Black liquor conbustion in Karft Recovery Boiler-Numerical Modelling

ISRN KTH/MSE--02/12--SE+ENERGY/AVH

ISBN 91-7283-301-7

Black Liquor Combustion in Kraft Recovery Boilers-Numerical Modelling

Doctoral thesis by

Reza Fakhrai

STOCKHOLM DEPARTMENT OF MATERIAL SCIENCE AND ENGINEERING

K UNGL

T EKNISKA

H ÖGSKOLAN

Black Liquor Combustion in Kraft Recovery Boilers-Numerical Modelling

Doctoral thesis by

Reza Fakhrai

Department of Material Science and Engineering Division of Energy and Furnace Technology

Royal Institute of Technology SE-100 44 Stockholm

Sweden

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm, framlägges för offentlig granskning för avläggande av teknisk doktorsexamen, onsdagen den 29 maj

2002 kl. 10.00 i E1, Elektroteknik, Kungliga Tekniska Högskolan, Stockholm

ISRN KTH/MSE--02/12--SE+ENERGY/AVH

ISBN 91-7283-301-7

Black Liquor Combustion in Kraft Recovery Boilers-Numerical Modelling

Reza Fakhrai

Dissertation for the degree of doctor of Philosophy in Energy and Furnace Technology (TeknD) 2000 Royal Institute of Technology

Department of Material Science and Engineering Division of Energy and Furnace Technology S-100 44 Stockholm, Sweden

Abstract

Black liquor is a by-product, which results from digestion of wood chip in alkaline pulping processes. After the evaporation process the solid in black liquor increases up to 80% and it is combustible. Black liquor is conventionally burned in a large unit called Kraft recovery boiler, for the dual purposes of energy production and recovery of the pulping chemicals.

Kraft recovery boiler model in the present context refers to the numerical simulation for solving partial differential equations governing the characteristics phenomenon in a Kraft recovery furnace. The model provides an analytical tool and it is best appreciated when the numerical simulations and the measurement techniques are linked to the real industrial problem and the industry that used it. The purpose of this study was to enhance the understanding of the processes involved in a Kraft recovery furnace through mathematical modelling and to keep the code in state-of-art.

It is essential to consider the path of every drop in the cavity of a Kraft recovery furnace. In this process the liquor may accumulate on the walls and depending on the gravity or the flow pattern at the wall it periodically sloughs off and falls to the bed. As new components in the general framework of the Kraft recovery boiler model, the interaction of burning drops and walls in a recovery boiler considering the above mentioned was modelled. The importance of a bed model and its effect on the predicted temperature in the furnace cavity was examined.

The heterogeneous conditions in a Kraft recovery furnace with significant local variation of concentration of constituent gas components and temperature level/gradient could affect NO production rate. The NOx model developed in this work considers the NO formation from fuel NO and prompt NO. It is assumed that the fuel nitrogen in black liquor is released either via devolatilization or char combustion.

Further work focussed on estimation of the temperature level near/on the bed based on the mass distribution on the char bed. The model was also used to examine the effects of changes in black liquor properties (used in Kraft recovery furnace model) namely effect of the swelling and solid content versus the Kraft recovery furnace performance.

The results illuminate also the potential of numerical modelling method as a promising tool to deal with the complicated combustion processes even for practical application in the industry.

ISRN KTH/MSE--02/12--SE+ENERGY/AVH

ISBN 91-7283-301-7

Supplements

The work presented here this thesis is mainly based on the following publications, referred by Roman numerical

I. Theoretical Analysis of Interaction between Fuel Drop and Walls during Black Liquor Combustion in A Kraft Recovery Furnace. Energy conversion & management- an International Journal, RAN2001 Special Issues, Nagoya, Japan Dec. 14-17, 2001

II. Combustion Performance of the Kraft Recovery Boiler Versus Black Liquor Properties – Numerical Study, Submitted to Energy Conversion & Management

III. Use of a Computer Model for Evaluation of Combustion and NOx Control Alternatives

in a Kraft Recovery Boiler, International Chemical Recovery Conference, Tappi, Tampa

Florida June 1-4 1998

Acknowledgment

The work in this thesis has been performed within the Energy and Furnace technology, Material Science department, Royal institute of technology (KTH) Stockholm Sweden, during the years 1997-2002. Energi Myndigheten (STEM), Ångpannföreningen forskningstiftelse (ÅF) and Värmeforsk financed the project.

I wish to convey my sincerest thanks to the leader of the Energy and Furnace division, Associate Professor Wlodek Blasiak, for giving me the opportunity to work in the group and to write my thesis under his direction, and for constantly providing me encouragement, guidance and moral support. I appreciate his commitment and utmost professionalism in all regards.

I also thank the other members of the Material Science department Prof. Seshadri Seetharaman, Prof. Pär Jönsson who made me feel like a colleague more than a student during the years I have worked at the department. I would also like to take the opportunity to thank my co-workers Jan Bong, Simon Lille who were my friends when I needed one.

I would like to thank my family, particularly my father, Abas who passed away 1999 and my mother Golestan, for their support and encouragement throughout my long academic career.

Finally, my heartfelt thanks to my dear wife “Neda” for her patience, concern and

understanding, my son “Sam” and my daughter “Ella Mina” who inspired me to aim high and

motivated me to achieve it.

Table of Contents

Abstract I

Supplements II

Acknowledgements III

Table of Contents 1V

Nomenclature VII

Thesis Summary

1. Introduction 1

1.1 Black Liquor 2

1.2 Recovery Furnace 2

1.3 Objectives 4

2. Liteature Review 5

2.1 Flow Field 5

2.2 The In-flight Combustion of Balck Liquor Droplets 6

2.3 The Char bed 8

2.4 Pollutant Formation 9

2.5 Gird Generation and Geometry 11

2.6 Model Validation 12

2.7 Concluding Remarks 13

3. Development of Model of Recovery Furnace Used in

This Work 14

3.1 Geometry of the Furnace Used in This work 14 3.1.1

Conventional Firing Strategy (CF) 15

3.1.2

Rotational Firing Strategy (RF) 17

3.2 Black Liquor Combustion 20

3.2.1 Spray 20

3.2.2 In-flight Drop Combustion 23 3.2.3 Char Bed Processes 24

3.2.4

The Interaction Between Drops and the Walls in the Recovery

Furnace

24

3.3 NO Modeling 28

3.3.1 Thermal NO 28

3.3.2 Turbulence Chemistry Interaction 29

3.3.3 Prompt NO 30

3.3.4 Fuel NO 31

4. Result and Disussion 33

4.1 Estimation of Surface Temperature and Mass Distribution

on a Char Bed 33

4.2 Effect of the Physical Properties of Liquor on The Furnace

Performance 36

4.2.1 Effect of the Swelling on the Path of a Droplet 36

4.3 Effect of the Wall-burning Model on the Overall Recovery

Furnace Model performance 40

4.4 Prediction of the NO Level in Recovery Furnace 42

5. Conclusions 46

References 48

Appendix

Nomenclature

A

int

Internal surface area of carbon in the bed (m

²

). The value of the internal surface area of Kraft chars was taken from the experimental data obtained with two experimental chars obtained

