EXOTHERMIC REACTION RELIEF SIZING AND THERMAL …

EXOTHERMIC REACTION

RELIEF SIZING AND THERMAL STABILITY

CASE STUDY

Relief Sizing Case Studies

2 of 19

MNL 057, Issued 26th January 2006, by J.E.Edwards of P&I Design Ltd.

Contents

1.0 Case Study

2.0 Reaction Considerations

2.1 Experimental Theory

2.2 Reaction Data

3.0 Emergency Relief System Design and Rating

3.1 Applicable Theory and Practice

3.2 Relief Sizing

4.0 Batch Reactors Thermal Stability and Dynamic Simulations

4.1 Dynamic Modelling of 4545L Reaction System

5.0 Equipment Sizing

5.1 Relief Header Sizing

Appendices

I Relief Sizing Calculations

II Physical Property Data

Transcal LT and Dowtherm J density, viscosity and heat capacity plots

III Appendix III Reactor Thermal Stability GUI

References

1. J. Wilday and J. Etchells, “Workbook for Chemical Reactor Relief System Sizing”

HSE Contract Research Report 136/1998.

2. “Emergency Relief System Design Using DIERS Technology”

The Design Institute for Emergency Relief Systems Project Manual, 1992.

3. “Sizing Selection and Installation of Pressure Relieving Devices in Refineries”

API 520, 7th Edition, January 2000.

4. “Guide for Pressure Relieving and Depressuring Systems”

API 521, 4th Edition, March 1997.

5. “Emergency Relief System Sizing Software Methods and Practice”

P&I Design Ltd, MNL 043, J.E.Edwards, 2002.

6. “Flow of Fluids” Crane Company, Publication 410M, 1998.


3 of 19


Nomenclature

Definition of symbols used unless defined otherwise in main text for specific equations.

SI units are the preferred but consistent units should be used as appropriate.

Some correlation constants require units to be used as defined in main text.

A cross-sectional area of relief device (m2)

Cd relief device discharge coefficient

Cp average liquid specific heat at constant pressure (J/kg°K)

D relief system (or pipe) diameter (m)

F environmental factor

G two phase mass flowrate per unit flow area (kg/m2s)

hfg latent heat of vaporisation (J/kg)

Kc relief device combination factor

MW vapour or gas molecular weight

me mass in experimental calorimeter (kg)

mR mass in reactor at relief pressure (kg)

Pf flowing pressure (N/m2 abs)

QH relief system external heat input (J/s)

QG peak rate of permanent gas evolution (m3/s)

qav average heat release rate per unit mass reacting mixture (J/kg s)

Tf flowing temperature (°K)

v0 specific volume at stagnation conditions at inlet to relief system (m3/kg)

vf liquid specific volume (m3/kg)

vfg difference between vapour and liquid specific volumes (m3/kg)

W mass flowrate (kg/s)

ρG gas density (kg/m3)

(dT/dt) adiabatic temperature rise (°K/s)

(dP/dt)e peak rate of pressure rise in experimental calorimeter (N/m2s)

(dT/dt)s temperature rise at set pressure (°K/s)

(dT/dt)m temperature rise at maximum design overpressure (°K/s)


4 of 19


1.0 CASE STUDY

This case study considers the proposed equipment to carry out a new exothermic batch

reaction.

The modelling thermodynamics were based on Ideal Vapour Pressure for the K value and

Latent Heat for the enthalpy which would not be conservative for a hybrid decomposition.

Bubble points are predicted from CHEMCAD library equations and may result in

prediction of lower relief temperatures than actual since there are dissolved solids in the

reaction mixture. Physical property data has been derived from experimental data or

predicted in CHEMCAD using appropriate correlations.

The study conclusions were:

• A 100mm diameter conventional high lift relief valve with integral graphite bursting disc with set pressure at 3.0 barg without vacuum support together with an

80mm diameter graphite bursting disc with set pressure at 4.0 barg, without

vacuum support provides adequate protection.

• Dynamic process simulation demonstrated that the 4545L reactor using Trancal LT could not maintain thermal stability under the proposed reaction condition, whereas

Dowtherm J wouldl provide thermal stability.


5 of 19


2.0 REACTION CONSIDERATIONS

2.1 Experimental Theory (1,2)

Closed cell Adiabatic Dewar Calorimeter experimental data needs correction for thermal

inertia φ. A higher φ leads to a slower reaction in a non-linear fashion and lowers the heat rate temperature. Plant size equipment tends to a φ approaching unity. A thermal inertia value of 1.05 was considered appropriate.

