Thermal combustion and oxygen chemisorption of wood exposed to low temperature long term heating 2

Water evaporation acts as a heat source term in the energy balance, and contributes to physical processes of heat and mass transfer in the heating of wood.. Water evaporation in hygrosco

Chapter Two: Literature Review

2 Introduction

The heating of wood involves physical changes such as enthalpy and moisture

content One of the major links between temperature and moisture changes is water

evaporation Water evaporation acts as a heat source term in the energy balance, and

contributes to physical processes of heat and mass transfer in the heating of wood This

chapter reviews first the chemical changes i.e pyrolysis and physical processes of heat

and mass transfer within the framework of wood combustion so that any addition,

alteration and omission of physical variables in the mathematical formulation could be

better understood in terms of its impact Because water evaporation is an important link

in wood heating, the different formulations on modeling of evaporation in wood heating

are also reviewed The objective is to elucidate the most optimum way to represent this

physical process in the modelling of wood heating and combustion, when the evaporation

front has recessed into wood

There have been different modeling approaches towards evaporation in wood heating

Using one approach instead of the other represents a different understanding to the

physical process of evaporation in wood drying Water evaporation in hygroscopic wood

is primarily concerned with the changes in equilibrium pressure of water vapour with

temperature and moisture content; this chapter hence first reviews the equilibrium and the

non-equilibrium approaches The different principles and formulations are discussed, and

the problems for applications in wood heating are evaluated with respect to both

low-temperature and high-low-temperature drying Alternative approaches such as the desorption

kinetics approach and the evaporation temperature approach are also discussed

2.1 Reviews of physical and chemical studies in wood combustion

Combustion is a complex problem involving solid-phase and gas-phase

phenomena For bench-scale methods such as Cone Calorimeter, analysis is mainly on

solid-phase phenomena; gas-phase diffusion and chemical kinetics are relatively

unimportant for this scale of evaluation, involving less complex geometry (Janssens

1991a) Chemical reaction and the heat and mass transfer processes constitute a complete

solid-phase phenomenon Chemical and physical processes however do not play equal

parts in thermal model This review considers a comprehensive combustion model that

includes pyrolysis as well as heat and mass transfer in the formulation of a mathematical

model

2.1.1 Heat and mass transfer in solid phase

In pure thermal models, heat transfer is solely accounted by conduction The flow

of pyrolysate gases (henceforth known as “volatiles”) is not considered in the energy

equation In the respective one-dimensional and three-dimensional model of Bamford et

term with thermal decomposition described by a first-order Arrhenius equation, acting as

a heat source term The convective heat transfer due to the flow of volatiles was not

included Such pure thermal models are often employed to limit the problems as a

conduction case, so that useful insights could be obtained to form analytical solutions

Janssens (1993) has used a thermal model to successfully correlate ignition with thermal

properties of wood slabs Besides, pure conduction problems are also widely used to

study ignition in materials that are irradiated on one side and lose heat by Newtonian

cooling (Simms 1960)

There came the findings from Kanury and Blackshear (1970a and 1970b) They studied

the convection of volatiles in a pyrolysing solid and demonstrated the importance of

internal convection to the overall heat balance They examined the relative magnitude of

convection term to conduction term, and showed that the Peclet number is greater than

0.1 Peclet number is a dimensionless number used in calculations involving convective

heat transfer; it is the ratio of thermal energy convected to the fluid to the thermal energy

conducted within the fluid Peclet number is in fact a product of Reynolds number and

Prandtl number, which can be expressed as ρ∗C p∗V∞∗(T1−T0) /l k∗(T1−T0) /l2 The finding that Peclet number was greater than 0.1 in this case strongly endorsed the

significance of internal convective heat transfer In addition, their research further

pointed out that the effect of convection would increase in tandem with the corresponding

increase in specimen’s size Internal convection of volatiles was subsequently included in

the energy equation of many pyrolysis models (Kanury and Blackshear 1970b, Kung

1972, Kung and Kalelkar 1973, Kansa, Perlee and Chaiken 1977, Boonmee 2004) The

energy transport equations in these works however did not include a convective heat

transfer term for the flow of water vapour; moisture was either not considered, or not

treated explicitly Kung (1972) discussed the significance of both the outward

convection of volatiles and char conductivity on the pyrolysis wave propagation, but did

not consider the evaporation of moisture in wood Kansa et al (1977) incorporated the

momentum equation for the movement of volatiles in solid but not one for volatiles

Boonmee (2004) considered the effect of water vaporisation to be insignificant in the

case of oven-dry wood and ignored convection of vapour on heat transfer

Vapour was added to the energy equation in some models on the ground that the

vaporisation could be significant on the overall heat balance Chan et al (1985), Fredlund

