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CONTENTS A COMPARISON BETWEEN ANALYTICAL AND NUMERICAL SOLUTION OF THE KROGH’S TISSUE CYLINDER MODEL FOR HUMAN BONE MARROW M. A. Islam 1 AN OXYGEN TRANSPORT MODEL OF HUMAN BONE MARROW FOR HEMOLYTIC SICKLE CELL ANEMIA M. A. Islam and R. Kumar 7 NUMERICAL ANALYSIS OF DROPLET COMBUSTION IN A CYLINDRICAL FURNACE H. N. Mondal and S. Roy 14 KINETICS OF DEHYDRATION OF AROIDS AND DEVELOPED DEHYDRATED AROIDS PRODUCTS M. Kamruzzaman and M.N. Islam 19 A NUMERICAL MODEL FOR BUBBLE SIZE DISTRIBUTION IN TURBULENT GAS-LIQUID DISPERSION M. A. K. Azad and Sultana R. Syeda 25 STUDY OF AN EVAPORATION SYSTEM FOR SODIUM HYDROXIDE SOLUTION Md. Atikur Rahman and Nymul Ehsan Khan 35 CORROSION CONTROL OF ELECTROLYZER, ANOLYTE TANK AND DECHLORINATION TOWER TANK OF A CHLOR-ALKALI PLANT BY AN INNOVATIVE METHOD Sazal Kumar Kundu 37 EFFECT OF SPARK ADVANCE ON A GAS RUN AUTOMOTIVE SPARK IGNITION ENGINE Md. Ehsan 42 TROUBLESHOOTING PLANTWIDE OSCILLATIONS USING NONLINEARITY INFORMATION M. A. A. Shoukat Choudhury 50 MONITORING AND TREND ANALYSIS OF AIR-BORNE PARTICULATE MATTER (PM10 AND PM2.5) AT MAJOR HOT-SPOT AREAS: MOHAKHALI AND FARMGATE IN DHAKA CITY Md. Mominur Rahman, Feroz Kabir, Bilkis Ara Begum and Swapan Kumar Biswas 61

JOURNAL OF CHEMICAL ENGINEERING The Institution of Engineers, Bangladesh Vol. ChE 24, No. 1 January 2006-December 2006

Reg: No. 13/76 ISSN: 0379-4318

Editor Dr. Engr. M. Serajul Islam, F/3118 Department of Chemical Engineering

Bangladesh University of Engineering and Technology

Dhaka – 1000, Bangladesh

Editorial board

Engr. Mohammad Mohsin Ali, F/1525 Vice-President (Academic and International), IEB

Chairman

Prof. Dr. Engr. Dil Afroza Begum, F/3522 Chairman, Chemical Engineering Divisional Committee, IEB

Vice chairman

Engr. Khan Monjur Morshed, F/3030 Honorary General Secretary, IEB

Member

Engr. Sukriti Saha, F/3547 Vice-Chairman, Chemical Engineering Divisional Committee, IEB

Member

Engr. Md. Akhteruzzaman, F/ 5888 Secretary, Chemical Engineering Divisional Committee, IEB

Member

Prof. Dr. Engr. Iqbal Mahmud, F/791 Chairman, BPERB

Member

Prof. Dr. Engr M Sabder Ali, F/1875 Dean, Engineering Faculty, BUET, Dhaka

Member

Engr. Dr. Syeda Sultana Razia, M/18037 Associate Professor, Chemical Engineering Department, BUET, Dhaka

Member

Disclaimer

The Institution of Engineers, Bangladesh does not take any responsibility of the opinions, comments or suggestion expressed in this journal.

JOURNAL OF CHEMICAL ENGINEERING The Institution of Engineers, Bangladesh

Chemical Engineering Division, IEB Divisional Committee, 2006-07

Dr. Engr. Dil Afroza Begum , F/3522 Chairman

Engr. Sukriti Saha , F/3457 Vice Chairman

Engr. Md. Akhtaruzzaman , F/5888 Secretary

Engr. Serajul Majid Mamoon, PEng., F/1040 Immediate Past Chairman

Engr. Sunil Kumar Mondal, F/6253 Immediate Past Secretary

Engr. Salma Akhter, M/15150 Member

Engr. Md. Idris Ali, M/17076 Member

Engr. Mohammad Sazzad Hossain, M/19938 Member

Engr. A.K.M. Humayun Kabir, F/6300 Member

Dr. Engr. Syeda Sultana Razia, M/18037 Member

Acknowledgement

The Editorial Board would like to thank Engr. Syeda Zohra Halim, Lecturer, Department of Chemical Engineering, BUET, for her assistance in compiling this Journal.

Journal of Chemical Engineering, IEB. Vol. ChE. 24, No.1, January 2006 -December 2006

1

A COMPARISON BETWEEN ANALYTICAL AND NUMERICAL SOLUTION OF THE KROGH’S TISSUE CYLINDER MODEL FOR

HUMAN BONE MARROW

M. A. Islam* Department of Chemical Engineering and Applied Chemistry,

University of Toronto, 200 College Street, Toronto ON, M5S 3E5, Canada

Abstract The Danish physiologist, August Krogh is the founder of the theory of oxygen transport to tissues. It was his famous tissue cylinder model developed for skeletal muscle, together with his colleague mathematician Erlang that laid down the foundation of the mathematical modeling of oxygen transport to tissues. Here an analytical solution of the Krogh’s model has been presented based on justifiable assumptions in order to validate the numerical approach used to solve more realistic oxygen transport models. The numerical solution of Krogh’s model is performed using computational fluid dynamics (CFD) software CFX 4.4. From the analytical solution, it is demonstrated that variation from the numerical result is less than 0.2% which in turn justifies the use of computer software in developing mathematical model for such physiological systems like BM.

Introduction The mathematical modeling of oxygen transport processes in the human bone marrow (BM) is a very important arena of biological systems modeling that offers numerous clinical or medical applications. The BM is the sole site for effective hematopoiesis or blood cell production in the adult human being and oxygen is the principal nutrient for differentiation and proliferation of BM hematopoietic cells. So it is very important to have a better understanding of oxygen tension/concentration (pO2) levels in the BM. At present, direct in vivo measurements of pO2 are practically impossible in BM and so, detailed modeling is the only available means to provide reasonable estimates. August Krogh’s pioneering work of tissue cylinder model is the cornerstone of such mathematical modeling. Due to the physical inaccessibility of the BM, no major study has been undertaken to-date that investigates the effect of oxygen and its distribution within the BM microenvironment. However, several sophisticated models have been developed for other tissues including the brain, muscle, skin and kidney. Although Krogh’s model has been the starting point, in general, for all these models, in which the tissue is approximated as a cylinder with a single capillary at its centre, mathematical modeling of pO2 distribution in the human BM is very different and more challenging to that of other tissues due to the complexity of the vascular structure and the heterogeneity of the tissue region. The use of numerical method necessitates the verification of the solution obtained and typically the

validation is via experimental results. However, as stated previously, the physical inaccessibility of the human bone marrow has hindered any detailed analysis through experimental methods. Using simplifying, but reasonable assumptions, an analytical solution to the oxygen transport model has been presented here. This in turn has been compared to the numerical solution obtained for the Kroghian model from the CFD software CFX 4.4. The geometry for the Kroghian system is presented in Figure 2, utilized to obtain a numerical solution. Krogh’s Tissue Cylinder Model The foundation of the theory of “oxygen transport to tissue” was established by August Krogh, a Danish physiologist, who provided the first insights into the role of the smallest micro vessels in the supply of oxygen to striated or skeletal muscle. Together with his colleague, mathematician Erlang in 1918, Krogh developed the famous mathematical model named ‘Krogh’s cylinder model’, which described how oxygen is delivered by a single capillary of a uniform array of capillaries to a surrounding tissue cylinder2. He theorized that the rate of transport is dependent upon the number and distribution of capillaries. In addition, he presumed that the capillaries are the sole supplier of oxygen to blood and each one obtained all of its oxygen by convection (bulk flow) from the terminal arterioles. Each capillary, in turn, served as an independent diffusive source delivering oxygen to a single distinct volume of tissue with homogenous oxygen consumption. Thus, Krogh’s model predicted a linear decrease in hemoglobin oxygen content along each capillary3. The model also captures the

∗ Corresponding author’s e-mail: [email protected]


2

longitudinal and radial O2 gradients within the capillary and surrounding tissue, further providing significant insights into the dynamics of oxygen delivery to the tissues2. The essence of Krogh’s model lies in the assumption that the tissue can be subdivide into circular cylindrical units, each of which has a capillary oriented along the axis and the units do not exchange oxygen with each other (Figure 1). In formulating this geometrical model, Krogh had in mind the capillary geometry in skeletal muscle where muscle fibers have a preferential direction and capillaries tend to be oriented along the fibers.

Fig 1. Geometry of the Krogh’s tissue cylinder

model5.

The assumptions for formulating an equation governing tissue oxygen transport, are, 1) pO2 distribution in the tissue cylinder is axisymmetric, 2) the permeability of tissue to oxygen or the Krogh diffusion coefficient, K=Dtαt is independent of spatial position; 3) O2 in the tissue is not bound to a carrier. Under these assumptions, the equation governing oxygen transport in the tissue can be written in the form4

MzP

rP

rrr

1KtP

2t

2tt −⎥

⎦

⎤⎢⎣

⎡∂∂

+∂∂

∂∂

=∂∂

tα (1)

At the outer boundary of the tissue cylinder the flux of oxygen is zero in accordance with the assumption that adjacent units do not exchange oxygen. Hence

Rrat 0r

Pt ==∂∂ (2)

Krogh further assumed that, 4) a steady state condition (the term ∂Pt/∂t in equation 1 is zero), 5) a constant oxygen consumption rate, 6) negligible axial diffusion (the term ∂2Pt/∂z2 is small) He did not consider the transport of oxygen in the capillary; rather the pO2 at the capillary wall was specified: cwt Rrat PP == (3)

The solution of equation 1 with boundary conditions 2 to 3 is

( ) ( ) Rrln

K2MRRr

4KMzPP

c

22

c2

wt −−+= (4)

This equation gives the radial distribution of tissue pO2 in terms of capillary and tissue cylinder radii and tissue permeability. In particular, it permits the calculation of the minimum tissue pO2, which occurs at the outer rim of the tissue cylinder, i. e. at r= R. The Oxygen Transport Equation Substance diffusion is an equilibration process in which substance molecules are transferred from loci of higher concentration to ones of lower concentration and this is the basis of oxygen transport in blood. The basic law that is applicable in this study is Fick’s second law of diffusion and the Henry-Dalton law, and its application yields the following equation: pK

tp 2∇⋅=∂∂α (5)

where α is the O2 solubility, ∂p/∂t is the change in pO2 with time and 2∇ is the Laplace operator. In addition to the diffusion processes there are other mechanisms that exert their influence on the local oxygen distribution; these include1:

1. Physiological oxygen sink; which may vary with local pO2 (michaelis-menten kinetics).

2. Presence of O2 carrier, hemoglobin (Hb) implies the release or binding of oxygen.

3. This carrier bound O2 (Hb-O2) represents a second oxygen species. The exchange between carrier-bound and free O2 is quantified via the release rate R; which constitutes the link between these equations.

4. Facilitated diffusion enhances free O2 diffusive transport.

5. Local convection displaces free and Hb-O2 at a rate depending on the velocity vector (v). The change in local O2 and Hb-O2 concentrations is proportional to the magnitudes of v and the concentration gradients.

Fig 2. Krogh’s tissue cylinder.


3

Taking into account the above factors, the O2 transport equation can be written as1, 4:

[ ] RpKpvt

pbbb

bb −∇∇=⎥⎦

⎤⎢⎣⎡ ∇+∂∂

..α (6) (3.2)

[ ] RDHvt

H HTT +∇∇=⎥⎦⎤

⎢⎣⎡ ∇+∂∂ γγγ .. (7) (3.3)

where R represents the net rate of carrier O2 release. Under most conditions, it is further possible to reduce the above set of equations to form a single equation under the assumption that the reaction rate described is extremely fast and thus the two states are always in equilibrium. Accordingly, the hemoglobin saturation (γ) solely depends on the partial pressure (pO2). Thus equations 6 and 7 can be reduced to:

[ ] [ ] )8( ..

..

γ

γγα

∇∇+∇∇=

⎥⎦⎤

⎢⎣⎡ ∇+∂∂

+⎥⎦⎤

⎢⎣⎡ ∇+∂∂

HTbb

Tbb

b

DHpK

vt

Hpvt

p

Applying the following chain rule, the above equation can be written as

( )t

pp

tp

ptbb

b ∂∂

=∂∂⋅

∂∂

=∂∂ 'γγγ , ( ) pp ∇=∇ 'γγ (9)

( ) ( )

[ ] ( )[ ] )10( '.

'.'

bHTbb

bb

Tbb

b

ppDHpK

ppvtp

pHpvtp

∇⋅∇+∇∇=

⎥⎦⎤

⎢⎣⎡ ∇+

∂∂

+⎥⎦⎤

⎢⎣⎡ ∇⋅+∂∂

γ

γγα r

Simplification of the above equation gives

( ) ( ) bHb

Tbb

b

b

Tb ppD

KHKpv

tp

pH∇⎥⎦

⎤⎢⎣

⎡+⋅∇=⎥⎦

⎤⎢⎣⎡ ∇⋅+∂∂

⎥⎦

⎤⎢⎣

⎡+ '1'1 γγα

α

(11)

( ) ( ) bHb

Tbb

bb ppD

KHKpv

tp

m ∇⎥⎦

⎤⎢⎣

⎡+⋅∇=⎥⎦

⎤⎢⎣⎡ ∇⋅+∂∂

+⇒ '11 γα

(12) where ( )p'

H m

b

T γα

= and ( )p'γ is the first derivative

of ( ) n

n

⎟⎠⎞⎜

⎝⎛+

⎟⎠⎞⎜

⎝⎛

=

50

50

pp1

pp

pγ .

