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VESSFIRE A Calculation System for

Blowdown of Process Segments and Process EquipmentExposed and Unexposed to Fire.

Technical Reference Manual


VessFire A Calculation System for Blowdown of Process Segments and Process Equipment Exposed and Unexposed to Fire. Technical Reference Manual Written by Dr. Geir Berge Petrell as Kjøpmannsgata 19 NO-7013 Trondheim Phone: + 47 73 80 55 00 Fax: +47 73 80 55 01 Mobile: +47 932 000 20 Email: [email protected] page: www.petrell.no © 2005 Copyright Petrell as. This document is intended for licensees of VessFire. Use of information in the document is subject to the rules of Copyright. No part of this document may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the distributor.

mailto:[email protected]


RP-VessFire-02 Date: 16-04-03 of 29

TABLE OF CONTENTS

1 INTRODUCTION............................................................................................................ 4

2 SYSTEM OVERVIEW.................................................................................................... 4

3 TECHNICAL DESCRIPTION....................................................................................... 6 3.1 THE SHELL .................................................................................................................. 6

3.1.1 Boundary conditions ...................................................................................... 7 3.2 THE INVENTORY.......................................................................................................... 8 3.3 THE FLAME ............................................................................................................... 11 3.4 THERMODYNAMIC..................................................................................................... 13 3.5 HEAT TRANSFER........................................................................................................ 14

3.5.1 Liquid-gas..................................................................................................... 15 3.5.2 Wall-gas ....................................................................................................... 15 3.5.3 Wall-liquid.................................................................................................... 17

3.6 DESCRIPTION OF RUPTURE MODEL............................................................................. 19 3.7 MATERIAL PROPERTIES FOR STEEL AND INSULATION ................................................ 20

4 VALIDATION................................................................................................................ 22 4.1 EXPOSURE OF A SPOOL PIECE (CYLINDER), DRY AND PARTLY FILLED WITH WATER ... 22

4.1.1 Dry cylinder exposed to heat........................................................................ 22 4.1.2 Cylinder partly filled with water .................................................................. 23

4.2 BLOWDOWN OF A VESSEL FILLED WITH AIR............................................................... 25 4.3 VESSEL PARTLY FILLED WITH PROPANE AND EXPOSED TO FIRE ................................. 26 4.4 CONCLUSION............................................................................................................. 28

5 REFERENCE LIST ....................................................................................................... 29



1 Introduction Behaviour of process equipment and inventory during blowdown, whether exposed to heat or not, is an important factor for safety in process plants as well as transportation of chemicals. During the latest years, it has been increased focus on storage of hazardous chemicals, in particular with respect to fire. New research has created insight that has made it necessary to review established standards and design methods. In addition, an increased focus on safety in the society is leading to call for new engineering tools and methods that are more accurate. This is the background for the creation of the simulation system VessFire. VessFire offers a method to predict effects on process equipment during blowdown exposed or not exposed to fire. It can predict temperature and stresses of the component shell and the conditions of the inventory. The operation of VessFire is described in the User Manual. This manual is a technical manual that describes the theory behind VessFire and presents some validation results. VessFire can be applied for vessels as well as pipe calculations. The orientation of the vessel can be horizontal or vertical. The ability built into VessFire complies with the requirements in the new standards developed for process design.

2 System overview VessFire is built around a 3-dimensional simulation of heat conduction in a cylinder shell influenced by the inventory and the external conditions. Figure 1 shows the geometry that is basis for VessFire. The inventory can be all gas, liquid or a mixture. The outside exposure can be a specified heat load as function of time. The heat load can be given as a combination of radiation and convection, only radiation or only convection. VessFire can also take input from a fire simulation.

Figure 1 Illustration of the shell geometry used by VessFire. A part of the shell is exposed to fire.



Figure 2 illustrates the principle physics considered for the inventory. Heat conducted through the shell is transferred to the gas and liquid zone and results in evaporation or condensation, increased or decreased pressure dependent on the scenario described. The inventory can have a combination of up to 20 different substances, including pseudo components. It is also possible to define new components. To calculate temperature distribution in the shell, 12 control volumes in radial direction is applied. The shell can have 4 different layers using 4 different materials. The number of layers in use is divided on the 12 control volumes. The strength-carrying layer is always the innermost.

To

TgTg

Tl

qo

qig

qil

lgm• lgm•

fm•

gVgV

lVlV

Tso

Tsi

12 layers distributed on up to 4 different materials

glm• glm••

•

•

gmgm

lmlmh l

h gh g

Figure 2 Principle illustration of the physical heat and mass transportation treated in VessFire.

A blowdown scenario is considering that the insulation valves for a blowdown segment have been closed and the inventory is at rest. The liquid level that is given in the scenario description defines the mass of liquid and gas. The vessel inventory composition is a result of a flash calculation by the mixture entering the vessel. For that reason liquid and gas inside the vessel has in general a different composition compared to the inlet composition defined by the user. Both Pressure Safety Valves (PSV) and Blowdown Valves (BDV) are included and can be operated separately. The BDV can have delayed opening. There are three kinds of PSV included (see User Manual). In the scenario definition file the location of PSV and BDV is given. The location of the outlet compared to the liquid level decides if liquid or gas is released. VessFire calculates the stress in the shell. This stress is compared to the stress the material is able to maintain at the elevated temperature. When the calculated stress exceeds what the material is able to maintain, a rupture is predicted. There is a temperature variation through the shell. The temperature used to find the allowed stress is the average temperature calculated as



∫ ⋅Δ⋅⋅Δ⋅=Rys

Risav dRzRT

VT θ1

Ris and Rys is the inner and outer radius of the strength bearing shell. (Insulation is not included.)

