Tuynel Thong

Imperial College London Arnaud

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Modelling and Optimisation of a Tunnel Kiln Process

Arnaud Schalk

September, 24th

2010

Supervised by: Professor Stratos Pistikopoulos

Dr. Kostas Kouramas

Mr. Christos Panos

A thesis submitted to Imperial College London in partial fulfilment of the requirements for the

degree of Master of Science in COURSE TITLE and for the Diploma of Imperial College

Department of Chemical Engineering and Chemical Technology

Imperial College London

London SW7 2AZ, UK


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List of contents

Abstract...........8

Acknowledgments..........9

1. Introduction..........10

2. Literature

review............................................................................................11

2.1 Mathematical Model and Optimization..............................................................11

2.1.1 General Mathematical Model....................................... ...........................11

2.1.2 Temperature fields in tunnel kiln............................................................ 12

2.1.3 Integral Equation......................................................................................12

2.2 Heat transfer coefficient and Experimental studies...........................................13

2.2.1 Heat transfer coefficient...........................................................................13

2.2.2 Experimental Studies...............................................................................13

2.3 Design and Simulation......................................................................................14

2.3.1 Design......................................................................................................14

2.3.2 Simulation................................................................................................15

3 Motivation...............................................................................................................16

4 Process.....................................................................................................................17

4.1 Tunnel Kiln Operation.......................................................................................17

4.2 Characteristic of the firing process....................................................................18

4.3 Process and methodology..................................................................................19

5 Mathematical Model...............................................................................................21

5.1 Assumptions......................................................................................................21

5.2 Model for One Column.....................................................................................22

5.2.1 Variables used in the model.....................................................................22

5.2.2 Properties.................................................................................................26

5.2.3 Properties equations.................................................................................27

5.2.4 Design characteristics..............................................................................28

5.2.5 Mass

Balance.....................................................................................................28

5.2.6 Calculation of the heat transfer coefficient of the gas.............................31

5.2.7 Pressure drop............................................................................................31

5.2.8 Energy Balance........................................................................................32

5.2.9 Heat loss...................................................................................................34

5.3 Parameters assigned for our project..................................................................35

5.4 Index of the model.............................................................................................37

5.5 Initial Conditions...............................................................................................37


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6 Simulation Results for one column.........................................................................39

6.1 Simulation with a fuel Flow rate of 0.02 kg/s...................................................40

6.1.1 Evolution of the gas temperature.............................................................40

6.1.2 Evolution of the Tiles and car temperatures............................................42

6.1.3 Pressure drop............................................................................................44

6.1.4 Heat

loss...........................................................................................................45

6.2 Simulation with a fuel Flow rate of 0.005 kg/s.................................................46

6.2.1 Evolution of the gas temperature.............................................................47

6.2.2 Evolution of the Tiles and car temperatures............................................48

6.2.3 Heat

loss...........................................................................................................48

7 Simulation Results for more than one column........................................................49

Conclusion....................54

Future Work.....................55

References........................56

Appendices....................58

A1. gPROMS Model entity Column.................................................................58

A.2 Model Entity AIR SOURCE......................................................................65

A.3 Model Entity FUEL....................................................................................66

A.4 Model Entity SECONDARY.....................................................................67

A.5 Model Entity MATERIAL.........................................................................68

A.6 Model Entity PROPERTIES......................................................................69

A.7 Model Entity Firing_Column.....................................................................71

A.8 Process Entity Firing Column....................................................................72

A.9 Model Firing Column Topology................................................................73


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List of Figure, Graph and Table

Figure 1: Schematic representation of a Tunnel Kiln.........................................................10

Figure 2: Top schematic view of a tunnel kiln....................................................................17

Figure 3: Picture of two columns of tiles in a Tunnel Kiln...............................................18

Figure 4: Characteristic of the Tunnel kiln..........................................................................18

Figure 5: Example of an experimental temperature distribution......................................19

Figure 6: Theoretical temperature distribution....................................................................20

Figure 7: Side cut of the firing section..................................................................................22

Figure 8: gPROMS one column interface............................................................................39

Figure 9: gPROMS 36 columns interface...........................................................................49

Figure 10: Schematic representation of two connected column......................................50

Graph 1: Inlet temperature of the gas, Ffuel=0.02 kg/s...................................................40

Graph 2: Outlet temperature of the gas, Ffuel=0.02 kg/s...................................................41

Graph 3: Tiles temperature, 3D graph, Ffuel=0.02 kg/s.....................................................42

Graph 4: Tiles temperature, 2D graph, Ffuel=0.02 kg/s.....................................................42

Graph 5: Car temperature, Ffuel=0.02 kg/s.........................................................................43

Graph 6: Pressure drop inside the kiln, Ffuel=0.02 kg/s....................................................44

Graph 7: Heat loss through the walls and roof, Ffuel=0.02 kg/s.......................................45

Graph 8: Kilns Walls Temperature, Ffuel=0.02 kg/s........................................................45

Graph 9: Kilns roof Temperature, Ffuel=0.02 kg/s...........................................................46

Graph 10: Inlet temperature of the gas, Ffuel=0.005 kg/s..................................................47

Graph 11: Outlet temperature of the gas, Ffuel=0.005 kg/s...............................................47

Graph 12: Tiles temperature, Ffuel=0.005 kg/s...................................................................48

Graph 13: Heat loss, Ffuel=0.005 kg/s.................................................................................48

Graph 14: Tiles temperature, 3D graph, Column 2...........................................................51


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Graph 15: Tiles temperature, 2D graph, Column 2...........................................................52

Graph 16: Car temperature, 2D graph, Column 2.............................................................52

Graph 17: Outlet temperature of the gas, Column 2..........................................................53

Table 1: Model Variables......................................................................................................22

Table 2: Air, Secondary air and Fuel flow rate, temperature, pressure and

composition................................................................................................................................35

Table 3: Inlet temperature car and tiles................................................................................35

Table 4: Design characteristic of the Kiln, Car and Tiles..................................................35

Table 5: Physical properties of the Kiln, Car and Tiles......................................................36

Table 6: Other constants used in the model.........................................................................36

Table 7: Molecular Weight...................................................................................................36

Table 8: First column Inlet.....................................................................................................50

Table 9: Second column Inlet...............................................................................................50

Table 10: Second column Outlet/Third column inlet........................................................51


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Nomenclature

A Area

Cp Heat capacity

Dh Hydraulic Diameter

f Friction factor

F Flow rate

h Heat convection coefficient

H Enthalpy

i Component i

k Thermal conductivity coefficient

L Length

Height

M MAss

MW Molecular Weight

Nu Nusselt

P Pressure

Per Perimeter

Pr Prandt

Q Heat

r reaction progress

Re Reynolds

Roug Rougness

T Temperature

Thick Thickness


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t Time

u Velocity

V Volume

W Width

x mass fraction

Greek letters

Absorptivity

Emissivity

Density

Stefan-Boltzmann constant

Viscosity


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Abstract:

This work presents the mathematical model developed for the firing section of a tunnel

kiln.

Tunnel kilns are widely used in industry of ceramics and brick making processes. This

is a dynamic process which has not received enough attention in the open literature.

The work presented is mainly based on a model developed in Imperial College

London and on the work made by S. Kaya, E. Mancuhan and K. Kucukada [4] from

Marmara University, Istanbul.

First of all, a model for a unique column of tiles is developed describing all the

physical phenomena happening inside the kiln. This model is then simulated in

gPROMS. Several results based on the simulation are then obtained regarding the

relation between the amount of fuel fed in the tunnel and the inlet temperature of the

gas as well as the temperature distribution inside the tiles.

Secondly, a generalisation of the model for more than one column is attempted and

proved by two separated simulations of one column.


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Acknowledgments

Sincere thanks to Professor Stratos Pistikopoulos and Dr Kostas Kouramas for

their dedicated guidance support throughout the project.