A

sp

Internal specific surface area of char, taken as 11000, m

²

/kg C

C, bed

Molar concentration of carbon in the bed, mol/m

³

C

SO4

Sulphate concentration, mol SO

4

/mol Na

2

C

C

Carbon concentration, mol C/mole Na

2

C

Na2, bed

Sodium concentration, moles Na

2

/bed volume, mol/m

³

M

d

Mass of the drop/parcel, kg

M

char, Na

Total amount of sodium in the drop parcels, kg M

char, S

Total amount of sulphur in the drop parcels, kg.

M

d0

Initial mass of the drop/parcel, kg

M

i

, M

j

Molecular weight of corresponding gas species

P

g

Local pressure of gas mixture at the cell adjacent to the char bed, bar R

O2, overall

Overall oxidation rate,

R

CO2, overall

Overall CO

2

gasification rate R

H2O, overall

Overall H

2

O gasification rate

V

bed

Char bed volume per unit surface area (m

³

/m

²

), X

H20

Mass fraction of water

X

VM

Mass fraction of volatiles X

C

Mass fraction of char X

Smelt

Mass fraction of smelt

X

Na

, X

S

Initial mass fraction of sodium and sulphur in the drop parcel.

Y

CO2

, Y

H2O

Molar fractions of carbon dioxide, water vapour, the cell adjacent to the char bed.

Y

CO

, Y

H2

Molar fractions of carbon monoxide, and hydrogen at the cell adjacent to the char bed.

Y

O2

Local oxygen mole fraction at the cell adjacent to the char bed.

β Multiplier for Cameron-Grace reduction rate

η Sumnicht factor, for carbon surface area available for direct oxidation. and has

a value of 0.6, which corresponds to 50% completion of sulphur reduction

⁵⁸

from the Institute of Paper Chemistry’s drop tube furnace, which had a value

of about 11 m

²

/g.

1. Introduction

In the 1970’s the paper industry in Sweden started to make large scales structural changes to the production of paper. These modifications continued during the 1980’s and 1990’s. The number of the paper making units was 47 in 1998, a reduction by 8 units since 1988.

Nevertheless, the total energy used by the industry increased because of environmental regulation [1]. The industry is almost independent on oil, but it requires heat for evaporation plant. Higher electricity costs as a result of nuclear phase-out seems to be the real threat to the industry [2]. In order to reduce the energy consumption, the building new production line or modernisation of the existing one, are possible alternatives. The other option would be, to increase production of the required heat by using the spent liquor. The industry has a long tradition in using residual oil. Heat extraction, from compound found in wood as a resulting of the chemical pulping process can supply a major part of the energy needed by the industry.

Of the total energy used, its bulk is from the internal fuel (black liquor and bio-mass). 74% of the total energy used, is self-produced with black liquor contributing 63% in 1998.

Chemical recovery is a technique used to recover the valuable cooking chemicals, generating large amounts of heat energy by burning the organic material in black liquor and eliminating the black liquor as a danger to the environment. The main objective of the Kraft recovery steps is to minimize, as efficiently as possible, the loss and subsequent makeup of the chemicals used in preparation of the cooking liquor (commonly called white liquor), [Green et al. (3)]. The recovery boiler in this regard is crucial and the bottleneck to the process. In order to improve recovery boiler performance, it is necessary to understand the effects of furnace design furnace operating variables, and liquor quality e.g. fouling and plugging rates, air emissions and combustion stability etc.

One of the tools available in improving the desired operation and design conditions is mathematical modelling. Mathematical modelling of a Kraft recovery furnace is the study of fluid dynamics, combustion and has been under constant development for years. It is commonly accepted as referring to the broad topic encompassing the numerical solution, by computational methods, of the governing equations which describe fluid flow, the set of the Navier-Stokes equations, for example continuity, energy /species concentrations. In Karft recovery model, In-flight burning of liquor and bed burning are the other important components, which are included and affect the gas phase. The essence of the subject of Kraft Recovery furnace is that of judicious compromise between theory and experiment. The goal of using the model is to use the model as a tool in order to enhance the understanding of the phenomena in question and in this case, the recovery furnace in a Kraft cycle.

In the next section, terms: black liquor, recovery boiler and black liquor combustion are

clarified and the relevant processes are introduced.

1.1 Black Liquor

Black liquor is an important resource for steam generation in the pulp and paper industry. It is a substance unique to the pulping process and represents a readily available renewable energy source. It is also one of the few fuels to have been locally produced and used in the countries with a pulping industry. From the point of view of fluid mechanics, black liquor is a liquid.

However, it has two states, fluid and solid. Its main components are inorganic cooking chemicals, lignin and other organic constituents removed from the wood during pulping in the digester, and water. These organic constituents are combined chemically with sodium hydroxide (NaOH) in the form of sodium salts such as Na

2

S, Na

2

CO

3

, Na

2

SO

4

. Some organics may be recovered in the chemical recovery process, such as the mixture of resin and fatty acids known as tall oil, or the turpentine recovered in a liquid separation sequence.

The exact composition of black liquor depends on the wood species, the pulp yield, and the alkali charge used. Considerable differences exist between liquors from different species, and especially between those from hardwood and softwood. An important aspect of black liquor combustion is elemental analysis of the liquor solids, that is, of the percentage by weight of each chemical element in the black liquor solids. Five elements are always present: sodium (Na), sulphur (S), carbon (C), hydrogen (H), and oxygen (O). In some cases, potassium (K) and chorine (Cl) are also present. The approximate composition of black liquor is given in Table 1.

Table 1: Typical elemental composition of black liquor solids and char

Element Present (wt%)

Na 19.17%

S 4.76%

C 35.93%

H 3.56%

O 35.20%

K 1.02%

Cl 0.12%

Inerts 0.24%

Total 100.0%

1.3 Recovery Furnace

A recovery boiler is both an ordinary steam boiler with tubes in the walls, bottom and top of

the furnace that delivers the steam required by the mill and a chemical reactor where sodium

sulphate is reduced to sodium sulphide. A unique characteristic of such boilers is the use of

char bed in the lower furnace. These boilers were developed by Tomlinson, in cooperation

with Babcock and Wilcox, in the early 1930s and contributed to the predominance of the

Kraft process, in which the recovery boiler is a crucial element. The boiler has three critical

functions. First, it uses the chemical energy in the organic portion of the liquor to generate

steam for the mill; second, it plays a major role in the sulphate process as a chemical reactor;

and third, it destroys dissolved organic matter and thus eliminates one type of environmental discharge.