3 Technical description 3.1 The Shell The temperature distribution in the shell is governed by the energy equation solved for temperature

qzT

zT

rrTr

rrtTc p

&+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=∂

∂λ

θλ

θλ

ρ2

11

T – Temperature [K] ρ - Density [kg/m3] cp - Specific heat capacity [J/kg K] t - Time [s] q& - Added heat per volume and time [W/m3] r - co-ordinate in radial direction [m] θ - Co-ordinate in circumferential direction [m] z - Co-ordinate in longitudinal direction [m] The equation is integrated over a control volume ΔV = rΔθΔrΔz See Figure 3, and the equation takes the form

∑ ++Δ

+= −

nppcp

pnnpp TSST

tc

TaTa 1ρ

where ap and Tp is the respective central coefficient and the temperature for the control volume, n is the number of neighbour control volume, an and Tn are the respective coefficient connecting the neighbour control volumes and the temperature in the neighbour control volumes and Sc and Sp is constant terms of a linearized source term. Tp

-1 is the temperature from the former time step.



r

Δr

Δz

Δθ

ri

ry

Figure 3 Control volume for the shell used in VessFire

The coefficients in r direction are

rzrar Δ

ΔΔ=

θλ , using ri for the inner coefficient and ry for the outer coefficient

in the θ direction

θλθ Δ

ΔΔ=

rZra

in the z direction

zrra z ΔΔΔ

=θλ

and

∑+Δ

=n

np

p at

ca

ρ

3.1.1 Boundary conditions The equation system for the control volumes in the shell is solved using the cyclic Thomas algorithm. The algorithm is well documented in ref. 2. That means there are no boundary conditions in the θ direction. At the boundary in the z direction is used a Von Neumann

condition, 0=∂∂

zT . In the radial direction, the boundary conditions are linked to the heat

transfer. This is done by setting the innermost and outermost coefficient in the r-direction to zero and include the heat transfer to the sour term. For the inner most control volume this will then be

fi

ic Trr

rS

Δ= α

rrr

S iip Δ

−= α



where Tf is the temperature of the fluid the control volume has contact with and αi is the heat transfer coefficient for the inside surface. Calculation of the heat transfer coefficient is discussed under chapter 3.5. As the liquid height is changing during the simulation, there will be control volumes partly in liquid and partly in gas. The inner surface of these volumes is than divided between the liquid and gas zone and both temperatures are considered. The boundary condition at the outer most control volume is treated in the same manner as the inner most. The source term is nevertheless different. The modelling of the flame is treated in the chapter 3.3 The Flame. 3.2 The Inventory The process taking part in the inventory is governed by separate energy equations for liquid and gas. A mixture that includes water is treated by separating water from the mixture and performing flash calculations for each. The thermodynamic of water is quite complicate and the separation is done in order to be able to treat higher content of water in mixtures. Mixing between fluids and water is assumed a mechanical mixture. That means no molecular forces are considered between components of the fluid and water. As the mixing is assumed complete, water and fluid will have the same temperature. This is enforced by heat transfer between fluid and water in the energy equation. A mean temperature is calculated using

( ) ( )( ) ( )

waterpfuelp

waterpfuelp

lm mcmc

TmcTmcT

+

+=

Heat transferred between liquid fuel mixture and water is

( ) ( )lmwaterwaterplW TTmcH −=Δ Even if water and fuel have separate energy equation, the same terms occur. Heat exchange between the wall and liquid is split between water and liquid mixture according to the mass ratio. For liquid the equation is

lwfllslglradglglililglbdll HmhFAqAqAqmhmh

tPV

tH

Δ±−++++−∂

∂=

∂∂

− &&&&&& lg

The gas phase are treated in the same manner as the liquid phase with respect to water (or vapour). For gas the equation is

gwfgglgligigglbdgg HmhAqAqmhmh

tPV

tH

Δ±−−+−+∂

∂=

∂∂

&&&&& lg

The gas is assumed transparent. The nomenclature is

Hl – Enthalpy for the liquid [J]

Hg – Enthalpy for the gas [J]

ilq& - Heat transport from the shell into the liquid phase [J/m2]



ilA - Vetted area for heat transport to the liquid [m2]

igq& - Heat transport from the shell into the gas phase [J/m2]

igA - Dry area where heat is transported to the gas [m2]

glq& - Heat transport from the gas phase to the liquid phase due to convection [J/m2]

glA - Area of the interface between liquid and gas [m2]

dh - Specific enthalpy at dew point [J/kg]

bh - Specific enthalpy at bubble point [J/kg]

gh - Specific enthalpy of gas [J/kg]

lgm& - Evaporated liquid entering the gas phase [kg/s]

glm& - Condensed gas entering the liquid phase [kg/s]

fm& - Gas flow through the BDV and PSV system [kg/s]

slF − - Form factor between liquid and the dry inner surface of the shell [m2]

radq& - Net radiated heat between the liquid and the dry inner surface of the shell [J]