Cm

CmCm

SS

CCSS ++++====φφφφ

Where mS sample weight CS sample specific heat

mC cell weight CC cell specific heat

Method for Evaluating Gas Evolution from Closed Cell

To determine the gas evolution rate from a closed cell test the following formula (2-A2.3 p139)

is used:

−−−−

====m

m

dt

dT

T

V

dT

dP

P

VQ

ee

G

The experimental self heat rate power output, Qe, is determined from the reactant mass,

me, reactants specific heat, CPR, and adjusted rate of temperature rise (dT/dt)e as follows:

====dt

dTCmQ

e

PRee

2.2 Reaction Data

A test was conducted to determine the temperature and pressure effects associated with the

normal reaction in the event of a loss of cooling. Reaction self heat rate data is shown :

REACTION SELF HEAT RATE

0.10

1.00

10.00

90 95 100 105 110 115 120 125 130

Measured Temperature (degC)

Measured SHR (degC/m

)


6 of 19


2.2 Reaction Data (Cont.)

Liquid Specific Heat Prediction

Reaction mix liquid specific heat has a major effect on the calculation of the reaction heat

output and the relieving flowrate. A lower value results in a reduction in the heat output and

the mass release rate is less conservative. Note this is a key consideration.

A liquid specific heat of 1730 J/kg°K at 100°C has been used in the relief sizing calculations. The significant lowering of the liquid specific heat value above 70°C indicates the onset of the exothermic reaction.

A Pseudo User Component (COMP) was created in CHEMCAD to provide an estimation

of the reaction mix ppd specifically for liquid density and specific heat. The pseudo

component was created by copying a similar component from the component library and

then regressing the liquid specific heat and density data into COMP.

Liquid Density

The reaction mix liquid density is another key parameter relief sizing calculations as it is

used to determine the initial reactor operating level and vapour volume fraction. A base

value of 1590 kg/m3 at 20°C was used for ppd prediction in CHEMCAD over the operating

temperature range.

EXPERIMENTAL DATA

Liquid Specific Heat Prediction

1200.0

1300.0

1400.0

1500.0

1600.0

1700.0

1800.0

1900.0

2000.0

40 50 60 70 80 90 100

Measured Temperature (degC)

Liquid Specific Heat (J/kg K)


7 of 19


3.0 EMERGENCY RELIEF SYSTEM DESIGN AND RATING

3.1 Applicable Theory and Practice (1,2,3,4,5)

Relief Device Discharge Coefficients

Device factor KC cd====

Cd = 0.975 for relief valve

= 0.953 for relief valve and rupture combination

= line factor for rupture disc alone with 0.625 as default

= 0.625*0.6 = 0.375 for rupture disc with vacuum support

Derating Kc Factor

Kc = 1 for relief valve alone

= 1 for bursting disc alone

= 0.9 for safety valve certified per the rule of ASME

= 0.9 for relief valve and bursting disc combination

Relief Valve Device Factor

Reverse calculation of flow data provides discharge coefficient of 0.625 which is adjusted

to 0.5625 by applying the derating correction factor above. This value has been used in the

relief sizing calculations.

Method for Evaluating Gas Density

The gas density at relief device inlet conditions is calculated using the following general

relationships. Non ideal behaviour is considered by determining the compressibility factor

Z which can be estimated using compressibility charts provided the pseudocritical absolute

temperature Tc and pressure Pc are known by evaluating the ordinates from the following

P

PP

T

TT

c

fR

c

fR ======== and

The gas density is calculated from the following:

m/kgT

273

Z

P

415.22

M 3

f

fWG

××××××××====ρρρρ


8 of 19


3.1 Applicable Theory and Practice (Cont.)

Method for Evaluating Relief Flow for Tempered Reactions (1,2)

Leungs Method (2-6.3.2, 3)

is used to determine the relief mass flow rate for tempered

runaway reactions involving two phase flow:

(((( ))))

∆∆∆∆++++

====

TCv

h

m

V

qmW

p5.0

fg

fg

R

5.02

avR

Using the rate of temperature rise at the relief device set pressure (((( ))))dtdT s and the

maximum rate of temperature rise at the maximum design overpressure (((( ))))dtdT m the

average value of heat release rate per unit mass of reacting mixture qav is calculated from:

++++

====dt

dT

dt

dTC5.0q

ms

pav

where Cp is the average liquid specific heat (kJ/kg K).