Concentrated black liquor enters the recovery furnace as droplets fired through liquor guns in the walls. Traditionally, two systems are used: either wall firing using one or two oscillating guns, or suspension firing with many oscillating guns located on two of the four walls around the furnace. The droplets then go through a series of processes involving drying, pyrolysis, char gasification and finally homogeneous combustion. Burning of the solid char residue that remains after pyrolysis of the black liquor occurs largely in the char bed that covers the floor of the furnace.

Older recovery boiler designs incorporated tangent tubes or tubes with flat studs backed by refractory. These water wall constructions had thick casing plates on the outside in order to keep the flue gases within the furnace. The walls of modern recovery furnaces are welded walls, also known as membrane walls. They are constructed of vertical tubes, typically 6.4 to 7.6 cm in diameter, set in rows. The tubes are either placed immediately adjacent to one another and continuously welded along the lines of contact or are spaced approximately 1.25 to 2.5 cm apart, connected by a flat fin. In chemical recovery boilers the water wall tube is normally made from ordinary carbon steel.

A series of ducts and boxes introduce the combustion air into the furnace. These open though the boiler walls at various levels, and with different numbers of openings at each level.

Dampers located in the ports, wind boxes, ducts or near the forced draft fan control the air flow.

Primary air nozzles are located approximately 1 m above the furnace floor. Approximately 35 primary air nozzles are located on each of the four walls of a recovery furnace designed for a 1000 ton per day mill. The size of these ports is approximately 5 by 25 cm.

Secondary air nozzles are located approximately 2 m above the furnace floor. The secondary air nozzles are generally large and less numerous than the primary ports. There are 4 to 16 ports on each wall of the furnace, ranging in size from 5 by 25 cm to 12.5 by 67.5 cm.

Tertiary air nozzles are located above the liquor guns approximately 8 m above the floor of the furnace. Tertiary air nozzles are the largest and are usually located on two opposing walls, normally the front and rear walls. Typically, 3 to 8 tertiary ports ranging between 10 by 45 cm and 15 by 75 cm are used on both walls.

The formation of Na

2

S requires local under-stoichiometric conditions. This reduction step is

critical. The only part of the recovery cycle where oxidised sulphur compounds can be

converted to sulphide is during combustion. The inorganic compounds melt and flow out of

the furnace as a mixture of molten salts called “smelt”.

Figure 1 Typical recovery furnace

1.4 Objectives

The work presented here has the following general objectives:

1. Enhance understanding of recovery furnace behaviour.

2. Develop new models and modify the existing model where necessary to keep the recovery furnace model state-of-the-art.

To achieve these goals, attention has been directed to the following:

• Estimating the temperature level near/on the bed based on the mass distribution on the char bed.

• Developing a model that incorporates the interaction of the droplets and the walls in a recovery furnace

• Implementing the NO

x

production/reduction mechanism in the recovery furnace.

• Examining the effects of changes in the properties of black liquor, particularly the effect of swelling and solid content on the performance of a recovery furnace.

It is hoped that the results provided in this thesis illustrate some of the ways CFD can be used

to supplement existing engineering tools and that researchers will be encouraged to tackle

new problems using modelling and to develop new methods as well as extensions and

improvements of the methods presented here.

2. Literature Review

The combustion of black liquor has been studied for more than 40 years. During the1980s there was extensive research in this area in the USA, Canada, Finland and Sweden. These findings underlie the present work. However, achievements in other fields have also contributed to our present understanding of recovery furnace operation. The rapid development of numerical simulation methods has made it possible to simulate a recovery furnace and accurately predict its performance [Blasiak et al. (4)] and has the potential to enhance our understanding of the processes occurring in a recovery furnace.

2.1 Flow field

Among the early achievements using recovery furnace models in literature is the isothermal simulation of the flow field and mixing pattern in a recovery furnace. The gas flow patterns are determined primarily by the furnace geometry, air inlet geometry. In view of this, considerable efforts have been devoted to determine the flow pattern in the recovery furnace.

Jonse and Grace (5) studied the general flow pattern in a recovery furnace, comparing the results of their computational model with experimental cold flow. The framework for the computational modelling techniques was FLUENT. The results showed that the flow pattern and the furnace exit gas velocity distributions have a tremendous effect on the deposition rate on the superheater tubes.

Grace et al. (6), 1989, described the construction of and preliminary results from a three- dimensional mathematical modelling of a Kraft recovery furnace. Their results indicated that gas flow patterns are primarily determined by the geometry of the air inlets. The bed shape, on the other hand, can be affected by the gas flow patterns.

.

Llinares and Chapman (7) used flow modelling to examine a three-level air system. The model was used to evaluate designs in order to determine the best location for introducing air into the furnace. The article gives no information regarding the modelling.

Perchanok et al. (8), investigated the flow pattern in a recovery boiler the results indicated that the flow is often grossly unstable. This unsteadiness was also observed in the physical model of boiler as well.

Bergman and Hjalmarsson. (9) introduced Rotafire, a new firing strategy applied to a number of the secondary air nozzles. Reducing the total open area of these nozzles produced an initial jet velocity of 70–80 m/s. Since the jets work together, this velocity caused vigorous rotation of the gas in the lower furnace. Mathematical modelling was used to support the theory.

Jones and Chapman (10) used computational fluid dynamics to describe two models in order to examine a refined secondary air system. They used big/small air nozzles configuration in secondary level. The results predicted a dramatic improvement in combustion behaviour using big/small secondary design

Salcudean and Gartshore (11) investigated flow pattern and associated transport phenomena

in black liquor recovery boilers and found that aerodynamics is critically important to the

performance of these boilers. They concluded that buoyancy effects are most likely secondary

over large parts of the boiler.

Salcudean et al. (12) presented preliminary computations of the cold flow in a simplified geometry of a recovery boiler. They did not take into account the effect of the char bed shape on the flow since the char bed was not modelled. However, the results indicated that the flow in the secondary level interacts strongly with the upwards flow in the central region of the boiler to form the upwards-rising core.

All of the research discussed so far used symmetry boundary conditions. Modelling just half of the furnace further reduced the mesh size requirements. The resulting mesh provided the optimum resolution and run-time performance possible at the time.