P - Pressure of inventory [Pa]

Vg - Volume of gas [m3]

Vl - Volume of liquid [m3] The composition defined in the vessel.scn file is assumed the composition of fluid entering the vessel or the pipe spool considered. The first step in a simulation is to define the conditions of the gas and the liquid phase and the corresponding masses. Therefore, a flash calculation is performed based on the temperature and pressure that is defined in the input file. The flash calculation gives the composition of the gas and liquid and the properties for each phase. For instance, the initial enthalpy for use in the energy equations, the molecular weight for the liquid and gas phase and other properties for the mixture are found. The mass of liquid is found based on the vessel dimension, the liquid height and the liquid density. Similarly, the mass of gas is found based on gas volume and initial gas density. In addition to the energy-equation, there is a mass conservation equation for each phase. For the liquid phase

lg

1

mmmtmm

flglll &&& −−=

Δ− −

For the gas phase

lg

1

mmmtmm

fglgg &&& +−−=

Δ

− −



In principle, both gas and liquid can be evacuated from the vessel. If the blowdown line for the PSV and BDV system is located below the liquid height, liquid will flow through the line. When the line is in the gas zone, gas will be evacuated. The release rate for gas is calculated based on the assumption of isentropic flow. The theory is outlined in most standard textbooks, for instance ref. 3.

The mass flow of gas is calculated using the pressure ratio 0P

P where P is the pressure at the

minimum flow area. If the pressure ratio is less than the critical ratio, the pressure is the critical pressure Pc. If the pressure ratio is greater or equals to the critical ratio the pressure is the backpressure downstream the restriction (for instance the orifice).

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=

−κ

κκ

ρκ

κ1

0

2

000 1

12

PP

PPPACm fcf&

Here P0 – is the pressure inside the vessel ρ0 - is the density of the gas inside the vessel Af – is the minimum physical flow area, including PSV and the blowdown system. For the

blowdown system, this usually is the orifice. Cc – is the contraction factor. This is an area ratio between the effective flow area and the

physical flow area. κ - is the ratio cp/cv, where cv is the specific heat capacity for constant volume. The critical pressure ratio is calculated using

1

0 12 −

⎟⎠⎞

⎜⎝⎛

+=

kc

PP

κ

κ

For liquid the flow rate is calculated using Bernoulli equation

ρρρPPuP

ll

Δ++=

2

20

where

22

22 uudlfP ξρρ +=Δ

This can be rearranged to

ξ

ρρ++

−==

dlf

PPACuACm fcfcfl

1

)(2 0&



where l - is the length of the flow pipe d – is the inner diameter of the flow pipe

f - is the friction factor depending on the Reynolds number (υdu

=Re )

ξ - is the valve friction coefficient chosen to 1.2 u - is the bulk velocity ν - is the kinematic viscosity [m2/s] For Re < 4000

Re64

=f

For Re ≥ 4000

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+−≈

11.1

10 7.3/

Re9.6log8.11 dk

f

where k is the roughness height. For the purpose of process pipes k is estimated to 0.000005 The following procedure is used to calculate the inventory:

1. At beginning of each step a flash calculation is performed based on the pressure and enthalpy from the last time step. A new temperature is calculated as part of the flash calculation.

2. A new mass balance for each phase is calculated based on the condensed and evaporated mass, resulting from the flash calculation and the release rate.

3. A new volume for the liquid is calculated by use of the updated liquid density and the mass balance for liquid.

4. New gas volume and liquid height is calculated.

5. A new gas density can now be found from the new gas volume and calculation of the new mass of gas.

6. Having found the new gas density the pressure is calculated using the new temperature.

7. The enthalpy for the next step is solved including the heat transfer from the wall.

8. At last, the release rate for the next step is calculated.

Flash calculations and properties are found using a thermodynamic package described in chapter 3.4. 3.3 The Flame This chapter deals with implementation of heat loads from flame when the heat is defined as a given number.



Just defining a heat load does not necessary implies a unique implementation and understanding of the exposure. Specifying a heat load also implies to inform how the heat load should be understood. Heat exchange between a flame and an object can be described as

reflectionbackradconvectionflameradnet qqqqq &&&&& −−+=

A stated heat load, for a flame exposure can be one of four options: loadq&

1. netdload qq && =2. convectionflameradload qqq &&& += 3. dconvectionload qq && =4. flameradload qq && =

In addition, the question whether the emissivity factor is included or not brings in an additional parameter. The result can be quite different depending on what choice is made. VessFire use the first interpretation considering the emissivity for the flame and the surface to be one. That option will be discussed in this chapter. When the heat source is located apart from the radiated object, the radiation load to the object is dependent on a radiation shape factor. Most of the recommended values for heat from flames given in standards assume that the object is engulfed by the flame. In that case, the radiation shape factor is one. VessFire assume engulfment. For cases where the flame is apart from the object, the heat load should be corrected due to radiation shape factor before it is given as input to VessFire. The flame temperature can be set independently from the heat load. For heat radiation and convection the following equations apply:

