Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

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Instrument Sizing 347

f~ = mass fraction in the liquid phase

F k = ratio of specific heats factor (k/1.40)

k - ratio of specific heats (Cp/C v)

K = superheat correction factor

K D = coefficient of discharge

P~ = inlet pressure, psia

P2 =

outlet pressure, psia

AP = pressure drop, psi

q = fluid flow rate

QI = liquid flow rate, gpm

gas flow rate,ft3/h at 14.7 psia and 60~

SpGrf = specific gravity of fluid

SpGr~ = specific gravity of liquid

SpGrg -specific gravity of gas - M Wt of gas/M Wt of air

T = flowing temperature, ~ (~ + 460)

V e = effective specific volume of the stream

Vg- specific volume of the inlet gas

V~ = specific volume of the inlet liquid

X T - pressure drop ratio factor (from manufacturer)

W = steam flow, lb/h

RELIEF VALVE SIZING

Introduction

Safety relief valves serve a valuable function in protecting against

overpressure of pipework and process equipment. This may occur due

to operational malfunction, such as equipment failure, fire or human

error. Proper sizing of a relief system is therefore essential. This requires

the determination of proper relieving conditions (e.g., flows, pressures

,and temperatures) so that relief valves and their associated pipework

can be properly sized for the worst scenario. Designers are responsible

to obviate all conceivable conditions, and good judgment must be

exercized in setting the relief requirements (set pressure, for example)

in all design facets during hazard and operability studies. Here, five

relief conditions are considered [ 11 ]:

9 gas or vapor

9 steam

9 liquid

348

Fortran Programs for Chemical Process Design

9 air

9 fire

In addition, noise suppression, preferred location of relief valves, and

pressure drop requirements for stable operation involving inlet pipe to

the valve and tail pipe are reviewed.

Typical Relief Valves

There are two main types of safety relief valves. The conventional

type is shown in Figure 5-3. A balanced safety relief valve shown in

Figure 5-4 is designed to limit the effect of back pressure on opening

pressure, closing pressure, lift capacity, and relieving capacity. The bal-

anced valves are mainly the piston type and the bellows type.

Because of its design, a conventional relief valve encounters any back

pressure accumulated in the discharge header so that the relieving pres-

sure is affected. For example, a relief valve set at 450 psig relieving into

a closed header system with 10 psig back pressure caused by loads from

other units will not open until the vessel is at 460 psig. Normal practice

allows only 10 percent of the set pressure "buildup" in a unit for most

emergencies. Conventional relief valves, therefore, may often force the

designer to increase the header size to limit back pressure. The balanced

relief valve does not encounter the accumulated pressure and can

relieve at design rates even when back pressure is 30-50 percent of its

set pressure. Therefore, for services with high back pressure in the header,

the balanced relief valve is much preferred.

Gas or Vapor Sizing

The expression used to determine the relief area for vapor discharge

when the back pressure is less than the critical flow pressure is:

A- W T.

(C)(K)(P)(K b ) M (5-46)

where C can be expressed as:

I ( / (k+l) 10.5

C-520 k 2

k+l

(5-47)

CONVENTIONAL SAFETY-RELIEF VALVE

Figure 5-3. Conventional safety relief valve. (Reprinted courtesy of the American Petro-

leum Institute.)

349

BALANCED SAFETY-RELIEF VALVE

Figure 5-4. Balanced safety-relief valve. (Reprinted courtesy of the American Petro-

leum Institute.)

350

Instrument Sizing 351

The values of k for some gases are given in Chapter Three.

K b

is the

back pressure correction factor due to back pressure and is dependent

on the type of relief used. Figure 5-5 gives

K b

for conventional spring

reliefs and Figure 5-6 for balanced bellows reliefs, repectively.