(1988), Alves and Figueiredo (1989) and Yuen (1998) have included moisture

evaporation as an additional heat source term, treating the latent heat of evaporation as

heat of reaction Convective heat transfer due to vapour was also added alongside

convection of volatiles in the energy transport equation The inclusion of moisture

evaporation as a heat source term creates a heat sink in the energy balance as it draws

heat from inside the solid to vaporise the moisture Zhang and Datta (2004) showed that

the conventional treatment of moisture evaporation as a heat source term could create

problems for low rate drying or low heating of wood The heat sink effect by moisture

evaporation causes the temperature to fall below the actual temperature where the initial

temperature remains fairly constant for initial drying

For models that accounted for the production of volatiles, alone or in combination with

water vapours, many of these models (Kung 1972, Kung and Kalelkar 1973, Kansa et al

1977, Chan et al 1985, Boonmee 2004) have assumed that these volatiles and vapours

escape instantaneously to the surface once they are formed In doing so, these models

have assumed, as well as limited, the flow of volatiles and vapour strictly in the

longitudinal direction, since wood has a large permeability along grain, of which the ratio

of axial to transverse permeability for softwoods is approximately 20,000 (Siau 1984);

the large axial permeability permits relative ease of escape The velocity of the volatiles

and vapour are given by the flow field which of course has to satisfy the continuity

equation There is no accumulation of volatiles and vapour, thereby eliminating

accumulation term in the continuity equation Since it is not a pressure-driven flow,

pressure is assumed constant Such simplification in mass transfer is often made so that

analytical models ascribed to certain complex combustion phenomenon can be made

tractable (Boonmee 2004)

Driving forces sometimes arise naturally in cases where there is a steep pressure build-up

resulting in a pressure gradient, or concentration difference that promotes diffusion In

both Fredlund’s model (1993) and Yuen’s model (1998), a pressure equation is provided

as a driving force In their models, mass transfer of volatiles and vapour is based on gas

flows driven by pressure gradients, the flow of which conforms to Darcy’s law Both

models allow the pressure to change with porosity of the wood slab, thereby creating the

pressure in the system The total pressure is then obtained according to Dalton’s law as

the sum of the partial pressures of water vapour and volatiles Mass source terms are

created in the continuity equation to allow accumulation of volatiles and evaporation of

vapour The only difference between the two mass transfer models is that in Fredlund’s

work, additional pressure changes arising from elevating temperature that cause gases to

expand in a constant volume according to the universal gas law have been provided for

Nonetheless, this additional pressure term is small as compared to pressure change

arising from vaporisation of water in rapid heating rates In the latter, rapid vaporisation

results in steep pressure gradient

In both Fredlund’s and Yuen’s models, moisture flow takes place mainly in vapour phase

Moisture flow can occur in liquid phase, but Fredlund and Yuen have both adopted the

high-temperature drying model proposed by Alves and Figueiredo (1989) which ignored

free water movement The same assumption of eliminating free water movement has also

been adopted in all the foregoing models that do not use pressure-driven flow For vapour

and volatiles transport, all models have implicitly (those with pressure driven flow) and

explicitly (those do not employ pressure-driven flow) excluded vapour diffusion The

assumption that water vapour/ carrier gas diffusion is much slower than vapour

convection reduces the model validity to high-temperature drying i.e above water boiling

point

2.2 Evaporation zone in drying model

Modelling of internal evaporation rate will be needed when internal evaporation is

later stage of drying when diffusivity of liquid becomes small due to diminishing

moisture content The escaping water flux through the surface decreases, resulting in a

drier surface and a decreasing surface evaporation rate Eventually, the evaporation front

moves inwards

Figure 2.1 shows a conceptual model of high-temperature drying in wood where

evaporation zone has retreated inwards, creating an evaporation zone within the

pyrolysing wood (Stanish, Schajer and Kayihan 1986, Farid 2002) Evaporation takes

place in this evaporation zone since it is the location where there is the largest moisture

gradient (Ilic and Turner 1986) The water vapour partly migrates towards and escapes

through the exposed surface A fraction also migrates in the opposite direction, and

re-condenses at a colder inner region This high-temperature drying model also models the

formation of cracks and fissures at the char surface, since high-temperature drying occurs

just incipient of or in tandem with flaming combustion The formation of cracks and

fissures greatly affects the heat and mass transfer between flame and the solid, and hence

the equilibrium of vapour pressure profile at the surface

Figure 2.1: Conceptual model of high-temperature drying in wood

(Drying model adapted from Janssens 2004, ©Fire and Materials)

