Relief System Sizing

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

11/20/2011 2 METU-NCC

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

11/20/2011 3 METU-NCC

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

11/20/2011 4 METU-NCC

Required Vent Area, 2-f Flow

0 25 50

Overpressure, %

Ven

t A

rea,

m2

0.05

0.0

0.1

10

design

range

11/20/2011 5 METU-NCC

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

11/20/2011 6 METU-NCC

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

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.

11/20/2011 7 METU-NCC

Spring Relief Area for Liquids

bs

ref

bpvo

v

PPKKKC

QA

25.1

/

gpm38

psiin 2/12

API correction factors included for wide applications:

11/20/2011 8 METU-NCC

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)

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

11/20/2011 9 METU-NCC

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

11/20/2011 10 METU-NCC

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.

11/20/2011 11 METU-NCC

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

11/20/2011 12 METU-NCC

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

11/20/2011 13 METU-NCC

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

11/20/2011 14 METU-NCC

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

11/20/2011 15 METU-NCC

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

11/20/2011 16 METU-NCC

11/20/2011 METU-NCC 17

Backpressure correction Kb for conventional spring-

type reliefs in vapor or gas service. Source: API RP 520

11/20/2011 METU-NCC 18

Backpressure correction Kb for balanced-bellows

reliefs in vapor or gas service. Source: API RP 520

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

11/20/2011 19 METU-NCC

PC

QA

ref

o

v

/

38.0gpm

)psi(in 2/12

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

11/20/2011 20 METU-NCC

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

11/20/2011 21 METU-NCC

11/20/2011 METU-NCC 22

A tempered reaction system

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

homogeneous venting 11/20/2011 23 METU-NCC

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

11/20/2011 24 METU-NCC

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

11/20/2011 25 METU-NCC

Patterns of two phase flow

11/20/2011 26 METU-NCC

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

11/20/2011 27 METU-NCC

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.

11/20/2011 28 METU-NCC

11/20/2011 29 METU-NCC

11/20/2011 30 METU-NCC

11/20/2011 METU-NCC 31

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.

11/20/2011 METU-NCC 32

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.

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

11/20/2011 33 METU-NCC

11/20/2011 34 METU-NCC

11/20/2011 METU-NCC 35

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.

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

11/20/2011 36 METU-NCC

11/20/2011 37 METU-NCC

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

11/20/2011 38 METU-NCC

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

11/20/2011 39 METU-NCC