4Tq εσ=&

surfacesurface ετ −=1

)T– (T surfaceflameα=convectionq& When the object has its initial temperature, following equation holds

loadnet qq && = This equation is used to split the radiation and the convective term. It is assumed that radiation from the flame maintains constant as long as the heat load is constant. Using equation above gives the radiation term for a given flame emissivity

4)]([ initsurfacesurfaceflameloadflameflamerad TTTqq −+−−= σαε &&



The last term is necessary in order to take care of the background radiation. When the simulation starts, the temperature of the object is considered to be in balance with the surroundings. The net heat transferred to the object during the heating process is than calculated as

4)( surfacesurfacesurfaceflameflameradsurfacenet TTTqq σεαε −−+= &&

In the equations above, the flame temperature is missing and has to be defined. This is done by solving the following equation for Tflame

0)( 44 =−+−− − flameinitsurfacesurfaceflameload TTTTq σσα& During the simulation, the flame temperature and radiation term are kept constant as long as the heat load is constant. When the heat load is changed a new flame temperature and radiation term are calculated. As an alternative, the flame temperature can be specified. This is relevant for cases where the flame is not impinge the object, but just exposing it by radiation. To give a fixed flame temperature, specify a temperature lower than the radiating temperature. The lowest value will be used. The heat load is included in the energy equation for the outer most control volume using the source term. 3.4 Thermodynamic VessFire are using two software packages for calculation of thermodynamic and transport properties, one for fluid mixtures and one for water and steam. The thermodynamic flash calculation for fluids is performed by use of SUPERTRAPP, a software package delivered by NIST, ref. 4. The package can handle pure components or mixtures up to 20 substances. The database shipped with the program includes 201 different substances. It is possible to modify existing substances or add new one. The Peng-Robinson equation of state is used to determine the phase equilibria. For the property evaluation, either the Peng-Robinson or the extended corresponding state is applied. The methods are described among others in ref. 5. The uncertainties in the calculated properties vary considerably depending on the fluid, property and thermodynamic state. The Peng-Robinson equation of state is most suitable for nonpolar molecules near saturated conditions. Care should be taken when applying this software for polar substances. The acentric factor, ω, represents the eccentricity or nonsphericity for molecules. For monatomic gases, ω is essentially zero. ω is widely used as a parameter that is supposed to measure the complexity of molecules with respect to geometry and polarity. Material with high acentric factors may indicate increased uncertainties. VessFire use SUPERTRAPP for flash calculations. The kind of flash calculations that is performed is P-H flash (pressure and enthalpy is known) for calculation of mass balance



between phases, composition for each phase, temperature and properties like density for liquid, viscosity, conductivity, compressibility, etc. To find pressure a T-D flash (temperature and density is known) is used. Performance of flash calculations is described in most textbooks on thermodynamic. For instance ref. 5. SUPERTRAPP support mixtures including water only up to 5% mol fraction of water. To be able to handle higher content of water a special package for water is applied, ref. 6. For that reason VessFire treats water mixed with other fluids as mechanical mixtures. That means there is no molecular adherence or other forces considered for the water in the mixture. For calculation of water and steam is applied the NIST/ASME Steam Properties database, Version 2.2. The equilibrium thermodynamic properties for water are calculated from the 1995 Formulation for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, issued by the International Association for the Properties of Water and Steam (IAPWS). 3.5 Heat transfer To calculate heat transfer between shell and fluid, between flame and shell and between oil and gas, VessFire is using heat transfer coefficients for the heat transport. These are of the type Nu = K f(Re, Pr, Gr) Here Nu is the Nusselt number, K is a constant, Re is the Reynolds number, Pr is the Prandtl number and Gr is the Grashof number.

λαLNu =

υuL

=Re

λμpc

=Pr

3

32

μρβ TLgGr Δ

=

L - Characteristic length u - Velocity ΔT - Temperature difference g - Gravitational acceleration cp - Specific heat capacity α - Convective heat transfer coefficient β - Coefficient of cubical expansion λ - Heat conductivity ρ - Density μ - Dynamic viscosity (= ν.ρ) ν - Kinematic viscosity It is common in heat transfer theory to divide the transfer mechanism into groups based on flow situations, geometry or change of faces. The type of problems VessFire is focusing on is



including most of the transport mechanism. Inside the vessel, there is heat transfer from solid surface to liquid and gas including free and forced convection, condensing and evaporation on vetted walls and boiling including different boiling regimes. Outside the vessel there is heat transfer including radiation and convection from jet fire and surroundings in combination or separately. The nature of the physics VessFire is dealing with is quite complex and a great effort has been put into the development to get the results as accurate as possible. The result has been tested as much as possible. The problem is good experiments for verification. This process will be continued, as new experiments will be available. The functions available in literature, that expresses Nusselt numbers, are largely focusing on one group (or physical phenomena) at a time. There are also complex functions that try to include several physical phenomena in one expression, but these are not used in VessFire. The strategy chosen is to use the basic expressions for free convection along a flat plate and forced convection for flow inside pipes and than make modifications and combinations based on the particular geometry used in VessFire.