Tao et al. (13) studied Rotafire air system designs. They showed that Rotafire creates a more effective mixing of gases than conventional firing methods, making it possible to achieve higher combustion and thermal efficiency and more evenly distributed gas temperatures and species..

2.2 The In-flight Combustion of Black Liquor Droplets

It has long been understood that black liquor behaves in very unconventional fashion during combustion. Its combustion behaviour is more like that of solid fuels, such as coal, than that of oil or other liquid fuels. During the combustion period, the droplet undergoes drying, devolatilisation, char burning and smelt reaction.

The amount of literature associated with spray modelling in general is huge, and comprehensive results have been presented for a droplet trajectory problem that involves drying, vaporisation and burning [Dwyer (14), Lintries (15), Stockel, (16), Bousfield et al.

1990].

Spielbauer et al. (17), presented droplet size distribution data for the spray from splash-plate and swirl-cone black liquor nozzles. They showed that the distribution is square root normal.

The result also indicated that normalised size distribution does not change, or changes very little, as a function of nozzle geometry, flow conditions and fluid parameters.

Horton et al. (18) studied spray variables including mean droplet size, breadth of spray distribution, and the angle at which liquor is sprayed into the furnace. However, little information is given about the parameters used in the model and symmetry plane was used in order to save CPU.

Empie et al. (19) evaluated two types of commercial nozzles, splash-plate and swirl-cone, with a number of liquors from different mills and found the same qualitative trends for both nozzles, despite differences in the quantitative dependence of droplet diameters on the parameters studied. The two most important variables were the velocity of the jet and the viscosity of the liquor. Increases in the velocity produced sprays with decreasing diameters and increases in the viscosity produced sprays with increasing diameters. Increasing jet diameters also increased the droplet sizes. Correlations showed that the type of liquor did not appear be important. Droplet diameters in these studies generally ranged between 2 and 3 mm.

Helpiö et al. (20) using splash-plate nozzles, focused on the effect of temperature on

atomisation, especially above the boiling point of the liquor. They found that even though the

temperature increase near the boiling point results in an increase in droplet diameters, the phenomenon of flashing, which occurs several degrees above the boiling point, leads to significantly smaller droplet sizes. Droplet diameters in these experiments (liquor with S = 0.698) ranged mostly between 3 and 4 mm, but decreased sharply with temperature to about 2 mm several degrees above the boiling point.

Hupa et al. (21) introduced the use of the single droplet burning technique to measure and characterise the swelling of black liquors during combustion. In their study, they observed a droplet swelling factor (d/d

0

) of 1.3 to 1.8 almost immediately upon contact with the hot gas, which remained constant during the drying period. The average value for a set of 19 determinations was 1.55, with a standard deviation of 0.11. Rapid and much more drastic expansion ensued during volatilisation, reaching maxima exceeding linear ratios of 3 (volumetric up to 35) at the end of that stage. Diameters decreased during char combustion, falling below those of original droplets before burnout.

Hupa et al. (22) published an article on black liquor combustion in which they defined the stages of black liquor combustion as drying, devolatilisation and char burning. Their work with a laboratory furnace enabled them to define three time-periods describing the entire droplet combustion process: drying time, t

i

, from the initial contact with the gas to ignition;

devolatilisation time, t

v

, from the appearance of the flame to maximum expansion; and char- burning time, t

c

. Good empirical correlations were established for all three: t

i

is proportional to the initial droplet diameter, and both t

v

and t

c

are proportional to the 5/3 power of that diameter. They were also able to generate profiles of the swelling and of the droplets’

temperature as a function of the liquor combustion time.

Fricke (23) performed extensive studies of the properties of black liquor and defined some of them by mathematical expressions (Appendix 1).

Jones (24) as well as Grace et al. (6), presented models which included some critical features of Kraft recovery boilers, such as the combustion of black liquor droplets in flight and in the char bed.

Frederick (25), (26), studied the combustion rate models for each of the combustion stages of black liquor. The drying and devolatilisation were limited by the rate of heat input to the particle. In the char burning stage, the burning rate was controlled by mass transport. These studies provided much needed data on such aspects of black liquor combustion as droplet surface temperature, the yield of volatiles during pyrolysis, and the impact of the temperature of the gas flame on swelling behaviour. They also succeeded in simplifying the swelling process somewhat by considering the change in dimensionless droplet diameter (the ratio between the minimum and maximum diameter) as a function of the dimensionless devolatilisation time (the fraction of pyrolysis time). An empirical expression was developed such that the dimensionless droplet diameter was roughly equal to the dimensionless time to the power of 0.8.

Walsh (27) and Hyöty et al. (28), 1989, developed a sub-model for in-flight combustion of

black liquor droplets. Horton et al. (29) studied the key parameters of this model using a

recovery furnace model. The model traces a droplet’s flight path as it simulates the rates and

stages of combustion as well as the locations where water, volatile organics, char carbon, and

inorganic ash portions of the black liquor were transformed from one phase to another. In all

these studies a symmetrical plan was used to save CPU time. However, Quick et al. (30)

pointed out that even when a boiler was geometrically symmetric, flow instabilities and jet interactions could cause major asymmetries in the flow patterns.

Malmgren (31) used analytical solution of partial differential equations to investigate the movement of droplets. The simulation showed that the trajectory of a droplet was influenced by the drag coefficient, mass transfer, its initial properties and variations in its size or density during flight. Rotation of a droplet was less important and the risk of the droplet breaking up due to aerodynamic forces was small in a recovery boiler.

Grace et al. (32) presented a new model of elemental-based black liquor drop burning. The processes of drying, devolatilisation and char burning were treated as occurring in parallel, eliminating the need for arbitrary criteria for transitions between steps. The model gave rate equations for the transfer of individual elements in the black liquor to the gas phase and included a proper treatment of char gasification as well as oxidation.

2.3 The Char Bed

A char bed with a wide active layer ensures stability and consistency in the combustion process in a recovery boiler. However, controlling the burning process and combustion rate in and on a char bed is very difficult. One of the critical issues for recovery boilers is the avoidance of blackout. Blackout occurs when

• heat released above the bed does not reach the bed surface and the gasification process stops (thermal feedback)

• the shape and height of a char bed are such that primary air nozzles are blocked, resulting in incomplete combustion of the released gas [Hough et al. (33), 1985]:

Sumnicht (34), 1989, presented a sub-model for char bed combustion that incorporates several factors that are important for the design of such a model, including the char combustion rate [Brown et al. (35), 1989] and the surface roughness of the char bed. The results suggested that the bed influences gas flow patterns as well as playing an important role in overall char combustion.

