The Pressure Relief System Design for Industrial Reactors

A quick and simple approach for reactor—emergency relief system design—for runaway chemical reactions is presented. A cookbook for system sizing with all main characteristic dimensions and parameters is shown on one realistic example from process industry. System design was done based on existing theories, standards, and correlations obtained from the literature, which were implemented for presented case. A simple and effective method for emergency relief system is shown, which may serve as an example for similar systems design. Obtained results may contribute to better understanding of blow down system frequently used in industrial plants, for increasing safety, decreasing explosion damage, and alleviating the ecological problems together with environmental pollution in case of industrial accidents.


Introduction
In process industry, raw materials are converted into various commercial products using different techniques.One frequently used method is their conversion by exothermic chemical reactions which can lead to a reactor thermal runaway if the heat generation rate exceeds the heat removal rate during process [1].Pressure build-up during the runaway is caused by an increasing vapor pressure of liquid components and by the production of noncondensable gases.Apart from the loss of reactor inventory due to an uncontrolled conversion process, a runaway reaction may lead to severely damaged equipment or even a physical explosion if pressure build-up inside the reactor exceeds the design pressure.The emergency relief system is composed of vent area, vent rupture membrane, safety relief valve, vent pipes, blow down tank, horizontal condenser, scrubber with absorber and vertical condenser, outflow chimney, corresponding pumps, fan, pipes, fitting, and supply system with electricity, cooling water, and neutralization medium.In case of reaction runaway, the vent rupture disc opens and the reactor mixture blows out into the vent pipes and flows into blow down tank.Due to short residence time of reactor mixture in the blow down tank, the volume changes and the pressure decreases at isothermal conditions, which results in the condensation of reaction mixtures.Remained two phases flow instantaneously blows into horizontal condenser, where it cools down, condensates, and flows into absorber with vertical condenser, where it is neutralized [2][3][4].
In present study, a detailed design of emergency relief system is shown based on Design Method for Emergency Relief Systems (DIERSs).It incorporates the state-of-theart knowledge obtained from mechanical, electrical, and process engineering based on a long year experiences in the process industries all over the world.All components were designed based on API RP 520 and API STD 526 standards [5,6].In case of problems, reaction runaway may appear due to loss of cooling water in the reactor, overor miss-charged reactant, external fire, and loss of agitation or wrong reaction temperature in reactor.Such cases are difficult to predict, almost not possible to control, and can lead to explosion.Therefore, a proper and correct sized emergency relief system is appropriate method to prevent fatal accidences and environmental pollutions.
The purpose of present study is to (i) show the main mechanical, electrical, and process fundamentals for this system, (ii) design emergency relief system with corresponding scrubber, absorption column, and corresponding connections.Designed emergency relief system is presented in Figure 1.A real industrial example from process industry composed from twelve equal 30 m 3 batch reactors equipped with pressure and temperature sensors, cooling and heating mechanism, and rupture discs was taken.In reactors, an exothermic phenol formaldehyde reaction takes place.For reactor cooling towers with capacity of 700 m 3 ⋅h −1 of cooling water at 13 ∘ C/26 ∘ C, cooling temperature regime was used.
Based on the reaction runaway the emergency relief system design was made in stages from plant vent system, blow down tank, and scrubber with corresponding heat exchangers and absorption column.

Pressure Relief Devices
Pressure relief devices design was made according to API RP 520 standard [5].Detailed pressure relief system on the reactor is presented in Figure 3 and is composed of safety relief valve (SVR) and rupture disc (RD) with dimensions presented in Table 1.The pressure at which SVR piston opens depends on the physicochemical characteristics of reaction system.In present study, it is designed so that SVR opens when the reaction medium pressure is above 70 ⋅ 10 3 Pa.In case of runaway, the outflow medium from reactor blows into vent pipes connected to blow down tank.Very high tip velocities cause a phenomenon known as blow-off where the flame front is lifted and could eventually turn into a blowout.Therefore, determination of the right pipe diameter is important as far as operation of the system is concerned.The vent size is a crucial step at emergency relief system design.In this study, an approach proposed by Fauske [1] and Leung et al. [3] was used.For pressure temperature relation, Antoine equation was used to calculate the vapor pressure at reaction runaway as follows: The two phase discharge flow rate per unit area was evaluated according to the homogeneous equilibrium model which can be approximated in the low quality region by relation proposed by Leung [2] as follows: where / was replaced by differential form of (1) and the two phase discharged flow per unit area was evaluated.The analytical vent sizing equation for homogeneous vessel venting is [2][3][4] where and all necessary physical and chemical data are presented as follows.
Physical-chemical parameters use for blow down system design:  ( Formation enthalpies (Perry and Green (2007) [7]): Reaction chemistry at runaway is very complex and depends on the type of used catalyst and other process conditions [1][2][3][4].In present study, a "worst-case scenario" was used for the thermal runaway of reaction.Design bases of (/)  and (/)  were obtained from the literature [2][3][4]8] and are presented in Table 1.Calculated vent area was compared to the nomogram method from study by Fauske [9] and yield a vent area of 0.326 m 2 or 0.65 m vent area pipe diameter which is in good agreement with the calculated results.Pressure relief devices designs were made according to API RP 526 standard [5].Detailed presentation of pressure relief devices are presented in Figure 3 with main dimensions shown in Table 1.In present design, it was suggested that RD is located between reactor and SRV.RD protects SRV piston from vapors and opens when tank pressure is above allowable reactor pressure.Maximal pressure which appears at reaction runaway was not known and was obtained from the literature reported data [9].A design pressure of 2.21 ⋅ 10 5 Pa was used for system design with 20% safety factor.In present study, a vent membrane had a pressure relief from −0.75 bar to 0.75 bar.At pressures higher than 0.75 bar, the rupture disc opened and the material was discharged into the blow down tank.

