Emergency Pressure Relief Calculations Using the Computer

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ELSEVIER

Journal of Hazardous Materials 46 (1996) 131-143

Emergency pressure relief calculations using the com puter

package: RELIEF

J.S. Duffield*, R. Nijsing, N. Brinkhof

European Com mission, Joint Research Centre - Ispra Establishment, 21020 Ispra Va), Italy

Received 4 August 1994; accepted 5 December 1994

Abstract

The computer package RELIEF has been specifically designed to model the transient

one-dimensional fluid dynam ic behaviou r of multicompo nent chemically reacting mixtures in

batch-type chemical reactors or storage vessels. The physical m odel that describes the above

phenomen a is coupled to a sophisticated input/outpu t processor that creates an environment in

which a problem can be easily set up and executed and the results investigated. A complete

“stand alone” packag e is thus created in which muc h attention has been devoted to minimising

the input requirem ents and model running time. This has made the packa ge an ideal tool for

performing parame tric studies of relief scenarios, and highlighting the key phenom ena that

control the process being studied. A numb er of emergency pressure relief calculations are

presented that illustrate the capabilities of REL IEF.

Keywords: Run away reaction; Emergency pressure relief; Two phase; Scaling; Com puter

simulation

1. Introduction

An uncontrolled thermal runaway reaction in a batch-type reactor or storage vessel

is one of the accidenta l events still occurring frequently in the chem ical ind ustry. These

events result from many cau ses including operator error, stirrer failure, reactant

accumulation, external fire loading, segregation of components, spontaneous de-

composition, etc.

Often coupled to this is a lack of detailed knowledge concerning the physical

properties, chemical kinetics and information regarding un wanted side-reactions

under runaway conditions. The consequences of such events can be benign (but still

costly in terms of lost production) when the products are safely vented to a catch tank

*Corresponding author.

0304-389 4/96/$15 .00 0 1996 Elsevier Science B.V. All rights reserved

SSDI 0304-3894(95)00065-8



132

AT

Duf ield et al./Journal of Hazardous Materials 46 (1996) 131-143

or simila r device, or can in certain circum stances be disastro us in terms of the effect on

the environment when the products are released to the atmosphere. One only has to

remember Bhopal and Seveso.

Public concern has led industry to address seriously the environmental issues, and

currently industry is investing 2 5-30% of the total process cost in achieving this. In an

existing plant, retro-fitting equipm ent is frequently performed and since the capital

cost of such equipmen t is high, it is very important that it is sized correctly. In a

new plant there is a growing tendency to design out the runaway potential, but this is

not always possible and goes against the trend of manufacturing multipurpose

equipment.

There exists a genuine requirement for an engineering tool that is quick runn ing

and easy to use, requesting the minimum of input data, such that, at an early stage in

a process design, the various safety options can be modelled, assessed and costed.

In view of the importance, the area of runaway reactions and emergency pressure

relief has received much attention in recent years. A significant contribution in this

area has been the work performed in the DIER S project under the auspices of the

American Institute of Chem ical Engineers, and latterly the “Industrial Hazards”

programme of the JRC .

2. Reactor relief phenomena

The situation considered can be generalised as being a vessel containing a multi-

component liquid mixture in which a chemical reaction occurs. If the generation of

reaction heat in this mixture exceeds the heat removal rate of the control system,

a thermal runaway process w ill occur which is strongly enhanced by the Arrhenius-

type temperature dependency of reaction rate. When operational measures can no

longer control the situation, the tempe rature will rise to levels where the volatile

components of the liquid reactant mixture will start to evaporate, and in addition, gas

can be produced as a result of a decomposition reaction. This volume production

leads to an increase of system pressure and , in order to prevent over-pre ssurisation of

the vessel, it is necessary to discharge the fluid mixture from the vessel at a sufficient

rate.

A computational model mu st therefore describe the chemical conversion, the heat

and mass transfer between the liquid and vapour phases, the distribution of compo-

nents in both ph ases, the two-phase fluid dynamic behaviour and the interactions

between these processes.

3. Two phase fluid dynamic behaviour

During the progress of a runaway reaction, there is a volumetric source in the liquid

phase resulting from evaporation and/or reaction gas production. The bubbles of

vapour or gas generated within the liquid will rise through the liquid and disengage at

the liquid su rface. If the rise velocity is sufficiently high droplet entrainm ent can occur.



J.S. Duj fi el d et al . Journal of Hazardous M at eri al s 46 1996) 131-143 133

The bubbles during their residence in the liquid o ccupy a volume and so cause the

liquid level to rise or “swell”.