Karvinen et al. (36), 1989, developed a char bed model in which the surface of the bed was assumed to be insulated and the air flow of primary jets was uniformly distributed across the whole bed surface. The heat released when droplets hit the bed was also assumed to be uniformly distributed. This model did not take into account the interaction between flowing air, incoming material and burning in the char bed.

Frederick and Hupa (37) developed a char bed model that took the chemical reactions into account and gave the temperature profile of an active zone, the rate at which carbon was burned The model required the mass flow rate of char to the bed and its composition and temperature as input.

Sutinen et al. (38) presented a two-dimensional char bed model linked to the gas atmosphere

above the bed in the furnace. The velocity, temperature and concentrations of gas in the

furnace were solved numerically for the vicinity of the char bed and linked to the chemistry of

the char bed.

Wessel et al. (39) extended the work done by Fiveland et al. (40), 1988. Their model included carbon monoxide oxidation kinetics but did not considered the H

2

and CH

4

in homogeneous chemistry. The char bed surface temperature was given, but no information was supplied regarding the nozzles and conversion rates.

Tao et al. (41) examined char bed geometry using the partial three-dimensional approach.

Their results showed that aerodynamics in the furnace had a strong impact on the performance of a Kraft recovery boiler. Any changes to the air system configuration and the char bed geometry would significantly influence the flow field in the furnace.

Tao et al. (42), 1997, presented a char bed model based on and incorporated into a recovery boiler model. They based their work on the fact that the reaction rate is influenced by the rate of mass transfer of the reacting gases (oxygen, carbon dioxide and water vapour) to the char bed as well as by the kinetics of the reactions of these gases with the carbon in the bed.

Grace (43), 1996, reviewed computer models of recovery boilers and identified two factors that currently limit the ability of models to deal with issues concerning char bed shape and inventory. One is a lack of an adequate model for the char bed inventory. The other is the lack of consensus on what constitutes a good bed, especially in a quantitative sense.

2.4 Pollutant Formation

Control of pollutant emission is an important factor in the design of a modern recovery boiler.

Pollutants of concern include particulate matter, such as soot and fly ash, metal fumes, and various aerosols; the sulphur oxides, SO

2

and SO

3

; unburned and partially burned hydrocarbons, such as aldehydes; oxides of nitrogen, NO

x

, which consist of NO and NO

2

; carbon monoxide, CO; TRS (total reduced sulphur), and greenhouse gases such as N

2

O and CO

2

.

Some of these gaseous emission such as TRS, CO, and volatile organic compounds (VOCs) are destroyed by oxidation. Adjusting the stoichiometry and improving the mixing in the furnace is sufficient to ensure the destruction of these gases. There is thus no need to simulate these species using source/sink methods.

Turns (44) however, pointed out that CO is a major species in rich-combustion products, and that substantial amounts of CO will be produced whenever rich mixtures are used. The other source of CO is quenching by cold surfaces.

In a recovery boiler the flow is unstable. Consequently, there will be local areas of rich and poor combustion. The CO concentration is highly uneven and therefore CO emission could be locally high.

Sricharoenchaikul et al. (45) reported that 30 to 60% of the carbon originally in the black liquor converted to tar. Secondary pyrolysis reactions then produced CO and CO

2

. These results were conformed by several studies.

Sricharoenchaikul et al. (46) investigated sulphur species transformation and sulphate

reduction during the pyrolysis of Kraft recovery liquor. He found that sulphur was released

from the burning liquor droplets and developed an algorithm for modelling SO

2

behaviour in

the furnace.

Frederick et al. (47) proposed an empirical model for predicting the rate and total amount of sulphur releases during devolatilisation of black liquor. The rate of sulphur release is assumed to be proportional to the rate of carbon release, while the total amount of sulphur released is a fraction of the total sulphur in black liquor.

Although NO

x

is a minor species in the combustion process, it is important because of its contribution to air pollution and has a large quantity of literature devoted to it.

Someshwar et al. (48) investigated the mechanism of fuel NO

x

and thermal NO

x

in relation to NO

x

formation in a Kraft recovery furnace. The results showed that NO

x

formation is most likely a result of fuel NO

x

formation rather than thermal NO

x

. The impact of an increase in the solid content on NO

x

emission was unclear in that study.

Jonse et al. (49) studied NO

x

formation and found that it increased above 75% solid content in black liquor, primarily due to additional thermal NO

x

formation.

Nichols et al. (50) reviewed NO

x

formation mechanisms in a recovery boiler. The limited data available showed an increase in NO

x

as the solid increased from 62% to 80%. The observed increase was much less than predicted by the temperature dependence of thermal NO

x

.

Nichols et al. (51) studied the formation of fuel NO

x

during black liquor combustion. They observed that fuel NO

x

is formed during devolatilisation and char burning. The formation of NO

x

was found to be moderately sensitive to temperature in the range of 800–1000°C. It was also found that conversion of only 25% of the nitrogen in the black liquor could account for the level of NO

x

measured in the flue gas from furnaces.

Aho et al. (52) studied fuel nitrogen released during black liquor pyrolysis. Their results indicated that ammonia was the main fixed nitrogen species formed and that the rate of fixed nitrogen released increased with increasing temperature.

Adams et al. (53) used the results from CFD calculations for a recovery boiler to estimate the maximum contribution of the thermal NO

x

mechanism to the ultimate NO

x

emission from the furnace. The results were compared for cases run at 67% and 80% black liquor solid content.

In both cases the estimated total thermal NO

x

was very low, 0.09 ppm and 8.3 ppm respectively. Information regarding the max temperature in the furnace was not given.

Forssen et al. (54) studied char nitrogen oxidation in single droplet experiments. At higher gas temperature (>800°C) and higher oxygen concentrations (>1%), the char nitrogen was oxidised at the same time as char carbon, and NO was formed. At low temperatures and low oxygen contents, however, the nitrogen was not released until all of the char carbon was consumed. If oxidation was stopped in the middle of carbon oxidation, the N remained in the char. During gasification in 20% CO

2

there was little formation of NO, and approximately two-thirds of the original char nitrogen was retained in the residue.

Brink (55) proposed a NO model for black liquor droplets. The model assumed that the fuel N

was released in the gaseous phase via devolatilisation and char combustion. During

devolatilisation, the amount of nitrogen released depends on temperature and increases as the

temperature increases. Laboratory studies have found that approximately 70% of the fuel

nitrogen is released during devolatilisation, mainly as NH

₃

and N

₂

.

Iisa et al. (56), 2000, reviewed the NO

x

formation and reduction mechanisms in a recovery boiler. They proposed algorithms for predicting NO

x

in a recovery boiler based on the three NO

x

formation mechanisms; thermal, prompt and fuel NO

x

. The basic information on reduction of the NO

x

in a recovery boiler is also available and interacts with the NO

x

formation mechanism.