Method for Evaluating Relief Flow for Hybrid Reactions (1,2)

Leungs Method (2-8.3.1, 3)

is used to determine the relief mass flow rate for tempered hybrid

runaway reactions involving two phase flow:

(((( ))))

∆∆∆∆++++

====

TCp

p

v

h

m

V

qmW

p5.0V

fg

fg

R

5.02

avR

External Fire

Heat input rates as a result of external fires have received extensive investigation by

several organisations including API, NFPA and OSHA. The operating pressure determines

the applicable standard as follows:

API 520 (3) / API 521

(4) operating pressure > 15 psig

In API 520/API 521 the heat input QH is determined from:-

With adequate drainage and fire fighting equipment QH = 21000 FA0.82

Without adequate drainage and fire fighting equipment QH = 34500 FA0.82

Where, QH = total heat absorption Btu/hr

A = total wetted surface ft2

F = environmental factor (API 521 Table 5)


9 of 19


3.2 Relief Sizing

The initial charge volume was set using a density of 1590 kg/m3 at 20°C.

Reactor dimensions used are shown in Appendix III and sample calculation shown in the

Calculations Section.

Due to the toxic nature of the initial reaction mix the relief design is based on a containment

strategy subject to the pressure protection of the process equipment. The 4545L reactor

maximum design pressure was 6.83 barg with a maximum design temperature of 200°C.

A primary 100mm diameter relief valve/bursting disc combination with a set pressure of 3.0

barg and an 80mm diameter bursting disc, with no vacuum support, set at 4.0 barg were

provided.

The relief sizing was based on a tempered runaway reaction model using a temperature rise

of 1.5 °C/m. Furthermore the system can handle the API 520 (F=0.3) External Fire Case with a coincident heat of reaction equivalent to 400 MJ/h, see calculation. Note 348 MJ/h is

evolved at 110°C reaction temperature.

For relief sizing, the vessel model used was Homogeneous Equilibrium (HEM) and the vent

flow model HEM. These assumptions result in a conservative relief device sizing and forces

two phase flow conditions.(1,2,5)

The stagnant conditions for relief device sizing together with conditions at vessel design

pressure and relief calculation summaries are shown below:

Experimental Data for the Reaction

Set

Pressure

Bubble

Point

Temperature

Accumulated

Pressure

Bubble Point

Temperature

dT/dt

Set Pressure

dT/dt

Accumulated Press

bara °C bara °C °K/min °K/sec °K/min °K/sec 4.0 169 4.3 172 1.5 0.025 1.5 0.025

5.0 179 5.5 186 1.5 0.025 1.5 0.025

CHEMCAD Calculations Primary Relief Valve/Bursting Disc, Set Pressure 3.0 barg

Relief

Scenario

Vessel

Level

Relief

Temperature

Relief

Rate

Disc Area Disc

Diameter

m °C kg/h m2

m

Design-001 1.01 172 38735 0.006873 0.093

Rating-002 1.01 172 46046 0.00817 0.100

CHEMCAD Calculations Secondary Bursting Disc, Set Pressure 4.0 barg

Relief

Scenario

Vessel

Level

Relief

Temperature

Relief

Rate Disc Area

Disc

Diameter

m °C kg/h m2

m

Design-003 1.01 186.1 18888 0.002154 0.05237

Rating-004 1.01 186.1 44015 0.00502 0.0799


10 of 19


4.0 BATCH REACTORS THERMAL STABILITY AND SIMULATIONS

4.1 Dynamic Modelling of 4545L Reaction System

The installed cooling used recirculating heat transfer fluid Transcal LT at 27.5 m3/h.

The dynamic plots below have been obtained using the thermal heat output for the reaction

at an initial temperature of 100 degC. The reaction time was set at 2.37h giving a

conversion rate of 10.78 mol/m. The agitator speed was set at 120 rpm and three high flow

jacket inlet nozzles were allowed.

The above plots demonstrate that with the simulation parameters used and the reaction

conditions prevailing the cooling system is inadequate to hold the reaction temperature at

100°C. Also as the reaction temperature increases the reaction thermal output will increase hence the plot shown above will reach atm BP at an earlier stage than indicated. The jacket

temperature selected gives the optimum cooling characteristics for Transcal LT where

viscosity becomes controlling at lower temperatures, see viscosity data presented in

Appendix I.


11 of 19


4.1 Dynamic Modelling of 4545L Reaction System (Cont.)

The dynamic simulations were repeated using Dowtherm J heat transfer fluid recirculating

at 27.5 m3/h. The plots below have been obtained using an estimated heat output for the

reaction at an initial temperature of 90 degC. The detailed simulation conditions are shown

in Appendix II. The reaction time was set at 3.58h giving a conversion of 7.12 mol/m. The

agitator speed was set at 120 rpm and three high flow jacket inlet nozzles were allowed.