When the set pressure of the safety device is reached and the vessel relieves, the

pressur e falls and the evaporation or “flashing” increases marke dly. This causes the

liquid level, or mor e precisely the “two-p hase mixture level”, to rise further and, if this

level reach es the vent position, two-p hase venting will occur. The depressurisation

rate of a system is directly proportional to the v o l um l o w rate exiting the system, and

since the latter, under critical flow conditions, is inversely proportional to the mixture

density at the vent line entrance, the capacity to reduce the system pressu re by venting

is strongly reduce d when the mixture level reach es the vent position. Typically, relief

system s that have been designed for two-p hase flow conditions will be 2-10 times

larger than those designed for single-phase flow. If the volume production rate due to

evaporation and gas production is greate r than the vented volume flow rate the

system pressu re will increase. There fore, the ability to describe the motion of the

two-phase mixture level is one of the most important aspects of reactor relief

modelling.

In REL IEF the vessel is discretised in the vertical direction into control volumes

for which conservation laws pertaining to the phas es are applied. The description

of the relative motion of the phases is made with a mixture momentum equation and

an algebraic drift-flux mode l. Th e application of the drift-flux mode l is justified

12

11

O

25

50

75

100

125

TIME(s)

Fig. 1. DIER S TS a water blowdow n test pressure history.



134

J.S. Duj jield et al./Journal of Hazardous Materi als 46 (1996) 131-143

TIME(s)

Fig. 2. DIERS T8a water blowdown test vessel void fraction history.

as the acceleration and wall friction terms in the mom entum equation are negli-

gible when compared to the buoyancy term. The model in RELIEF describes

bubbly flow, churn turbulent flow and droplet flow by a continuously varying

function of drift-flux and void fraction; the founda tions of this model are

given in Refs. [l, 21. Figs. 1 and 2 show the predictions of pressure and average

vessel void fraction for one of the DIER S large scale water blowdown experi-

ments [3].

4. Chemical systems

Chem ical reactions are normally the cause of a pressure increase in closed vessels.

Even endothermic reactions can cause a pressure increase if the reaction products are

gases, or liquids which are more volatile than the reactants. Exothermic reactions are

potentially more dangerous, as in addition they raise the temperature of the reactants

and hence accelerate the chemical reaction. At present in RELIEF chemical reaction

is limited to the liquid ph ase where up to ten irreversible reactions of arbitrary order

can be modelled.

Often in the literature distinction is made between the mechanism of this pressure

rise so that sim plifications can be made to the mathem atical treatment of relief system



J.S. Duffield et al./Journal of Hazardous Materi als 46 (1996) 131-143

135

0

50

100

150

200

TIME(s)

Fig. 3. Acetic anhydride/methanol runaway pressure history.

50 100

150 200

TIME(s)

Fig. 4. Acetic anhydride/methanol runaway temperature history.



136 J.S. Dujield t aLlJournal of Hazardous Materials 46 (1996) 131-143

500.E + 03

450.E + 03

400.E + 03

350.E + 03

NE 3OOE+03

2

; 25O.E+03

5

2

I 2OOEi03

a

150.E + 03

100.E + 03

5O.OE + 03

0 00

420.

2 380.

2

LS

g 360.

P

g

340.

320.

0

2000.

4000.

6000.

TIME(s)

0. 2000.

4000.

6000.

TIME(s)

Fig. 5. Hydrogen peroxide decomposition: Pressure, temperature and mass fraction histories.

sizing. The following distinctions are usually ma de:

(a) “Vapour pressure” or “tempered” systems, in which the pressure generated by

the reaction is due to the increasing vapour pressu re of the reactants, produ cts and/or

inert solvent as the tempe rature rises.



J.S. Du j t i el d et al ./Journal of Hazardous M at eri al s 46 1996) 131-143 137

Lb ;; 1

reation of H,O due to chemical reaction

2

kg 0.40

B

Consumption of H,O, due to chemical reaction

3

\

0.20

___----------------___,_

\

v

o.oot~~‘~“~~““‘~‘~‘~~“~~~‘~“~“‘~~l~-j

:-_

-

0. 2000. 4000. 6000.

TIME(s)

Fig. 5. Continued

(b) “G assy” systems, in which the pressure is due to the production of a permanent

gas by the reaction.

(c) “Hybrid” systems, in which the pressure rise is due to both an increase in vapour

pressure an d permanent gas generation.

For such classifications a number of analytical tools and formulae can be used

to calculate the vent size for a particular overpressure. These “hand calculation”

methods usually treat the vessel as a single node h aving uniform properties.