The term Kb (1+…) is referred to as effective conductivity Keff. Hence, the oxygen transport equation for the blood region becomes

( ) [ ]beffbb

b pKpvt

pm ∇⋅∇=⎥⎦

⎤⎢⎣

⎡ ∇⋅+∂∂

+1α (13)

In cylindrical co-ordinates, the above equation can be written as,

( ) ⎥⎦

⎤⎢⎣

⎡∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=⎥⎦⎤

⎢⎣⎡

∂∂

+∂∂

+ 2

211zp

rpr

rrK

zpv

tpm bb

effbb

bα (14)

Replacing Keff by αbDb and dividing by αb,

( ) ⎥⎦

⎤⎢⎣

⎡∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=⎥⎦⎤

⎢⎣⎡

∂∂

+∂∂

+ 2

211zp

rpr

rrD

zpv

tpm bb

bbb (15)

For the tissue region, the O2 transport eqn can be written as

02

21 mzp

rp

rrr

Kt

p ttt

tt −⎥

⎦

⎤⎢⎣

⎡∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=⎥⎦⎤

⎢⎣⎡∂∂

α (16)

where m0 is the volumetric metabolic oxygen consumption rate of tissue (assumed constant). After dividing both sides by αb

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎥⎦

⎤⎢⎣

⎡∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎥⎦

⎤⎢⎣⎡∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛

t

ttt

b

tt

b

t mzp

rpr

rrD

tp

ααα

αα 0

2

21 (17)

Boundary Conditions The boundary conditions needed to solve equations 15 and 16 are as follows: Blood region: crrLz ≤≤≤≤ 0 and 0 (18)

BC 1: z =0, pb = pb(t) BC 2: z = L, ∂pb/∂z = 0 BC 3: r = 0, ∂pb/∂r = 0

BC 4: r = rc, pb = pt and Dbr

pD

rp t

tb

tb

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∂∂

αα

Tissue region: tc rrrLz ≤≤≤≤ and 0 (19)

BC 5: z = 0, ∂pt/∂z=0 BC 6: z = L, ∂pt/∂z=0 BC 7: r = rt, ∂pt/∂z=0 These two boundary conditions state that oxygen cannot leave the tissue region at either end by axial diffusion. Analytical Solution Solution of the above equations for the oxygen concentrations within the blood and tissue regions is a formidable problem which can be accomplished numerically with the help of computational techniques but, a reasonable analytical solution can be obtained with some simplifications and this was explored by Fournier6. The basic assumptions include, 1) steady-state condition, 2) m is constant, 3) negligible axial diffusion within the tissue region, 4) within the


4

capillary, negligible axial diffusion in comparison to axial convection. Applying these assumptions in equation 15 gives

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=∂∂

+r

pr

rrD

zp

vm bb

b 11 (20)

Radial averaging of the above equation gives

( )∫ ∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=∂∂

+c cr r

bb

b rdrrp

rrr

Drdrzp

vm0 0

1212 ππ (21)

( )c

c

r

bcb

r

b rp

rDrdrpdzdvm

∂∂

=+⇒ ∫ ππ 2120

(22)

The radially averaged pO2 level in the blood, bp can

be defined as

∫=cr

bcb rdrprp0

2 2ππ (23)

This allows equation 22 to be written as

( )cr

b

c

bb

drdp

vrD

zp

m2

1 =∂

∂+ (24)

Applying BC 4 in the above equation, we have

( )cr

t

bc

ttb

drdp

vrD

zp

mαα2

1 =∂

∂+ (25)

The basic assumptions simplifies equation 17 to the following form

rD

mdrdp

rdrd

tt

t

α0=⎟

⎠⎞

⎜⎝⎛ (26)

Integration of the above equation two times followed by application of the boundary conditions 4 and 7 in equations 18 and 19 gives the following result.

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

ctt

t

ctt

cbt r

rD

rrr

Dmrzpzrp ln

21

4,

22

02

αα (27)

Equation 27 is the analytical solution of the oxygen concentration equation in the tissue region. Differentiation of Equation 27 with respect to r at r = rc gives the following equation

ctt

t

tt

c

r

t

rDmr

Dmr

drdp

cαα 22

02

0 −= (28)

Using this result in equation 26 gives

( )c

ctt

t

tt

c

bc

ttb

rDmr

Dmr

vrD

zp

m ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

∂

∂+

αααα

222

1 02

0 (29)

( )( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

−=⇒ 11

2

0

c

t

b

b

rr

vmm

dzpd

α (30)

This equation may be integrated to give the following result,

( ) ( )( ) zrr

vmm

pzpc

t

binbb

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

−= 11

2

0

α (31)

Equation 31 is the analytical solution of the oxygen concentration equation in the capillary region. Results and Analyses The results obtained by using CFD software CFX 4.4 for the numerical solution of the Kroghian model have been compared with the results of the aforementioned analytical solutions in a view to justify the use of CFX 4.4 for developing more realistic mathematical model of bone marrow7. Figure 3 depicts the comparison between analytical and numerical solution for the tissue region at an input oxygen partial pressure of 80 mm Hg and a radial distance of 160 µm in the capillary region. It clearly demonstrates that the oxygen partial pressure gradually decreases with the increase of radial distance in the tissue region, which signifies that the oxygen concentration distant from the supplying region experiences lower oxygen content. This in turn can affect the cellular functions residing in this region, such as granulopoietic cells. The small variation in the partial pressure of oxygen is due to the choice of the lowest consumption rate for the cells (granulocytes).

Fig 3. Plot of numerical vs. analytical solution for

tissue region at pO2 = 80 mm Hg and Z = 160 µm.


5

Fig 4. Plot of numerical solutions in different

capillary distances for the tissue region at pO2 = 80 mm Hg.

Fig 5. Percentage error in between numerical and

analytical solution for the tissue region at pO2= 80 mm Hg.

Fig 6. Comparison between numerical and analytical

solution for the capillary region at pO2 = 80 mm

Fig 7. Percentage error between numerical and

analytical solution for the capillary region at pO2 = 80 mm Hg.

Figure 4 illustrates the varying oxygen tension with radial distance in the BM microenvironment, at different axial distances in the capillary region. The main objective of this section is to high-light the minimal error between the numerical solutions obtained from CFX when compared to an analytical solution, and in Figure 5 the error between analytical and numerical solution is between (0.05-0.35) %; which is within the acceptable margin of error (1%). Furthermore, the error decreases exponentially as the radial distance increases. Figure 6 is the comparison of analytical and numerical solutions for the capillary region, while Figure 7 is the error of the solutions for the capillary. The only notable difference from the solutions for the tissue region is that for capillary, the trend of decreasing oxygen partial pressure is linear which demonstrates the homogeneity of the capillary region. Hence, the error is also much lower than the capillary region and in some instances the error almost diminishes. Conclusion Given the small error between the expected and the simulated data, the numerical method utilized within this work is assumed to be predictive, with a high level of confidence. This in turn validates the use of CFX 4.4 to develop more realistic mathematical models for normal as well as pathological BM with potential clinical applications. Acknowledgement The author is indebted to commonwealth scholarship commission, UK for funding this project.


6

Nomenclature

Db Diffusion coefficient of blood in tissue cm2s-1

Dt Diffusion coefficient of oxygen in tissue cm2s-1

HT Volume fraction of hemoglobin in blood %

M Modified Hill Constant for CO2

1/mmHg

m0 Volumetric oxygen consumption rate mol O2 cm-3s-1

Keff Effective Krogh coefficient

mol O2 cm-3s-1

mmHg-1

K Oxygen permeability mol O2 cm-3s-1

mmHg-1

Kb Oxygen permeability-blood

mol O2 cm-3s-1

mmHg-1

Kt Oxygen permeability-tissue

mol O2 cm-3s-1

mmHg-1

pO2 Oxygen tension (Partial pressure) mm Hg

pt Oxygen Tension in tissue mm Hg

pb Oxygen Tension in blood mm Hg

rt Radius of the tissue cylinder µm

rc Radius of the sinus µm

Greek Symbols αb Oxygen solubility-blood mol O2 cm-3

mm Hg-1

αt Oxygen solubility-tissue mol O2 cm-3 mm Hg-1

γ Oxygen saturation function -

References 1. Groebe, K. and Thews, G., Basic mechanisms of

diffusive and diffusion-related oxygen transport in biological systems: a review. Adv Exp Med Biol . 317(Oxygen Transport to Tissue XIV): 21-33, 1992.

2. Kreuzer, F., Oxygen supply to tissue: the Krogh

model and its assumptions, Experientia, 38: 1415–1426, 1982.

3. Ellsworth, M.L. and Pitman, R.N., Arterioles

supply oxygen to capillaries by diffusion as well as by convection, Am J Physiol, 258: H1240–H1243, 1990.

4. Popel, A.S., Theory of Oxygen Transport to

Tissue, Critical Reviews in Biomedical Engineering, 17(3): 257-321, 1989.

5. Reneau, D.D. Jr, Bruley, D.F. and Kinsley, M.H.,

A mathematical simulation of oxygen release, diffusion, and consumption in capillaries and tissue of the human brain, Chemical Engineering in Medicine and Biology, Hershey, D. (ed.) (Plenum Press, New York, USA), pp 135, 1967.

6. Fournier, R.L., Basic Transport Phenomena in

Biomedical Engineering, Crc Press Llc; 1 edition, 1998.

7. Islam, M.A., Simulating Oxygen Transport in the

Human Bone Marrow: Hemolytic Sickle Cell Anemia Study, MSc Thesis, Imperial College London, 2005.


7

AN OXYGEN TRANSPORT MODEL OF HUMAN BONE MARROW FOR HEMOLYTIC SICKLE CELL ANEMIA

M. A. Islam*

Department of Chemical Engineering and Applied Chemistry University of Toronto, 200 College Street, Toronto ON, M5S 3E5, Canada

R. Kumar

Petrofac Engineering, 76-86 Chertsey Road, Woking Surrey, GU21 5BJ, UK

Abstract The human bone marrow (BM) is a complicated tissue with intricate vascular and heterogeneous extravascular (tissue) architecture. Oxygen is an important modulator of differentiation and proliferation of the BM hematopoietic cells under normal and pathological conditions. Currently, due to the inaccessibility of the BM, it is not possible to measure the spatial distribution of the oxygen tension (concentration) levels in the tissue. Thus, the present treatise utilizes mathematical modeling to offer a greater insight on the effects of oxygen on the BM cellular components. Here, we present simulation results that are correlated with known in vivo data of BM along with proposing a model for the two state description of allosteric hemoglobin molecule under hemolytic sickle cell anemia condition of BM.

Introduction Hematopoiesis is the process of blood cell formation that takes place primarily in the bone marrow (BM) in adults. This produces three types of blood cells; namely, red blood cells (RBC), white blood cells (WBC) and platelets, contributing approximately one trillion cells per day to the human circulatory system. The BM factory requires the constant availability of oxygen, the principal nutrient for the energy metabolism of active tissues. Since cessation of oxygen supply results in loss of function (BM proliferation and differentiation) within seconds, continual feed of adequate amount of oxygen to tissue is the pivotal task for nutrient delivery vehicles; the BM microcirculation. In addition, due to the intricate structure of tissue, the metabolic oxygen requirements are spatially varied and highly heterogeneous. It is for this reason that understanding the mechanism affecting the oxygen delivery to the tissue is of great importance. The experimental techniques available to-date have been inadequate for studying the oxygen concentration and its distribution within the BM due to the inaccessibility of the BM, and thus modeling provides an attractive alternative to have a better understanding of the BM function under normal and pathophysiological conditions. In the present work, we develop models to study the oxygen transport between the extravascular space (tissue) and the delivery system of the BM. The model is essentially based on symmetry description of oxygen loading and unloading between the two conformational states of hemoglobin; deoxyhemoglobin and

oxyhemoglobin. The model is extended to study the bone marrow under pathological condition, which is sickle cell anemia in this case. The transport model under normal conditions combines oxygen transport in the sinusoidal region with the extravascular space surrounding these vessels. In addition, as the famous Hill equation has been utilized for the representation of the oxygen saturation curve, to account explicitly for the effect of pH and carbon dioxide on the oxygen transport, the variable Hill coefficient model has been implemented. The development of such physiologically relevant models for oxygen tension distribution in the human BM could offer numerous clinical/medical applications including understanding of the effects of oxygen tension on drug efficacy (chemotherapy) to the hematopoietic compartment, and assisting in the reconstitution of ex vivo bone marrow engineering constructs. Sickle Cell Anemia Sickle cell anemia is a disorder/disease of the blood which has been subjected to intense scrutiny at the vascular, clinical, cellular, biochemical and molecular levels over the last few decades in order to have a better understanding of the pathophysiology of the disease which portends the development of effective therapy. It is an inherited disorder that is uniquely accompanied by a severe clinical phenotype of vascular occlusion. The disease, caused by inherited abnormal hemoglobin (an oxygen-carrying protein within the red blood cells), results in a sudden increase



8

in the destruction of red blood cells called hemolysis (Figure 1).