2.5 Grid Generation and Geometry

Very few studies have addressed the issue of grid generation and geometry. A full-scale boiler is approximately 30 m high and has a cross section of 100 m

²

. It features one or two liquor guns on each wall. The bull nose is located some 30 m above the floor and occupies about one-half of the furnace cross-section. The combustion air system in the boiler has three levels:

• Primary air, nozzles located on all four walls, about 1 m above the floor and 100 x 50 mm in size.

• Secondary air, nozzles located on all four walls, about 2–3 m above the floor and 200 x 50 mm in size.

• Tertiary air, nozzles located on two walls (the front wall and the rear wall) about 9.1 m above the floor.

In some cases there is a fourth level, at an arbitrary height. Comparing the size of the air inlets and the height of a furnace shows the need for high local grid resolution, particularly in the air nozzle regions.

Jones et al. (57) described the first stage in the development of a three-dimensional recovery furnace model, namely, the simulation of cold flow in an existing furnace design. One of the limitations mentioned in the work was the use of staggered nodes to describe a diagonal surface (i.e. the bed surface).

Grace et al. (43) listed the limitations in the simulation of a recovery boiler at that time. They included problems in reaching convergence and the use of symmetry plane to limit the number of computational cells.

Salcudean et al. (12) addressed two issues in their simulation of transport phenomena in recovery boilers. The first of these is the need for high local resolution, especially at the air nozzle levels, and the second is the slow convergence rate of the solution algorithm for the large domains typical of recovery boilers. They suggested the adoption of a multigrid solution algorithm in order to increase the convergence rate. However, they also used a symmetrical model (only half of the furnace was modelled).

Tao et al. (58) investigated the flow field in a recovery boiler and showed that use of an unstructured grid and local mesh refinement made it possible to simulate the complex flow and geometry in a Kraft recovery boiler with optimum resolution and run-time performance.

Studies of the isothermal flow field that combined mathematical and physical modelling verified that this approach gives satisfactory accuracy regarding general flow characteristics.

It minimises the need for compromises in describing the geometry of the boiler when setting

up a problem with a reasonable number of computation cells or elements. Air nozzle

arrangements do not have to be adjusted to fit grids and line up with other nozzles and the

geometry of the air nozzles can be correctly described.

Salcudean et al. (59) examined the numerical solution and convergence. Their results showed that an accurate solution of the flow field in a recovery boiler could only be obtained with very high numerical resolution and excellent convergence characteristics. The computer code developed at the University of British Columbia and used in the work uses a multigrid method and segmentation technique.

Yang et al. (60) presented a CFD study of jet flows near the char bed in recovery furnaces.

They examined the effects of step and smooth char bed surfaces on gas velocity, shear stress, and heat transfer rates. Comparing a step bed model with a smooth bed model showed that a step boundary could be used to predict main gas phase flow patterns, but that the velocity errors caused by the step boundary result in large errors in shear stress and heat transfer coefficient distributions. A step boundary also resulted in overestimation of the surface area and led to an error in the total heat transfer rate. A smooth boundary was recommended if the surface transport process needed to be accurately calculated. The results indicated that the primary air jets produce high shear stresses on bed surfaces and are therefore important in controlling bed shape. The geometries of the nozzles affect shear stress distributions, and therefore also the mass and heat transfer processes that play important role in char bed combustion.

2.6 Model Validation

It has proved very difficult to measure lower furnace gas temperatures, species concentration or bed temperature with any degree of reliability. The basic problems are the extreme dirtiness of the furnace atmosphere and interference from the sodium and water vapour present.

Borg et al. (61) measured the temperature inside a Kraft recovery furnace under various operating conditions. Temperatures were measured inside the bed (5–25 cm below the surface). They distinguished cold spots and hot spots on the surface of the char bed. The hottest zones were where the primary (and high primary) air hit the bed surface. They found that the average bed temperature was usually quite stable, as if controlled by a themostat and close to the melting point of the system. This study gave a normal temperature distribution vertically in the furnace.

Blackwell (62) used two simple techniques to check the validity of the results of physical flow modelling: a) cold-flow air tests on a full-scale boiler, b) camera observations in an operating boiler. The work aimed to examine a new air system.

Blasiak et al. (63) studied the isothermal flow pattern in a recovery furnace model using a water model. Flows calculated using isothermal models were tested against data from water flow models of two different recovery boilers with reasonable success.

Vaclavinek et al. (64) studied the stability of the flow field in a recovery furnace using a water flow model. The results were verified by mathematical modelling, which indicated that the overall flow predictions were reasonable.

Karidio et al. (65) measured the velocity distributions of cold air flow at the liquor gun level.

The velocity boundary conditions for the mathematical modelling were determined from the

pressure measurements at the primary and secondary windboxes. Subsequent comparison of

the measurements and the computations yielded good agreement, showing that balanced air

flow through opposed walls resulted in a central region of high velocity upwards flow.

Wessel et al. (66) compared the modelling results for flow, combustion and fume formation to the performance test data for an operating Kraft recovery boiler. However, the gas flow and temperature distribution were not measured during performance tests. Visual inspection of furnace brightness through observation doors in the upper furnace was used. It indicated a bias in the temperature distribution towards the left-hand corner of the front wall.

2.7 Concluding Remarks

Indeed a great deal of research has been performed on issues related to the combustion of black liquor and mathematical modeling of recovery boiler. While in some instances the results reported by different researchers are consistent with one another, in a surprisingly large number of cases, the results are contradictory. Some of these inconsistencies are undoubtedly due to differences in modeling methods and approaches but many result from the complex nature of recovery furnace and lack of needed CPU power at the time. It highlights the difficulty of studying such a complex phenomena.

One of the phenomena that did give consistent results about a recovery furnace was the influence of the operation strategy on flow field i.e. “central chimney“ in a recovery furnace.

Central chimney is formed as the primary and secondary air from the four walls converge, usually in the middle of a recovery furnace, displaying a strong upward flow. But influence of the furnace geometry on the flow field deserves further study. Research on the influence of the furnace geometry on the flow field has not provided consistent results and as such the impact of the variables like the relation between the total inlets area and the char bed surface area is still not fully understood.

The issue that how the liquor-dependent parameters affect a recovery performance is one of the uncertainties. Dealing with these parameters in the in-flight model requires more study.

Despite, a considerable effort to characterise and understand the recovery furnace, there is still no good explanation regarding the furnace performance based on the known properties of the liquor. Swelling is a good example in this regard. At the present swelling factor made in the laboratory under arbitrary conditions can be used as a basis for describing swelling in the furnace.