Great thanks to Mr Christos Panos for all his encouragement, great support,

guidance, stimulating suggestions and patience during my project.

Many thanks to all my Imperial College lecturers from whom I gained

invaluable knowledge and without which this thesis would not have been possible.

A particular thanks to Mr Mayank Patel for his thoughtful help during my

project.

Very special thanks to my family for their encouragement and support.


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1. Introduction

Tunnel Kilns are widely used in industry for ceramics and brick making processes. A

definition of tunnel kilns system is given in the U.S. Patent number 4,718,847 of

January, 12th, 1988 [1]: [The tunnel Kiln system] is a very long kiln which can be 20

to 100 yards (18m to 92m) in length and through which are continuously moved from

one end to the other a series of carts or cars supporting the materials to be treated. The

kiln is divided into temperature zones varying with distance from the kiln heat source

either by merely utilizing the length of the kiln or by interposing hot gas flow control

systems and movable doors at various locations. In general, a tunnel kiln is composed

of three zones namely (See figure 1): the preheating zone, where bricks are heated to

evaporate the remaining water and to avoid cracking due to the thermal shock, the

firing zone, where the temperature of the bricks is gradually increased to about

1000C, the cooling zone, where heat is recovered.

Figure 1. Schematic representation of a Tunnel Kiln

Many researches and publications have been done about Tunnel Kiln system. We can

identify four main research areas in these studies: The first one is the studies whom

deal with Mathematical Model and Optimization of the process with the objective of

minimizing the costs and the energy. The second one is the calculation of the Heat

transfer coefficient and the analysis of Experimental work. Researches were done

regarding different Design for the tunnel kiln such as small tunnel kiln or rotary tunnel

kiln and also Simulations of tunnel kiln were run via developed software. The last area

is the development of controller in order to run a safe operation, to get the highest

product quality, and to find the most economic operation.


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2. Literature review 2.1 Mathematical Model and Optimization

2.1.1 General Mathematical Model

D.R. Dugwell and D.E. Oakley [2] developed two different models to simulate one

and two dimensional temperature profiles along the tunnel kiln. The model represents

the kiln as a series of plug-flow regions, in which heat transfer to ware occurs,

interspaced by well-stirred adiabatic regions, in which burners and air inleakages are

introduced. The models estimated the gas temperature and composition in addition to

the refractory ware temperature. The two-dimensional form gives good agreement

with measured ware temperature profiles. The simpler one-dimensional form predicts

gas temperature profiles accurately, and estimates representative ware temperatures.

Both models solve the unsteady conduction equation with strongly nonlinear boundary

conditions due to radiation.

In 2005, Ebru Mancuhan and Kurtul Kucukada [3] analysed the operation of a tunnel

kiln producing coal admixed bricks, bricks with a low or high calorific value coal

added as an energy source in the brick body. They considered two different fuels;

pulverized coal (PC) and natural gas (NG), and based their optimization on a particular

plant. The objective was to minimize the cost of the fuels used and the energy lost

through the stack. Solving their 1D model by linear programming, they showed up that

it was advantageous to use admixed coal (AC) for both cases, which are using PC or

NG in the firing zone. The results showed that the using of AC supplies a significant

percentage from 15% to 39% of the energy required for this particular plant. They

showed as well that the optimum energy requirement was between 2040 and 3510

kj/kg brick depending on the properties of the fuels used.

Following this work, Ebru Mancuhan, Kurtul Kucukada and Sinem Kaya [4]

demonstrated how the optimal operating conditions could be predicted by using a

mathematical model representing in the simplest form the phenomena of heat transfer,

combustion of AC and PC, together with gas flow. The work focused on the firing

zone of a tunnel kiln. Using the same 1D-Model and the same objective function than

the previous work, they came up to the conclusion that the heating values of AC and

PC are the key parameters to obtain minimum fuel cost. Using AC with higher heating

values will reduce the required PC while keeping the carbon percentage in the brick

body in the permissible limits and thus the total fuel cost will decrease. They also

determined that the secondary ambient air is blown into the firing zone from 30% to

80% of the dimensionless firing length with a flow rate of 0.175kg/kg while the PC is

fed into the firing zone between the about 18 and 93% of the dimensionless firing

length. The model proposed is specific to coal admixed bricks, and does not consider

the conditions favouring the formation of CO and SO2. The effect of these two

reactions should be included as process constraints in the future.

The same group of research of the Marmara University [5] was interested of the heat

recovery in the cooling zone of a tunnel kiln. As all their previous work, the model


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proposed is still a 1D-model using green bricks. This work was realized to improve the

heat recovery by optimizing the ambient air inlet flow rate at the brick exit side, the

suction and blowing air flow rates along the cooling zone. As the pressure drop along

the cooling zone is a function of the flow rates and temperature of the air, the objective

function to be minimized was defined as the total pressure drop. They determined that

there should be four distinct regions formed of two sets of suction and blowing

regions. This work just gave an estimation of the heat transfer and fluid flow

phenomena and the optimum operating conditions in the cooling zone of a tunnel kiln.

Ebru Mancuhan [6] analysed and optimised the drying of green bricks in a Tunnel

dryer. A drying process is required for the removal of most of the water in the green

brick body to reduce the water content of the brick to about 10% before firing in the

tunnel kiln. Without this preheating step, the water within the clay body turns to

stream at the firing process and damages the bricks severely. The objective function of

this 1D-model is the total cost of the energy required for drying. The cost of the

electricity consumed by the fans for the circulation of the drying air is also included in

the objective function. The optimization of the drying process is realized by linear

programming using Microsoft Excel solver, to find the optimal values of the hot and

outdoor air mass flow rates per kilogram of the brick. The results showed that for

different manipulated variables, it was found that 59 to 62% of the total energy is used

for drying per unit of green bricks.

2.1.2 Temperature fields in tunnel kiln

An approach of a determination of temperature fields in tunnel kiln for brick

production is developed by J. Durakovic and S. Delalic [7]. They claimed their

mathematical model was appropriate for analysis and checking of a stationary

temperature field in brick products and in the furnace. They executed simulations of

temperature distribution in furnace during a brick production process in real conditions

by using a computer program, which has been developed on Delphi 3 programming

language base at Faculty of Metallurgy and Materials Science, University of Zenica.

2.1.3 Integral Equation

In 1985, G. Halasz elaborated a new heat-exchanger model of simulation of heat

treatment in a tunnel kiln. The nonlinear 1D multipoint boundary-value problem has

been handled in the form of an integral equation. Its kernel function characterizing the

mixing and boundary conditions is assumed to consist of a finite number of

elementary kernel functions of its subsystems and the parameters of this kernel

function are directly measurable on a real kiln. A new effective integral equation-

based algorithm solved this equation. Two years later, G. Halasz, J. Toth and K.M.

Hangos [8] applied this model to an existing tunnel kiln in china and proposed a

simple method of determining the energy optimal conditions of this tunnel kiln.


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In 2000, R.H. Essenhigh [9] analysed the tunnel kiln performance to determine the

relation between input energy and useful output energy by applying the integral energy

equation which shown to lead to a firing equation of standard form.

2.2 Heat transfer coefficient and Experimental studies

2.2.1 Heat transfer coefficient:

In 1972, V.G. Abbakumov and G.Sh. Ashkinadze [10] investigated the best

calculations for the coefficient of the heat transfer by convection in tunnel kilns

depending of the structure and the surface of the setting. Based on previous

investigations only, about convective heat exchange from variously orientated

surfaces, and written as an Equations review, they analysed and discussed the

equations to use. They ended up with several recommendations: In calculating the

coefficients of heat transfer by convection in tunnel kilns for the longitudinal surfaces

of the setting with a latticed column structure the following equation is recommended:

Nu=0.08Re0.7

where

is the Nusselt factor;

is the Reynolds

criterion; is the heat transmission coefficient, d the equivalent diameter of the

channel; the coefficient of thermal conductivity of the gases; w the velocity of the

gases and v is the kinematic viscosity of the gases. For the longitudinal surfaces of the

setting with solid columns the following expression for the average Nusselt criterion

for the channel is recommended: Nu=0.018Re0.8 where the coefficient takes into

account the increase in the intensity of the heat exchange with an unstabilized flow in

the setting channels. For transverse surfaces in the setting

where r is the size of the

gap (transverse gap between the products of the setting), is half the thickness of the

column, and S=1 for surface arranged with the flow and S=0 with surfaces arranged

opposite the flow.