Fig 1. Normal hemoglobin (HbA) and sickle

hemoglobin (HbS)3 The varied clinical manifestations of sickle cell anemia are generally attributable to either microvascular occlusion or accelerated red blood cell destruction. While possible determinants of vasocclusion have received much investigative attention, fewer studies have addressed the hemolytic component of this disease2. The sickle RBCs (Fig 1) appear to be more susceptible to fragmentation and disintegration than normal RBCs. Hence, the aim of this research project is to develop a model to analyze the effect of the hemolytic rate on the oxygen distribution in the bone marrow. Models for Allosteric Proteins Monod and Jacob5 introduced the term ‘allosteric’ in a discussion on end-product inhibition. Presently, allosteric term refers to any mechanism in which protein can exist in two (or more) distinct conformations, which differ in their affinity for a ligand. More specifically, hemoglobin is an allosteric protein as the binding of oxygen at one hemoglobin site is coupled with the binding of other substances at other sites, due to the conformational change of the molecule9. From a mechanistic perspective, there are two hypotheses that describe the conformational changes in the allosteric molecules: the symmetry or two-state model of Monod et al, known as MWC model6and the sequential or induced-fit model model of Koshland et al, known as KNF model7. The MWC or two-state model of co-operativity has at its core the axiom that only a single R (Relaxed)-state

and T (Tension)-state exist, and co-operative functioning and allosteric modulation occur simply by a switching between different population distributions of the R- and T-states. The sequential or induced-fit model involves four subunits, one binding site per subunit, and one type of ligand. The assumptions in the induced-fit model are that each subunit can exist in either of two conformational states, the A and B states, with the equilibrium constant Kt= (B)/(A) characterizing the relative stability of the conformations. Oxygen Transport in Blood Hemoglobin is basically an iron containing pigment of vertebrate red blood cells that functions primarily in the transport of oxygen from the lungs to the tissues of the body. This molecule in almost all vertebrate is tetramer consisting of four peptide chains, each with an incorporated heme group. During the oxygenation of hemoglobin molecule, the Fe of each heme group binds O2 molecule to cause conformational change of hemoglobin which in turn affects its ability to further bind oxygen or other molecules. The binding affinity of hemoglobin for oxygen molecule is influenced by hemoglobin-oxygen saturation (SO2) which is defined as the fraction of available oxygen-binding sites occupied by oxygen and is expressed as either a fraction or a percent9.

The ability of a medium to dissolve free oxygen is characterized by a parameter called the Bunsen solubility coefficient and is denoted by α. According to Henry’s law: [O2] = αP (1)

where [O2] is the concentration of dissolved oxygen and P is the partial pressure of oxygen (oxygen tension), pO2

9.

Fig 2. Oxyhemoglobin Dissociation Curve10.


9

The plot of oxygen-hemoglobin (Hb-O2) saturation vs. oxygen tension (pO2) is a sigmoid curve called Oxyhemoglobin Dissociation Curve (ODC) or Oxygen-Hemoglobin Equilibrium Curve (OHEC) (Fig 2). In order to do the mathematical modeling of oxygen transport to various tissues, accurate expressions for SO2 as a function of pO2 and other parameters are very important. The available expressions for describing the ODC curve fall into two categories. Those that are derived from the kinetic models of hemoglobin-oxygen reaction, and those that are constructed empirically without the aid of kinetics. In 1910, Hill proposed the first kinetic model, which expressed the sigmoidal shape of the ODC curve, can be explained by the following reaction: ka Hb + n O2 Hb(O2)n (2) kb where n represents the number of molecules of oxygen that bind with hemoglobin (Hb) to form oxyhemoglobin [Hb(O2)n] and ka and kb are the association and dissociation rate coefficients, respectively. In equilibrium, the Hb saturation can be described using:

[ ][ ]n

n

OKOKS

2

2

1+= (3)

where K= ka/kb is the equilibrium constant and [O2] is the concentration of free oxygen in hemoglobin solution. Using Henry’s law (Equation 1), we can rewrite equation 3 in the following form:

( )( )n

n

PPPP

S50

50

/1/

+= (4)

where P50 = 1/(Knα) is the value of pO2 at which the hemoglobin is 50% saturated. Equation 4 is reasonably accurate within the saturation range 20 – 80% with n ≈ 2.7 for human blood. This equation is called the Hill equation8, its simplicity has resulted in being used within numerous mathematical simulations. However, for a more realistic presentation some authors have also applied a more complicated expression for the dissociation curve; namely the Adair’s four step mechanism1, 11. ka O2 + Hb4(O2)i-1 Hb4(O2)i, i= 1,2, 3, 4 kb (5) In equilibrium, the above equation yields the Adair equation:

( )4

43

32

21

44

33

221

14432

PaPaPaPaPaPaPaPa

S++++

+++= (6)

where S is expressed as the ratio of the number of oxygen molecules to the total number of hem groups:

( )[ ]

( )[ ]∑

∑

=

== 4

1ii24

4

1ii24

OHb

OHbiS (7)

Constants ai’s are called Adair constants9. The mathematical complexity of the Adair’s model has retarded its use in mathematical simulation of oxygen transport. Mathematical Model Oxygen Transport Simulation Majority of the oxygen transport models developed to-date are usually based on the Adair type reaction scheme or its modifications, the basic equations of which are presented as9, 12

[ ] RpKpvt

pbbb

bb −∇∇=⎥⎦

⎤⎢⎣⎡ ∇+∂∂

..α (8)

[ ] RDHvt

H HTT +∇∇=⎥⎦⎤

⎢⎣⎡ ∇+∂∂ γγγ .. (9)

The ‘R’ term is the reaction term corresponding to the addition or subtraction of oxygen from the surrounding plasma. The cases analyzed in this section include: 1) the oxygen transport model with constant Hill’s coefficient (Equation 10), 2) explicit expression for the carbon dioxide in the Hill’s equation (Equation 11), and 3) variable Hill’s coefficient (Equations 12-14). The following equations summarize these cases:

( )1 ( )t df pR N k

f pγ⎡ ⎤−

= ⎢ ⎥−⎣ ⎦ (10)

2

2

( )( )1 ( )

n

n

Kp Of pKp O

⎡ ⎤= ⎢ ⎥+⎣ ⎦

(11)

2

2 2

( )( )1 ( ) ( )

n

n

Kp Of pKp O mp CO

⎡ ⎤= ⎢ ⎥+ +⎣ ⎦

(12)

0 2

0 2

( )( )1 ( )

n

n

K p Of pK p O

⎡ ⎤= ⎢ ⎥+⎣ ⎦

(13)

( ) ( )

( ) ( )

2

2

22 6

0

21 5

1

'

1

pl rbcCO rbc

L pl

plpl rbc

CO rbcpl

H pCOK K r

r HK K H

H pCOK K r

r H

α

α

+

+−+

+

+

⎛ ⎞⎛ ⎞ ⎛ ⎞⎡ ⎤⎣ ⎦⎜ ⎟⎜ ⎟ ⎜ ⎟+ +⎜ ⎟⎜ ⎟ ⎜ ⎟⎡ ⎤⎣ ⎦⎝ ⎠ ⎝ ⎠⎜ ⎟⎡ ⎤= ⎣ ⎦ ⎜ ⎟⎛ ⎞ ⎛ ⎞⎡ ⎤⎣ ⎦⎜ ⎟⎜ ⎟ ⎜ ⎟+ +⎜ ⎟⎜ ⎟ ⎜ ⎟⎡ ⎤⎜ ⎟⎣ ⎦⎝ ⎠ ⎝ ⎠⎝ ⎠

(14)

where, ( )23'nL

O rbcK K r α=

The variable Hill constant model and the modified Hill equation were presented by Sharan et al.14 and Sharan & Singh13, respectively. All the variables in these equations have also been defined in the nomenclature


10

section of this paper, and can also be found in the appropriate papers.

Fig 3. A. Oxygen saturation against dimensionless axial

distance within the sinus. The simulation results are presented under steady state condition for maximum (GMax) and average (GAvg) granulocyte consumption rates in the homogeneous tissue environment. B. The oxygen tension distribution within the BM microenvironment for the conditions in A.

Although no quantitative verification can be offered that validates the simulation results, we can, however, present qualitative description of the oxygen transport process that does offer a partial authentication of the results. It is known that the saturation level decreases by approximately 15% during the transport process under normal conditions12, and as can be seen in Fig 3, the saturation for the hemoglobin does decrease by 15% under maximum granulocyte consumption. The BM is a highly heterogeneous tissue with a multimodal distribution of cellular components, and in turn implying a wide variation in the consumption rate

values. The literature data is based on the consumption rates of cells in brain tissue, which has a closer oxygen uptake rate to the progenitor granulocytes than other cell types. One of the main limitations of the Hill equation, despite its simplicity offering a tremendous advantage, is its inability to capture the ODC throughout its entire plasma oxygen partial pressure range. The above representations of the Hill equation attempts to overcome this deficiency. Figure 4 manifests a comparison between the saturation levels and the oxygen tension distribution for the different representations of the Hill equation (Equations 10-14).

Fig 4. A. Oxygen saturation against dimensionless axial

distance within the sinus. The simulation results are presented for a one residence time of blood flow and average granulocyte consumption rate. Variable Hill Coefficient (V), Constant Hill coefficient (C), and Modified Hill Equation (M). B. The oxygen tension distribution within the BM microenvironment for the conditions in A.

The results in Figure 4 shows that the variable Hill constant model predicts a lower average tissue partial


11

pressure and a lower oxygen distribution within the tissue environment (B), while the saturation decrease is at a slower rate than predicted by other models. Although such results can be considered to be negligible under the present circumstances, it is, however, more likely to be important under pathological conditions where any sensitivity in the model simulation can impart significant effects on the oxygen distribution in the tissue region. In Figure 5, the transient development of the oxygen tension in the tissue is presented for four time points. As expected, during the early part of the simulation, majority of the tissue remains in hypoxic state, while some regions of the tissue can be anoxic. With increasing time, the tissue emerges from the hypoxic state and approaching the steady state oxygen tension values (indicated by rightward shift in the tissue profiles).

Fig 5. The transient development of oxygen tension

distribution within the BM microenvironment for the conditions in Fig 4. The simulation results are presented for average granulocyte consumption rate.

Two State Model Development: Hemolysis Alternative description to the Adair’s stepwise mechanism is the two state schemes; which has been described earlier. The model presented in this section is based on the existence of the two conformational states of the hemoglobin, i.e. the oxy- and the deoxy-hemoglobin. The transport model for normal condition (Equations 15-26) is extended to hemolytic sickle cell anemia. Sinus Region

[ ] RpKpvt

pbbb

bb −∇⋅∇=⎥⎦

⎤⎢⎣⎡ ∇⋅+∂∂

α (15)

[ ] RNDNvt

NHOHHO

HO +∇⋅∇=⎥⎦⎤

⎢⎣⎡ ∇⋅+

∂∂ (16)

[ ] RNDNvt

NHHH

H −∇⋅∇=⎥⎦⎤

⎢⎣⎡ ∇⋅+∂∂ (17)

Tissue Region

[ ] 0mpKt

ptt

tt −∇⋅∇=⎥⎦

⎤⎢⎣⎡∂∂

α (18)

where

( )( ) ⎥

⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

= HOHd Npf

pfNkR1

(19)

( ) 0

01

n

n

K pf pK p

⎡ ⎤= ⎢ ⎥+⎣ ⎦

(20)

where, k0 = variable Hill constant13

Obb DK α= (21)

[ ]( )Hbb2

0 10997.11 −×+= αα (22)

where [Hb] is in millimolars.

mM/Torr 10459.1 3350 0

−×=C

α (23)

[ ] [ ] [ ]( ) s/cm 1008.28078.262148.95032.14 2732 −×−+−= HbHbHbDH

(24) [ ] [ ] [ ]( ) s/cm 101794.53107.05056.40719.2 2532 −×+−−= HbHbHbDO

(25) where [Hb] is in g/cc solution and valid at 25°C. Boundary Conditions

BC 1: w

tt

w

bb r

pK

rp

K∂∂

=∂∂ (26)

BC 2: wtwb pp =

BC 3: 0=∂∂

=∂

∂

w

HH

w

HOH r

NDr

ND

In Figure 6, the results are presented for the two state model under normal conditions. The boundary conditions for the oxy- and deoxy-hemoglobin at the sinusoidal/tissue interface maintain the total concentration of hemoglobin to be constant. During the oxygen transport process, the release of oxygen from the oxy-hemoglobin is transferred to the deoxy-hemoglobin, and to the plasma region; and the concentration gradient between the tissue and the blood drives the plasma pO2 into the tissue region. This process is clearly demonstrated in Figure 6(A). The hemolytic model assumed random destruction of the erythrocytes and the ‘death’ term is present only in the equations for the oxy- and deoxy-hemoglobin.


12

Future Works The hemolytic model presented in this paper is still in the early stages of development and significant amount of work is yet to be carried out to actually reach a point where a working model is attained; but mathematical modeling represents an excellent alternative to examining the pathological implications of sickle hemoglobin and the related changes in the bone marrow oxygen transport. Given that, at present, only a simplified model for the RBC destruction has been considered, it is fitting that we advance the model so that more realistic features of the in vivo sickle cell disease are captured involving both the intravascular and extravascular destruction of erythrocytes.

Fig 6. A. The variation in concentration of oxy- and

deoxy-hemoglobin for normal oxygen transport, against dimensionless axial distance within the sinus. The simulation results are presented at 0.75s and average granulocyte consumption rate. The Hill constant with Variable Hill Coefficient (V), is utilized in the model above. B. The axial variation in oxygen tension conditions within the vessel. Further model parameters are presented in Appendix.

The model advancements can proceed on three major fronts: microcirculation structure, extravascular arrangement of cellular components, fluid dynamics of the blood flow and its components and RBC destruction mechanism. Accounting for all these factors would indeed formulate a more complete model that can lead to true predictions of the disease. However, such a model would be appropriate for a long-term research goal, but for the immediate case, we propose features that can be incorporated into the present hemolytic model from the aspects of using CFD software CFX. To account for the propensity for RBC interaction with macrophages, we propose a multiphase model that includes both RBCs and macrophages and under certain conditions, this can lead to RBC hemolysis. To account for the extravascular destruction of the RBC, the heterogeneous geometrical presentation can be extended to include random destruction of cellular components through the use of source terms. As a final point, although the strategy is yet undetermined, the hemolysis model can be combined with Sickle Cell polymerization aspects; such a model is a step towards the real in vivo situation. Acknowledgement The author would like to thank Commonwealth Scholarship Commission for funding the project.