One critical need is to tie the NO forming processes more closely to the combustion model and to define the rate formation and nature of it in the recovery boiler. A step in right direction is to identify the mechanism, dominating the NO production. NO model could answer some of the question regarding the NO forming processes.

A wall in a recovery furnace is an important part of the burning surface when it comes to

smelt reduction. In an ordinary recovery furnace the surface of the walls is ten times larger

than the surface of the char bed. A droplet reaching a wall may continue interacting with

gases in the furnace. In order to handle droplets reaching the furnace walls correctly, it is

necessary to have a model considering the interaction of the droplets and the walls in a

recovery furnace.

3. Development of Model of Recovery Furnace model Used in This Work

It is clear from the literature survey that several issues are involved in obtaining an accurate representation of the flow field in a recovery boiler. The problems include the high numerical resolution required, especially at the air nozzle levels, and the large amount of computer time required to obtain convergence. Slow convergence of the solution algorithms is generally due to persistence of low frequency errors that are not effectively removed by a grid that is fine relative to the wavelengths of the errors.

Kaul et al.’s (67) suggestion of using an unstructured grid system with local mesh refinement was adopted for the recovery furnace model. Several studies done by Tao et al. between 1992 and 1997 [13, 41, 42, 58] at the division of Energy and Furnace Technology, KTH, confirmed that use of an unstructured grid and local mesh refinement makes it possible to simulate the complex flow and geometry in a Kraft recovery boiler with realistic computing power.

The code used in this work is a steady state/transient, finite difference, computational fluid dynamics program that can solve three-dimensional fields for pressure, velocity, temperature, kinetic energy of turbulence, dissipation rate of turbulence, and several chemical species. The code operates by solving the governing differential equations of the flow physics by numerical means on a computational mesh and is able to predict gas velocity, temperature profile, and concentration fields.

The code is also modified to accommodate the unique characteristics of black liquor combustion. The black liquor combustion models interact with the gas fields and provide source/sink terms to the CFD equations. Black liquor burning rates depend on the gas fields and, in turn, influence them through the source/sink terms (Appendix 3). The boiler model is limited to the furnace cavity itself and terminates at the nose arch. However, it may be possible to carry flow and temperature calculations through the superheater.

3.1 Geometry of the Furnaces Used in This Work

Combining the body-fitted meshing capabilities with unstructured non-orthogonal grids, local mesh refinement and arbitrary coupling between mesh blocks gives great flexibility in representing highly complex geometries. However, the geometry of a recovery boiler and recovery furnace in particular is not complicated. Eliminating the boiler bank on top of the furnace from the calculation makes the geometry even simpler. This elimination is reasonable since no information is available regarding the cooling mechanism of the passing gases, the mechanism of deposition of the carried-over materials on the tube and the correct presentation of gas passage area. The main problem in regard to the geometric representation of a recovery boiler is the shape of the char bed. A description of the char bed geometry as a boundary in the model will be given at a later stage.

Two furnaces were chosen for study. The first operates with the conventional firing method

with three elevations for air delivery, while the second boiler has four elevations for air

delivery and uses a Rotafiring strategy on the secondary level.

3.1.1 Conventional Firing Strategy (CF)

Air is delivered to the studied recovery boiler using the conventional firing method at three elevations. Primary and secondary nozzles are located in all four walls, but the tertiary nozzles are located only in the side walls. The furnace is 10.248 x 9.912 m

²

in cross-section.

The height to the midpoint of the bull nose is 27.4 m. Combustion air enters the unit through 179 inlets that can be individually set.

Figure 2 The computational domain for the CF recovery boiler.

Primary air enters the furnace through 24 air nozzles on the right and left walls, and 26 on

the front and back walls. The primary air system on all four walls is located 1.050 m above the floor. 30% of the combustion air enters the furnace through these nozzles. The temperature of the air at this level is 153°C. The velocity of the air entering the combustion chamber through these nozzles is between 18 and 36 m/s.

Figure 3 The computational grids illustrating the shape of the primary nozzles.

Figure 4 Mesh defining the primary air nozzles.

Secondary air enters the furnace through 16 air nozzles on each wall (64 in total). The secondary air system on all four walls is 2.4 m above the floor. These nozzles introduce 55%

of the combustion air. The temperature of the air at this level is 128°C. All the nozzles at this level were open at the time of measuring. The air is delivered to the combustion chamber through these nozzles with a velocity between 63 and 81m/s.

Figure 5 Mesh defining the secondary air nozzles.

Tertiary air enters the furnace through 14 air nozzles, 6 on the front wall and 8 on the back

wall. These nozzles introduce 15% of the combustion air. The tertiary air system is located 9.1 m above the floor. The temperature of the air at this level is 35°C. The velocity of the air entering the combustion chamber through these air nozzles is between 50 and 60 m/s.

The geometry of this CF recovery boiler was represented in a three-dimensional data model

consisting of a mesh with 242 000 cells. See Figure 6.

Figure 6 The computational grids used in the simulation of CF recovery boiler.

3.1.2 Rotational Firing Strategy (RF)

Air is delivered to the studied recovery boiler using the Rotafiring strategy at four elevations.

There are primary and secondary nozzles in all four walls but the tertiary and the fourth nozzle levels are located only in the side walls.

Rotafiring was done by the secondary air nozzles, a number of which were closed. Reducing the total open nozzle area on the secondary level produced an initial jet velocity of 70 to 80 m/s. Since the jets work together, vigorous rotation of the gas in the lower furnace is achieved.

The furnace is 10.5 x 10.5 m

²

in cross-section. The height to the midpoint of the bull nose is 28.5 m.

Figure 7 RotaFire secondary air nozzles configuration.

Primary air enters the furnace through 33 rectangular nozzles on each side, 1.2 m above the

floor. 38.6% of the combustion air enters the furnace through these nozzles. The temperature of the air at this level is 223°C. The air entering the combustion chamber through these nozzles has a velocity of between 18 and 36 m/s.

Secondary air enters the furnace through nozzles arranged as follows:

Front and back walls

Port 1–3 and 13 are 100% open Port 14–16 are closed

Ports 3–12 have their opening areas decreased by 10%

Right and left walls

Ports 1–3 and 11 are 100% open Ports 12–14 are closed

Ports 3–11 have their opening areas decreased by 10%

These nozzles introduce 43% of the combustion air. The temperature of the air at this level is 99°C.

Figure 8 Secondary air nozzles configuration used in this work.