Steam Sizing

The equation for steam service is a modification of Napier steam

flow given in the ASME Boiler and Pressure Vessel Code. ASME Power

Boiler Code applications permit 3 percent overpressure. The equation

for steam relief is [ 12]:

W (5-48)

(51.5)(P, )(K d )(K N )(Ks. )

Liquid Sizing

The requisite orifice area for a safety relief valve used in liquid service

(nonviscous) requiring liquid capacity certification is"

)0.5

A - W SGL (5-49)

(38)(K a)(K w)(K~) PI - P2

ILl

(./3

I.IJ

I---

0 ,,

0 10 20 30 40 90 100

k:1.5

.~. ~, ~ ~._e

i""

50 60 70 80

% ABSOLUTE BACK PRESSURE =

BACK PRESSURE + 14.7

(SET PRESSURE + OVER PRESSURE + 14"7) x 100

Figure 5-5. Constant back pressure sizing factor, K b, for conventional safety relief valves

in vapor or gas service. (API Recommended Practice 520, Sizing, Selection and Instal-

lation of Pressure Relieving Devices in Refineries, Part 1, 5th ed., 1990. Reprinted

courtesy of the American Petroleum Institute.)

352 Fortran Programs for Chemical Process Design

LIJ

IX.

",t

CC3

"1"

I-"

0.50

0 5

10 15 2O 25

' ~

Oercent

~reSSure

' r

30 35 40 45

% GAUGE BACK PRESSURE =

BACK PRESSURE, PSIG

SET PRESSURE, PSIG

x 100

Figure 5-6. Back pressure sizing factor, K b, for balanced-bellows pressure relief valves

in vapor or gas service. (API Recommended Practice 520, Sizing, Selection and Instal-

lation of Pressure Relieving Devices in Refineries, Part 1, 5th ed., 1990. Reprinted

courtesy of the American Petroleum Institute.)

K w is the capacity correction factor due to back pressure on balanced-

bellow relief valves. If the back pressure is atmospheric K w = 1. This

correction factor is given is Figure 5-7. When sizing a relief valve for

viscous liquid service, the orifice area is first calculated for nonviscous

service to obtain a preliminary discharge area. The next standard orifice

size is used to calculate the Reynolds number. The K v factor is then

calculated and applied to correct the preliminary required discharge area.

The Reynolds number is expressed as [10]:

Re - Q(2800)(SGL) (5-50)

g(ADES) ~

where

K v - -2.38878 + 1.2502(ln Re) + 0.1751(ln Re) 2

+ 0.01087 (ln Re)3 _ 0.00025 (ln Re)4

(5-51)

Air Sizing

The required orifice area for a relief valve sizing for air at constant

back pressure is"

Instrument Sizing 353

ILl

I--

I.a.I

I--

I.a.

I.--

l.a.I

1.00

0.95

0.90

0.85

~. ,1,,,

= =

9 ~ 1 ..... ! , - -

,. L t., \,,,.

0.70

0.65

0.60

0.55 ----------------

' '

0.50

0 10 2O 3O 40 5O

% GAUGE BACK PRESSURE = BACK PRESSURE, PSIG

SET PRESSURE, PSIG

x 100

Figure 5-7. Capacity correction factor, K w, due to back pressure on balanced-bellows

pressure relief valves in liquid service. (API Recommended Practice 520, Sizing, Selec-

tion and Installation of Pressure Relieving Devices in Refineries, Part 1, 5th

ed., 1990.

Reprinted courtesy of the American Petroleum Institute.)

A (V)(T) ~

~ (5-52)

(418)(K d)(P)(K b)

Fire Sizing

In the case of a fire, there is a pressure buildup and the required relief

capacity can be determined provided that the heat absorbed can be esti-

mated. API 520 gives recommendations for heat of absorption during

vapor relief [ 12]. Not all the causes will happen simultaneously, but the

pressure relief or safety relief should be sized for conditions that require

the greatest relief.

354 Fortran Programs for Chemical Process Design

Inconsistencies for sizing relief valves for fire emergencies arise

among published codes. This is because of varying interpretations of

the heat flux caused by fire exposure. These variations are based on the

area in which the heat flux applies and the protection factors used to

characterize the installations. Crozier [13] has summarized these varia-

tions and evaluated the pertinent correlations. Here, the API 520 corre-

lation is used because it contains an implied protection factor of 0.5 for

good drainage.