The resulting coefficients of heat transfer can be made more accurate by multiplying

them by the value determined from where Pr is the Prandtl

criterion and Tf the Temperature factor.

In a same review manner, G.A. Kovelman and A.A. Barenboim [11] studied the

variation of the coefficient of heat transfer from the gases to the setting and they

concluded that a study of the heat exchange permits to determine in a proper manner

the direction of the work to be carried out for further increasing the efficiency of

tunnel kilns without proposing any models or improvements.

2.2.2 Experimental Studies:

An experimental study led by S.A. Karaush, Yu. I. Chizhik and E.G. Bober [12]

showed that the factor that affects the rate of heat absorption by ware most strongly is

the size of the transverse channels in the setting as it determines the setting density. By


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varying the channel size, it is possible to control heat absorption by the ware and the

throughput of the kiln and to balance them in the proper ratio.

O.B. Goltsova, V.S. Klekovkin, O.B. Nagovitsin and S.V. Antonychev [13] described

what provides experimental studies about heat losses in a tunnel kiln for brick firing.

From an experimental study, it was found that the destructions of several joints

between concrete blocks in firing zones leads to thermal losses. They showed up that

experimental studies provided the following:

- accuracy in identifying heat loss zones, their sizes and configurations;

- identifying the type of destruction of the enclosing structure or thermal

insulation, which would be impossible without breaking the heat-insulating layer if the

thermal imager had not been used; this has made it possible to develop justified

recommendations for repairing the kiln lining or thermal insulation;

revealing the need for additional thermal insulation in zones with large heat losses

even when the lining or thermal insulation are not destroyed;

the possibility of saving up to 5% thermal energy, i.e., cutting the consumption of

natural gas for brick firing by 27 m3/h.

2.3 Design and Simulation

2.3.1 Design:

Many method of firing or design of the tunnel have been tested, analysed and

improved. In 1983, a group of research of the Moscow Engineering and Construction

Institute [14] focused its studies on a system for firing a small tunnel kiln operating on

natural gas. The purpose was to improve the method of firing refractories in an

existing plant in order to increase the production and decrease the specific fuel

consumption. Many factors had a negative influence on the kiln operating, and

therefore the specified operating condition, a required temperature of 1740-1780C,

was not reached. Based on an experimental model, they equipped the small tunnel

kiln with a combined firing system with ejector supply of hot air to the burners which

provided stable operation at firing required temperature and increased the production

while the specific fuel consumption decreased by 25%.

In October 1982 the first high-temperature rotary tunnel kiln for firing of refractories

was placed in service at the Kazogneupor Plant. After a year and half of operating

experience the group of the Kazogneupor plant [15] published, as a scientific

publication, the first results of the system. The operation of the kiln was characterized

by the high service reliability of its design elements, including the hearth system, and

insignificant costs for routine repairs of the kiln equipment. At this time, specialists of

the institute and the plant were still doing further work on improving the technical and

economic indices of the new equipment, acceleration of the refractory firing processes


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in it, increasing the temperature of the kiln, and broadening the range of production

fired.

While they were studying the first results of the first high-temperature rotary tunnel

kiln for firing of refractories, N.A. Tyutin, B.I. Kitaev, and V.G. Avdeeva [16]

investigated the aerodynamics of a tunnel circular kiln. The operating effectiveness of

a production kiln depends significantly upon the aerodynamics of the gases in the

working space, which influences the intensity and uniformity of heating or cooling of

the parts being heat-treated. One of the characteristics of the gas aerodynamics is the

velocity field in the cross section of the kiln space. Based on experimental results, they

established that the uniformity in the velocity field across the width of the kiln cross

section depends upon the composite influence of the charge parameters and the

geometric and dynamic factors of the curvature.

2.3.2 Simulation:

In 1997, J.F.M. Vellhuis and J. Denissen [17] outlined a procedure to optimize

industrial dryers for ceramics. The optimization was done through DrySim, which is a

flexible computer model for simulations of dryers. Lab dryer experiments and

measurements were done before implementing the model on DrySim. Two examples

of simulations was given to illustrated the procedure: the optimization of a chamber

dryer and the optimization of a tunnel dryer. In the first example, it was shown that it

was possible to reduce the drying time by 2, making possible to double the production.

An increase of 10% of the production was shown if the tunnel kiln was running at

critical conditions in the example 2.

O.B. Goltsova, V.S. Klekovkin, O.B. Nagovitsyn, and N.L. Dmitriev [18] identified

experimentally the different defects appearing in firing brick in a tunnel kiln: Bulges,

nonuniform tint on the brick surface, cracks or full destruction of product and black

core. They identified their causes and proposed some recommendations in order to

avoid these defects in firing brick. The statistical analysis of defects shows that they

are caused by the violation of the technological and thermotechnical processes due to

the absence of automated control of gas-air mixture supply, unstable performance, and

imperfect design of the gas burners, and the absence of the appropriate temperature

regime in the preheating zone.


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3. Motivation

The most widely used firing unit in the roof tile and general the heavy clay industry is

the tunnel kiln. The tunnel kiln is a counter flow kiln since the kiln cars loaded with

green roof tiles travel in the opposite direction of the air thus causing a steady

exchange of heat between the air and the tiles. The tunnel kiln consists of three main

zones: preheating, firing and cooling zones. The green ware (tiles) is heated in the

preheating zone from the hot exhaust gases from the firing zone. In the firing zone the

product is heated to the required temperature. The main energy source for the heating

of the tiles is the radiation emitted from the combustion of the fuel. The final product

is then cooled down to the intended exit temperature with air in the cooling zone. In

general, the tunnel kiln operation is an intensive and energy consuming process. The

distribution of the temperature inside the kiln plays an important role for the quality of

the final product.

The advanced control and energy management of the intensive kiln process requires

the development of detailed mathematical models. This has not received enough

attention in the open literature and is one of the key issues for the optimization and

control of the kiln process. Optimization of the kiln process is required in order to

achieve the best quality of the tiles while minimizing the energy consumption. The

objective of this project was to develop a mathematical model for the firing zone of the

kiln process and optimize the process to reduce the fuel consumption. [22]


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4. Process 4.1 Tunnel Kiln Operation

In tunnel kiln operation the bricks and gas move in opposite directions which means

that the air and brick flow is counter current as shown in Figs. 1 and 2. In general, a

tunnel kiln is composed of three zones namely; preheating, firing and cooling as

shown in figure 1. The bricks leaving the drying kiln with a moisture content of

around 12% enter the preheating zone. In the preheating zone, bricks are heated to

evaporate the remaining water and to avoid cracking due to thermal shock. The inlet

temperature of bricks coming from the preheating zone is about 700 C. It increases

gradually to about 1000 C along the firing zone as a result of the heat released by the

combustion of Natural Gas fed through the holes on top of the kiln. The combustion

reaction deals with the combustion of the natural gas introduced at the top of kiln with

the oxygen of fresh air as depicted in the figure 2.

