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

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Instrument Sizing 357

the AP will cause it to flash. Therefore, the size of the valve and dis-

charge pipework must be increased to accommodate the larger volume.

Further flashing in the downstream piping will increase the gas-liquid

mixture through the two-phase regimes. If this is not arrested, slug flow

will develop along the pipeline resulting in the mechanical damage to

the pipework.

Discharge Reactive Forces

The total stress imposed on a safety valve or its piping is a result of

the sum of the following:

9 internal pressure

9 dead weight of piping

9 thermal expansion or contraction of either the discharge line

9 the equipment upon which the valve is mounted

9 the bending moment caused by the reaction thrust at the discharge

The discharge reactive force is based on the assumption that critical

flow of the gas or vapor is obtained at the outlet of the relief device and

the discharge is horizontal to the atmosphere. For any gas or vapor, the

reactive force can be expressed as:

10.5

W kT

F- (k + 1)M

_ w (5-56)

366

Relief Valve Location

The location of a relief device often influences its size and material

of construction. Relief devices must be sited so that the risk of blockage

by debris is minimized. It is poor practice to mount relief valves at the

end of long horizontal pipe through which there is no flow. The possi-

bility of liquid phase entering a vapor relief system must also be avoided.

Locating a relief device upstream of equipment that has AP due to flow

allows the relief valve to be smaller because increased AP is available.

Reduced costs of a relief system may be obtained by installing relief

valves in a more conducive position with regard to temperature and

corrosion. Figure 5-8 shows alternative positions. Position 1 is preferred

when the relief valve is tied into a closed relief system because of ease

of maintenance. It assures a relatively short line to the relief header and

358

Fortran Programs for Chemical Process Design

i ii i| |

I i

( )

Figure 5-8. Alternative positions for a relief valve.

lower temperature for relief when air fan coolers are used. Position 2 is

preferred for relief to atmosphere. Position 3 is used on low pressure

towers designed for the same top and bottom pressure. Figure 5-9 illus-

trates key areas for design verification of relief system. Manufacturers'

orifice areas and corresponding valve sizes are shown in Table 5-4.

Nomenclature

A - valve discharge area, sq in.

A w - wetted surface area of the vessel, sq ft

ADES - next largest valve orifice, sq. in, from the manufacturer's stan-

dard orifice area

Piping

Header System

,if i, ....

_f-h_ 5

4 ~A Protective Device X s)

Isolation ~Relief Requirement 3

ected Equipment 1 ~" Source of Overpressure 1

I or System

i .

KEY AREA

Sources of Overpressure

Equipment or System

protected by Relief

stream

Require Relief Rate

Isolation

Protective Device(s)

5a. Devices in Series

Piping

Headers or Common Vents

BASIC CONSIDERATIONS

Which have been considered?

(i) All equipment is

identified.

(ii) Design press, and temp.

limits cannot be exceeded.

Design codes for protected

equipment and devices are

compatible.

What is it?

Is any fitted?

If so, how is continuity

assured?

Under or oversized?

Suitability of device(s).

Correct ~P maintained

across devices.

Interspace moni tored/alarmed

Correctly sized.

Pressure drop O.K.

Supports O.K for reaction

loads. Suitable for fluid.

Drainage/blockage.

Is there one?

Sized for all streams.

Back pressure O.K.

Damage to/from other streams.

Figure 5-9. Pressure relief design verification.

359

360

Fortran Programs for Chemical Process Design

Table 5-4

Orifice Sizes for Relief Valves

Orifice Designation

Orifice Area Valve Size

(sq. in.) (in.)

D 0.110 1-2

E 0.196 1-2

F 0.307 1.5-2

G 0.503 1.5-2.5

H 0.785 1.5-3 or 2-3

J 1.287 2-3 or 2.5-4

K 1.838 3-4

L 2.853 3-4 or 4-6

M 3.600 4-6

N 4.340 4-6

P 6.379 4-6

Q 11.050 6-8

R 16.000 6-8 or 6-10

T 26.000 8-10

C = coefficient determined by ratio of specific heats of the gas or

vapor at standard conditions

F = reaction force at the point of discharge to the atmosphere, lb

FI = factor for insulation (for non-insulated vessel FI is 1.0)

K = effective coefficient factor due to backpressure (0.975 for

vapor flow)

K b =

capacity correction factor due to backpressure is 1.0, when

backpressure is 55% of absolute relieving pressure

K d = coefficient of discharge (0.953)

K N = correction factor for Napier equation, K N, is 1.0, where

P < 1515 psia

overpressure correction factor for direct spring-operated valves

only, Kp is 1.0

KsH = correction factor due to amount of superheat in the steam. Val-

ues range from 0.88 (maximum superheat) to 1.0 for saturated

steam.

Kv = viscosity correction factor

K w = backpressure correction factor for balanced-bellows spring-

operated valves only (K w is 1.0)

k = ratio of specific heat capacities (Cp/C~)

Instrument Sizing 361

M = molecular weight

M w = molecular weight of vapor (or process fluid)

P = upstream relieving pressure, psia

Pb =

total backpressure, psig

Pi = set pressure at which relief valve begins to open, psig

Q = flow rate, in U.S. gallons per min

Qr = rate of heat input due to fire, Btu/hr

SGL = specific gravity of liquid at flowing temperature referred to

water as 1.0 at 70~

T = absolute temperature of inlet vapor ~176 + 460)

V, = required air capacity, standard ft3/min

W = flow of any gas or vapor, lb/hr

Z = compressibility factor

= latent heat of vaporization at the boiling point of the liquid,

Btu/ib

= absolute viscosity at the flowing temperature, cP

TWO-PHASE FLOW RELIEF SIZING

FOR RUNAWAY REACTION

Introduction

Many methods have been used to size relief systems: area/volume scal-

ing, mathematical modeling using reaction parameters and flow theory,

and empirical methods by the Factory Insurance Association (FIA). The

Design Institute for Emergency Relief Systems (DIERS) of the AIChE

has carried studies of sizing reactors undergoing runaway reactions. Intri-

cate laboratory equipment and analysis have resulted in better vent sizes.

