]

If both gas and sub-cooled liquid phases are present, add up the values of the Mrt, as determined for each phase separately, then multiply the sum by the density of the venting phase to get the value of W.

Negative values of Q signify a cooling load.  The vent stream is then the vacuum relief flow.

I.  Vaporizing Liquid

If a liuqid is at its boiling point at relieving pressure, heat input will generate vapor flow at the flowing rate:

W = (q /λ) (νg - νf) / νg

Where, W = relief rate lbs/min.

q = emergency heat load, BTU/min

ν = specific volume ft3 /lb., f denotes liquid and g denotes vapor

λ = laten heat of vaporization, BTU / lb.  ( for mixtures, use average based on vapor composition)

The quantity, (νg - νf) / νg can be set equal to one(1) for the usual conditon of low gas density.  Note an emergency                  cooling load will required a condensing rate equal to the above flow.

19.  Two-phase Venting
The level of a boiling or gas-sparged liquid can rise out the vent if enough gas “bubbles” accumulate in the liquid.  The             gas hold-up will be high even at low gas rates if the liquid is viscous or foamy.  The non-foamy liquids can swell over               also at high gas rates.  The actual gas/liquid ratio in the vent can be estimated. However, it is appropriate for non-                     reacting fluids to deal only with the extremes of the vent quality (weight flow fraction vapor).  That is designs will be             based either on a quality of unity (single-phase vapor venting), or on a quality equal to the over-all vapor content in               the vessel itself (“homogeneous” or “uniform froth” two-phase venting).  Designs for reacting fluid require special                   consideration and should be referred to a process safety specialist.

Test for Boil over (Two-phase flow test)

Check for boil over (two-phase venting) by the following steps

A)     If the fluid is viscous (over about 500 cp, or foams upon boiling (such as latex), design for two-phase venting.

B)     If the fluid viscosity is in the range 100 to 500 cp, design for two-phase venting unless it is known that the fluid has              no foaming tendency.

C)      If the fluid viscosity is less than 100 cp and foaming tendency is slight, assume all vapor venting.  Proceed with the following steps to check this assumption.

D)     Calculate the vapor velocity in the vessel:

∪s = W / ρg Ac

∪s =  velocity in vessel just above liquid surface, ft/min

W = relief flow rate lbs./min

ρg = gas density, lb./ft3

Ac = cross-section flow area at liquid surface, ft2

If the flow area decrease with increasing level, use the minimum area (maximum possible level).  Example are spheres                or horizontal tanks over half full.  If no reasonable minimum area can be assigned, design for two-phase venting.

E)        Calculate the bubble rise rate parameter:

∪∞  = [ 3.0 (61,000 δ /ρf) ( 1 - ρgf)] 0.25

∪ = rise rate ft./min.

δ = surface tnesion, dyne/cm

ρf,  ρg = liquid and vapor density, lb/ft3

Surface tensioin data may be hard to find for a particular fluid.  The answer is insensitive to the surface tension                       value, so data for similar fluids can be used.

F)         Calculate the dimensionaless parameter Ψ.

Ψ =    ∪s / ∪

IF most of the gas is from a bottom sparger rather than from a boiling liquid

Ψ = 2 ∪s/ ∪

G)        Read average α for this vlalue of Ψ from the  α vs Ψ curve.  Note that average α is the volume fraction of vapor                         hold- up in the liquid for a given value of Ψ.

H)         Calculate the actual volume fraction gas phase in the vessel:

α = 1 - (liquid volume / vessel volume)

I)           Compare this  α on the the α vs. Ψ curve.

a.    if α is above the curve then flow is single-phase vapor

b.    if α is below the curve then the flow is two-phase.

19.1     Phase Change on Mixing

Sudden changes in vapor volume can occur as the result of condensation, dissolutions or vaporization during the                    addition of one fluid to another.  An example is the contacting of water and HCl gas.  The water will dissolve the gas              and heat up causing lower pressure in the vapor space.  Another example is the contact of a hot liquid with a more                  volatile sub-cooled liquid.  The net super-heat will go to the vaporization and increase the vapor space pressure.

The volume changes that occurs during these mixing events can be calculated quite readily.  However, the rate of                    change will depend on the rate of mixing, mass transfer, etc.  Consult a process safety specialist for assistance with              problems of this type.

Once the designer has determined his relief rate required to keep the vessel pressure below what is allowed under                 the code then he must select a relief device orifice size based on performing an orifice size calculation for the type               of fluid being relieved.  That fluid may be liquid, gas, vapor, steam, or two-phase.  If two-phase then consult safety                 expert.