During the firing period, the crystal growth activates the formation of solid bridges

within the brick body. Finally, the bricks move to the cooling zone where they give off

most of the heat to the cooling air. Blowing of the ambient air into the kiln at different

locations along the cooling zone cools rapidly the bricks and increases the pressure

drop. Suction of the hot kiln air reduces the pressure drop and recovers the heat

content of the bricks. During the cooling zone, the bricks are cooled down to their

desired exit temperature of around 30 - 50 C. There is a null pressure line between

the cooling and firing zone. It was achieved by blowing of the ambient air at the very

beginning of the cooling zone to avoid the reversal of the air flow from the firing to

the cooling zone. [4]

Figure 2. Top schematic view of a tunnel kiln


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4.2 Characteristic of the firing process (figure 4)

- 29 meters long made in low conduction material

- 2.3 meters high

- 4.8 meters long

- The length of the car is the one of the kiln as shown on the figure 3

- There are 6 cars, each carrying 6 columns which leads to a total of 36

columns involved in the process, moving very slowly throughout the

tunnel.

- Pure Fuel is fed through the burners in the firing zone.

- Two air sources are coming in the firing zone: the air source which come

directly from the cooling zone and the secondary air source which is the

hot air extracted from the cooling zone which is fed from the top of the

tunnel.

Figure 3. Picture of two columns of tiles in a Tunnel Kiln

Figure 4. Characteristic of the Tunnel kiln


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4.3 Process and methodology:

This project will mainly be based on a mathematical model for the preheating section

of the tunnel kiln developed at Imperial College London on the work made by S. Kaya,

E. Mancuhan and K. Kucukada [4] from Marmara University, Istanbul.

It will be developed a stable mathematical model of the firing zone in order to reach

the wanted temperature of the tile by minimizing the fuel consumption.

Specifically, the project will comprise the following three stages:

1. Development of the mathematical model for one column of tiles on a car

in the firing section. This model will be based on the model for the

preheating section. We will have to take in consideration the heat

exchanged by radiation between the gas and the tiles and the heat loss by

radiation and convection through the walls and roof of the kiln.

2. Using gPROMS, the mathematical obtained is simulated. gPROMS

ModelBuilder 3.0.3, is a software package for the modeling and

simulation of processes combining discrete and continuous

characteristics [23].

3. Using gPROMS, we will attempt to simulate the whole process by

connecting 36 columns together.

The objectives of the development of a mathematical model and of the simulation of it

in gPROMS are:

- To get a temperature distribution inside the kiln the closest of the

theoretical distribution shown in Figure 6:

Figure 5. Example of an experimental temperature distribution


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Figure 6. Theoretical temperature distribution

- To show that the model developed is stable and can be applied in real.

- To optimize the system in order to minimize the fuel consumption.


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5 Mathematical Model

5.1 Assumptions:

The mathematical model requires appropriate selection of simplifying assumptions:

- Modelling of one column of tiles instead of the entire car

- The gas has uniform temperature and velocity. No variation of temperature and

flow rate in the vertical direction.

- Complete oxidation of the fuel

- The fuel reacts with oxygen instantaneously. The reaction takes place before

getting in the column

- The three streams (fuel, air and secondary air) mixed before getting in the

column

- The composition of the gas flow getting in the column is the one after mixing

and combustion; and contains CO2, H2O, N2, Fuel and O2

- The air properties are function of the pressure, temperature and composition

- Heat is transferred between the gas and the tiles by convection and radiation

- The pressure of the gas after the mixing is assumed to be the pressure of the air

source as it is the main air flow

- The tiles temperature is distributed over the vertical axis

- The tiles properties are function of the temperature only

- The heat lost from the roof and the wall are based on previous work of O.B.

Goltsova, V.S. Klekovkin, O.B. Nagovitsin, S.V. Antonychev [13] and S.

Kaya, E. Mancuhan, K. Kucukada [4]

- We do not consider the radiative transfer between the bricks and the walls,

only radiative exchanges between the gas and the tiles and the gas and the

walls/roof of the tunnel

- The mass of the tiles and of the car do not change over the time

- No reaction happens inside the tiles material

- The tiles and the car are moving throughout the tunnel at a constant velocity.


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5.2 Model for One Column:

Figure 7. Side cut of the firing section

The development of the following mathematical model for the firing section of the

tunnel kiln is based on a mathematical model developed in Imperial College London

for the preheating section of this same tunnel kiln. The heat transfer by radiation will

be taken in account as well as the heat loss through the walls and the roof of the

system. We have an illustration of the counter current process and how the mass and

energy balance will be done on figure 7.

5.2.1 Variables used in the model:

There are 111 variables in our model:

Variable

Names Name Units Number of variable

Acar Area of car m2 1

Afree Free area m2 1

Aroof Area of the roof m2 1

Atiles Area of tiles m2 1

Awall Area of the walls m2 1

cpcar Heat capacity of the car kJ/kg.K 1

cpgas_in Inlet heat capacity of the gas kJ/kg.K 1

cpgas_out Outlet heat capacity of the gas kJ/kg.K 1


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cptiles Heat capacity of the tiles kJ/kg.K 1

Dh Hydraulic diameter m 1

f Friciton coefficient / 1

Fair_in Inlet air mass flowrate kg/s 1

Fcar_in Imlet car mass flowrate kg/s 1

Fcar_out Outlet car mass flowrate kg/s 1

Ffuel_in Inlet fuel mass flowrate kg/s 1

Fgas_in Inlet gas mass flowrate kg/s 1

Fgas_out Outlet gas mass flowrate kg/s 1

Fsec_in Inlet secondary air mass flowrate kg/s 1

Ftiles_in Inlet tiles mass flowrate kg/s 1

Ftiles_out Outler tiles mass flowrate kg/s 1

h Heat transfer coefficient W/m2.K 1

Hair Enthalpy of the air kJ/s 1

hcar Heat transfer coefficient of the car W/m2.K 1

Hfuel Enthalpy of the fuel kJ/s 1

Hgas_in Enthalpy of the gas out kJ/s 1

hkiln Heat transfer coefficient of the wall W/m2.K 1

Hsec Enthalpy of the secondary air kJ/s 1

k Thermal conductivity coefficient W/m.K 1

kkiln Thermal conductivity coefficient for kiln W/m.K 1

Lkiln Length of the kiln m 1

kiln Height of the kiln m 1

Ltile Length of the tiles column m 1

tiles Height of the tiles column m 1

Mcar Mass of car kg 1


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Mi Mass of component i kg 5

Mtiles Mass of tiles kg 1

Mtotal Total Mass kg 1

MW(i) Molecular weight of component i kg/kmol 5

Nu Nusselt Number / 1

Pair_in Inlet air Pressure Pa 1

Pdrop Drop Pressure Pa 1

Per Perimeter m 1

Pgas_out Outlet air Pressure Pa 1

Pr Prandt Number / 1

Qloss Heat lost J/s 1

Qradiation Radiation kJ/s 1

Qroof Heat lost through the roof J/s 1

Qwall Heat lost through the walls J/s 1

r reaction progress of combustion kmol/s 1

Re Reynolds number / 1

Roug Rougness / 1

Tair_in Inlet temperature of air K 1

Tamb Ambient Temperature K 1

Tcar_in Inlet temperature of car K 1

Tcar_out Outlet temperature of car K 1

Tfuel_in Inlet temperature of fuel K 1

Tgas_in Inlet temperature of gas K 1

Tgas_out Outlet temperature of gas K 1

Thickroof Thickness of the roof m 1

Thickwall Thickness of the walls m 1


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Troof Temperature of the roof K 1

Tsec_in Inlet temperature of secondary air K 1

tstep Step Time s 1

Ttiles_in Inlet temperature of the tiles K 1

Ttiles_out Outlet temperature of the tiles K 1

Twall Temperature of the walls K 1

u Velocity of gas m/s 1

Vfree Free volume m3 1

Vtiles Volume of the tiles m3 1

Wstep Width step m 1

Wtiles Width of the tiles column m 1

xair_in Inlet air mass fraction / 5

xfuel_in Inlet fuel mass fraction / 5

xgas_in Inlet gas mass fraction / 5

xgas_out Outlet gas mass fraction / 5

xsec_in Inlet secondary air mass fraction / 5

gas Absorptivity of gas / 1

gas Emissivity of the gas / 1

kiln Emissivity of the wall / 1

tiles Emissivity of the tiles / 1

gas Density of gas kg/m3 1

Stefan-Boltzmann constant W/m2.K4 1

gas Viscosity of gas kg/m.s 1

Total

111

Table 1. Model Variables


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5.2.2 Properties:

The model involves five chemical components: Carbon dioxide, water, oxygen,

nitrogen and methane.