13

Nomenclature

Db Diffusion coefficient of blood in tissue cm2s-1

Dt Diffusion coefficient of oxygen in tissue cm2s-1

DH Diffusion coefficient of hemoglobin in blood cm2s-1

M Modified Hill Constant for CO2

1/mmHg

m0 Volumetric oxygen consumption rate mol O2 cm-3s-1

K Equilibrium Constant cm3g-1

Keff Effective Krogh coefficient mol O2 cm-3s-1

mmHg-1 kd Dissociation rate coefficient - ka Association rate coefficient -

Kb Oxygen permeability-blood mol O2 cm-3s-1

mmHg-1

Kt Oxygen permeability-tissue mol O2 cm-3s-1

mmHg-1 Km Michaelis-Menten Constant mmHg n Hill’s Coefficient - NH

O Molar concentration of oxyhemoglobin

mol Hb cm-3 blood

NH Molar concentration of deoxyhemoglobin

mol Hb cm-3 blood

NT Molar concentration of total hemoglobin

mol Hb cm-3 blood

S Sink or source term mol O2 cm-3s-1

mmHg-1

R Consumption rate mol O2 cm-3s-1

mmHg-1 [H+

] Hydrogen ion concentration nmol/cm3

pl Plasma - pt Oxygen Tension in tissue mm Hg pb Oxygen Tension in blood mm Hg

Greek Symbols

αb Oxygen solubility-blood mol O2 cm-3 mm Hg-1

αt Oxygen solubility-tissue mol O2 cm-3 mm Hg-1

µ Viscosity p ρ Density gcm-3 Г Diffusion coefficient - γ Oxygen saturation function - λ Thermal conductivity - φ General variable -

References 1. Adair, G.S., The Hemoglobin System. VI. The

oxygen dissociation curve of hemoglobin. J Biol. Chem, 63: 529-545, 1925.

2. Bensinger, T.A. and Gillette, P.N., Hemolysis in sickle cell disease. Arch Intern Med 133:624-631, 1974.

3. Bwh. Harvard, : What is sickle cell disease? http://sickle.bwh.harvard.edu/scd_background.html, 2002

4. Changeux, J-P and Edelstein, SJ, Allosteric receptors after 30 years. Neuron, 21: 959-980, 1998.

5. Monod, J. and Jacob, F., General conclusions: telenomic mechanisms in cellular metabolism, growth and differentiation. Cold Spring Harbor Symp Quant Biol 26:389-401, 1961.

6. Monod, J., Wyman, J., and Changeux, J-P, On the nature of allosteric transitions: a plausible model. J Mol Biol 12:88-118, 1965.

7. Koshland, D. E., Nemethy, G., and Filmer, D., Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry 5:365-385, 1966.

8. Hill, A.V., The possible effects of the aggregation of the molecules of hemoglobin on its dissociation curve. J. Physiol (London), (iv): 41, 1910.

9. Popel, A.S., Theory of Oxygen Transport to Tissue, Critical Reviews in Biomedical Engineering, 17(3): 257-321, 1989.

10. Wikipedia,:Hemoglobin http://en.wikipedia.org/wiki/Hemoglobin, 2004

11. Yap, EW, Hellums, J.D., Use of Adair four-step kinetics in mathematical simulation of oxygen transport in the microcirculation. Adv Exp Med Biol., 215: 193-207, 1987.

12. Groebe, K. and Thews, G., Basic mechanisms of diffusive and diffusion-related oxygen transport in biological systems: a review. Advances in Experimental Medicine and Biology. 317(Oxygen Transport to Tissue XIV): 21-33, 1992.

13. Sharan, M., and Singh, M.P., Equivalence between one step kinetics and Hill’s Equation. J Biomed Eng 6: 297-302, 1984.

14. Singh, M.P., Sharan, M. and Aminataei, A., Development of mathematical formulae for O2 and CO2 dissociation curves in the blood. IMA J Math Appl Med Biol 6:25-46, 1989.


14

NUMERICAL ANALYSIS OF DROPLET COMBUSTION IN A CYLINDRICAL FURNACE

H. N. Mondal* and S. Roy

Department of Chemical Engineering Bangladesh University of Engineering and Technology, Dhaka-1000.

Abstract The combustion performance and emissions of liquid fuels are mainly influenced by the atomization of the liquid fuel, the motion and evaporation of the fuel droplets and mixing of fuel and air. A reliable description and simulation of spray combustion requires a detailed understanding of droplet ignition and combustion. Recently, it has become apparent that an understanding of the mechanisms related to spray combustion is the key to the development of non-polluting and high performance devices. In this study liquid droplets of Toluene is taken into consideration and their burning characteristics are investigated for different combustor geometries and droplet sizes. Non-adiabatic presumed probability density function (PPDF) model is used with high Reynolds number k-ε model. Droplet breakups are handled with Reitz-Diwakar model. Preliminary investigation shows that droplet size, inlet pattern and oxidizer temperature have profound effect on combustion temperature distribution and pollutant formation.

Introduction In many technical systems sprays of small fuel droplets are burnt in the presence of air. The liquid fuel used as the energy source is atomized into smaller droplets in order to increase the surface area of fuel exposed to the hot gases and to facilitate rapid gasification and mixing with the oxygen rich ambience. Droplet burning has relevance to many practical combustion devices, including diesel, liquid rocket engine, and gas turbine engines, as well as oil fired boilers, furnaces, and process heaters. The liquid fuel is injected into the combustion chamber and the combustion occurs as the droplets vaporize and fuel vapor mixes with air. Hence spray dynamics and combustion studies are extremely important to determine flame stability behavior at widely varying loads, to ensure safety and efficient utilization of energy, as well as to better understand the mechanisms of pollutants formation and destruction. Numerical simulation of these processes is a very challenging task due to the stiffness of the chemistry and the coupling with the flow. Moreover, as the fuel is injected at high velocities, the flow nature is turbulent in the spray vicinity and therefore the turbulence-chemistry interactions need to be accounted for. A reliable description and simulation of spray combustion requires a detailed understanding of droplet ignition and combustion. Recently, it has become apparent that an understanding of the mechanisms related to spray combustion is the key to the development of non-polluting and high performance devices. An important

approach is to use advanced computer models for such fundamental studies and for developing practical devices. The development of advanced computers with high speed processors enables theoreticians to formulate and numerically solve comprehensive models with more detailed consideration of physical and chemical processes involved in spray combustion. The combustion of a single liquid droplet in a quiescent atmosphere has been studied extensively both experimentally and numerically. Most of the experimental researches deal with the fuel ethanol1, 2, 3,

4, 5 and n-heptane6, 7, 8, 2, 9. Numerical simulations have been presented for methanol droplets10 and n-heptane droplets11, 12, 13, 14. Only a little number of studies do not assume spherical symmetry and nevertheless consider the physics of the droplets and the chemical processes in detail. In this study, burning characteristics of toluene droplets in a cylindrical furnace is taken into consideration. Effect of different droplet sizes, different number of droplet parcels, different flow rates of primary and secondary air are investigated. Full three dimensional geometry without any cylindrical or periodic symmetry is taken as the computational domain. Governing Equations Droplet evaporation and subsequent combustion is modeled as dispersed multiphase flow consisting of a continuous phase, which may be gaseous or liquid, and one dispersed phase in the form of liquid droplets. In general, the motion of the dispersed phase will be



15

influenced by that of the continuous phase and vice versa. Here the dispersed phase is volatile, reactive, heat and mass transfer occurs between the phases. The conservation equation for droplets in the Lagrangian framework are as follows: The momentum equation for a droplet of mass md is

bampdrd

d FFFFdtudm

rrrrr

+++= (1)

where ur is fluid velocity, dur is droplet velocity,

drFr

is drug

force, pFr

is pressure force, amFr is virtual mass force,

and bFr

is the body force. In the presence of mass transfer, the droplet mass rate of change is given by

( )( )st

ttgs

d

pppp

pKAdt

dm

,

,lnν

ν

−

−−= ∞ (2)

where As is the droplet surface area, Kg is the mass transfer coefficient, and pt, pν,∞ and pν,∞ are the gas pressure and partial pressures of the vapor in the droplet surroundings and its surface, respectively. The droplet energy balance takes into account the mechanisms of surface heat transfer rates qd per unit surface area and loss/gain due to phase change, thus:

( )dt

dmhqAdt

Tcdm d

fgdsddp

d +−=, (3)

where cp,d the droplet specific heat and hfg the latent heat of phase change. Droplets may become unstable under the action of the interfacial forces induced by their motion relative to the continuous phase. For the break-up of liquid droplets in a gaseous stream a set of widely used models exist. Some of them are Reitz and Diwakar, Pilch and Erdman, Hsiang and Faeth etc. In this work Reitz and Diwakar is used which is briefly described below. Reitz and Diwakar model According to this model15, 16, droplet break-up due to aerodynamic forces occurs in one of the following modes: - ‘Bag break-up’, in which the non-uniform pressure

field around the droplet causes it to expand in the low-pressure wake region and eventually disintegrate when surface tension forces are

overcome. - ‘Stripping break-up’, a process in which liquid is

sheared or stripped from the droplet surface In each case, theoretical studies have provided a criterion for the onset of break-up and concurrently an estimate of the stable droplet diameter, Dd stable , and the characteristic time scale τb of the break-up process. This allows the break-up rate to be calculated from

( )b

stabledd DDdtdD

τ,−

= (4)

where Dd is the instantaneous droplet diameter. The criteria and time scales are as follows: Bag break-up: Here, instability is determined by a critical value of the Weber number, We, thus:

12 bd

d Cuu

We ≥−

≡σ

ρrr

(5)

where σd is the surface tension coefficient, and Cb1 is an empirical coefficient having a value in the range 3.6 to 8.4.12 STAR-CD uses Cb1=6 as the default setting. The stable droplet size is that which satisfies the equality in the above equation. The associated characteristic time is

21

23

21

42

d

ddbb

DCσρ

τ = (6)

in which π≈2bC . Stripping break-up: The criterion for the onset of this regime is

1Re sd

CWe≥ (7)

where Red is the droplet Reynolds number and Cs1 is a coefficient with the value 0.5.15 The characteristic time scale for this regime is

duudDdsC

b rr−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

21

22

ρρ

τ (8)


16

Here, the empirical coefficient Cs2 is in the range 2 to 20.15 The default setting in STAR-CD for Cs2 is 20. The continuous phase conservation equations are essentially the k-ε model of the time averaged Navier-Stokes equations, species transport and energy transport equations. PPDF with enthalpy transport In this model, the following transport equation is solved for enthalpy:

( ) ( )

)9( ~

1,

~1

sj

xi

u

ijj

xj

upp

ju

jx

pgtgjh

Fhj

uj

xhg

tg

+∂

∂+

∂

∂−

∂

∂+

∂

∂=−

∂

∂+

∂

∂

⎟⎠⎞⎜

⎝⎛

⎟⎠⎞⎜

⎝⎛

τ

ρρ

where h is the static enthalpy. The time average value of temperature, density and species concentrations are obtained using the following equation:

dffPf )()(ˆ1

0∫= φφ (10)

where φ̂ is any variable which can be uniquely related to the mixture fraction, f. The equation for the mixture fraction is of the standard form, whereas the transport equation for its variance gf is given below 17:

j

gD

C-

2f

21 ~

κε

ρ

σ

µρ

σµ

ρ

ρ

j

f

g

tg

fj

xg

D

gu

jx

jxg

t

jxf

ggtg

∂

∂⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=⎟

⎠⎞⎜

⎝⎛

∂

∂

∂∂

∂

∂+

∂

∂

(11)

The presumed pdf form, P(f), is a β function10

∫ −−

−−

−

−= 1

0

11

11

)1(

)1()(

dfff

fffpba

ba (12)

in which

[ ]

af

fb

gffgfa ff

)1(

)1(

−=

−−≡

The temperature is obtained from the mass fractions and transported enthalpy. It is also assumed that the density is related to pressure, temperature and chemical species via the ideal gas law. Description of the unit The basic geometry is shown in Fig. 1. Primary air inlet consists of two concentric layers of holes with a total surface are of 0.0141 m2. There are three secondary air inlets with surface areas. The areas of secondary air inlet 1, 2 and 3 are 0.012, 0.009 and 0.009 m2 respectively. The outlet has a surface area of 0.08 m2. Input parameters are velocity, number and parcels of droplets, and primary and secondary air velocities. Result and Discussion Different droplet sizes, number of parcels, droplet numbers in each parcel and effect of secondary air variation are investigated by numerical simulation. Fig. 2 and Fig. 3 show the droplet generation and subsequent evaporation as it carried up by the swirled primary air from the bottom of the cylindrical furnace.

Fig. 1. Geometry of the model considered. Volume of the cylinder is 0.0964 m3. Total area of primary air inlet is 0.0141 m2. The areas of secondary air inlet 1, 2 and 3 are 0.012, 0.009 and 0.009 m2 respectively. The injected droplet diameter of Fig. 3 is 1.6 times the injected droplet diameter of Fig. 2 and as a result Fig. 3 shows that droplets with bigger diameters take longer time to vaporize completely and hence travels longer path along the furnace.

Secondary Air Inlet 3



Fuel Inlet

Primary Air Inlets

x z

y


17

Fig 2. Droplet generation and evaporation for droplet diameter of 0.15 mm with 360 parcels with each parcels contains 70,000 droplets.


Fig 6. Temperature distribution diameter of 0.25 mm with 360 parcels with each parcels contains 35,000 droplets.



Fig 7. Temperature distribution diameter of 0.15 mm with 180 parcels with each parcels contains 70,000 droplets. (Reduced Secondary Air)


18

Fig. 4 and Fig. 5 compare the resulting absolute temperature distribution for different droplet diameters. In Fig. 4, due to smaller diameter, the droplets vaporize quickly so the maximum temperature occurs near the bottom of the furnace. Whereas in Fig. 5, complete vaporization of the bigger diameter droplets takes longer time and as a result higher temperature occurs near the top of the furnace. Fig. 5 shows the effect of the number of droplet parcels compared to Fig. 3 and Fig. 4. Fig. 6 shows the effect of reduced secondary air on the temperature distribution of the furnace. It becomes clear that no secondary air at all or reduced secondary air helps to spread the flame near the wall of the furnace which is not desirable due to the requirement of high temperature resistance materials. Conclusions In this study burning characteristics of liquid Toluene droplets are investigated for different combustor geometries and droplet sizes. Droplet breakups are handled with Reitz-Diwakar break-up model. Combustion calculations and turbulence modeling are handled using non-adiabatic presumed probability density function (PPDF) model and high Reynolds number k-ε model respectively. Investigation showed that droplet size, inlet pattern and oxidizer temperature have profound effect on combustion temperature distribution and pollutant formation. References 1. Marchese, A. J., Dryer, F. L., Vedha-Nayagam,

M., and Colantonio, R., "Microgravity Combustion of Methanol and Methanol/Water Droplets: Drop Tower Experiments and Numerical Modeling", Twenty-Sixth International Symposium on Combustion, Pittsburgh, PA, p. 1209, 1996.