3.5.1 Liquid-gas The heat transfer between liquid and gas is based on

( )lgglgl TTq −= α& The heat transfer coefficient can be calculated from Nu= a (Gr⋅Pr)b

Included in the Grashof number is a typical height of a vertical surface and a temperature difference. As temperature difference is used the difference between liquid (Tl) and gas (Tg). As typical height is used the elevation difference between the liquid surface and the top of the gas zone in the vessel. The constants, a and b, are dependent of the Grashof number and the temperature difference as shown in the table below, ref. 7.

ΔT Gr·Pr a b Tg > Tl 0.25 0.27

> 2.107 0.333 0.14 Tg < Tl< 2.107 0.25 0.54

The heat transfer between liquid and gas due to convection is seen to be small compared to the heat transport due to the evaporation and condensing process.

3.5.2 Wall-gas The heat transfer between wall and gas is consisting of convection and radiation. Most gasses absorb radiation within narrow wavelength bands and the absorbed energy is small compared to convective energy. For that reason the gas is considered transparent. The dominant transfer mechanism is the convective transport. The expression for heat transferred per square meter is

( )giigig TTq −= α&



The flow regime inside the vessel is complex. Different approaches have been used in the literature. Quite common it has been argued that buoyancy forces is a governing mechanism and consequently expressions including Grashof numbers has been applied in combinations with expressions including Reynolds number. It seams logic to believe that the temperature difference between wall and gas is a driving force, especially in a situation where a segment is insulated by valves and there is no flow through the system. Two other flow regimes seam to influence strongly as well. When the blow down valve or the pressure safety valve opens a flow situation will be created inside. Another flow regime appears caused by evaporation or condensing. It seams as these two flow regimes in certain situations will dominate over the buoyancy effect, modelled by use of Grashof numbers. The heat transfer model applied is a combination of free flow and forced flow conditions. For free flow conditions is applied

( ) 25.0Pr555.0 ⋅= GrNuGr for Gr < 109 and

)( 4.0Pr021.0 ⋅= GrNuGr for Gr > 109 These two equations are relevant for a horizontal flat plate and well documented, ref. 9 and 12. Inside the vessel, the surface is curved. It is considered that on the top and bottom the conduction is dominant. That correspond to Nu = 1. In between, the heat transfer is considered to vary with the vertical portion of the surface. That means a sinus function. In addition, there is reason to believe that the free convection heat transfer is a function of the diameter of the vessel. Free convection becomes stronger for increasing diameters, within an upper limit. The resulting correction is than

⎥⎥⎦

⎤

⎢⎢⎣

⎡ − )+= 5.1|.0|

4.01.0sin( Nu1. Nu

2

GreDω

The brackets [ reads maximum of a and b while ]ba | ba | is read minimum of a and b. ω is the angle between the vertical centre line and the centre of the control volume. The angle is zero at the top of the vessel. The equivalent diameter, De, is used as length scale in the expressions for Nu

v

ge L

VD

π4

=

Here is Lv and Vg respectively the length and the gas volume of the vessel. Forced convection is modelled using the expression for turbulent pipe flow, ref. 9 and 12

4.08.0Re PrRe023.0=Nu

The length scale used is De. Forced convection is caused when a valve is opened and gas is flowing out. Boiling liquid also initiate a kind of forced convection. Boiling also leads to transport of small droplets that might be in contact with the shell surface and evaporate rapidly. The transport of droplets to the wall is more marked for small vessel (pipe) diameters.



The velocity used in the Reynolds number are expressed as

22Re evbl VVV +=

Here Vbl is the velocity caused by the release rate

gg

fbl A

mV

ρ&

=

Here Ag is the gas flow cross section area, normal to the vessel length and

glgVev A

mkV

ρlg&=

The kv is a function of the height from the liquid surface to the top of the vessel, lg. For small heights more droplets will be in contact with the shell surface, this will soon diminish as the height is increased. The function is

01.0|.1|l0.2200k

5

gV

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

Whether free, forced or a combination of convection effects are present is decided by the ratio Gr/Re2. If Gr/Re2 > 1.12, free convection is dominant. If Gr/Re2 < 0.9 forced convection is dominant. In between there is a combination calculated as Nu = (NuGr

3 + NuRe3)1/3.

3.5.3 Wall-liquid Heat transfer between liquid and wall is a typical boiling heat transfer situation with change of phase. The theory is explained in most textbooks for heat transfer, for instance ref. 9. Figure 4 shows a typical curve for heat transfer between wall and liquid (water) in a boiling situation without forced flow. In most situations relevant for process equipment, it is considered that the heat transfer situation will be similar to zone 1 and 2. It is not considered that the heat load is high enough to pas the critical heat limit between zone 2 and 3. Never the less, the knowledge within this area especially for hydrocarbon and other substances are little known and care should taken especially for substances with low evaporation heat.



0.5 5 50 500 5000

30

1600

Log

q/A

[k

W/m

2 ]

ΔT [K]

Pure convection heat transfer by superheated liquid rising to the liquid-vapour interface where evaporation take place.