To each of them will be attributed a number used further in the model:

i=1: CO2

i=2: H2O

i=3: O2

i=4: N2

i=5: CH4

Several physical properties of the three different streams are needed in the model.

They depend of the temperature, the pressure and the composition of each stream

considered. Some of them will be calculated by the Physical property packages of

gPROMS[20] and some other will be calculated by correlation from literature.

Enthalpy: Enthalpy is a function of temperature and pressure. Values for the more

common substances have been determined experimentally and are given in the various

handbooks. [21] We will use the package for this property in our model.

H = H(T, P, n)

Density: Enthalpy is a function of temperature, pressure and composition. We will use

the package for this property in our model.

= (T, P, n)

Viscosity: Values for pure substances can usually be found in the literature. It is

function of the temperature, the pressure and the composition when it is for a mixture.

We will use the package for this property in our model.

= (T, P, n)

Heat capacity: It depends of temperature, pressure and the composition of the stream

and will be calculated by the physical properties package.

Cp=Cp(T, P, n)

Thermal conductivity: A correlation will be used. It is the one used by S. Kaya, E.

Mancuhan, K. Kucukada, in Model-based optimization of heat recovery in the

cooling zone of a tunnel kiln [5].


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5.2.3 Properties equations:

Property Equation Number

of

Equation

Equation

Number

Enthalpy of

air

Hair = Hair(Tair, Pair, Fair*xair(i))

1 1

Enthalpy of

secondary air

Hsec= Hsec(Tsec, Psec, Fsec*xsec(i))

1 2

Enthalpy of

fuel

Hfuel= Hfuel(Tfuel, Puel, Ffuel*xfuel (i))

1 3

Enthalpy of

gas after

combustion

Hgas = Hgas(Tgas_in, Pgas_in, Fgas_in*xgas_in (i)) 1 4

Density of the

gas

gas= gas(Tgas_in, Pgas_in, Fgas_in*xgas_in (i)) 1 5

Viscosity of

the gas

gas= gas(Tgas_in, Pgas_in, Fgas_in*xgas_in (i))

1 6

Heat capacity

of the inlet

gas

Cpgas_in=Cpgas_in(Tgas_in, Pgas_in, Fgas_in*xgas_in (i))

1 7

Heat capacity

of the outlet

gas

Cpgas_out = Cpgas_out (Tgas_out, Pgas_out, Fgas_out*xgas_out (i))

1 8

Thermal

conductivity

1 9


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5.2.4 Design characteristics:

Some design characteristics will be needed for the mathematical model depending of

the characteristics of the kiln and the columns themselves:

5.2.5 Mass Balance:

Gas:

We assume that:

- the mixing of the three inlet streams happens just before getting in the column,

- the reaction of combustion of the fuel happens just before getting in the column,

during the mixing,

- the fuel is fully oxidised (total reaction),

- the inlet gas flow rate and the outlet gas flow rate are constant and even,

- the composition of the inlet gas flow rate is the one after combustion,

- the composition of the outlet gas flow rate is the same than the inlet gas flow rate

because no reaction happens inside the column,

- the pressure of the inlet gas flow rate is the pressure of the inlet air as it is much

bigger than the two others.

Perimeter:

1 10

Area free:

1 11

Area tiles: 1 12

Area car:

1 13

Area walls: 1 14

Area roof: 1 15

Volume free: 1 16

Volume tiles:

1 17


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Before mixing:

Flow rate: 1 18

Composition: 5 19, 20,

21,

22,

23

Reaction:

CH4 + 2O2 CO2 + 2H2O

From the assumption that the fuel is fully oxidised, we need a condition on the on the

different air flows to keep the excess of oxygen:

We have

from the assumption; we therefore need a minimum amount of

Oxygen which is:

which leads to:

The oxygen comes from the air source and the secondary air source:

Therefore, for a viable process we need the fuel flow rate 19.05 times less than the

sum of the two air flows.

Reaction

progress: 1 24

After the mixing and the passage through the column:

Mass

conservation:

1 25

1 26

1 27

1 28

1 29


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The total mass of the gas is the sum of the mass of each component in the gas:

Total mass

1 30

The total mass is also related to the density of the gas:

Total mass 1 31

Composition:

Composition 5 32, 33,

34,

35,

36

Velocity:

Velocity 1 37

Car:

We assume that:

- The mass of the car does not change over the time,

- The car is moving through the tunnel at a constant velocity.

Mass conservation and flow rate:

Mass

1 38

Flow rate

1 39

Constant

flow rate 1 40

Tiles:

We assume that:

- The mass of the tiles does not change over the time,

- No reaction happens inside the tiles material,

- The tiles are moving through the tunnel at a constant velocity.


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Mass conservation and flow rate:

Mass

1 41

Flow rate

1 42

Constant

flow rate 1 43

5.2.6 Calculation of the heat transfer coefficient of the gas:

The heat transfer coefficient of the gas is a function of the temperature of the gas, the

pressure and the velocity of the gas through the column. As the temperature of the gas

is not constant, the heat transfer is not either:

The Nusselt number is a function of the heat transfer coefficient and the hydraulic

diameter:

Nu

1 44

Dh

1 45

It is function of the Reynolds and Prandt Numbers:

5.2.7 Pressure drop:

Due to the friction between the gas and the tiles, a pressure drop can be observed. The

pressure drop needs to be the smallest possible in order to minimize the energy lost

due to the friction.

The pressure drop is a function of the friction coefficient:

Pdrop 1 49

1 50

From [3], the pressure drop is described as a differential:

Nu 1 46 Re

1 47

Pr

1 48


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The friction factor is a dimensionless parameter. We assume that the gas is fully

developed turbulent flow; we therefore use the Colebrook equation for the friction

factor.

Friction factor

1 51

5.2.8 Energy Balance:

Combustion:

The heat needed to heat up the tiles comes from the combustion of the methane.

In order to control the firing process we need to know precisely the amount of energy

released by the combustion. It can be done by an enthalpy balance.

The difference between the total inlet enthalpy and the total outlet enthalpy (after

combustion) gives the heat of combustion, or in other words the amount of energy

released by the oxidative reaction. This can be then related to the temperature of the

gas after the reaction, just before getting in the column. The heat released is equal to

the energy needed to increase the temperature of the gas from the temperature at the

reaction took place to the temperature after reaction:

The difference between the inlet temperature (the sum of the three enthalpies of the

three flows) and the outlet enthalpy (just after the reaction took place, during the

mixing) gives the heat of combustion. The standard enthalpy of each component can

easily be found in the literature but as we are operating at high temperature, the

enthalpy is function of the temperature, the composition and the flow rate. All these

parameters are taken in account in the gPROMS physical properties package.

Temperature of

the gas after

combustion

1 52

Gas:

By going through the column, the gas exchanges heat with the tiles to heat them up

and with the car. This heat is transferred by convection and radiation as we are


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operating at very high temperatures. At the same time, some heat is lost by radiation

with the walls and the roof.