1 3

11

14

Right and left air delivery configuration

Front and back air delivery configuration 16 12 3 1

Tertiary air enters the furnace through 8 nozzles, 4 on the front and 4 on the back wall. These

nozzles introduce 15% of the combustion air. The tertiary air system is located 10 m above the floor. The temperature of the air at this level is 36°C.

Fourth air enters the furnace through 4 nozzles, 2 on the front and 2 on the back wall. These

nozzles introduce 2% of the combustion air. The temperature of the air at this level is 36°C.

Figure 9 Computational grids used in the simulation of the RF recovery boiler.

3.2 Black Liquor Combustion

A model of black liquor combustion was built using STAR-CD. Such a model has to be able to account for what happens to a droplet based on its modelled trajectory. A droplet of liquor burns in a number of different ways in the recovery furnace, all of which must be accounted for. It may burn in flight, on the char bed, or on the walls, or may exit the furnace only partially burned (carry-over). The fully coupled recovery boiler model in this work has several interactive components:

• Built-in models in STAR-CD describing the flow, heat transfer and chemical reactions in the gas phase.

• A droplet trajectory model.

• An in-flight droplet combustion model describing the characteristics of liquor sprays, droplet motion and the physicochemical behaviour of droplets subject to local furnace conditions.

• A char bed model describing the interaction between the char bed reactions and the gas flow above the bed.

• A wall model describing the interaction between the walls and the gas flow.

• A NO

x

emission model, which considers NO formation from thermal NO, fuel NO and prompt NO mechanisms.

3.2.1 Spray

Several types of commercial nozzles are used to inject black liquors into recovery boilers. The splash-plate type is the most common, but swirl-cone and V-jet types are occasionally used.

While it would be expected a priori that droplet size would be determined by both properties of liquors and nozzle design, the relative importance of the various parameters has to be determined empirically.

A successful black liquor distribution system must control the droplet size in order to minimise carry-over and deliver relatively dry liquor to the bed surface. To do this, liquor guns are arranged in a symmetrical pattern that distributes liquor evenly across the full cross- section of the furnace. The mechanisms for stream break-up exiting the liquor gun nozzle generally fall into two basic regimes: ordered and chaotic. The most common commercial spray nozzles and atomisers fall into the latter category, as do all current black liquor nozzles used in recovery boilers in pulp and paper mills [Green et al., (68)].

The injection velocity, that is, the velocity of the liquid fuel as it exits the nozzle and enters the furnace, and the viscosity of the liquor are the most important parameters in a spray calculation. They strongly influence the atomisation and break-up processes, the spray penetration, the interphase transfer processes, and droplet–droplet and droplet–wall interactions. In general, modelling of the spray can be done in two ways:

• Using the nozzle geometry (e.g., the diameter, D, of the nozzle hole) as a parameter [Adams (69)].

• Setting up the initial conditions obtained under laboratory conditions.

Although these two approaches have different starting points, they should produce fairly

similar results. The size distribution of the droplets should fall within the initial conditions,

for these were set up to simulate the injection of the droplets by liquor guns into the furnace.

The current model uses the second option. This option was chosen because setting up the initial conditions as the input parameter shortens the CPU time tremendously.

In mathematical modelling of spray, groups of droplets with similar initial conditions are commonly assigned to classes or parcels. Each parcel is distinguished by the initial position, velocity, diameter, temperature and density of a typical droplet as well as by the number of droplets within it. A single droplet possessing the properties of that class represents an individual parcel. The trajectory and heat/mass transfer between the phases is then calculated based on the local gas phase conditions as a droplet parcel moves through the flow field [Star- CD (70)].

The characteristics of a black liquor spray are defined by its

• Initial position and velocity.

• Temperature and density.

• Size distribution.

The two first points can be can be obtained from known plant operation conditions and are given in Table 2.

Table 2: Initial liquor conditions

Recovery Furnace Initial position (m) Above the floor

Initial velocity (m/s)

Temperature (K)

Load m_total (kg) ds/s

CF 6,2 8 120 24,67

RF 6 7,4 115 19,67

In the present model, the velocity and size distributions of a black liquor spray are determined using the following relations. The mass carried by an individual droplet is:

d total

d n

m

=

m

(1)

A Rosin-Rammler size distribution is assumed for the diameters of droplet parcels. The size distribution function has the following form [Tao (41), 1997]:

d d

d dm

CV

q

= −



 





  

  ln

100

/

100

1

(2)

where d

_dm

is the mean droplet diameter for a given nozzle, CV is the cumulative volume and

q is a parameter that describes how wide the distribution of diameter is for the nozzle. Two

parameters must be specified: the mean diameter and the distribution parameter. A splash-

plate nozzle has the following spray distribution parameters: d

_dm

= 3 mm and q = 2.7. These

parameters have been applied in the present work. Ten droplet diameters are used to represent the size distribution in the calculations. These diameters d are calculated by the following

_dⁱ

relations:

q

j dm

j d CV

d

/

ln

1

100 100

 





 





 





 





= − (

3)

j

CV_j

= 10

j

= 0 , 1 , 2 , 3 ,...., 9 , 9 . 9 )

(

. 5

₁

0 +

₊

=

_{j j}

i

d d d

d i

= 1 , 2 , 3 ,...., 10

j

= 0 , 1 , 2 ,..., 9 , 9 . 9 The number of droplets in a droplet parcel is given by:

d i d i p d

d N M

π

³

ρ 6

=

(4)

The initial velocity vector of a droplet parcel is determined from known spray angles (horizontal and vertical) and known mass distribution within the spray angles. In the present work, a group consisting of ten droplet parcels with the diameter distribution described above is assigned a unique initial velocity vector.

The magnitude of the relative velocity between the droplet and the gas implies that the Reynolds number is less than 10

³

and thus that the drag force is important in this case.

The model uses the average gas velocity in a given computational cell to determine the drag on a liquor droplet passing through the cell. The trajectory used in this work takes into account the changes in mass and physical size of the droplets as they burn (Appendix 3).

Knowledge of droplet velocity makes it possible to determine the position of a droplet at any

moment, when it could be on the hearth, at a furnace wall, on the char bed or be being carried

out of the furnace by flue gas. One current method for calculating droplet trajectories is based

on the force balance. This method is not particular to recovery boilers and has yielded reliable

models in other applications. The initial velocity and droplet size are liquor gun–dependent

variables and should be considered carefully. The trajectory model should also account for the

swelling/deswelling of a droplet during combustion. In this work the swelling/deswelling of a

droplet is treated empirically. Generally there is a need to find a swelling/deswelling model

that is dependent on the liquor properties and furnace environment. Trajectory calculations

directly determine the amount of carry-over [Fakhrai (71)].