The above plots demonstrate that with the simulation parameters used and the reaction

conditions prevailing the cooling system is adequate to hold the reaction temperature at

90°C using Dowtherm J as the heat transfer fluid. In fact inspection of the relevant spreadsheet in Appendix III indicates that thermal stability is achievable at reaction

temperatures up to 100°C.


12 of 19


5.0 EQUIPMENT SIZING

5.1 Relief Header Sizing

The relief header sizing was based on a maximum straight length of 10m, four (R/D=1)

bends and one exit from pipe is shown.

A 200 mm diameter line with as short a route as is practicable and the minimum number of

bends should prevent choking.

The model and results for the primary relief system rating case are shown below:

For an adiabatic thermal flow condition the outlet vapour mass fraction is 0.286 and for the

isothermal flow condition the outlet vapour fraction is 1.0.

On this basis, it is estimated that for an HEM vessel model and HEM vent flow model

there will be approximately 2400 kg of material collected in the liquid section of the

blowdown drum.


13 of 19


Appendix I – Relief Sizing Calculations Calculation # : 001

Remarks: Design Basis

Device type = Relief valve / Rupture disc in series Valve type = Conventional valve

Vent model = HEM (Homogeneous Equilibrium Model) Vessel model = Homogeneous vessel model Design model = Tempered runaway reaction

Design, Pressure vessels. Vertical vessel

Head type = Ellipsoidal Head K factor (dpth / R) = 0.5

Vessel dimensions: Diameter m = 1.829

Length (T to T) m = 1.425 Vessel volume m3 = 5.3458 Liquid level m = 1.01

Initial vapor volume fraction = 0.57851 Height above ground m = 2

Fluid properties: Vapor mass kg = 23.191

Liquid mass kg = 3214.9 Vapor density kg/m3 = 7.4989

Liquid density kg/m3 = 1426.9 Surface tension N/m = 0.012774 Liquid viscosity cP = 0.25533

Vapor Z factor = 0.92945 Cp/Cv = 1.1616

Vapor MW = 60.053 Liquid heat capacity kJ/kg-K = 2.231 Latent heat kJ/kg = 398.18

Relief device analysis:

Set pressure bar = 4 Back pressure bar = 1.341 % Overpressure = 10

Temperature C = 172.38 Discharge coefficient = 0.5625

C0 radial distribution parameter = 1.5 Kb Backpressure correction factor = 1 dT/dt rate of T rise at Pset K/s = 0.025

dT/dt rate of T rise at P K/s = 0.025 Length/Diameter of pipe = 38

Calculated nozzle area m2 = 0.0068728


14 of 19


Appendix I – Relief Sizing Calculations

Calculation # : 001

Page: 2 The following calculation is base on vent area 0.0068728 m2.

Calculated vent rate kg/h = 38735 Calc critical rate kg/h = 38736

Calc critical press bar = 3.8647 Nozzle inlet vapor mass fraction = 0.0071618

Device inlet density kg/m3 = 605.74 Nozzle inlet vapor vol. fraction = 0.57851

Inlet/outlet pipe size analysis: Compressible flow parameter = 29.098

Inlet pipe diameter m = 0.1 Inlet pipe length m = 0.1 Inlet pipe roughness m = 4.572e-005

Mixture viscosity cP = 0.1152 Inlet Fanning friction factor = 0.0042252

Inlet pipe P drop bar = 0.00041731 % Inlet P drop / Differential P = 0.01615

Outlet pipe diameter m = 0.2 Outlet pipe length m = 38.3

Outlet pipe roughness m = 4.572e-005 Mixture viscosity cP = 0.013673 Outlet Fanning friction factor = 0.003586

% Allowable outlet P drop = 10 Outlet pipe length m = 63.384 (Allowable)

Outlet pipe reaction force (thrust) analysis: Reaction force (slip flow) kgf = 166.85

Reaction force (homogeneous) kgf = 166.85

Device Inlet Stagnant Conditions Temp C 169.2778 Pres bar 4.0000*

Relief Conditions Total Vapor Liquid Temp C 127.3823 127.3823 127.3823 Pres bar 1.3410 1.3410 1.3410

Enth MJ/h -2.8436E+005 -65738. -2.1862E+005 Vapor mole fraction 0.24113 1.0000 0.00000

Total kmol/h 645.0166 155.5307 489.4859 Total kg/h 38735.1831 9340.0844 29395.0978 Total std L m3/h 24.3657 5.8752 18.4905

Total std V m3/h 14457.17 3486.01 10971.16 Flowrates in kg/h

COMP 38735.1831 9340.0844 29395.0978


15 of 19



Calculation # : 005

Device type = Relief valve / Rupture disc in series Valve type = Conventional valve Vent model = HEM (Homogeneous Equilibrium Model)

Vessel model = Homogeneous vessel model Design model = API-520/521

Rating, Pressure vessels. API 520-521, Adequate firefighting and drainage facilities exist.