Nucleate boiling regime Transition boiling regime

Stable film boiling regime

Zone 1 Zone 2 Zone 3 Zone 4

Figure 4 Typical boiling curves for a wire, tube, or horizontal surface in a pool of water at

Atmospheric pressure. ΔT is the temperature difference between the liquid and surface.

For heat transfer in zone 1, VessFire is using an expression recommended in ref. 10,

( ) 3/1Pr16.0 GrNu =

As characteristic length in the Grashof number is used the liquid height, hliq. For nucleate boiling in zone 2, there are a number of models available. The most well known is by Rohsenow ref. 11. Most of these models are quite inaccurate and complex. For the purpose of VessFire, they have been evaluated as less relevant. The heat transfer is quite high in the liquid area during boiling. The steel temperature is consequently dominated by the liquid temperature. For the purpose of rupture prediction, the most critical steel temperature is in the gas zone. The importance of heat transfer to the liquid is to predict evaporation rate. Whether the temperature difference between liquid and steel are 3 or 20 K are for this purpose of less importance. The total heat transferred to the liquid is little influenced by this temperature difference. Experiments performed with water, ref. 13 also confirm a small temperature difference of about 3 K. The model applied is based on

( ).1,min boilst TTAq

−=α

where Tst and Tboil is respective the steel and the boiling (bubble temperature) temperature for the mixture. The transition between the two models are based on

⎥⎥⎦

⎤

⎢⎢⎣

⎡= αλα |

liqliq h

Nu



]The brackets [ reads maximum of a and b. ba | 3.6 Description of rupture model VessFire calculates the stress in the shell based on the steel temperature and the pressure inside the vessel. The model used is strictly applicable for thin walled vessels. However, the model represents a conservative approach for thick walled vessels and as such is on the safe side. The tensions are calculated along two axes, the longitudinal and the circumferential direction. The tension in longitudinal direction is calculated using

12

0

−⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

i

yl

RR

PPσ

The circumferential tension

( )( )b

RRPP ic

Δ+−= 0σ

where

bERPR

R iy=Δ

ΔR is the increased radius caused by the pressure in the vessel, b is the wall thickness, E the modulus of elasticity, Ri the inner radius, Ry the outer radius and P0 the atmospheric pressure.

The resulting tension is calculated based on the von Mises-hypothesis

clcle σσσσσ −+= 22 The equivalent tension σe is compared with the material stress that is decided as rupture criteria. For the time being, there is no general agreed rupture criteria defined. It is little known about the rupture mechanism for a vessel shell exposed to fire. The rupture criteria used in VessFire is consequently a choice among many possibilities. Figure 5 shows a stylistic stress–strain relationship for carbon steel. For carbon steel, yield stress is a definite point that can be observe. For most materials, the yield point is not easy to observe. For that reason, the yield stress is replaced with a 0.2% deformation limit. Figure 6 shows a stylistic stress–strain relationship typical for most metallic materials. The ultimate tensile stress is at the point where the material breaks.



σ p,T

σ y,T

σ u,T

εp,T

Stress σa

Strain εFigure 5 Stress-strain relationship for

carbon steel including hardening

σ 0.2,T

σ u,T

ε0.2,T

Stress σa

Strain ε Figure 6 Stress-strain relationship for steel

Exposed to heat the stress-strain curve flattens as the material temperature increase. This effect is expressed with a reduction factor as function of temperature for the respective stress definitions. For the yield stress this is defined as

20,2.0

,2.0)(σσ TTF =

VessFire is using the yield stress as acceptance criteria for the vessel integrity. As long as σe < σ0.2,T integrity of the vessel is maintained. When σe ≥ σ0.2,T the vessel is outside the criteria.

An alternative could be to use the ultimate tensile stress, but the safety margin is then reduced. This is a question about safety philosophy and not dependent on VessFire as such. 3.7 Material properties for steel and insulation Besides the thermodynamic properties for the inventory as described in chapter 3.4, VessFire is using material properties for steel and insulation. The properties used are: density, specific heat capacity, thermal conductivity and the reduction function for the yield stress. Examples for the properties are showed below for carbon steel as function of temperature. The density for steel and insulation material is not considered a function of temperature in VessFire. Density for steel is set constant to 7850 kg/m3, density for insulation is dependent on the material.



Specific heat for carbon steel

0

1000

2000

3000

4000

5000

6000

300 500 700 900 1100 1300Temperature [K]

J/kg

K

Figure 7 The figure shows specific heat capacity for carbon steel as function of temperature. The

curve is taken from the European standard prEN 1993-1-2.

0

0.2

0.4

0.6

0.8

1

1.2

300 500 700 900 1100 1300Temperature [K]

F-fa

ctor Yield Stress

Figure 8 The figure shows the F-factor for yield stress (σ0.2,T) of carbon steel as function of

temperature. The curve is taken from the European standard prEN 1993-1-2.



Conductivity for carbon steel

0

10

20

30

40

50

60

300 500 700 900 1100 1300Temperature [K]

W/m

K

Figure 9 The figure shows the thermal conductivity for carbon steel as function of temperature.