2. Vieille, B., Chauveau, C., Chesneau, X., Adide, A., and Gökalp, I., “ High-Pressure Droplet Burning Experiments in Microgravity”, Twenty-Sixth Symp. (Inter.) on Comb. 1, The Comb. Inst., Pittsburgh, pp. 1259–1266, 1996

3. Okai, K., Moriue, O., Araki, M., Tsue, M., Kono, M., Sato, J., Dietrich. D. L. and Williams, F. A., “Combustion of Single Droplets and Droplet Pairs in a Vibrating Field Under Microgravity”, Proceedings of the Combustion Institute, 28, pp. 977-983, 2000.

4. Chauveau, C., Vieille, B., Gökalp, I., Segawa, D., Kadota, T., And Nakainkyo, “A. Effects of

gravitational acceleration on high pressure combustion of methanol droplets”, Journal de Chimie Physique, 96, 1031-1037, 1999.

5. Shaw, B.W, H. A. Dwyer and J. B. Wei, "Studies on Combustion of Single and Double Streams of Methanol and Methanol/Dodecanol Droplets", Combustion Science and Technology, ,174: pp. 29-50, 2002.

6. Faeth, G.M., and Olson, D.R., SAE Transactions, pages 1793–1802, 1968.

7. Hara, H . and Kumagai, S. Proc. Combust. Inst. 23 (1991) 1605-1 61 0, Pittsburgh, USA.

8. Jackson, G.S., and Avedisian, C.T., Proceedings of the Royal Society of London A. Mathematical, Physical and Engineering Sciences, 446:255–276, 1994.

9. Nayagam, V., Haggard, J.B., Colantonio, R.O., Marchese, A.J., Dryer, F.L., Zhang, B.L., and Williams, F.A., AIAA Journal, 36:1369–1378, 1998.

10. Cho, S.Y., Choi, M.Y., and Dryer, F.L., In Twenty-Third Symposium (International) on Combustion, The Combustion Institute, pages 1611–1617, Pittsburgh, 1990.

11. Cho, S. Y., and Dryer, F. L., Combustion Theory and Modelling, 3:267–280, 1999.

12. Marchese, A. J., Dryer, F. L., and Nayagam, V., 1999, Combustion and Flame, 116:432–459, 1999.

13. Schnaubelt, S., Moriue, O., Eigenbrod C., and Rath, H. J., Microgravity Science Technology, XIII/1:20–23, 2001.

14. Moriue, O., Mikami, M., Kojima, N. and Eigenbrod, C., “Numerical Simulations of the Ignition of n-Heptane Droplets in the Transition Diameter Range from Heterogeneous to Homogeneous Ignition”, Proceedings of the Combustion Institute, 30, pp. 1973-1980, 2005.

15. Nicholls, J.A. ‘Stream and droplet breakup by shock waves’, NASA SP–194 (Eds. D.T. Harrje and F.H. Reardon), pp. 126–128, 1972.

16. Reitz, R.D., and Diwakar, R. ‘Effect of drop breakup on fuel sprays’, SAE Technical Paper Series, 860469, 1986.

17. Methodology Manual, STAR-CD Version 3.15, Computational Dynamics Ltd, 2001.


19

KINETICS OF DEHYDRATION OF AROIDS AND DEVELOPED DEHYDRATED AROIDS PRODUCTS

M. Kamruzzaman* and M.N. Islam

Department of Food Technology and Rural Industries, Bangladesh Agricultural University, Mymensingh, Bangladesh

Abstract The study was concerned with the dehydration kinetics of aroids in mechanical dryer at different drying condition such as variable air dry bulb temperature and air velocity. Fresh aroids with 3, 5 mm slice and 8 mm cube were used as raw materials for drying. The experimental results showed that drying rate constant and thickness can be expressed as power law equation. The exponent of the equation for aroids was 1.15 indicating presence of significance external mass transfer resistance. Increasing loading density gave decreased drying rate constant and when air velocity of dryer was increased, drying rate constant was also increased, as higher air velocity reduces the external resistance to mass transfer and also higher temperature gave faster drying rate. The activation energy of diffusion of water from aroids during drying as per Arrhenius equation was found to be 5.12 k cal/g-mole. The chemical compositions of fresh and dried aroids were determined and it was observed that all the constituent remained almost constant, only fat decreased slightly possibly due to oxidation. Organoleptic taste testing showed that “chapatti” prepared from aroids powder (aroids powder: wheat flour = 1:4) were adjudged to be the best by the panelists using 1-9 hedonic scale and ranked as like moderately securing score 7.3.

Introduction Aroids (Colocasia esculenta) locally known as “kachu” is a tropical tuber crop cultivated in Bangladesh for its leaves, corms and cormels. Different types and sizes of aroids are grown in Bangladesh and mainly cultivated in greater Mymensingh. From the economic point of view, the aroids are important root crops for most of the tropical developing and some of the developed countries. Flour made from aroids is an excellent starchy food and was prescribed to cereal allergy sufferers8. Chowdhury5 reported that the nutritive value of corms of aroids seems to be comparable with that of the other starchy foods. Notwithstanding their high starch content, edible aroids have a higher content of protein and amino acids than many other tropical root crops14. Protein quality is essentially the same for all aroids determined with lysine as first limiting amino acid4. A comparative chemical analysis per 100 g of rice, potato and corms of two of the aroids indicates that besides being comparable in respect of some nutrient contents, the corms seem to be richer in Ca and Fe16. Flour made from aroids is an excellent starchy food and is highly digestible due to small grain size6. According to Gerpacio et al.7 the advantage of using aroids for preparing infant food is that it contains an appreciable amount of protein and it does not contain hydrocyanic acid or any toxic substance in amount which is generally found in case of cassava. Its higher digestibility is an added advantage for its suitability for

this purpose. Converting tubers into flours and starches may be an important process that could contribute to minimizing losses and to allow the commercial food industry to store the tuber throughout the year by using appropriate drying technology. Preservation by drying of this vegetable can prevent the wastage and make them available in the off-season. Processing of this vegetable into shelf-stable products using efficient drying procedure and effective utilization of the finished products will enhance availability of the vegetable throughout the year. Moreover, this will stimulate increased production, bring better returns to the farmers and improve nutritional status of the people. Drying can be accomplished in a mechanical dryer, direct sunlight or solar dryer. In the mechanical dryer, desired temperature and airflow could be maintained. Compared to sun/solar drying higher airflow and temperature can be used in mechanical drying. As a result higher production rates and improved quality products are achieved. Moreover mechanical drying is being independent of sunlight it can be done as and when necessary. So the objective of this work was to study the dehydration kinetics of aroids using mechanical dryer and develop aroids flour that could be used as a supplementary raw material for the production of “chapatti” and to assess the overall acceptability of the developed products.



20

Materials and methods Fresh aroids grown in Mymensingh were used for drying process to develop dried aroids slices and aroids powder. Aroids were sliced into desired thickness and placed in trays as to form a single layer and drying commenced in dryer. Weight loss was used as a measure of extent of drying. Initial moisture content was determined as per method of Ranganna17. AOAC2 methods were used to determine crude fat and protein content of the aroids. Experimental Apparatus Forced convection hot air type cabinet dryer (Figure 1) was used for drying of aroids.

Fig 1. Schematic diagram of forced convection hot

air type cabinet dryer The dryer consisted of an insulated cabinet containing a circulating fan, which was fixed over the heating element (heater) and above the cabinet chamber. When the equipment was run, the circulating fan drew air through the heater and this heated air was forced to the chamber through the adjustable louvers at the inlet port. This heated air then passed into the chamber and over the product which was placed on trays. The heated air, having less moisture content, picked up moisture from the exposed food materials placed on the trays and having a higher moisture content. The moist air then left the chamber and went out through exhaust port. The exhaust air was controlled by an adjustable louver at the outlet port. The velocity of air was measured (0.6 and 1.25 m/sec.) by an Anemometer. Characteristics dimensions of dryer: Size =2mx1mx0.84m Chamber size =1mx0.64mx0.66m Temperature range = 380C to 3400C

Analysis of experimental data Since food dehydration is most frequently assumed to take place by diffusion process, Fick’s second law of diffusion can be applied for describing mass transfer during drying. The expression is

tMδδ

= MDe2∇

Where, M = Moisture content T = Time De = Effective diffusion co-efficient The solution of the above unsteady state diffusion equation for one dimensional transport for the case of initial uniform moisture distribution in the sample was derived by Brooker et.al3 and Islam12 when dried from one major face is:

MR=8

=−−

eo

et

MMMM

=2

8π

∑=

α

0n2)12(

1+n

Exp

⎥⎦

⎤⎢⎣

⎡ +−2

22)12(L

tDn eπ------ (1)

For low Me values and for moisture ratio (MR) less than six, equation (1) reduces to,

o

t

MM

= 2

8π

22 / LDete π− = 2

8π

e-mt ------ (2)

Where, Mt = Moisture content at any time M0= Initial moisture content Me = Equilibrium moisture content L = Sample thickness T = Time

m = 2

2

LDeπ

= drying rate constant, sec-1

Consequently, a straight line should be obtained when plotting lnMR versus time (t). The slope of the regression line is the drying rate constant, m from which the effective diffusion co-efficient, De is calculated. The diffusion co-efficient, De has an Arrhenius type of relationship with air-dry bulb temperature (abs). The relationship is as follows9:

lnDe = lnDo - abs

a

RTE

----------(3)

Where, D0 = the constant of integration and is usually referred to as a frequency factor when discussing Arrhenius equation; Ea = activation energy of diffusion of water, cal/g-mole;R=gas constant, cal/g-mole°K; and Tabs = absolute temperature, °K.


21

From the semi-theoretical equation as shown in equation (2), symbolically ‘m’ may represented as: m = A( L )-n or, logm = logA – nlog L ------(4) Where, A = π2De and n = 2 The above relationship shows that if external resistance to mass transfer is negligible and if simultaneous heat and mass transfer effects are taken into account, the value of the exponent of the power law equation should be 2. But the above conditions are not always satisfied and experimentally determined ‘n’ value is found to be less than 2 as reported by co-author12. Results and discussions Experiment was conducted to determine the effects of loading density (mass/unit area) as well as thickness of aroids on drying rate at three different temperatures (55°C, 60°C and 65°C) in a cabinet type of mechanical dryer. Experiment was also conducted to investigate the effect of air velocity on drying rate at constant temperature. Effect of loading density on drying time To determine the influence of loading density on drying time, 1.2 kg/ m2 and 2.4 kg/ m2 aroids slices were dried at different dry bulb temperature (55°C, 60°C and 65°C) at constant air velocity in a cabinet dryer. The drying rate constants were calculated by a regression analysis for each sample thickness using equation (2) and moisture ratio (MR) versus drying time (hr) were plotted on a semi-log scale (Fig.2) and rectangular scale (Fig.3).

Fig 2. Effect of loading density on drying rate at

55°C. The following regression equations were developed: MR = 1.0289e-0.2384t for 1.2 kg/m2

MR = 1.049e-0.223t for 2.4 kg/m2

From Fig 2 and 3 it is seen that as loading density of aroids increases the rate of drying decreases, but drying rate constant does not decreases proportionately as loading density increases. Using 1.2 kg/m2 loading density, the rate constant was 0.238 hr-1 at 550C, whereas for twice the loading density at similar condition the rate constant was 0.223 hr-1. This phenomenon can be advantageously used for increased dryer thoroughput. However, care should be taken not to increase loading density to such an extent that may increase drying time to a level at which the products are spoiled. Influence of thickness on drying rate To investigate the effect of thickness on drying behavior aroids slices were dried at constant air dry bulb temperature (600C) and constant air velocity (0.6 m/s). The results were analyzed by using equation (2) and are shown in Table-1. The equations developed are as follows: MR = 1.0026e-0.3987t for 2 mm slice MR = 1.0397e-0.2567t for 3 mm slice MR = 1.0842e-0.1521t for 5mm slice By putting MR value = 0.13 in the above equations, it is seen that for removal of 87% moisture 2mm aroids slice takes only 5 hours whereas 3 and 5mm aroids slices needed 8 and 14 hours respectively. So the products can be made shelf stable within these time. From Fig. 3 and Table 1 it is also clear that thickness of the sample directly influences total drying time. Table 1: Thickness dependence of drying rate constant of aroid slices

Thicknes (cm) Drying rate constant (sec-1) 0.2 1.10x10-4 0.3 7.13x10-5 0.5 4.22x10-5

The relationship between drying rate constant (m) and sample thickness (L) was developed (Fig. 4) from the plot of drying rate constant versus sample thickness on log-log scale using equation (4). This relationship can be represented by a power law (regression) equation, which is as follows. m = 0.9445L-1.1451


22

Fig 3. Effect of thickness on drying behavior of

aroid slices at 60°C. From the above equation, it is seen that the value of index ‘n’ of the power law equations is 1.14 at 600C. This value is lower than 2 as predicated by equation (4) and it indicates that the external resistance to mass transfer is highly significant under the given conditions. This also indicates that higher airflow rates will give higher drying rates. Islam12 showed an ‘n’ value of 1.70 while drying potato using higher airflow rates (2.5 m/s). The above discrepancy of ‘n’ values is primarily due to airflow rate and sample thickness, and shows the relative importance of external or internal mass transfer resistance. However, product structure and composition and simultaneous heat and mass transfer effects also play an important role in this regard. Islam12 while working with potato, showed that by taking into account of the simultaneous heat and mass transfer effect value of ‘n’ could be corrected to 2 from 1.7.