Blow Down Tank Design
The purpose of the blow down tank is to capture the two phase material flow from reactor and to decrease the pressure of outflow material [9].Blow down tank design was done based on API RP 520 standard [5].Blow down tank volume was calculated from the reactor volume as and is reported in Table 1.A factor 2 in (6) was used as engineering safety coefficient which decreases the pressure from reaction runaway by half.It may also be called additional safety margin.The pressure decrease in a blow down tank was calculated by applying the ideal gas behavior at constant temperatures as follows: and was 1 ⋅ 10 5 Pa.The maximal allowable working pressure (MAWP) for blow down tank was calculated according to API RP 520 standard [5] and was 2.5 ⋅ 10 5 Pa.MAWP was higher than peak pressure at 2.21 ⋅ 10 5 Pa.Due to volume change, the MAWP in blow down tank will not be reached during reaction runaway.In blow down tank, a solid part of two phase runaway material is captured.

Horizontal and Vertical Heat Exchanger Design
Various procedures for heat exchanger design may be found in the available literature [9,10,13].Only brief calculation procedure is presented [5,7,10].
(i) Assume pipe diameter, length, inside, and outside fouling factor.(ii) For the pipe construction, an INOX AISI 316 was used with corresponding characteristics presented in Table 1.(iii) Corresponding energetic balances for horizontal and vertical heat exchanger were written as Equation ( 8) enables calculation of heat duty, , and the hot medium outflow temperatures and results are presented in Table 1.
(v) Based on the experiences and literature data, divided flow shell and even tube passes were assumed for both condensers.Following the procedure proposed by Richardson et al. [10], parameters   , , and   were obtained from the corresponding diagrams.Obtained parameters enabled calculation of mean temperature difference: (vi) Overall heat transfer coefficients were assumed from the data reported in the literature [10] within their minimum and maximum values and were between 700 W⋅m 2 ⋅K and 1000 W⋅m 2 ⋅K.Predicted heat transfer coefficients enabled calculation of minimum and maximum provisional area which were taken as average for heat exchanger design: Next, main parameters used for heat exchanger design were calculated using ( 12)- (18).Pressure drops and the heat transfer coefficients for heat exchanger were calculated using ( 19)-( 25) for the shell and tube site, respectively.
Equations used for horizontal and vertical heat exchanger design are as follows: (vii) The heat transfer coefficient ℎ tube for turbulent flow was calculated by using next correlation: (viii) The overall heat transfer factor was calculated on "outside pipes flow": (ix) The overall heat transfer factor was calculated on "inside pipes flow": (x) The tube-side pressure drop was calculated: Calculated parameters for horizontal and vertical condenser design are reported in Table 1.

Vertical Heat Exchanger Design
For the vertical heat exchanger design, exactly the same procedure as proposed for the horizontal heat exchanger was used.Firstly, the amount of condensed vapor was calculated from the ratio of vapor pressures at reactor release in the blow down tank and after the volumetric expansion: where  1 and  2 were the saturated pressures calculated from (1).Obtained   was used for calculation of gas flow which needs to be neutralized and cooled down in vertical heat exchanger: where  HZT and  vent are the reactor runaway flow and flow through horizontal condenser reported in Table 1.Calculated  HZT flow was used for vertical condenser design at the exact same procedure as for horizontal condenser.In the next step,  HZT flow needed to be cooled down and neutralized in absorption column using sodium hydroxide solution before it was left in the surrounding. HZT flows from blow down reactor with temperature which is equal to the temperature of runaway flow due to short residence time.Similar predictions were obtained at design of other blow down processes [3,8,9].All calculated parameters are presented in Table 1.During  HZT neutralization reaction, heat was formed.The heat which needs to be cooled down was calculated as the sum of vapor gas heat and the heat produced by neutralization reaction: where Q react was calculated using reaction enthalpy as follows: and the heat pro recycles using