The obvious difficulty arises when this assumption is not valid and when it is

not known a priori w hat type of system is expected. RELIEF does not suffer

from these restrictions and the type of reaction system can be deduced from the

results.

Figs. 3 and 4 illustrate the runaway of a vapour pressure system. The reaction

considered is the esterification of acetic anhydride and methanol with the experi-

mental data provided by [4]. The close coupling between tem perature and pressure is

clearly seen.

Some of the more difficult prob lems to be solved are the hybrid systems, since the

temperature and pressure effectively become uncoupled due to the production of

noncondensable products. Unfortunately, this type of system is very comm on, as in

the runaway phase undesired decomposition reactions often occur. Fig. 5 shows the

runaway of an aqueous hydrogen peroxide solution which can be regarded as

prototypical of this type of system. The batch size is about 1 t containing 25% mass

fraction of hydrogen peroxide. One shou ld note that there is a rather long period of

time between the initial upset, leading to the opening of the relief valve, and the major

excursion in pressure and temperature, so that for control purposes it would be useless

observing only the system pressure.



138 JS. Duf Jield et al. JJour nal of Hazardous Materi als 46 (1996) 131-143

5. Scaling considerations

The size and aspect ratio of a system has much more influence on the hydrodynamic

behaviour than on the chemical behaviour. This is because chemistry is governed by

the elementary molecular reactions whereas the hydrodynamics are governed by

bubbles and droplets with typical dimensions in the range l-10 mm . Over this range,

bubbles generated within a liquid will rise at a reasonably constant speed [SJ;

therefore, their residen ce time will be longer for a tall vessel, leading to an increased

level swell, compared to a short vessel. The effect of this is demonstrated by a RELIEF

calculation shown in Fig. 6. Two vessels of equal volume but differing aspect ratios (a

factor 10) have been modelled in which a vapour pressure runaway reaction (bulk

polym erisation) proceeds. In all other respects the calculations are identical. One can

see that a pressure excursion occurs in the tall vessel but not in the short one. The

increase in the level swell for the tall vessel causes the two-ph ase mixture level to reach

the vent location resulting in two-phase venting and a reduced relief capacity.

A similar calculation is shown in Fig. 7, but instead of a vapour pressure system,

a decomposition or hybrid system has been modelled. In this case the trend is exactly

the opposite

30.0

t

TIME(s)

Fig. 6. Influence of vessel height on pressure history: Vapour pressure system (polymerisation).



J.S. Duj fi eld et aLl Journal of Hazardous M ateri als 46 (1996) 131-143

139

60.0

c

TIME(s)

Fig. 7. Influence of vessel height on pressure history: Hybrid system (decomposition).

For this type of system, the pressure response is extremely sensitive to the amount

of mass vented early on in the runaway phase. Only with the aid of a dynamic

simulation of the runaway can one appreciate some of these differences. This makes

the search for simple scaling rules difficult.

6. Design strategies

The flexibility and ease with which R ELIEF can be used as a design tool can be

illustrated by the following exam ples. The first considers the addition of a solvent to

temper or moderate the runaway in a hybrid system. The system studied is the

aqueous solution of hydrogen peroxide. The relief line was sized such that a significant

pressure excursion occurred, and then in successive calculations a proportion of the

water w as substituted with methanol. Figs. 8 and 9 show the pressure and temper-

ature histories in which it can be seen that the effect of addin g methanol is not so

straightforw ard. Initially it has a deleterious effect raising the peak pressu re, and only

when a significant amount of methanol is added is the reaction tempered.

RELIEF has the capability of modelling several vent lines located at any position

on the vessel. This enables various design strategies to be studied, such as the

operation of multiple staggered relief valves, and combined top and bottom venting.



140

J . S.Duf ield et al./Journal of Hazardous Materi als 46 (1996) 131-143

8.0e + 06

7.0e + 06

6.0e + 06

h 5.Oe + 06

E

5 4.0e + 06

w

5

3.0e+06

B

2.0e + 06

l.Oe + 06

0.0 L-f--+,

- ---

1

T-i-a

a

’

m

A

n

’

I-* sn n m’ c

’ ’

.__.. ._.._.___

1000 2000 3000

4000

5000 6000

7000 8000

TIME(s)

Fig. 8. Effect of methanol as a tempering agent: Pressure history (decom position reaction).

600

525

500

? 475

kj

450

@ 425

9

g 400

375

40% methanol

\

55% methanol

Fig. 9. Effect of methano l as a tempering agent: Temperatu re history (decom position reaction).