Fig 4. Influence of air velocity on drying rate at

60°C for 3 mm slice. Influence of air velocity on drying time From Fig. 5 and 6 it is obvious that when air velocity is

increased, drying rate constant is also increased, as higher air velocity reduces the external resistance to mass transfer. The decrease in external resistance leads drying to be controlled by increasing internal resistance to mass transfer as is important for analyzing drying data according to Fick’s diffusion equation. However, doubling the air velocity did not increase the rate constant twice as much. Moreover, for certain drying conditions, there may be a fixed air velocity above which increase in velocity will not result in increased drying rate12. Influence of temperature on drying time From Fig 7 it is seen that the moisture ratio (MR) decreases with time and time to dry to a specific moisture ratio decreases with increasing temperature. Thus higher temperature would give faster drying rate. At very high temperature and low humidity drying rate may initially increase, but as drying progresses resultant case hardening would reduce drying rate drastically and deteriorate the quality of the product due to cooking instead of drying. High temperature also may scorch the product and thus selection of optimum temperature for drying is of significance during drying particularly, mechanical drying with counter current operation13,15. From the drying rate constants determined by regression analysis, the diffusion co-efficients were determined. Diffusion co-efficient (De) versus inverse absolute temperature (Tabs

-1) was plotted on a semi-log co-ordinate and regression lines were drawn. From the slope of the resultant straight line (Fig. 8), activation energy (Ea) for diffusion of water was calculated and found to be 5.12 Kcal/g-mole. The calculated activation energy is lower than 12.5 Kcal/g-mole of activation energy for diffusion of water from potato by Saravacos and Charm 18, those found by Afzal Babu et al.1 for onion (26.83 Kcal/g-mole) and for cucumber (8.50 Kcal/g-mole), and cauliflower (7.76 Kcal/g-mole) found by Iqbal10 but higher than that found for mango (4.4 Kcal/g-mole) by Islam et al.11 .That means the activation energy value is within the range of values reported by many researcher. The differences in activation energy may arise from differences in product characteristics as well as process parameters. The dependence of diffusion coefficient on absolute temperature can be represented as De = 0.0015 e-2574.3 Tabs

-1

Where, De = Diffusion coefficient (cm2/s) and Tabs = Absolute temperature (°K)


23

Table 2: Influence of temperature on diffusion coefficient

Temperature (OC)

Diffusion coefficient ( cm2/s)

55 4.43x10-7 60 6.50x10-7 65 1.07x10-6

Fig.5: Effect of temperature on drying rate at

constant loading density (1.2 kg/m3) Comparison of composition of fresh and dried aroids The fresh aroids contained 91.2% moisture, 0.38% protein, 0.22% fat, 1.24% ash and 6.96% carbohydrate where as the mechanical dried aroids contained 11.4% moisture, 2.52% protein, 0.09% fat, 7.86% ash and 78.13% carbohydrate (Table 3). During drying most of the water in the aroids are vaporized so the moisture content is so less and consequently solid content increased. This increased solid content results in the increased protein, ash, and carbohydrate content. The fat content decreased in the dried sample, which may be due to the oxidation of fat during drying. Table 3: Comparison of composition of fresh and dried aroids

Parameters Fresh aroids (%)

Dried aroids (%)

Moisture 91.2 11.4 Protein 0.38 2.52

Fat 0.22 0.09 Ash 1.24 7.86

Total carbohydrate 6.96 78.13

Development of product The dried aroids were grinded in a laboratory grinder and aroids powder was obtained. Then “chapatti” was prepared by mixing wheat flour and aroids powder at

different ratio. The products are then tested organoleptically. Sensory evaluation of developed product The consumer's acceptability of developed products was evaluated by a taste testing panel. The 1-9 hedonic rating test was used to determine this acceptability. A two way analysis of variance (ANOVA) was carried for color, flavour, texture and overall acceptability preference of developed product and the results are shown in Table 2. As shown in Table 2 (DMRT) the sample 1 was the most acceptable product securing the highest score 7.3 (out of 9) among the samples and ranked as “like moderately”. However, sample 2 and 3 were equally acceptable at 5% level of statistical significance securing score 6.2 and 5.5 respectively and ranked as “like slightly”. But sample 4 secured the lowest score (4.8) and was ranked as “neither like nor dislike”. Table 2. Mean score for color, flavor, texture and overall acceptability of “chapatti”

Sensory attributes Sam-ple

Color Flavor Texture Overall

Acceptability

1 7.0a 6.3b 7.1a 7.3a 2 6.1b 7.6a 5.8b 6.2b

3 5.6bc 5.3c 5.1b 5.5bc

4 5.1c 4.4d 4.3c 4.8c

Sample 1: Aroids powder: wheat flour = 1:4 Sample 2: Aroids powder: wheat flour = 1:3 Sample 3: Aroids powder: wheat flour = 1:2 Sample 4: Aroids powder: wheat flour = 1:1 Conclusions This study demonstrated that the aroids flour could be conveniently incorporated into wheat flour for the production of “chapatti” in order to produce “chapatti” of acceptable quality. Hedonic rating test for organoleptic quality indicated that 20% of aroids flour could be added in the production of “chapatti” to maintain acceptable scores for color, flavour and texture of the product. Every year a substantial amount of aroids are cultivated in Bangladesh. The study showed that there is a good prospect of processing of aroids through diversified and value-added products. By processing aroids its market value may be increased and production can be maximized. Therefore, it may be concluded that, aroids can be successfully and economically preserved during its peak season by drying process.


24

Mechanical drying systems may be used for large-scale production. References 1. Afzal Babu, S. M. M., Kowser Sarker, M. A. S. and Islam, M. N. Kinetics of mechanical, Solar and Sun drying of onion. Bangladesh J. Agril. Engg. 8 (1&2): 49-61, 1997. 2. AOAC methods. Officials Methods of Analysis 12th edition. Association of Official Agricultural Chemists, Washington D.C. USA, 1984. 3. Brooker, D. B., Bakker, F.W. and Hall, C.W. Drying cereal grains: Theory and simulation of cereal grain drying. The AVI Pub. Co. Inc. USA. 185(1974). 4. Bradbury, D.H. and Holloway, W.D. 1988. Chemistry of tropical root crops. ACIAR, Canberra (1988). 5. Chowdhury, B. The nutritive value of edible aroids grown in Bangladesh. M.S. Thesis. Dept. of Biochemistry, Bangladesh Agricultural University. Mymensingh (1975) 6. Coursey, D. G. The edible aroids. World Crops. 20: (4), 25-30(1968). 7. Gerpacio, A. L., Roxas, D B., Ulchanco, H. M., Roxas, N. P., Custudio, C. C., Marcado, C., Gloria, L. A., and Castillo, L. S. Tuber meals as carbohydrate sources in broiler rations. TPI conf. Proc. Animal Fees of Trop. & Subtrop. Region. 151-154 (1974). 8. Greenwell, A. B. H. Taro with special reference to its culture and uses in Hawaii. Econ. Bot. 1: (3), 276-289 (1947).

9. Heldman, D. R. Food Process Engineering. AVI Pub. Co. Inc. Westport. Connecticut. U.S.A (1974). 10. Iqbal, A. Processing and preservation of cauliflower and cucumber by dehydration and fermentation. M.S. Thesis. Dept. of Food Technology and Rural Industries, Bangladesh Agricultural University. Mymensingh (2003). 11. Islam, M.N., Uddin, M.B. and Islam, N.M. Development of shelf-stable dehydration mango products. Bangladesh j. of Agril. Engg. 4:(1&2), 65-73 (1997). 12. Islam, M. N.Use of solar energy for development of shelf-stable potato product. Ph.D. Thesis. Royal Veterinary and Agricultural University, Copenhagen, Denmark (1980). 13. Karel, M., Fennema, O.R. and Lund, D.B. Principles of Food Science, Part-II, Physical Principles of Food Preservation. Marcel Deker, Inc.New York and Basel (1975). 14. Kay, D. E.. Crop and product digest No. 2: Root crops. 2nd Edition. London: Tropical Development and Research Institute. 380 (1987) 15. Potter, N.N. Food Science, CBs Publishers and Distributors, Shahdara, Delhi. 78(1978). 16. Rashid, M.M. Transferable Techniques in tuber crops. Tuber crop research centre, BARI. Joydebpur, Gazipur. 14(1991). 17. Rangarna, S. Handbook of Analysis of Fruit and Vegetable Products. Tata McGrow Hill Cl. Ltd. 1-30. New Delhi. India (1992). 18. Saravacos, G. D. and Charm, S. E. A study of the mechanism of fruits and vegetable dehydration. Journal of Food Technology.16: 78(1962).

Journal of Chemical Engineering, IEB.Vol. ChE. 24, No.1, January 2006 -December 2006

25

A NUMERICAL MODEL FOR BUBBLE SIZE DISTRIBUTION IN TURBULENT GAS-LIQUID DISPERSION

M. A. K. Azad and Sultana R. Syeda*

Department of Chemical Engineering Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh

Abstract In present study a numerical model for bubble size distribution is developed that considers both breakage and coalescence in turbulent gas liquid dispersion. Two-step mechanisms are considered for both breakage and coalescence of bubbles. The bubble breakage is structured as the product of the bubble-eddy collision frequency and breakage efficiency in gas-liquid dispersions. The coalescence function considers the product of bubble-bubble collision frequency and coalescence efficiency. The model overcomes several limitations observed in previous efforts such as empirical parameters, narrow range of operating conditions, and narrow range of geometries. Favorable agreement is found between the predicted bubble size distribution and the experimental data reported in the literature. The percentage of error obtained for the average bubble size was found within ± 17%.

Introduction

Bubble columns are employed in many mass transfer processes. They are used in a variety of industrial applications ranging from stripping and absorption columns to three phase slurry beds and activated sludge ponds. Bubble columns have broad application as reactors and separation units in the chemical, mining, pharmaceutical and biochemical industries. Bubble columns are also used as aerobic biochemical reactors in fermentation systems. There is considerable interest in developing means of predicting bubble-size distributions in turbulent two-phase dispersions. An understanding of the physical mechanisms determining bubble size is crucial to any detailed theory of the transfer of heat, mass and momentum between phases, and is also necessary for the framing of the design of reduced-scale laboratory models to simulate bubble and droplet flows in industrial plant. Bubble size distribution in a vessel is not constant, but may change due to bubble-bubble interactions that can lead to breakage or coalescence. No broadly applicable model for the determination of these two rates has yet been presented due to both the unsatisfactory understanding of the physical mechanisms that lead to breakage and coalescence and the enormous difficulty in obtaining reliable data, especially for high gas flow rates. Most of the studies investigating bubble size distribution in turbulent flow, dealt with breakage and coalescence separately. The primary-contributions to the study of Bubble breakup in turbulent flow are those of Kolmogoroff1 and Hinze2. These authors independently suggested that the maximum size of bubble stable against breakup by the turbulence could be estimated by means of dimensional analysis based

on the hypothesis that the key parameter characterizing the structure of turbulence fluctuations is the rate of energy dissipation in the flow. Similar line of argument applied to coalescence, suggests that in a turbulent environment there is a minimum size of bubble stable against coalescence Shinnar3. Following the footsteps of Kolmogroff and Hinze a number of studies were carried out that dealt with either breakage or coalescence phenomena separately 4,5,6,7,8,9. Prince and Blanch10 are among the very few researchers who proposed a phenomenological model for the rates of bubble coalescence and bubble break up in bubble columns. They modeled bubble coalescence by considering bubble collisions due to turbulence, buoyancy and laminar shear and by analyzing the coalescence efficiency of collisions. Bubble break up was estimated in terms of bubble interactions with turbulent eddies. They developed a method to measure the coalescence and breakup events in turbulent systems and used the measurements to validate their model. However, lack of information on several parameters makes the model difficult for application. Colella et. al.11 studied the interfacial mechanisms that dealt with both coalescence and breakage of bubbles. They tried to develop a new methodology to analyze breakage and coalescence phenomena in bubble columns based on the physics of bubble columns and by considering wake and shape effect. Again, several adjustable parameters included in the model, made the model case sensitive. The present study is aimed at developing a general theory based model to determine equilibrium bubble size distribution in gas liquid dispersion without including any adjustable parameter. The objectives will be fulfilled through the following steps.



26

1. Formulation of the turbulent break up and coalescence events.

2. Development of an algorithm where both breakup and coalescence are considered simultaneously towards attainment of equilibrium bubble size distribution.

3. Comparison of the predicted bubble size distribution with experimental data available in literature.

Model Development Initial bubble size distribution Initial bubbles, i.e., bubbles just after leaving sparger orifices or nozzles are different in size from the bubbles rising through the main part of the column under the operating conditions normally used in practice. The size of the majority of bubbles at equilibrium distribution depends mainly on input bubble size and a balance between the coalescence and breakup rates. Experimental data showed that the initial bubble size was independent of the properties of system such as surface tension, liquid viscosity and liquid and gas densities12. It is also reported that the size distribution of such bubbles is log normal distribution13. The distribution function F(x) is defined by ( ) ( )∫=

x

0

dxxfxF (1)

Where f(x) is the probability density function. The probability density function f(x) can be expressed by

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −

−=2mxln

21exp

2)(x1)x(f

Σπσ

(2) Where m is the natural logarithm of the geometric mean bubble size (dg), and Σ is the standard deviation. Here geometric mean is assumed equal to the average mean of bubble size. The average bubble size of initial bubbles depends on the orifice diameter do and the gas velocity through the orifice u0 12.

( ) )gd/u(88.1dd3/1

ooog = (3)

From dimensional analysis and the experimental data, the following correlation was obtained for the standard deviation of bubble size distribution.