The difference of energy is the sum of the heat carried by the gas when it gets in the

column, the heat carried by the gas when it gets out of the column, the energy

transferred by convection to the tiles and the car and the heat lost through the walls

and the roof:

Energy balance

for the gas

1 53

Car:

The difference of heat for the car is only due to the convection between it and the gas:

Energy balance

for the car

1 54

Tiles:

The difference of heat for the tiles is due to the convection between it and the gas and

also by radiation:

Energy balance

for the tiles

1 55

The radiative heat transfered between the gas and a surface (here the tiles) is:

Radiation

1 56


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5.2.9 Heat loss:

According to O.B. Goltsova, V.S. Klekovkin, O.B. Nagovitsin, S.V. Antonychev

[13], the thermal loss has the following form:

Qloss=Qwalls+Qroof

Where Qwalls and Qroof is the heat lost through the walls and the roof by convection and

radiation.

According to Sinem Kaya, Ebru Mancuan and K. Kucukada [4], the heat loss is

significant in the firing zone. By writing the heat balance equation on the wall and the

roof given by the following equation, the wall and roof temperatures at any location

along the firing zone and the heat loss for the length increment can be calculated:

Heat transfer

by convection between

air and wall/roof

+

Heat transfer to kiln walls

by radiation from gas

=

Heat transfer through the

kiln walls/roof by

conduction

We therefore have the following equations in our model:

Heat losses 1 57

Qwalls

1 58

Qroof

1 59

Temperature of the walls and temperature of the roof:

Twalls

1 60

Troof

1 61


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5.3 Parameters assigned for our project:

Several parameters have been assigned for the simulation of our model in gPROMS.

The inlet flow rate, temperature, pressure and composition of the fuel, the secondary

air and the air sources as well as some physical properties that we assume remaining

constant during the process.

The inlet flow rate and temperature of the car and the tiles are also known as well as

the physical properties that we assume remaining constant during the process.

Air, secondary air and fuel inlet:

Air Secondary air Fuel

Flow rate (kg.s-1

) 0.5 0.2 0.02

Pressure (Pa) 200000 100000 100000

Temperature (k) 800 700 298.15

XCO2 0 0 0

XH2O 0 0 0

XO2 0.21 0.21 0

XN2 0.79 0.79 0

XCH4 0 0 1

Table 2. Air, Secondary air and Fuel flow rate, temperature, pressure and composition

Material source:

Tiles Car

Mass 20 20

Temperature 500 500

Table 3. Inlet temperature car and tiles

Dimensions for tiles, car and kiln:

Tiles (Column) Car Kiln Wall Roof

Length (m) 4 Kiln length 4.8 / /

Height (m) 1.9 / 2.3 / /

Width (m) 0.6 Wstep / / /

Thickness (m) 0.3 0.3

Table 4. Design characteristic of the Kiln, Car and Tiles


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Properties of the Tiles, car and kiln:

Tiles Car Kiln

Heat capacity, Cp (kJ/kg.K) 0.8364 0.7967 /

Heat transfer coefficient

(W/m2.K)

/ 1 1

Emissivity coefficient (/) 0.93 / 0.85

Thermal conductivity coefficient

(W/m.K)

/ / 0.75

Table 5. Physical properties of the Kiln, Car and Tiles

Some constant used for the model:

Properties Value

gas (/) 0.8

air (/) 1

(Stefan-Boltzmann constant) (W/m2.K) 5.67*10-8

Roug (/) 1

Tstep (s) 180

Table 6. Other constants used in the model

Molecular weight:

Compound Molecular weight (kg/kmol)

CO2 44

H2O 16

O2 28

N2 32

CH4 18

Table 7. Molecular Weight


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5.4 Index of the model:

We have 111 variables:

11 differential variables

100 Algebraic variables

54 Assigned

This leads to 57 unknown variables.

We have 57 equations in our model.

We have 11 algebraic variables so we need 11 initial conditions to get an Index-1

Model.

5.5 Initial Conditions:

We have eleven differential equations in our model; we therefore need eleven initial

conditions:

Equation number (39) and (42), the material mass balance, we need two initial

conditions toward the mass of the car and the mass of the tiles:

Mcar=Mcar(assigned)

Mtiles=Mtiles(assigned)

Equation number (26) to (30), the five mass balance for the outlet composition of the

gas, we need four initial conditions toward the initial composition. If we know four of

the five mass fractions, the fifth is also known by the condition: . We then

need a fifth initial condition. It will be on the inlet flow rate of the gas because the

composition is related to the inlet gas:

xgas_in(1)= xgas_out (1)




Fgas_in=Fgas_out (4)


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Equation number (53), the enthalpy balance of the gas, we need an initial condition

toward the inlet temperature of the gas:

Tgas_in=Tair_in

Equation number (54), (55) and (56) lead us to have three initial conditions on the inlet

temperature of the gas, the car and the tiles:

Tgas_in= Tgas_out

Tcar_in =Tcar_out

Ttiles_in =Ttiles_out


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6. Simulation Results for one column

After the development of the mathematical model the main part of the project has been

to simulate it on gPROMS. The mathematical model comprises a set of integral,

partial differential and algebraic equations (IPDAEs). gPROMS ModelBuilder 3.3.1 is

a software package for the modeling and simulation of processes combining discrete

and continuous characteristics. gPROMS allows the direct modeling of systems

described by a combination of partial differential equations combined with algebraic

ones [23].

Four this process we separate the column of the three gas sources and of the material.

We consider each source as independent for the simulation. This enables us to

change the inlet parameter easily as shown on figure 8.

The column was the section where we put our mathematical model. With the three

sources separated we can control the inlet Temperature of each streams as well as their

flow rate, composition and inlet pressure (See Appendix A.9)

The purpose of separating all the different section was to facilitate the connection of

more than one column as we will discuss later.

Figure 8. gPROMS one column interface


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6.1 Simulation with a fuel Flow rate of 0.02 kg/s

For our first model we fixed the inlet temperature of the the three gas streams and of

the materials source. The inlet temperature of the air coming from the cooling zone

was fixed at 800K, with a pressure of 1Bar, a flow rate of 0.5 kg/s and the composition

of air (21% O2, 79%N2). For the secondary air, the inlet temperature was fixed at

700K, the pressure at 1Bar a flow rate of 0.5 kg/s and the composition of air. The fuel

is 100% methane, coming in the tunnel at ambient temperature at 0.02 kg/s and with a

pressure of 1Bar.

The inlet temperature of the car and the tiles is supposed to be equal and of 500K.

(See Appendix A.1, A.2, A.3, A.4, A.5, A.6, A.7 and A.8 for the gPROMS code)

6.1.1 Evolution of the gas temperature

The first thing we can observe after the simulation of the model is that we reach

quickly the required temperature for the inlet gas. The graph 1 shows the evolution of

the temperature over the time. We can see that the combustion takes place

instantaneously and increased the temperature of the gas from 800K to 1126K.

Graph 1. Inlet temperature of the gas, Ffuel=0.02 kg/s


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On the graph 2 we can observe that the temperature of the outlet gas increases after

passing through the column. It is observed an increase of 4 degrees between the two

temperatures. This is certainly due to the numerical solving and not to a real physical

effect.

It represents an increase of only

.

We can then consider that the inlet and outlet temperature remains constant. It tells us

that the quantity of heat released by the combustion is really important, or that the

amount of heat exchanged and lost is low.

Graph 2. Outlet temperature of the gas, Ffuel=0.02 kg/s


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6.1.2 Evolution of the Tiles and car temperatures

The simulation shows that the temperature of the tiles increases quickly up to 1043K

in less than 100s. The graph 3 shows the distribution of the temperature in the tiles.

We can see that the temperature distribution inside the column is uniform. There is no

variation of the temperature depending of the height of the column.

Graph 3. Tiles temperature, 3D graph, Ffuel=0.02 kg/s

The graph 4 shows that it is a really quick process and the desired temperature is

quickly reached.