J.S. DufJield et aLl Journal of Hazardous M at eri al s 46 1996) 131-143

141

The second example studies the performance of a combined top and bottom safety

relief system, and again the system chosen is an aqueous solution of hydrogen

peroxide. Two calculations were made, the first being a simple top venting with a relief

line sized as in the above examp le and the second m aintaining the same total vent area

as the first calculation but distributed such that half the vent area is at the top and half

4.0e+06 ,,,,,,,,, ,,I,,,,,, ,,,,,,,,, ,,,,,,,,, ,I ,,,,,,, ,I,,,,,,, ,,,,,,,,, ,,,,,,,,, <

3.6e + 06

3.2e + 06

Top venting only

2.8e + 06

“E 2.4e +06

t

-

2

2.0e + 06

2

Y

1.6e+06

d

p 1.2e+06

Combined top and bottom

venting

8.0e + 05

4.0e + 05 \14,1,. ------_____ ,

0.0 “~“~~~~“““~~“‘~~‘~‘~~~~‘,~~~‘~~“’~~~~’~ ~~I~~~~‘~~~~‘~ ~~’~~~~’~~“‘~~~~

5800 5900 6000 6100 6200 6300 6400 6500 6600

TIME(s)

k? 425

2

2 400

315

Top venting only

Combined top and bottom

5800 5900 6000 6100 6200

6300 6400 6500 6600

TIME(s)

Fig. 10. Hydrogen peroxide decomposition reaction: The effect of combined top and bottom venting.



142

J.S. Dufi el d et al ./Journal o f Hazardous M at eri al s 46 1996) 131-143

0 II.IIII,I.III,IIII,,III.II,I..

5800 5900 6000 6100 6200 6300 6400 6500 6600

TIME(s)

Fig. 10. Continued.

at the bottom. The set pressure for the bottom vent line is given a value 0.15 bar above

the set pressure of the top vent line. Fig. 10 shows the pressure, temperature and m ass

flow rate histories for the two calculations. There appears to be no difference betw een

the two cases up to z 6000 s, but thereafter the results are very different. For the case

of top venting the maxim um pressure exceeds 60 bar, whereas with combined venting,

the peak pressure is limited to the set pressure of the bottom vent, i.e., 1.5 bar.

Referring to the ma ss flow rates, it is clear that bottom venting does not occur until

6100 s into the transient after which time significantly more mass is vented, thus

achieving the goal of venting reactant early on in the runaway phase.

A further exam ple could be the determination of the maxim um reactor filling that

would lead to only single-phase vapour being discharged in the event of a runaway.

This strategy would reduce the operational efficiency of the reactor as the reactor may

be only half full, but it wou ld significantly reduce the capital cost of the relief system

since no expensive separation equipment would be required and the products could be

simply routed to a flare stack.

7. Conclusions

Environmental issues concerned with the release of chemicals to the atmosphere are

being addressed seriously by the chemical industry. This work accounts for a signifi-

cant proportion of the total process cost. There appears to be a genuine requirement

for an engineering tool that is quick run ning and easy to use, requesting the minim um

of input data, such that at an early stage in a process design various safety options can

be modelled, assessed and costed. The computer package RELIEF has been specifi-

cally designed to fulfil this need.

In this paper a number of calculations have been presented that highlight the key

phenomena associated w ith runaway reactions and emergency pressure relief. In

addition, it has been shown how R ELIEF can be used to analyse v arious relief design



J.S. Duj fi el d et al ./Joumal of Hazardous M at eri al s 46 1996) 131-143

143

strategies. A n attempt has been made to illustrate the complexity of the problem and

show that som e results are indeed counter-intuitive. The quest to find simplified

formulae to describe these processes appears at the very least questionable.

In view of the large capital cost associated with downstream separation equipment

and containment vessels, it is important that the safety systems are incorporated into

the overall process design at the earliest possible stage.

eferences

[l] J.S. Duffield, G. Friz, R. Nijsing and I. Shepherd, in: G.F. Hewitt, J.M. Delhaye and N. Zuber (Eds.),

Multiphase Science and Technology, Vol. 6, Hemisphere, New York, 1992, pp. 107-141.

[Z] W.B. Wallis, One-dimensional Two-phase Flow, McGraw Hill, New York, 1969.

[3] Fauske and Associates, Inc., Phase III Large-Scale Integral Tests, DIERS 111-3, Experimental Results

for Series I Tests, FA1/82-20, 1982.

[4] G. Wehmeier and L. Friedel, private communication.

[5] F.N. Peebles and H.J. Garber, Chem. Eng. Prog., 49 (1953) 88.

Emergency Pressure Relief Calculations Using the Computer

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