Scrubber Design
Since the reaction enthalpy for the neutralization reaction of phenol acid with sodium hydroxide cannot be found in the available literature it was calculated from formation enthalpies and was 22.32 kJ/mol [10].Since the composition of the blow down gas is not known exactly, it was assumed that it is composed from phenolic acid [8].The neutralization reaction of phenolic acid with sodium hydroxide was written as Neutralization reaction gives the stoichiometric ratio of phenolic acid versus sodium hydroxide and enables the calculation of the amount of neutralization medium needed for neutralization.The necessary 50 wt.%neutralization liquid flow rate was calculated from the reaction and was 42.3 kg/s.To decrease the necessary volume of used sodium hydroxide, its recycling was assumed.The recycle flow was calculated using Recycle =  HZT  scrubber tank .
The recycle ratio gives scrubber volume of 4.5 m 3 and enables the calculation of the liquid and the gas flow rates used for absorption column design.Scrubber design was performed according to API RP 520 standard.All main scrubber dimensions are presented in Table 1.MAWP of scrubber was designed to be 1.5 ⋅ 10 5 Pa.

Absorption Column Design
Before outflow gas from blow down system was left into surrounding air, it was neutralized by sodium hydroxide in counterflow absorption column.A lot of literature for absorption column design can be found in available literature [11,14].Due to high flow of gas and neutralization fluid the chemical reaction was the limiting step of this process.A generalized approach proposed in the literature was used for column design [7,11,14].Firstly, (/) ⋅ (  /  ) 1/2 factor was calculated.Pump characteristics limited the pressure drop in absorption column to 1  water column per feet of packing.
Based on existing correlations, factor ( * 2 ⋅⋅ 0.1 )/(32.2⋅   ⋅ (  −   )) was obtained to be 1.8 and enabled to calculate the gas flux  * .A ceramic IMTP packing number 70 was taken as packing material, with main parameters presented in Table 1.Calculated parameters enabled to design an absorption column area and diameter from the following equation: Large absorption column diameter is a consequence of large gas flow at reaction runaway which was designed to be up to 59.5 m 3 ⋅h −1 ⋅m −2 , which is lower than allowed maximal liquid flow rate of 122 m 3 ⋅h −1 ⋅m −2 for IMTO packing number 70.Next, absorption column height was designed based on the procedure proposed by Seader et al. [11] and was obtained to be 3000 mm.All other column parameters are presented in Table 1 and enabled to design the absorption column pressure drop, which was 30 ⋅ 10 3 Pa.

Ventilator Fan Design
The vapor gas coming out from absorption column is mainly composed of different phenolic vapors which are heavier than air; therefore, a ventilator fan needs to be inserted into outflow chimney.The role of the fan is to suck the vapor gas coming out from absorption column and to blow it out via chimney into surrounding air.Equations used for the fan design are presented as follows [12].Design equations for ventilator fan design in outflow chimney.
Pressure of ventilator: Gas vapor velocity: where Ventilator motor power: Journal of Industrial Engineering  Axial fan velocity: The fan pressure and the fan capacity were designed based on capacity of 82.3 kg ⋅ s −1 of outcoming gas by (43)-(47).Radial velocity of ventilator fan speed V  was calculated from (47) and clearly indicates that an axial ventilator must be applied.All main designed technical characteristics of the ventilator fan are shown in Table 1.A 34 kW ventilator fan motor with corresponding ATEX protection with II 2G EEx de II B T4 code and motor thermal protection should be used since the motor is located in Ex cone.According to ATEX directive, the electric board with all main connections should be located outside Ex cone which is presented in Figure 2. Chimney height was obtained from standards and was approximately 6000 mm.All other chimney dimensions are presented in Table 1 [4,15].

Blow Down and Cooling Water Pipes Design
Blow down equipment is connected using thick wall pipes made of INOX AISI 316 due to highly corrosive medium, high fluid velocities, and large pressures at reaction runaway.For the vent size pipes, diameter design at reaction runaway frequently used technique proposed by Bleier [12] was used: where all parameters are explained in the Nomenclature.The pipe system with 400 mm pipe diameter was proposed as connection between horizontal heat exchanger and absorption column at given conditions.All other data are presented in Table 1 and Figure 2. Connection pipe system between reactors and blow down tank should be as short as possible, straight with no elbows, no reductions to decrease the amount of condensing flow and to prevent the appearance of plugs which may lead to fatal accidents.Additionally, such system configuration ensures easy maintain and fast pipe cleaning.In parallel, the pipe pressure drops were calculated by method proposed by Crane [16] to ensure smooth and easy flow.The pipe length was designed to be as short as possible with minimal pressure drop which will result in low amount of condensed fluid.High fluid velocities, low friction factors, and minimal pressure drops are expected which agrees with results obtained from the literature [16].
For the cooling water pipes diameter and sodium hydroxide pipe diameter design, a method proposed by Mays [17] which is based on the steady state incompressible energy equation utilizing Hazel Williams friction loses and continuity equation was used.The results are presented in Table 1 and in Figure 2.