Graph 4. Tiles temperature, 2D graph, Ffuel=0.02 kg/s


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In contrast with the tiles, we can observe a different variation of the temperature inside

the car. The temperature increases from 500K to 516K. The radiative exchange

between the gas and the car has not been taken in account in the model. This would

explain the small amount of heat exchanged between the gas and the car (Graph 5). It

is important that we minimize the exchange between the car and the gas. The energy

used to heat up the car is as much as fuel consumed, therefore the car has to be made

with a material with a very low heat transfer coefficient.

Graph 5. Car temperature, Ffuel=0.02 kg/s


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6.1.3 Pressure drop

The pressure drop was an issue in the process. It needs to be the smallest possible. We

can observe a very small pressure drop inside one column of tiles. We get a pressure

drop of 7.3*10-3

Pa which is almost null (graph 6). We can say that the pressure drop

after one column is null and the pressure remains the same.

Graph 6. Pressure drop inside the kiln, Ffuel=0.02 kg/s


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6.1.4 Heat loss

In order to minimize the fuel consumption we need to know how much energy is loss

in the system, through the wall and the roof. For one column we observe a loss of

4030 J/s (Graph 7). This energy is the energy required to heat up the roof and the walls

from 743K to 1060K according to the results of the simulation as shown on graph 8

and 9.

Graph 7. Heat loss through the walls and roof, Ffuel=0.02 kg/s

Graph 8. Kilns Walls Temperature, Ffuel=0.02 kg/s


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Graph 9. Kilns roof Temperature, Ffuel=0.02 kg/s

6.2 Simulation with a fuel Flow rate of 0.005 kg/s

An interesting result is observed while decreasing the amount of fuel fed in the tunnel.

Another simulation has been run with a flow rate of 0.005 kg/s of fuel instead of

0.02kg/s, which is four times less.

We can observe the same quick increase in temperature for the inlet gas flow (Graph

10), up to 1151K which is higher than the temperature got with the previous flow rate.

This means that the process does not need a big amount of fuel to work and that a too

high flow rate would have a negative effect on the process by decreasing the

temperature.


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6.2.1 Evolution of the gas temperature

Graph 10. Inlet temperature of the gas, Ffuel=0.005 kg/s

It can also be observed that the outlet temperature of the gas is now lower than the

inlet which is now coherent with the fact that the gas exchange heat with the tiles and

the tunnel (Graph 11). We can observe a loss of heat due to the exchange happening in

the column. Tgas_out=1149K.

Graph 11. Outlet temperature of the gas, Ffuel=0.005 kg/s


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6.2.2 Evolution of the Tiles and car temperatures

We also observe that the temperature of the tiles is higher than the previous

simulation. With a lower flow rate of fuel, we get a higher inlet gas temperature and a

higher tiles temperature, Ttiles_out=1061K (Graph 12):

Graph 12. Tiles temperature, Ffuel=0.005 kg/s

6.2.3 Heat loss

This result is important in order to minimize the fuel consumption.

At the same time, the heat loss remains almost the same (4121 J/s) as shown in the

graph 13:

Graph 13. Heat loss, Ffuel=0.005 kg/s


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7. Simulation Results for more than one

column

Figure 9. gPROMS 36 columns interface

The general idea with the generalisation of the model was to connect 36 columns

together.

The outlet gas flow rate of the first column was then the inlet gas flow rate of the

second column and so on for the 34 others. It is the same for the material. The outlet

flow rate of material of the 36th

column was the inlet flow of material for the 35th

column and so on until the first one.

This is shown on the figure 9.

Fgas_in_2=Fgas_out_1 and Ftiles_in_35=Ftiles_out_36 which is the same for the car than the tiles.

To connect the columns together we worked step by step. We could not connect them

all together due to high temperature and large flow rate resulting of the addition of the

column and secondary air/ fuel sources.

Some problems have been encountered while simulating the whole process.

In this project, it has not been possible to run the process with only two connected

columns. A solver issue that we have not been able to fix.

Nevertheless, it has been possible to test if the model could run for more than one

column. For this, the results got after the second simulation (after decreasing the fuel

flow rate) have been implemented for a new simulation as the input of the new

simulation (figure 10):


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Column

1

Fuel

Ffuel=0.005 kg/s

Tfuel=298.15K

Secondary air

Fsec=0.05 kg/s

Tsec=700K

Air

Fairc=0.05 kg/s

Tair=800K

Fgas_out_1=Fgas_in_2

Tgas_out_1=Tgas_in_2

x(i)gas_out_1=x(i)gas_in_2

Column

2

Fgas_out_2=Fgas_in_3

Tgas_out_2=Tgas_in_3

x(i)gas_out_2=x(i)gas_in_3

Fuel

Ffuel=0.005 kg/s

Tfuel=298.15K

Secondary air

Fsec=0.05 kg/s

Tsec=700K

Figure 10. Schematic representation of two connected column

First simulation (Table 8):

Fgas_in_1=Fair_1 Ffuel_1 Fsec_1 Flowrate (kg/s) 0.5 0.005 0.5

Temperature (K) 800 298.15 700

Pressure (Pa) 100000 100000 100000

x(1) 0 0 0

x(2) 0 0 0

x(3) 0.21 0 0.21

x(4) 0.79 0 0.79

x(5) 0 1 0

Table 8. First column Inlet

We got, after the first simulation the following results (Table 9):

Fgas_in_2=Fgas_out_1 Ffuel_2 Fsec_2 Flowrate (kg/s) 1.005 0.005 0.5

Temperature (K) 1150 298.15 700

Pressure (Pa) 99999.99 100000 100000

x(1) 0.014 0 0

x(2) 0.01 0 0

x(3) 0.19 0 0.21

x(4) 0.786 0 0.79

x(5) 0 1 0

Table 9. Second column Inlet


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We then obtain the following results after the second simulation for the second

column, with a random temperature for the tiles and the car of: Ttiles=1000K and

Tcar=516 (Table 10):

Fgas_in_3=Fgas_out_2 Ffuel_3 Fsec_3 Flowrate (kg/s) 1.51 0.005 0.5

Temperature (K) 1334 298.15 700

Pressure (Pa) 99999.98 100000 100000

x(1) 0.018 0 0

x(2) 0.014 0 0

x(3) 0.183 0 0.21

x(4) 0.785 0 0.79

x(5) 0 1 0

Ttiles (K) 1255

Tcar (K) 537

Table 10. Second column Outlet/Third column inlet

This simulation shows that with constant values for the inlet flow, we can run the

simulation. As it is a dynamic simulation, the parameters of the new inlet flows are

variables and change during the simulation, and it seems to be the problem of the fail

of the simulation.

From the following graph (Graphs 14, 15, 16, 17), the results are coherent with the

simple simulation in point (5.2):

Graph 14. Tiles temperature, 3D graph, Column 2


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Graph 15. Tiles temperature, 2D graph, Column 2

Graph 16. Car temperature, 2D graph, Column 2


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Graph 17. Outlet temperature of the gas, Column 2


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Conclusion

This work focuses mainly on the development of a stable mathematical model for the

firing section of the tunnel kiln. Based on previous work and assumptions, a dynamic

model was first of all developed for one column of tiles going through the tunnel.

The model describes all the physical phenomena inside de kiln such as the combustion

of the fuel, the heat transfer by convection and radiation between the tiles and the gas,

the heat transfer loss through the walls and roof by convection and radiation, the

pressure drop due to the friction of the gas with the tiles and the mass balance for the

gas and the materials.

By simulating this model with gPROMS, it was shown that the model was stable and

coherent. By several simulations, it has been shown that the amount of fuel fed in the

tunnel was a key point for a proper cooking of the tiles. It was shown that a too high

amount of fuel could lead to an effect which is against the effect desired: decreasing

the temperature of the inlet gas.

A simulation for the whole process was attempted without success. In order to prove

that the model could work for more than one column, two separated simulations were

run. It proved that the model could run and give coherent results. An increased of

temperature was observed for the gas, the tiles and the car.