The curve is taken from the European standard prEN 1993-1-2.

4 Validation 4.1 Exposure of a spool piece (cylinder), dry and partly filled with water Some small-scale experiment was performed on a 1060 mm long cylinder with inner diameter 177 mm and material thickness of 12 mm. The cylinder was exposed to heat load varying from 20 to 260 kW/m2. The exposure was done by an element heated by electricity. The experiments are documented in ref. 13. The cylinder was completely closed in one end. At the other end there was a 50 mm opening to the atmosphere, see Figure 10.

Figure 10 Experimental upset. The cylinder is surrounded by heat element consisting of a thin

nickel foil.

Two cases where calculated with VessFire. On case (case 5) where the dry cylinder is exposed to heat and another case (case 7) where the cylinder is partly filled with water and exposed to heat.

4.1.1 Dry cylinder exposed to heat This calculation correspond to the experiment no. 5 in ref. 13. The radial emissivity for the cylinder surface was 0.8 and the heat element emissivity was 0.9. The emissivity for the heat element was estimated based on measurements.



Maximum and minimum heat flux

0

20 000

40 000

60 000

80 000

100 000

120 000

140 000

0 1 2 3 4 5 6 7

Time [min]

Hea

t flu

x [W

/m2]

8

Maximum heat flux Minimum heat flux Experimental heat load

Figure 11 The figure shows the heat load from the experiment compared to the heat load used in

the calculations as function of time. Here the maximum and minimum heat load is the same.

Maximum and minimum temperature in vessel shell

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7

Time [min]

Tem

pera

ture

ves

sel s

hell

[°C

]

8

Average calculated temperature T1 Top 0.5 T5 Top 0.25

Figure 12 The figure shows the steel temperature for the case. The temperature T1 is measured on

top of the cylinder 500 mm from the exit opening. The temperature T5 is measured 250 mm from the exit opening.

4.1.2 Cylinder partly filled with water This calculation correspond to the experiment no. 7 in ref. 13. The cylinder was initially filled with 1 kg water. The radial emissivity for the cylinder surface was 0.8 and the heat element emissivity was 0.9. The emissivity for the heat element was estimated based on measurements.



Maximum and minimum heat flux from flame

0

10 000

20 000

30 000

40 000

50 000

60 000

70 000

0 1 2 3 4 5 6 7 8 9 1

Time [min]

Hea

t flu

x [W

/m2]

0

Maximum heat flux Minimum heat flux kW/m2

Figure 13 The figure shows the heat load from the experiment compared to the heat load used in

the calculations as function of time. Here the maximum and minimum heat load is the same.

Maximum and minimum temperature in vessel shell

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0 1 2 3 4 5 6 7 8 9 10Time [min]

Tem

pera

ture

ves

sel s

hell

[°C

]

Max. steel temperature Min. steel temperature T1 Topp 0.5

T4 Bottom 0.5 T6 Bottom 0.25 T5 Topp 0.25

Figure 14 The figure shows the steel temperature for case 7. The temperature T1 is measured on top of the cylinder 500 mm from the exit opening. The temperature T5 is measured 250 mm from the exit opening. The temperatures at the bottom, T4 and T6, are located at the bottom of the cylinder in respective 500 and 250 mm from the cylinder exit.



Time History of the Temperature of Gas and Liquid

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0 1 2 3 4 5 6 7 8 9 10

Time [min]

Tem

pera

ture

[°C

]

Calculated temperature mist Calculated temperature waterT7 Water mist T8 Water

Figure 15 The figure shows the temperature in the water and the water mist compared to the

calculations.

Time History of Mass in the Vessel

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10Time [min]

Mas

s liq

uid

[kg]

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

Mas

s ga

s [k

g]

Mass liquid Sum Mass Mass water Mass gas Mass steam

Figure 16 The calculated mass balance of the cylinder is shown in the figure . The “mas gas” line

indicate the air content.

4.2 Blowdown of a vessel filled with air This case is based on an experiment performed at Cowley, England in 1968, ref. 14. A horizontal cylindrical gas storage vessel, about 48 m long and 4 m in diameter (volume 525 m3 and dry weight 127 000 kg) was pressurized with air. The tank had an initial pressure of 21.5 bar a. It was than depressurized during a period of 2 hours with a constant release rate. The documentation available does not indicate how this was done, but having reached a sub-critical pressure inside the vessel (1.8 bar a) it is assumed in the calculations that a sub-critical flow is established. It is also assumed that the vessel and the air temperature initial were of the same magnitude. The result of the calculation is shown in the figure below.



-40.00

-35.00

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

0 50 100 150 200

Time [min.]

Tem

pera

ture

[°C

]

-

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Rel

ease

rate

[kg/

s]

Calculated steel temperature Air temperature, experimentSteel temperature, experiment Calculated air tempeperatureCalculated release rate

Figure 17 The figure shows calculated and measured air and steel temperature. The release rate is also indicated. After 2 hours, it is assumed that the orifice flow is sub-critical.