Pump Design
Neutralization process characteristics demand 100 m 3 ⋅h −1 of 50 wt.%sodium hydroxide.For this, a corresponding pump with 5.5 kW electrical motor and capacity of 120 m 3 ⋅h −1 at approximately 4⋅10 5 Pa is proposed.A corresponding electric schema with all relevant parts is presented in Figure 2. Since the pump is situated in Ex cone, a correct motor with motor II 2G EEx de II B T4 code and correct connection according to ATEX standard must be used [18].Electric board with necessary connections should be located outside the Ex cone.A pressure sensor (PC) is proposed on the pipe from vertical heat exchanger to absorption column.PC has two tasks, to ensure that neutralization medium is pumped all the time from scrubber tank on the absorption column and to prevent the centrifugal pump running dry, which can result in pump failure and in the worst case in pump rotor damage.It needs to be mentioned that reaction mixture which appears at reaction runaway is very viscous, which may result in appearance of plug in designed pipes, equipment, and huge pressure drops.This problem will be avoided by decreasing the connection pipe length without reductions and low pipe elbow number.Horizontal heat exchanger which is located above the blow down tank decreases the fluid temperature which results in fluid condensation, that is why lower amount of gas need to be neutralized in absorption column.Less required gas for neutralization results in lower NaOH consumption which decreases operational costs of designed system.Additionally, horizontal heat exchanger produces huge pressure drop which results in lower gas velocities and higher gas/liquid mass transfer coefficients which increases the efficiency of absorption columns [14].

Conclusions
Designed results of this study demonstrate that proposed method can be used for emergency relief system design.Based on calculated data the following conclusions were made.
Emergency relief system for exothermic reaction for reactor volume up to 30 m 3 was designed.A 60 m 3 blow down tank, with 700 m 3 ⋅h −1 of 13 ∘ C/26 ∘ C cooling water, and two condensers-horizontal and vertical-with cooling area of 54 m 2 and 5 m 2 are proposed.An absorber column with diameter of 1.5 m and 3.0 m height, 4.5 m 3 scrubber tank, and corresponding outflow chimney were designed.All other system parameters are presented in Table 1.It is hoped that the presented procedure will serve as an engineering tool for emergency relief system design in various process industries all over the world.

𝐿:
L e n g t h ( m )   : Th e r m a lc o n d u c t i v i t y (W⋅m −1 ⋅K −1 )  cold : Specific heat of cold medium (J⋅g −1 ⋅K −1 )  hot : Specific heat of hot medium (J⋅g −1 ⋅K −1 ) Cooling water: Specific heat of cooling water (J⋅g −1 ⋅K −1 ) Q: H e a t t r a n s f e r ( W )  hin : T e m p e r a t u r eo fh o tm e d i u m ( ∘ C)   : Reactor charge (kg) : A r e a ( m 2 ) : R e a c t o r v o l u m e ( m 3 ) : Density (kg⋅m −3 ) q  : Heat release per unit mass cold medium (W⋅kg −1 ) qℎ : Heat release per unit mass hot medium (W⋅kg −1 ) : D i s c h a r g e m a s s fl o w r a t e p e r unit area (kg⋅m 2 ⋅s −1 ) : Pressure (Pa) : Temperature (K) /: Self heat rate in runaway reactions (K⋅min 1 ) : E n e r g y r e l e a s e r a t e ( J ⋅kg −1 ) Q hot : Heat of hot medium (W) Q Pipe diameter (mm) : R a t i o n ṁ: Mass flow (kg⋅s

Figure 2 :
Figure 2: Electrical connections for pump and fan motor.

Figure 3 :
Figure 3: Rupture disc and safety relief valve connection to reactor.
cold : H e a to fc o l dm e d i u m( W )  ℎ,out : T e m p e r a t u r eo fh o tm e d i u m ( ∘ C) LMTD: Log mean temperature difference ( ∘ C)   : Parameter for temperature correction factor prediction : Parameter for temperature correction factor prediction   : Temperature correction factor   : Mean temperature difference ( ∘ C) : Overall heat transfer coefficient (W⋅m −2 ⋅K −1 ) : Average provisional area (m 2 )   : N u m b e ro ft u b e s :

Table 1 :
Calculated system dimensions and characteristics for vent area, horizontal and vertical heat exchanger, blow down and scrubber tank, absorption column, and outflow chimney.