Regarding the optimisation of the process, it was planned to run an optimisation in

order to minimize the fuel consumption. As the simulation of the whole process has

not worked, the optimisation has not been done. It would be a future work.


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Future Work

According to what is mentioned above, the project concentrates on the modelling of a

stable dynamic model for the firing zone of a tunnel kiln, and the simulation of this

model in gPROMS. Several results have been obtained for one column going through

the tunnel.

However the simulation for more than one column has not been possible in this

project. The model seems to work but it needs more attention to make it work for two

columns and then the whole process with its 36 columns.

Additionally, after the simulation of the whole process, the optimization of the system

in order to minimize the fuel consumption should be run.


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References:

[1] United States Patent, Kiln System, Patent number 4,718,847; Jan. 12, 1988.

[2] D.R. Dugwell, D.E. Oakley, A model of heat transfer in tunnel kilns used for firing

refractories, Int. J. Heat Mass Transfer 1988, 31:2381-2390

[3] E. Mancuhan, K. Kucukada, Optimization of fuel and air use in a tunnel kiln to

produce coal admixed bricks, Appl Therm Eng 2006; 26:1556-1563

[4] S. Kaya, E. Mancuhan, K. Kucukada, Modelling and optimization of the firing

zone of a tunnel kiln to predict the optimal feed locations and mass fluxes of the fuel

and secondary air, App Energy 2009; 86:325-332

[5] S. Kaya, E. Mancuhan, K. Kucukada, Model-based optimization of heat recovery

in the cooling zone of a tunnel kiln, App Therm Eng 2008; 28:633-641

[6] E. Mancuhan, Analysis and optimization of drying of green bricks in a tunnel

dryer, Drying Technology; 27:5:707-713

[7] J. Dukakovic, S. Delalic, Temperature field analysis of tunnel kiln for brick

production, Materials and Geoenvironment 2006, Vol 53, 3:403-408

[8] G. Halasz, J. Toth and K.M. Hangos, Energy-optimal operation conditions of a

tunnel kiln, Comput. Chem. Engng 1988, 12:183-187

[9] R.H. Essenhigh, Studies in Furnace Analysis: Prediction of Tunnel Kiln

Performance by Application of the Integral Energy Equation, Energy and fuels 2001,

15 :552-558

[10] V.G. Abbakumov, G.Sh. Ashkinadze, Convective Heat Exchange in Tunnel Kiln,

Refractories and Industrial Ceramics 1972; 13:3:20-27

[11] G.A. kovelman, A.A. Barenboim, Heat exchange during heating of fine ceramics

in tunnel kilns, State Institute of Ceramics Industry 1974, 10:20-21

[12] S.A. Karaush, Yu. I. Chizhik, E.G. Bober, Optimization of ceramic setting as a

function of their heat absorption from the radiating walls of the furnace, Steklo i

Keramika 1997, 6:25-27


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[13] O.B. Goltsova, V.S. Klekovkin, O.B. Nagovitsin, S.V. Antonychev, Heat losses

in a tunnel kiln for brick firing, Steklo i Keramika 2006, 4:24-25

[14] A. F. Utenkov, E. A. Sinitsyn, V. G. Abbakumov, M. S. Glazman, V. F.

Konstantinov, Yu.F. Sachkov, L. I. Krigman, A. A. Ionin, and B. A. Unaspekov ; A

system for firing a Small tunnel kiln operating on natural gas , Ogneupory 1983, 3 :33-

39

[15] V. G. Abbakumov, G. A. Taraka~chikov, S. I. Vel'sin, Yu. G. Golod, E. I.

Telkman, E. A. Drozdov, A. A. Kulikov, A. G. Belogrudov, I. V. Zimnukhov, N. A.

Domrachev, and A. S. Potapov ; A circular tunnel kiln for firing of refractories,

Ogneupory 1985, 2 :40-44

[16] N.A. Tyutin, B.I. Kitaev, V.G. Avdeeva, Investigation of the aerodynamics of a

tunnel circular kiln, Orgneupory 1982, 6:20-27

[17] J.F.M. Vellhuis, J. Denissen, Simulation model for industrial dryers: reduction of

drying times of ceramics and saving energy, Drying technology, 15:6, 1941-1949

[18] O.B. Goltsova, V.S. Klekovkin, O.B. Nagovitsyn, N.L. Dmitriev, Cause-and-

effect relations with respect to defects in brick firing in tunnel kilns, Steklo I Keramika

2005, 3:26-28

[19] P. Michael, S. Manesis, Modelling and control of industrial tunnel-type furnaces

for brick and tile production. Proceeding of the5th international conference on

technology and automation. Greece: Thessaloniki; 2005. p. 21621.

[20] gPROMS Physical Properties Guide

[21] R.K. Sinnott, Chemical Engineering Design Volume 6, Coulson and Richardsons

Chemical Engineering Series, Fourth Edition

[22] Chemical Engineering Department, MSc Handbook, Imperial College London

2009

[23] PSE, http://www.psenterprise.com/


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APPENDICES

A1. gPROMS Model entity Column

PARAMETER

# Number of components

NoComp AS INTEGER

phys_prop AS FOREIGN_OBJECT "PhysProp"

Tileheight AS REAL

DISTRIBUTION_DOMAIN

Y AS [ 0 : Tileheight ] # normalised domain

UNIT

properties as PropertiesTileCar

Material_Source001 AS Material_Source

PORT

Air_Inlet AS Air_Flowrate

Air_Outlet AS Air_Flowrate

Fuel_Inlet AS Fuel_Flowrate

Secondary_Inlet AS Sec_Flowrate

Material_Inlet AS Material_Flowrate

Material_Outlet AS Material_Flowrate

VARIABLE

#Flowrate

Fair_in as MassFlowrate

Ffuel_in as MassFlowrate

Fsec_in as MassFlowrate

Fgas_in, Fgas_out as MassFlowrate

Mtotal as Mass

M as array(NoComp) of Mass

FcarIn, FcarOut as MassFlowrate

Mcar as Mass

FtilesIn, FtilesOut as MassFlowrate

Mtiles as Mass

xair_in as array(NoComp) of NoType

xfuel_in as array(NoComp) of NoType

xsec_in as array(NoComp) of NoType


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xgas_in, xgas_out as array(NoComp) of NoType

# Combustion

r as MolarFlowrate

#Velocity

velocity as Velocity

# No-type constants

# Time constants

StepTime as notype

# Characteristic Numbers

Re as notype

Pr as notype

Nu as notype

friction as friction

# General Variables

Combined_variable as notype

Dh as Length

Per as area

Afree as area

Atiles as area

Acar as area

Vfree as volume

Vtiles as volume

Awall as area

Aroof as area

#Pressure

Pair_in as Pressure

Pgas_out as Pressure

P_drop as Pressure

Psec_in, Pfuel_in as Pressure

#Heat

QLosses as Heat

Qwall as Heat

Qroof as Heat


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#S as notype

#Temperature

Tair_In as Temperature

Tfuel_In as Temperature

Tsec_In as Temperature

Tgas_In, Tgas_out as Temperature

TcarIn as Temperature

TcarOut as Temperature

TtilesIn as DISTRIBUTION(Y) OF Temperature

TtilesOut as DISTRIBUTION(Y) OF Temperature

Twall as Temperature

Troof as Temperature

#Heat and Radiation coeff

h_convection as convection

k_conductivity as conduction

#Radtiles as heat

# properties

MolecularWeight as array(NoComp) of molecular_weight

density_air as density

viscosity_air as viscosity

cp_gas_out as HeatCapacity

cp_gas_In as HeatCapacity

#Enthalpy

H_in1,H_in2,H_in3, H_out as Heat

random as Heat

set

Phys_prop :=

"IPPFO::mass:

" ;

NoComp := Phys_prop.NumberOfComponents ;

Air_Inlet.no_components := NoComp;

Air_Outlet.no_components

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