( )08.0g

08.2l

3 )gD/U()/gD(60.5ln −−= υΣ (4)

Bubble concentrations can be obtained from gas hold-up and bubble size data. Taking the number of bubbles as equal to the volume of gas divided by the average bubble size one obtains:

( )i3

bi

T2

Ti xf

r34

HRn φ= (5)

Here f (xi) = the fraction of bubbles with radius rbi For determining total number of bubbles initially present in the system f (xi) is considered as 1 and average bubble size is determined from the Eq. 3.

3bi

T2T

T

r34

HRn φ= (6)

The correlation of Hikita et.al.14 allows one to estimate the global gas hold up based on the physical properties of the phase.

107.0062.0131.0

3

4578.0

672.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛=

−

c

d

d

c

l

cdc gµµ

ρρ

σρµ

σµµ

φ (7)

In present study the bubble size distribution within 12.5 cm from the bottom of the column is considered to have initial bubble size distribution. Bubble coalescence theory Coalescence of two bubbles in turbulent flows occurs in three steps.

1. Collisions of bubbles and trapping of liquid between them.

2. Flattening of bubble surface and drainage of the trapped liquids.

3. Coalescence of two bubbles. From the first step it is seen that the coalescence rate is intimately connected to the collision rate. The second step is ordinarily the slower and hence determines the overall duration of the coalescence process. Collision occurs due to the following mechanisms:

i) Turbulence (Random motion of bubbles due to turbulence)

ii) Buoyancy (Bubbles of different sizes will have different rise velocities which may lead to collision)

iii) Laminar shear (Bubbles located in a region of relatively high liquid velocity may collide with bubbles in slower section of the velocity field)

It is assumed that collisions from these various mechanisms are cumulative.


27

Turbulent collision rate Collision takes place by mechanism analogous to particle collisions in an ideal gas. The primary reason for bubble collision is the fluctuating turbulent velocity of the liquid phase. The turbulent motion can be expressed as a function of bubble size, concentration

and velocity15 2/122 )(−−

+= tjtiijjiTij uuSnnθ

(8) Where ni , nj are the concentration of bubbles of radius rbi , rbj respectively. ut is the average turbulent fluctuating velocity of the bubble. Sij is the collision cross sectional area of the bubbles, given by

2)(4 bjbiij ddS +=π (9)

The following assumptions are made to develop the turbulent collision rate.

1. The velocity of bubbles in Eq. 8 is assumed to be the turbulent eddy velocity of the length scale of the bubble.

2. The turbulence is isotropic and that the bubble size lies in the inertial sub range.

This criterion is typically examined in terms of the inverse

radius or wave number, which is known as the inertial subrange:

ke<< kb<< kd (10) Where, ke is the wave number of the large energy containing eddies; kb is the wave number of the corresponding bubble size; kd is the wave number of the eddies of viscous dissipation. Batchelor15 defines the wave number for energy dissipation (kd), equivalent to the inverse of the micro scale of turbulence:

4/3

4/1

5.0υε

=dk (11)

Where ε is the energy dissipation per unit mass, υ is the kinematic viscosity An expression for the energy dissipation per unit mass is given by:

gus ×=ε (12) The kinetic energy and mass of the gas phase have been neglected in this formulation.

The size of the energy containing eddies is typically assumed to be equal to the vessel diameter. Thus ke is inverse of vessel diameter. According to Eq.10 the length scale of the bubble is well removed from that of both the energy containing eddies and eddies of viscous dissipation and falls in the inertial subrange. The turbulent velocity in the inertial subrange of isotropic turbulence is:

)3/1()3/1(04.1 bt du ε= (13) Where db= the bubble diameter. Substitution of this value in to Eq. 8 yields the turbulent collision rate.

2/13/23/23/12 )()(089.0 bjbibjbijiTij ddddnn ++= επθ

(14) Buoyancy-driven collision rate Collisions may result from the difference in rise velocities of bubbles of different size. The buoyant collision rate (θij

B) is given by Friedlander17 :

)( rjriijjiB

ij uuSnn −=θ (15) Where ur is the rise velocity of the bubble and can estimated by the following expression18:

( ) 2/1]505.0/)14.2[( bblr gddu += ρσ (16) Where ρl is the liquid density, σ is the surface tension. The equation is strictly applicable only to uncontaminated bubbles with mobile gas-liquid interfaces. Laminar shear collision rate The final contribution to the collision rate results from laminar shear in the liquid phase. Collisions occur in this situation as a result of the development of a gross circulation pattern in a bubble column at a sufficiently high gas flow rates. The circulation pattern gives rise to a radial velocity distribution. Because of this, it is possible for bubbles situated in a zone of relatively high liquid velocity to overtake another bubble of the same size and rise velocity. The functional form of the collision rate due to laminar shear is given by Friedlander16:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

dRUdrrnn

34 l3

bbjiLS

ij jiθ (17)

Where Ul= the liquid circulation velocity, R= the radial coordinate of the column


28

dRUd l = The average shear rate.

For evaluating the average shear rate, the velocity profile developed by Walters and Blanch17 for inviscid fluid is used. The exact velocity profile is a function of the position of the stagnant point, the radial distance at which there is no net upward or downward flow. For inviscid systems, Walter and Blanch state that the transition point occurs at a radial position of approximately 0.7RT. The velocity profile for this condition is ( )( )2

T2

max,ll R/R1UU α−= (18)

Where αRT = the transition point, Ul,,max = The velocity in the center of the column. The mean shear rate is found by averaging the local shear rate over the radial dimension of the column. If we substitute γ(R) for the local shear rate we find:

T

l

T

R

R

T

R

RU

R

RdRR

R

RdRRR

T

T

T

max,222

03.5

)1(

).(2

)(

).(2)( =

−+=∫∫

α

γ

α

γγ

α

α

(19) For turbulent flow the maximum liquid circulation velocity is given by

3/1

2L2M

max,l FdgHQ2U ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

π (20)

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−= 2

2

22L

1dD

11F (21)

)(

ln

21

2

12

2

PPPP

PQ

PP

QQLM

M −== (22)

Where, Q = gas rate per orifice, m3/s. QM = Mean gas rate, m3/s. P1= Pressure at the sparger, N/m2. P2= Absolute Pressure, N/m2. PLM= Log mean Pressure, N/m2. Substitution of Eq. 21 and Eq. 22 in to Eq.19 gives the laminar shear collision rate.

Collision efficiency Collision efficiency is the fraction of bubble collisions that leads to coalescence. The efficiency depends on the contact time between bubbles and the time required for bubbles to coalesce. An expression for the efficiency is given by Coulaloglou and Tavlarides 18:

)/texp( ijijij τλ −= (23) Where tij= The time required for coalescence of bubbles of radius rbi and rbj; τij = The contact times for the two bubbles. Coalescence times have been successfully modeled in stagnant fluids by examining the time required for the liquid film between bubbles to thin from an initial thickness to a critical value where rupture occurs. An expression for the thinning of liquid film between bubbles of equal size is taken from Oolman and Blanch19.

2/1

3b

22

gl2d h6

Ar2h)

dcd(

TRc4

R8

dtdh

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛++

−=

−π

σσρ

(24)

Where h= the film thickness, Rd= the radius of the liquid disk between the coalescing bubbles Rg= the gas constant, T= the temperature, A= the Hamaker constant c = concentration of a surfactant species. For the distilled water c = 0. The coalescence time can be found by integrating of Eq. 24:

f

o

2/1

l3

ijij h

hln16r

t ⎟⎟⎠

⎞⎜⎜⎝

⎛=

σρ (25)

Where ho = the initial film thickness, hf = the critical thickness where rupture occurs. Rd has been assumed to be bubble radius. This assumption is not strictly accurate; however, it is used for simplicity and because more detailed data is not available. For the case of bubbles of unequal size, rb in Eq. 25 has been replaced by the equivalent radius (rij). The equivalent radius is given by Chesters and Hoffman20 as:

1

bjbiij r

1r12r

−

⎟⎟⎠

⎞⎜⎜⎝

⎛+= (26)

The time that bubbles remain in contact is dependent on the bubble size and turbulent intensity. High levels of turbulence increase the probability that an eddy will separate particles, while large particle size provides


29

larger contact areas. Levich21 provides an estimate of the contact time in turbulent flows:

3/1

3/2

ετ b

ijr

= (27)

Values for the coalescence and contact time may be substituted in to Eq.23 to determine the efficiency. In turbulent dispersion a simple criterion for coalescence to occur is tij<τij. In other words unless the intervening film thins down to the critical rupture thickness h in the time available before bubbles are separated again, coalescence doesn’t occur. Combining the Eq.25 and 27 we obtain the result that coalescence is impossible unless d<dmin. Where

5/6

03/1

2/1

min

ln

)/(55.10

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

≈

f

l

hh

dε

ρσ (28)

Now it can be said that bubbles whose diameter exceeds dmin are much less likely to coalesce than smaller bubbles in the dispersion. Similarly bubbles slightly below the threshold size will not coalesce as easily as very small bubbles. Thus the equation gives a rough estimate of the size of the smallest bubble stable against coalescence Total coalescence rate The coalescence rate of bubbles of radii rbi and rbj is given by the total collision frequency multiplied by the efficiency.

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ −++=

ij

ijLSij

Bij

Tijij

texp

τθθθΓ

(29) The overall coalescence rate is then given by:

( )∑∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −++=

i j ij

ijLSij

Bij

TijT

texp

21

τθθθΓ

(30) The factor 1/2 is included to avoid counting coalescence events between bubble pair twice. Bubble breakup theory In order to develop the breakage model, the following simplifications are made.

1. The turbulence is assumed to be isotropic. 2. Only the binary breakage of fluid particles is considered. 3. The occurrence of breakup is determined by the energy level of the arriving eddy only. 4. Only eddies of length scale smaller than or equal to the particle diameter can induce particle oscillations. Collision of bubbles with turbulent eddies To obtain an expression for the break-up rate of bubbles, the turbulent collision rate of bubbles with eddies of the appropriate size is considered. The collision rate is given by22:

2/122 )(−−

+= tetiieeiie uuSnnθ (31) This Eq. is analogous to Eq.8 except that the diameter, concentration and velocity of one bubble are replaced by those of the eddy. To employ this equation, the number of eddies of a particular size must be determined. We assume that the turbulence is isotropic and that the eddy size of interest lies in the inertial subrange. Batchelor16 gives the spectral energy density in the inertial subrange of the energy spectrum as:

3/53/2 k7.1)k(E −= ε (32) Where, k is the eddy wave number (k=1/re, re being the radius of the eddy), ε gives the energy dissipation per unit mass and E(k) is the energy per unit mass and per interval of wave number. According to Azbel23, E(k) can be written as

e)k(N)k(E = (33) Where, N(k) denotes the number of eddies per unit mass of the liquid and per unit interval of wave numbers. Multiplication by the liquid density yields the eddy concentration. The energy of a single eddy is given by:

232

32

21

eefe urmue πρ== (34)

In Eq. 34, re, ue, and m denote the eddy radius, velocity and mass respectively and ρf denotes the fluid density. According to Kolmogorov’s for the inertial subrange of the energy spectrum, the eddy velocity is given as:

3/1

e k86.2u ⎟

⎠⎞

⎜⎝⎛=ε (35)


30

Eq.32 to 35 are used to determine the number and velocity of eddies. It must be noted that Eq. 33 is only valid for the inertial subrange. The number of eddies predicted by the equation becomes infinitely large as the eddy size approaches zero. Therefore the expression may not be useful to very small eddies which lie in the viscous dissipation range. In practice, therefore, it is necessary to consider an arbitrary size, below which an eddy will not cause breakage. For the present study, this value is set at eddies smaller than 20% of the bubble size. Such eddies are unlikely to contribute significantly to the overall break-up rate since they posses only 0.5% of the kinetic energy associated with an eddy equivalent to the bubble in size. Break-up efficiency Only a certain number of bubble-eddy collisions are likely to result in bubble break-up. The criterion of break-up relates the energy of the eddy to the surface tension forces of the bubble. The balance of disruptive and cohesive forces is generally expressed in terms of the dimensionless Weber number.