The rate at which the evaporation zone moves into the solid can be calculated by heat

conduction (Williams, 1953) The method divides the solid into two regions separated by

an isothermal plane – the 100°C plateau, the plane of vaporisation The rate at which this

plane moves at any depth r is assumed to depend only upon the net rate of heat transfer

by conduction to that depth The equation for calculating r at time tis given by

1/ 2

1/ 2

( )

constant2( )

7 Flame

3 Heat transfer

movement

2exp( )

z

β β

βπ

∞

Figure 2.2 shows the depth ( )r of the plane of vaporisation (interface B) calculated by the

heat conduction method It has been pointed out that in hygroscopic materials, there is no

abrupt interface between the dry zone (Zone A) and the wet zone (Zone C) (Schrader and

Litchfield 1992) The capillary effect still causes water diffusion and vapour generation

depends on moisture content (X) and temperature (T) So, evaporation takes place in a

zone instead of on a sharp interface as shown as “interface B” in Figure 2.2

Figure 2.2 Evaporation front calculated by heat conduction in high-temperature drying

(Simplified model of high-temperature drying reproduced from Alves and Figueiredo

1989, ©Chemical Engineering Science)

Incorporating the evaporation zone, instead of an evaporation front into a drying model

yields a high-temperature drying model that has been widely used in pyrolysis studies of

wood It has thus been commonly referred to as the “conventional high-temperature

X= 0 Zone A

Zone C

X = constant > 0

r

drying model” (See Figure 2.3) Vapours are generated in Zone B (evaporation zone)

when temperature reaches the moisture boiling point, or evaporation temperature

Janssens (2004) pointed out that since water is adsorbed to cell walls, evaporation

requires more energy than needed to boil free water and may occur at temperatures

exceeding 100°C Alves and Figueiredo (1989) proposed that the evaporation

temperature is governed by the moisture content (X) on dry basis For 1% < X < 14%, the

evaporation temperature is given as

Yuen (1998) suggested that when the moisture content in wood is less than 1%, the

evaporation temperature may be assumed to be 473K For wood with moisture content >

14%, the evaporation temperature can be assumed to occur at 373K, with negligible

discontinuity and error (Alves and Figueiredo, 1989; Yuen, 1998)

Figure 2.3: Conventional high-temperature drying model

(Drying model reproduced from Alves et al 1989, ©Chemical Engineering Science)

2.3 Formulation of evaporation rate

To include evaporation as an internal term in a drying model, there is a need to

describe the rate of evaporation R in the model, through the time to reach equilibrium ev

between liquid and vapour Equilibrium approach assumes that equilibrium between

water and vapour is reached instantaneously; the rate of evaporation is formulated with a

known vapour pressure p Non-equilibrium approach on the other hand does not assume v

water vapour to be in equilibrium with liquid water; vapour pressure remains an unknown

variable Non-equilibrium approach needs both the equilibrium vapour pressure and the

parameter indicating the rate of evaporation

Zone C T< Tev

Tev (X) Vapour convection

2.4 Equilibrium approach

Equilibrium approach assumes that vapour and water are in phase equilibrium at

any time (Plumb, Spolek and Olmstead 1985, Stanish et al 1986, Crapsite, Whitaker and

Rotstein 1988, Ni, Datta and Torrance 1999) According to ideal gas law, the amount of

vapour per unit volume V is given by

v v

p M V

RT

In equilibrium approach, vapour pressure is fixed so long as temperature and/or water

content are given, where

The assumption that vaporization is sufficiently rapid for complete saturation of vapour

in the pores – so long as there is water in the liquid phase at the point of consideration –

further simplifies the relations between p and v p v sat, set out in Equation (2.6), so that

,

v v sat

By determining the vapour pressure, V or p is no longer an independent variable in the v

system of conservation equations The rate of evaporation can be formulated from the

continuity equation and readily solved given the known state variables such as

temperature and pressure distribution In Yuen (1998) three-dimensional model of

pressure-driven flows, the rate of evaporation R , expressed in the continuity equation, ev

requires the solution of total pressure inside the system where

j=x y zdirections; η being the kinematic viscosity of gaseous mixture in the solid In tYuen’s model, the total pressure p is readily obtained according to Dalton’s law as the s

sum of partial pressures of vapour, volatiles and dry air, i.e p s = p g+ p v+ p i Alves and Figueiredo (1989) also formulated the rate of evaporation assuming local moisture-

vapour equilibrium from their heating model which does not consider mass transfer The

rate of evaporation R is formulated from their one-dimensional energy balance ev

comprising of a thermal decomposition scheme of six constituent components where