A selection of relief venting as the basis of safe operation is based

upon the following considerations [14]:

9 compatibility of relief venting with the design and operation of the

plant/process

9 identifying the worst scenarios

9 type of reaction

9 means of measuring the reaction parameters during the runaway

reaction

9 relief sizing procedure

9 design of the relief system including discharge ducting and safe

discharge area

362 Fortran Programs for Chemical Process Design

Runaway Reactions

A runaway reaction occurs when an exothermic system becomes un-

controllable. The reaction leads to a rapid increase in the temperature

and pressure, which if not relieved can rupture the containing vessel. A

runaway reaction happens because the rate of reaction and therefore the

rate of heat generation increases exponentially with temperature. Alter-

natively, the rate of cooling increases only linearly with temperature.

Once the rate of heat generation exceeds available cooling, the rate of

increase in temperature becomes progressively faster. Runaway reac-

tions nearly always result in two-phase flow reliefs. Runaway reactions

are generally classified into three systems.

Vapor Systems

Boiling is attained before potential gaseous decomposition, that is,

the heat of reaction is removed by the latent heat of vaporization. The

reaction is tempered, and the total pressure in the reactor is equal to the

vapor pressure. The principal parameter determining the vent size is

the rate of the temperature rise at the relief set pressure.

Gassy Systems

Gaseous decomposition reaction occurs without tempering. The total

pressure in the reactor is equal to the gas pressure. The principal param-

eter determining the vent size is the maximum rate of pressure rise.

Hybrid Systems

Gaseous decomposition reaction occurs before boiling. The reaction

is still tempered by vapor stripping. The total pressure in the reactor is

the summation of the gas partial pressure and the vapor pressure. The

principal parameters determining the vent size are the rates of tempera-

ture and pressure rise corresponding to the tempering condition. A tem-

pered reactor contains a volatile fluid that vaporizes or flashes during

the relieving process. This vaporization removes energy via the heat of

vaporization and tempers the rate of temperature rise due to the exo-

thermic reaction.

Adiabatic Calorimetry

Two-phase flow calculations are complex when conditions change

rapidly as in runaway reactions. Because of this complexity, several

Instrument Sizing 363

experimental and analytical techniques have been developed over the

past decade to obtain the relevant data for the relief vent calculations.

The data required for the runaway calculations are determined with labo-

ratory tools such as the Differential Scanning Calorimetry (DSC), the

accelerating rate calorimeter (ARC), the vent sizing package (VSP),

and recently, the laboratory calorimetric Reactive System Screening Tool

(RSST). The RSST determines the type of reaction and principal

parameters required for sizing reactor vents for vapor, hybrid, and gassy

systems. Figures 5-10A and 5-10B show the principal features of the

RSST. The principal data for relief sizing calculations are shown in Fig-

ures 5-11A, 5-11B, 5-11 C, and 5-11D, the temperature rate at the set

(text continued on page 366)

Figure

5-10A. The RSST vessel.

Figure 5-10B. The test cell and associated equipment.

i 'atmax,mumJ r

permitted pressure/ ~ |

IT at relief set ~

(~ t t+5 t+10

t+151t+20t+25

Time L

~ (min)

Venting time for vapour system j

E during which time the entire J

i0 vessel content is discharged Jr

0 1000 2000 3000 400(3

Time (rain)

Figure 5-11A. Temperature against time for an abiabatic system.

364

0 - ! ! .

0 1000 2000 30()0 40C)0

Time (rain)

Figure

5-11B. Pressure against time for an abiabatic system.

100

Slope = E _ T1T21n(-~12) ~ ''~

R 7"2 T1/

-Average rate of temperature rise/

"between relief set pressure and T at

"maximum permitted pressure/' maximum

............. .~ permitted

1.0 /]- pressure

,, ....~/ I T at

= ,,',2 J/1 Irelief

"~ /I set

r~ ressure

0.11

M' --',,.t 1 •

o.o~ /' T, T2

/ t"-- Onset temperature for

0.001 " / I a l m 3 reactor charge TF

' f. ~, . , 9 , . ,

.... ,. ,~. ,

20 40 60 80 100 120 140

Temperature (~

Figure

5-11C. Rate of temperature rise against temperature for an abiabatic system.

365

366

Fortran Programs for Chemical Process Design

Maximum //~dp l

/ dt

tmax

.. permitted pressure 1 /~-----'

- AP (vapour

A-T systems)

/I AP

/(gassy,

= ~ ;v / systew,,~)

Rel~ AT/ -

60 I I 80 I &O

120 140

Temperature (~

100

Figure 5-11D. Pressure and rate of pressure rise against temperature for an abiabatic

system.

(text continued from page 361)

pressure and the temperature increase, corresponding to the overpressure.

In addition, the heat of reactions can be determined from the tempera-

ture vs. time data of the heat capacities if the monomers and products

are available. Table 5-5 lists formulae for computing the area of the

three systems.

Simplified Nomograph Method

Boyle [15] and Huff [16] first accounted for two-phase flow with

relief system design for runaway chemical reactions. A computer simu-

lation approach to vent sizing involves extensive thermokinetic and

thermophysical characterization of the reaction system. Fisher [ 17] has

provided an excellent review of emergency relief system design involv-

ing runaway reactions in reactors and vessels. Fauske [18] has devel-

oped a simplified chart to the two-phase calculation. He expressed the

relief area as:

A~ = VPr (5-57)

GAt v