Relief System Sizing - CHERIC Relief Size I o Conventional spring-operated reliefs in liquid or...
Transcript of Relief System Sizing - CHERIC Relief Size I o Conventional spring-operated reliefs in liquid or...
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Relief System Sizing
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Calculating Relief Size I
o Conventional spring-operated reliefs in liquid
or vapor-gas service
o Rupture disc in liquid or vapor-gas service
o Two-phase flow during runaway rxn
o Reliefs for dust and vapor explosion
o Reliefs for external fire
o Reliefs for thermal expansion of process
fluid
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Calculating Relief Size II
Phase
Liquid
Gas
Two phase
Outcome
Process fluid
External fire
Dust & vapor
explosion
Rupture disc
Standard
Vent area
Low P Vent
High P Vent
Vent area
Vent area
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Relief Area Requirements
o Minimum flow to hold valve seat in open position: 25-30 % of maximum flow
- Low flow can lead to rapid opening and closing (chattering)
o Overpressures are designed to be 10 to 25 % above set pressures to prevent excessive vent sizes
o To hold pressures near the set pressures would require much larger vent sizes
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Required Vent Area, 2-f Flow
0 25 50
Overpressure, %
Ven
t A
rea,
m2
0.05
0.0
0.1
10
design
range
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Spring Relief Area for Liquids
Assume orifice flow through the valve port:
Qv u A ACo2gc P
PC
Q
u
QA
ref
o
vv
/
38.0gpm
)psi(in 2/12
Eqn 4-6, p. 114
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ū is the liquid velocity through the spring relief,
Co is the discharge coefficient,
ΔP is the pressure drop across the relief, and
ρ is the liquid density
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Computed Area for Liquids
A is computed area for device sizing as
contrasted to effective valve area during use
Max pressure in the API equation is 25 %
above the set pressure
For Co use the conservative value of 0.61
unless more information is available
Kv, Kp, Kb are correction factors for use of the
API equation with various liquid viscosities,
maximum pressures, and backpressure.
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Spring Relief Area for Liquids
bs
ref
bpvo
v
PPKKKC
QA
25.1
/
gpm38
psiin 2/12
API correction factors included for wide applications:
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A is the computed relief area (in2),
Qv is the volumetric flow through the relief (gpm),
Co is the discharge coefficient (unitless),
Kv is the viscosity correction (unitless),
Kp is the overpressure correction (unitless),
Kb is the backpressure correction (unitless),
(ρ/ρref) is the specific gravity of the liquid (unitless),
Ps is the gauge set pressure (lbf/in2)
Pb, is the gauge backpressure (lbf/in2)
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Correct Area for Viscosity: Kv
Higher the viscosity the higher the friction losses
through the valve
Higher the viscosity, the smaller the Reynolds
number, Re, and smaller the Kv and therefore the
larger the required A
Re usually is > 5,000. Then Kv is ~ 1.
For low Re , Kv is a strong function of Re
98.0Re
170
1V
K
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Viscosity Correction Factor: Kv
10 50 5000 Reynolds number
Vis
co
sit
y c
orr
ec
tio
n,
Kv
1
0.6
0.3
0.8
Spring relief, Liquids
Fig 9-2, p. 387
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Correct A for Overpressure: Kp
1.25 Ps- Pb = ∆P for 25 % overpressure (OP); use a correction factor, Kp , for OP within 10 - 50 %
OP correction factor: Kp = 1 for 25 % OP
Above 25 %, the vent area is fixed, so flow rate change only with pressure drop: Kp is a weak function of pressure in this range
Below 25 %, the vent area changes with pressure, so flow rate changes with pressure drop and with area: Kp is a strong function of pressure in this range.
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Overpressure Correction: Kp
10 25 50
Overpressure, %
Overp
res
su
re c
orr
ec
tio
n,
Kp
1
0.6
Spring relief for liquids
Fig 9-3, p. 387
Vent area
changes
Vent area fixed
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Pb in basic API equation corrects for effects of backpressures in conventional valves (set pressure and flow rate
Higher the backpressure, the lower the flow: larger the calculated required area, A
For balanced bellows valves, a correction factor, Kb, must be included because the set pressure does not increase as backpressure increases
The higher the backpressure, the smaller the Kb and the larger the required A for a given Qv
Ex 9-1, p 388 relief sizing
Correct Area for Backpressure: Kb
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Kb for Balanced-Bellows Reliefs
0 25 50
% Gauge Backpressure
Bac
kp
ressu
re c
orr
ecti
on
, K
b 1
0.7
0.5
0.9
Liquids, Overpressure = 25 %
Fig 9-4, p. 388
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Spring Relief Valves for Gases
In general, flow is critical with Pch > Pext:
(Qm )ch CoA P gc M
RgT
2
1
(1) /(1)
A Qm
Co Kb P
T z
M
gc
Rg
2
1
(1) /(1)
z, compressibility factor
P, max absolute discharge
pressure
Eqn 4-50
p. 133
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Vent Area Equation for Gases Separate Kb correction for each valve type:
- Standard valves, Fig 9-5, balanced bellows, Fig 9-6
- For larger backpressure, Kb smaller and A larger
Co: if not known use 0.975
M is average molecular weight
P is the maximum absolute relieving pressure:
P = Pmax + 14.7
ASME safety guidelines, Ps = gauge set pressure:
Pmax = 1.1Ps, unfired vessels
Pmax = 1.2Ps, vessels exposed to fire
Pmax = 1.33Ps, piping, Ex 9-2, p 392
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Backpressure correction Kb for conventional spring-
type reliefs in vapor or gas service. Source: API RP 520
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Backpressure correction Kb for balanced-bellows
reliefs in vapor or gas service. Source: API RP 520
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Rupture Disks for Liquids
Use expression for spring relief valves for liquids
- Discharge directly to atmosphere or short piping:
Discharge to a relief system:
Flow through the system of pipes and other components must be analyzed as considered in study of source terms.