4.3 Vessel partly filled with propane and exposed to fire This case is based on experiments documented in ref. 15. A LPG vessel is exposed to an engulfing fire from a pool of kerosene. Results are reported for different filling levels. The one used here is the 22 volume % filling. The vessel was filled with commercial propane. In the calculations, 95 mol% propane and 5 mol% normal butane were used. The outer diameter of the vessel was 1.7 m and the length 4.88 m (TT), giving a total volume of 10.25 m3. The wall thickness of the shell was 11.85 mm. The initial pressure was set to 5.5 bar a, and the initial temperature of the inventory was 5.7 °C. Two PSV each with an effective area of 8.87 10-4 m2 and an opening pressure of 14.3 bar a (fully opened at 15.5 bar a), where installed. The average heat flux measured with heat flux thermocouples is showed in Figure 18. The vessel was originally built as a road tanker. For that reason it is assumed, in the calculations that the vessel is made of stainless steel. The flame emissivity is set to unity and the surface emissivity to 0.7.



0

20 000

40 000

60 000

80 000

100 000

120 000

140 000

0 2 4 6 8 10 12

Time [min]

Hea

t flu

x [W

/m2]

14

Maximum heat flux Minimum heat flux Measured flux

Figure 18 Measured and applied heat flux for the case. It was reported that the fluxes varied

around the tank, but only the average flux where available. The highest flux is only applied for a small part of the vessel and did not influence the inventory. It was applied just to indicate the magnitude of the heat load necessary to achieve the highest steel temperature reported.

Maximum temperature in vessel shell

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0 2 4 6 8 10 12 14

Time [min]

Tem

pera

ture

ves

sel s

hell

[°C

]

Max. steel temperature Max.measured steel

Figure 19 The figure shows the maximum measured shell temperature and the maximum calculated temperature. Temperature differences were measured on the shell in the range of 170 °C.



Time History of the Temperature of Gas and Liquid

0.00

50.00

100.00

150.00

200.00

250.00

0 2 4 6 8 10 12 14 16

Time [min]

Tem

pera

ture

[°C

]

Calculated gas Calculated liquid Measured mean, gas Measured mean, liquid

Figure 20 Calculated temperature of liquid and gas compared to measured values.

Time History of Internal Pressure of Vessel

0

200

400

600

800

1 000

1 200

1 400

1 600

0 5 10 15 20 25 30 35 40

Time [min]

Pres

sure

[kPa

]

Calculated pressure Measured pressure

Figure 21 The figure shows the measured and calculated pressure history. The opening and closing of the PSV are dependent on the type PSV applied. It is not known what kind of PSV that was applied in the experiments. In the calculation, the triangular type (see User Manual) is used.

4.4 Conclusion The validation examples presented represents a range of dimensions and vessel inventory. The results are in good agreement with the experiments. Nevertheless, engineering judgement should always be practised whatever simulation is performed. Even if VessFire is designed carefully and tested for many applications, there might be a variation of the accuracy. This has to be considered for results from VessFire as well as for other simulation systems.



Development of VessFire is a continuous work. As more test cases are available, the validation will proceed giving a staidly better product. If for any reason there is doubt about the results that VessFire produce, please report to Petrell AS.

5 Reference list

1. “VessFire” User Manual, Geir Berge, Petrell as

2. C. Hirsch, Numerical Computation of Internal and External Flows, Volume 1, John Wiley & Sons1994

3. S.W. Yuan “Foundation of Fluid Mechanics”, Prentice-Hall International, Inc., London

4. NIST Standard Reference Database 4, NIST Thermophysical Properties of Hydrocarbon Mixtures Database. (SUPERTRAPP). Version 3.1. February 2003. U.S. Department of Commerce, National Institute of Standards and Technology, Gaithersburg, MD 20899

5. Robert C. Raid, John M. Prausnitz and Bruce E. Poling The Properties of Gases & Liquids. Forth Edition, McGraw-Hill International Editions, 1988

6. NIST Standard Reference Database 10, NIST/ASME Steam Properties, Version 2.2 U.S. Department of Commerce, Technology Administration, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Maryland 20899

7. W.L. McCabe and J.C. Smith “Unit Operations of Chemical Engineering”, 1976

8. DUBBEL, Taschenbuch für den Maschinenbau, 13. Auflage, Springer-Verlag 1970

9. Frank Kreith, Principles of Heat Transfer. Third edition. Intext educational publishers, 1973

10. M. Jacob, Heat transfer, Vol. 1, Wiley 1967

11. W.M. Rohsenow, A method of correlating Heat Transfer Data for Surface Boiling Liquids, Trans. ASME, 74, p969, 1952

12. Frank P. Incropera, David P. DeWitt, “Fundamentals of heat and mass transfer”. John Wiley & Sons. Forth edition. 1996

13. G. Berge & Ø. Brandt, ”Brannlast for prosessutstyr”, SINTEF NBL, report no. A03111, 2003.

14. W.H.Brigges and C.J. Marchant, “High Pressure Gas Storage Installations”, London & Southern Junior Gas Association, April 1969

15. K. Modie, L.T. Cowley, R.B. Denny and I. Williams, “Fire Engulfment Tests on a 5 Tonne LPG Tank”, J. of Hazardous Materilas, vol. 20, p55, 1988

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