Vertical vessel Head type = Ellipsoidal Head K factor (dpth / R) = 0.5

Vessel dimensions:

Diameter m = 1.829 Length (T to T) m = 1.425 Vessel volume m3 = 5.3458

Liquid level m = 1.01 Initial vapor volume fraction = 0.57851

Height above ground m = 2 Fluid properties:

Vapor mass kg = 23.191 Liquid mass kg = 3214.9

Vapor density kg/m3 = 7.4989 Liquid density kg/m3 = 1426.9 Surface tension N/m = 0.012774

Liquid viscosity cP = 0.25533 Vapor Z factor = 0.92945

Cp/Cv = 1.1616 Vapor MW = 60.053 Liquid heat capacity kJ/kg-K = 2.231

Latent heat kJ/kg = 398.18

Relief device analysis: Set pressure bar = 4 Back pressure bar = 1.416

% Overpressure = 10 Temperature C = 172.38

Discharge coefficient = 0.5625 C0 radial distribution parameter = 1.5 Kb Backpressure correction factor = 1

Exposed area m2 = 6.8224 Environmental factor = 0.3

* Additional heat rate MJ/h = 400 Heat rate MJ/h = 625.25

Check adequacy of device for rating case.

Specified nozzle area m2 = 0.00817 Calculated nozzle area m2 = 0.0080981


16 of 19



Calculation # : 005

Page: 2 The following calculation is base on vent area 0.00817 m2.

Calculated vent rate kg/h = 46046 Calc critical rate kg/h = 46047

Calc critical press bar = 3.8647 Nozzle inlet vapor mass fraction = 0.0071618

Device inlet density kg/m3 = 605.74 Nozzle inlet vapor vol. fraction = 0.57851

Inlet/outlet pipe size analysis: Compressible flow parameter = 29.098

Inlet pipe diameter m = 0.1 Inlet pipe length m = 0.1 Inlet pipe roughness m = 4.572e-005

Mixture viscosity cP = 0.1152 Inlet Fanning friction factor = 0.0042063

Inlet pipe P drop bar = 0.00058707 % Inlet P drop / Differential P = 0.02272

Outlet pipe diameter m = 0.2 Outlet pipe length m = 38.3 (Specified)

Outlet pipe roughness m = 4.572e-005 Mixture viscosity cP = 0.013673 Outlet Fanning friction factor = 0.0035774

% Allowable outlet P drop = 10 Outlet pipe length m = 42.865 (Allowable)

Outlet pipe reaction force (thrust) analysis: Reaction force (slip flow) kgf = 180.66

Reaction force (homogeneous) kgf = 180.66

Inlet Stagnant Conditions Temp C 169.2778 Pres bar 4.0000*

Outlet Conditions Total Vapor Liquid Temp C 129.2612 129.2612 129.2612 Pres bar 1.4160 1.4160 1.4160

Enth MJ/h -3.3803E+005 -75146. -2.6289E+005 Vapor mole fraction 0.23199 1.0000 0.00000

Total kmol/h 766.7632 177.8844 588.8788 Total kg/h 46046.4330 10682.4937 35363.9429 Total std L m3/h 28.9647 6.7196 22.2451

Total std V m3/h 17185.96 3987.04 13198.92 Flowrates in kg/h

COMP 46046.4330 10682.4937 35363.9429


17 of 19


Appendix II - Physical Property Data


18 of 19


Appendix II - Physical Property Data


19 of 19

MN

L 0

57, Is

sued

26

th J

anuary

2006, b

y J.

E.E

dw

ard

s of P

&I

Des

ign L

td.

Ap

pen

dix

III

Rea

cto

r T

her

ma

l S

tab

ilit

y G

UI

EXOTHERMIC REACTION RELIEF SIZING AND THERMAL …

Documents

Transcript of EXOTHERMIC REACTION RELIEF SIZING AND THERMAL …