Eqn 9-3, p. 385
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PC
QA
ref
o
v
/
38.0gpm
)psi(in 2/12
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Rupture Disks for Gases
Use expression for spring relief valves for gases
For low backpressure levels with no Kb factor:
For significant backpressure levels as into a containment system:
- Analyze discharge and flow through the entire containment system. Ex 9-3,4, p 395
Eqn 9-13, p. 394
A Qm
Co P
T z
M Assumes Co = 1
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Two-Phase Relief Behavior
Choked, two-phase flow through relief orifice
Two-phase flow through containment system
Runaway generally includes flashing during
relief; ∆Hv removed (reaction is tempered)
Reactor system, large vol/area, ~ adiabatic
Energy removal only by vaporization and
discharge
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A tempered reaction system
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Two-Phase Mass Discharge
Liquids at their saturation pressure, saturation temperature, Ts, the two-phase mass flow rate:
Mass flux with L/D correction factor, ψ, Fig 9-8, p. 397:
Eqn 4-104, p. 156
ps
c
gf
vm
CT
g
v
AHQ
gf
gf Vv
sp
c
gf
vT 9.0
TC
g
v
HG
Empirical 0.9 factor to
match data for
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Correction for 2-f Flashing Flow in
Pipes
0 200 400 L/D
Co
rrec
tio
n F
acto
r
0.75
0.5
0.1
100
Correction factor: ψ
300
Fig 9-8, p. 397
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Two-Phase Mass Discharge
Clausius Clapyron:
p
scT 9.0
C
Tg
T
PG
gf
v
vT
H
dT
dP
ψ = 1 for an orifice
2
v
gf
v
o
To /
TC
v
H
m
VGqmA
2
vs
o
To /
TC
dT
dPT
m
VGqmA
Heat terms:
generated by process,
removed by discharge
adsorbed by evaporate
∆T due to ∆P (OP)
qWith CC equation:
mo = mass before release
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Patterns of two phase flow
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Thermal Reaction Behavior
Measure heat input rate using a calorimeter, such as VSP, Fig 8-8, p. 366
Measure heating rate at the set pressure and the heating rate at the maximum pressure
Understand behavior of two-phase releases
Avoid scenarios that can result in two-phase releases, e.g., overheated polymerization reactor
ms
v5.0dt
dT
dt
dTCq
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Nomograph Sizing Method
A graphical method by Fauske for quick estimates of two-phase release areas uses only this information:
- Heating rate at the set temperature, (dT/dt)s
- Set pressure
- Mass of reactants
Obtain a vent size area using Fig 9-9, p. 403
- Assumes a discharge piping of L/D = 400 (a discharge coefficient = 0.5), and 20 % OP.
Adjust an area estimate for other L/D ratios and OP values.
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9-6 Deflagration Venting for Dust and Vapor
Explosions
o Vents for Low-Pressure Structures
by Runes P
LLCA 21
*
vent
A is the required vent area,
C*vent is a constant that depends on the nature of the
combustible material,
L1 is the smallest dimension of the rectangular
building structure to be vented,
L2 is the second smallest dimension of the enclosure
to be vented, and
P is the maximum internal pressure that can be
withstood by the weakest member of the
enclosure.
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o Vents for High-Pressure Structures
1/3
max
StG or Vdt
dPKK
KG is the deflagration index for gases and
vapors,
Kst is the deflagration index for dusts,
(dP/dt)max is the maximum pressure increase,
determined experimentally, and
V is the volume of the vessel.
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Reliefs for Fired Reactors
Reactors exposed to external fires: heating and
boiling of process liquids and excessive pressures
Usually exposure at a small part of reactor surface:
two-phase foam is smaller amount than from a
runaway reaction
Help prevent two-phase flow during external fire
relief: allow a large vapor space above the liquid
If reactor not protected, firing can lead to reactor
failure and result in a BLEVE (p. 282) and if liquid is
flammable, a VCE (p. 281)
Security results more from inherently safer designs
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vT
fgo
HVG
vQmA
Q is the constant heat input rate,
GT is the mass flux through the relief,
A is the area of the relief,
mo is the liquid mass in the vessel,
V is the volume of the vessel,
ΔHv is the heat of vaporization of the liquid.
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Reliefs for Thermal Expansion of Process Fluids
Liquids contained process piping
expands and damage pipes & vessels
Ex; Cooling coil in reactor
Contamination of reactor
Subsequent corrosion
Substantial plant outage
Large repair expense
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Reliefs for Thermal Expansion of Process Fluids
dT
dV
V
1
Then, the volumetric expansion rate is expressed
dt
dTV
dt
dT
dT
dV
dt
dVQv
Energy balance with external heating
)( aP TTUAdt
dTmC
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Reliefs for Thermal Expansion of Process Fluids
Then, the volumetric expansion rate is expressed
)()( a
P
a
P
v TTUAC
TTUAmC
VQ
Homework due on Jan/6(Thu)
Crowl, Problems 9-1, 2, 5, 19, 28
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