Liquid in liquid-filled vessels exposed to direct or radiated heat from

a fire will vaporize. The heat required to accomplish this will limit the

shell temperature of the tank to only a slight rise. The amount of liquid

vaporized depends on the rate of heat input from the fire and the reliev-

ing temperature. This can be determined by calculating the heat input to

the wetted surface of the vessel and dividing this by the latent heat

of vaporization.

Qr -- 21,000(FI)(Aw)

(5-53)

and

W = Qr (5-54)

The vapor to be relieved is the vapor in equilibrium with the liquid (that

is, saturated vapor at the conditions existing when the valve is relieving

at the rated capacity). Table 5-3 shows environmental factors for bare

and insulated vessels.

For a multicomponent mixture, )~m~ can be determined from

~. ~iYiMi

~' mix -

M (5-55)

i--I

To determine y~, it is necessary to know the equilibrium liquid-phase

mole fraction, x~, at the bubble point corresponding to the accumulated

relieving pressure.

The wetted surface area depends on the diameter and length of the

vessel. For working storage tanks, the wetted surface is obtained on the

average inventory. Surge drums usually operate about half full; thus the

wetted surface will be calculated at 50 percent of the total vessel surface.

Instrument Sizing

355

Table 5-3

Environmental Factor

Type of Equipment

Factor

Bare vessel

1.0

Insulated vessel (These arbitrary insulation conductance

values are in Btu/hrft 2 ~

0.3

0.15

0.075

0.67

0.05

0.5

0.4

0.0376

0.03

0.33

0.026

Water-application facilities on bare vessel

Depressurizing and emptying facilities

For approved water spray with approved insulation

For drainage

For approved water spray

1.0

0.15

0.5

0.3

Effect of Back Pressure

The maximum allowable back pressure (gauge) for a conventional

safety relief valve is 10% of the set pressure (gauge). If the maximum

allowable back pressure is exceeded during any relief situation, the size

of the relief lines or headers should be increased until the back pres-

sures are sufficiently reduced.

Noise Suppression

Expansion of gas or vapor usually gives rise to an unacceptable noise

level. However, this is not a problem with liquid relief. There are two

sources of noise:

356

Fortran Programs for Chemical Process Design

1. Noise due to turbulence at the point where the gas mixes with the

atmosphere. Suppression of this type of noise involves the fitting

of a silencer.

2. Noise due to pressure letdown (that is, relief valve) when sonic or

near sonic velocities are generated. This is transmitted through

the wall of pipe and, if the discharge is short, it is transmitted

through the open end. Noise from this can be reduced by length-

ening the discharged pipe and by insulation. Suppression of the

noise can also be overcome by fitting a silencer. Such silencers are

often installed in an exposed environment and are likely to accumu-

late dirt, vapor, or products from minor leakage of safety devices.

Effect of Pressure

Drop (AP) on

Pipework

The pipework should be designed with the following considerations:

9 The frictional AP through the inlet pipework, inlet fittings, and

valves at the maximum possible relief rate should not exceed 3%

of the set gauge pressure (psig). The calculation of AP should

include the entrance loss of the inlet pipework. The discharge

pipework must be such that AP is less than 10% of the relieving

pressure (that is, set pressure plus overpressure in gauge). The dis-

charge pipework should withstand the internal pressure and high

velocities, the reaction forces, and the sudden transient loading that

occur when a relief device suddenly comes into operation.

9 The inlet pipework should be of a size at least equal to the relief

valve, with its length minimized to reduce AP. It should also be

equal to the bending moments resulting from the forces that

develop when the valve or disc is discharging at full capacity.

9 A relief device should be installed vertically and preferably on a

nozzle at the top of the equipment (for example, vessel) or on a tee

connected to a pipeline. When discharging a gas or vapor, the fluid

reaches sonic velocity when passing through a relief device. Thus,

the gas flow rate or AP can be determined by a method as described

in Chapter Three.

For liquid discharges, the design of the pipework may be complex. If

the liquid is subcooled, the discharge pipework is sized by standard

liquid pressure formulae. If the liquid in the equipment is at or near its

saturation pressure, the relief device and discharge pipework should be

sized for two-phase flow. As the liquid flows through the relief valve,