σρ lb

edu

W2

= (36)

A critical Weber number will exist at the point where cohesive and disruptive forces balance, resulting in a maximum stable size. An expression for the maximum stable bubble size in turbulent gas-liquid flows provided by Kolmogoroff1 and Hinze2:

1.0

d

c6.04.0

6.0

max 12.1d ⎟⎟⎠

⎞⎜⎜⎝

⎛=

µµ

ρεσ

(37) Where dmax is the maximum stable bubble size, Vl is the total volume of liquid, and µc, µd are the viscosities of the continuous and dispersed liquid phase, respectively. All bubbles above the dmax will undergo the breakage process provided that the bubbles remain in the turbulent field for sufficient period of time. From this expression and Eq. 36 and 13, one may obtain a critical Weber number of 2.3 for air bubbles in water. This is translated in to a critical eddy velocity (uci) for break-up of a bubble of radius rbi

( )( ) 2/1lbici d/52.1u ρσ= (38)

It is necessary to determine which eddies have velocities that exceed this value. To do so, an energy distribution function is required. Angelidou et al.24

provide such an expression for a random distribution of energy:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ −=

−

e

e

ee

E

Eexp

E1)E(x (39)

Where x (E) = Energy distribution function, Ee= the kinetic energy of the eddy. Taking the energy of the eddy as proportional to the square of the velocity yields a function of the following form for the fraction of eddies with sufficient energy to cause rupture18

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2

te

2ci

uuexp)u(F (40)

Where F(u) = the fraction of eddies with sufficient energy to cause rupture and ute= the turbulent velocity of an eddy of radius re. Total break-up rate The break-up rate for a bubble of radius rbi is thus given by:

( )( )( )∑ −=e

2te

2ciiei u/uexpθβ (41)

Here the summation incorporates the contribution to break-up from eddies of various sizes. The total break-up rate for

all bubbles there fore is;

∑∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

i e2te

2ci

ieT uu

expθβ (42)

Model Development Algorithm of the model In present study a simulation program is used to determine the bubble sizes. Initial bubble size distribution is estimated for a particular superficial gas velocity. These initial bubbles are used to initialize the simulation. The population of bubbles is divided into discrete size categories. The bubbles are first checked for the inertial sub range. If bubbles lie within the sub range they are sent either to coalescence or to breakup depending on their size. If the bubbles are larger than dmax they are sent to break-up; if they are smaller than dmin they are sent to coalescence; and if they lie between dmax and dmin they are not subject to further coalescence or breakup. The resulting size distribution is recorded after a number of coalescence and break-up


31

0.00

0.05

0.10

0.15

0.20

0.25

1.0 2.5 3.6 4.7 5.8 6.9 7.9 9.0 10.1

d, mm

f

P rediction by the proposed Model

Exp data of Colella et.al.(1999)

0.00

0.05

0.10

0.15

0.20

0.25

1.0 2.5 3.6 4.7 5.8 6.9 7.9 9.0 10.1

d, mm

f

Prediction by the proposed ModelExp data of Colella et.al.(1999)

events. The procedure is continued until an equilibrium average bubble size is achieved, i.e. further iterations produce no change in the average bubble size or bubble size distributions. The algorithm to determine the equilibrium bubble size distribution by using the

proposed model is shown in Figure 1. Fig 1. Algorithm for equilibrium bubble size determination Results and Discussion The bubble size distribution determined by the model is compared with the experimental data obtained from bubble columns reported by Collela et. al.11 and Prince and Blanch10. The model is first executed with the bubble column used by Colella et al.11. The bubble column is made of Plexiglass with a diameter equal to 15.24 cm and a height of 109 cm. Bubbles were generated by a perforated plate with holes of 0.1 cm diameter, arranged in an equilateral triangle pattern with a pitch equal to 1cm. The distribution is measured for the gas superficial velocity of 0.59 cm/s and 1.13 cm/s. For both velocities the column is operated in homogeneous regime. Initial bubble size distribution is obtained from the equations 1 to 7. Figure 2 shows the initial size

distribution of the bubble column at gas velocities 0.59 cm/s and 1.13 cm/s. Fig 2. Estimated initial bubble size distribution for the bubble column used by Collela et.al. (1999). Fig 3. Comparison of the model with the experimental data of Collela et.al. (1999) for velocity 0.59 cm/s. The equilibrium size distribution measured at a distance 57.5 cm from the sparger by Collela et.al.11 is compared with the prediction by the proposed model. The result is shown in Figures 3 and 4 for velocities 0.59cm/s and 1.13 cm/s, respectively. The model is further executed with the bubble column used by Prince and Blanch10 . The bubble column consisted of a 27 cm diameter plexiglass cylinder with a liquid depth of 2m. The sparger was made up of two 20 cm long curved stainless steel tubes, each having six orifices of 2 mm diameter along the upper edge. The two tubes were oriented to maximize radial mixing of the gas streams in the lower section of the bubble column. The distribution was measured at a gas superficial velocity 5.2 cm/s. For this velocity the column is operated in heterogeneous regime, where turbulent collision and laminar shear collision become dominant.

Initial bubble size Estimation


32

0.000.050.100.150.200.250.300.350.40

0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15

V, cc

f

Predicted data by proposed Model

Exp Data of Prince & Blanch (1990)

0.000.040.080.120.160.20

0.00 2.00 4.00 6.00 8.00

d, mm

f

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1.0 2.5 3.6 4.7 5.8 6.9 7.9 8.0 9.0 10.1d , mm

f

Prediction by the proposedModelExp data by Colella et.al.(1999)

Fig 4. Comparison of the model with the experimental data of Collela et.al. (1999) for velocity 1.13 cm/s.

The estimated initial bubble size distribution is shown in Figure 5.

Fig 5. Estimated initial bubble size distribution for bubble column used by Prince and Blanch (1990). The equilibrium size distribution estimated by the out lined model is compared with the experimental data obtained by Prince and Blanch10 at a distance 200 cm from the sparger. The result is shown in Figure 6 for velocity 5.2 cm/s.

Fig 6. Comparison of the model with the experimental data of Prince and Blanch (1990) for velocity 5.2 cm/s.

Figures 3, 4 and 6 show satisfactory agreement between the experimental and predicted data, which validate the proposed model. Bubble size distribution When db>dmax, the inertial force becomes greater than the surface force and bubble breaks up. On the other hand, bubbles whose diameters are smaller than dmin are more prone to coalescence than the larger bubbles. There fore when bubbles are larger than dmax or smaller than dmin they are subject to break up or coalescence, respectively. Thus the equilibrium bubble size predicted by the proposed model would preferable lie between dmin and dmax. However, from Figure 4, 5 and 7 it is evident that the bubble size distribution spread out beyond dmax and dmin for both predicted and experimental data. The reason behind such spreading out is the very low rate of bubble break up and coalescence beyond dmin to dmax. It is noted that the distribution frequencies of very small bubbles predicted by the model is less than that of the experimental ones. This is due to the fact that the break up may not be a simple binary split as assumed in the model. Prince et al.25 and others have reported that the bubble breakup is often accompanied by production of two primary bubbles and a number of smaller fragments. Incorporation of this effect would significantly alter the number of smaller bubbles predicted by the model. Furthermore, the complete range of eddy size is not considered in the model. The expression used for eddy number is only applicable for eddies within the inertial sub range. Eddies smaller than 20% of the bubble size was ignored. Such eddies may contribute to the breakage rate. The model adopts a set of equations to predict the initial bubble size distribution. Those equations are based on the data for single orifice sparger and extended to the perforated plate sparger. This may cause error in initial bubble size determination, which in turn affects the equilibrium size distribution. In present model the values of dmax and dmin are used as break-up and coalescence criteria. The equation for dmin has been established by a number of researchers. On the other hand, the expression for dmax is based on a single study. Further research is needed in this regard. The equation used for determining Ul,max is limited to Newtonian fluid and turbulent flow. In case of laminar flow or Non-Newtonian fluid different equations need to be applied.


33

Conclusion A model for determining equilibrium bubble size distribution in a bubble column has been developed. Both coalescence and breakup of bubbles have been considered in the model. The coalescence event was modeled by considering the collision rate of bubbles and the likelihood of collisions resulting in coalescence. Collisions due to turbulence, buoyancy and laminar shear were considered. The coalescence efficiency was determined by comparing the time required for coalescence and contact time of two bubbles in turbulent flow. Bubble breakup was modeled by examination of bubble interaction with turbulent eddies. Breakup was assumed to occur when bubbles encountered eddies of appropriate size and sufficient energy to cause rupture. In all cases the turbulence was assumed to be isotropic and the particles were considered to lie in the inertial subrange. The favorable comparison of reported data with the present model suggests that the model may be used to predict dispersed phase mixing rates in uncontaminated gas liquid systems. The model also provides a framework to optimize bubble column performance with regard to mass transfer rates. Notation A= the Hamaker constant c= concentration of a surfactant species db= the bubble diameter, m dmax = the maximum stable bubble size, m dmin = the minimum stable bubble size, m dg = the geometric mean bubble size, m. D= tank or column diameter, m. Ee= the kinetic energy of the eddy, Kg. m2/s2. E(k) = the energy of eddies of wave number k, kg. m3/s2. h= the film thickness between coalescing bubbles, m. ho = the initial film thickness, m. hf = the critical thickness where rupture occurs, m . H = The un aerated liquid height, m. k = The eddy wave number (k=1/re, re being the radius of the eddy), m-1. ke = The wave number of the large energy containing eddies, m-1. kb= The wave number of the corresponding bubble size, m-1. kd= The wave number of the eddies of viscous dissipation, m-1. N (k) = the number of eddies of wave number k per mass of fluid and per unit interval of wave numbers. m = the eddy mass ni ,nj = The concentration of bubbles of radius rbi, rbj respectively, m-3. P1= Pressure at the sparger, N/m2.

P2= Absolute Pressure, N/m2. PLM= Log mean Pressure, N/m2 Q = gas rate per orifice, m3/s. QM = Mean gas rate, m3/s. R= the radius of the column, m. Rd= the radius of the liquid disk between the coalescing bubbles, m. re = the eddy radius. Sij= The collision cross sectional area of the bubbles, m2. tij= The time required for coalescence of bubbles of radius rbi and rbj, sec. ue= the eddy velocity, m/s ur= The rise velocity of the particle, m/s. Ul= the liquid circulation velocity, m/s. Ug= The superficial gas velocity, m/s. Ul,max = The velocity in the center of the column, m/s. x (E) = Energy distribution function Greek symbols ε= The energy dissipation per unit mass, m2/s3. υ= The kinematic viscosity, m2/s. ρc= the liquid density, Kg/m3. ρf= the fluid density, Kg/m3. σ = The surface tension, Kg/s2. φ = Gas hold-up υt = Turbulent Kinetic viscosity, τij = The contact times for the two bubbles of radius rbi and rbj , sec. µc, µd = the viscosities of the continuous and dispersed liquid phase respectively , Kg/m.s. Γ = gamma function. θB= buoyancy driven collision rate, m-3.s-1. θLS= collision rate due to laminar shear, m-3.s-1. θT= collision rate due to Turbulence, m-3.s-1. Subscripts b = Bubble c = continuous phase d = dispersed phase e = eddy f = final g = gas i, j = particle i,j l = liquid T= total Superscripts - = Mean Value.


34

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13. Lage, P. L. C., The non-uniform bubble size distribution in bubble columns: the choice of

bubble mean diameter for mass transfer, Proc. of XXVI ENEMP (Brazilian Congress on Particulate Systems) II: 631-636, 1996.

14. Hikita, H., Asai, S., Tanigawa, K., Segawa, K. and Kitao, M. , Gas hold-up in bubble columns, Chem. Eng. J., 20: 59-67, 1980.

15. Batchelor, G.K., The theory of homogeneous turbulence, Cambridge University Press, Cambridge 1970.

16. Friedlander, S. K., Dust, S., and Haze, A., Wiley, New York, 1977.

17. Walter, J., and Blanch, H. W., Liquid circulation patterns and their effect on gas hold up and axial mixing in bubble columns, Chem. Eng. Commun. , 19:243, 1983.

18. Coulaloglou, C. A., and Tavlarides, L.L., Description of interaction processes in agitated liquid-liquid dispersions, Chem. Eng. Sci, 32:1289, 1977.

19. Oolman, T. O., and Blanch, H. W., Bubble coalescence in air-sparged bioreactors, biotechnology and bioengineering, XXVIII, pp. 578-584,(1986).

20. Chesters, A. K., and Hofman G., Bubble coalescence in pure liquids, Appl. Scientif. Res., 38, 353, (1982).

21. Levich, V. G., Physicochemical hydrodynamics, Prentice-Hall, Englewood Cliffs, New Jersey, 1962.

22. Kennard, E. H., Kinetic theory of gases, McGraw-Hill, New York, 1938

23. Azbel, D., Two phase flows in chemical engineering, Cambridge University press, Cambridge 1981.

24. Angelidou, C., Psimopoulos, M. and Jameson, G. J., Size distribution functions of dispersions, Chem. Eng. Sci., 34: 671, 1979.

25. Prince, M., J. Walters, and H. W. Blanch, Bubble break-up in air sparged biochemical reactors, First Generation of Bioprocess Engineering, T K. Ghose, ed . 160, 1989


35

STUDY OF AN EVAPORATION SYSTEM FOR SODIUM HYDROXIDE SOLUTION

Md. Atikur Rahman* and Nymul Ehsan Khan

Department of Chemical Engineering Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh

Abstract The textile industry in Bangladesh uses a substantial quantity of caustic soda (sodium hydroxide) to clean and prepare fabrics for dyeing. In all textile mills dealing with finishing, particularly with the mercerizing of cotton and mixed cotton fabrics, dilute caustic soda solutions come out as effluent from mercerizing unit. Caustic soda is expensive and its disposal without neutralization is unacceptable. A considerable amount of caustic soda can be saved if the dilute solution leaving the mercerizing step can be collected, concentrated and recycled. The concentration of the dilute caustic soda solution can be carried out by means of evaporation. A single effect evaporation system to concentrate the dilute sodium hydroxide solution was constructed and operated. The operating results confirm the economic viability of such recovery scheme.

Introduction Evaporation of sodium hydroxide solution is performed on large scale and over a wide concentration range in the production of sodium hydroxide. The textile dyeing and finishing industry in Bangladesh use dilute solution of caustic soda in different operating steps such as desizing, washing and mercerizing. The concentrations of aqueous caustic soda vary from 4 to 20% by weight. At the end of such operations, the caustic solutions are discarded as effluents having lower caustic concentration, which pollutes the water body. The concentration of caustic solution leaving the mercerizing section as effluent is about 4% by weight. A laboratory scale setup capable of producing 25 kg/hr water vapor and resulting in a solution of 20% sodium hydroxide from a 4% by weight of caustic soda effluent was designed, built and tested. This paper deals with the operation of the laboratory scale evaporation setup and its application in the industry for recovering caustic soda from waste effluent. Experimental Study A 0.381 m ID and 2.44 m long cylindrical column with conical bottom made from 6.35 mm SS 304 Sheet was used as the flash separator for the boiling solution. A shell and tube exchanger (6 tubes – 1.52 m long, 9.14 mm ID, SS 304, 0.10 m ID CS Shell) was used for vaporization and a preheater of shell and tube type (4 tubes – 0.76 m long, 9.14 mm ID, SS 304, 0.076 m ID CS shell) was used to preheat the feed solution with vapor from the vapor separator. The steam used in the exchanger was at 16-20 psig. The setup is shown in Figure 1. Details of the setup are available elsewhere1.

The system was designed to evaporate of 25 kg/hr of water from 31.25 kg 4% feed solution of sodium hydroxide to yield 6.25 kg 20% solution. The flash tank would constantly contain 40 kg of 20% solution. The dilute feed solution, after passing through the preheater, would mix with a circulating stream of concentrated solution from the tank and pass through the evaporator. The mixture of liquid and vapor enters the flash tank where the vapor separates from the liquid and leaves through the top of the flash tank to pass through the preheater to preheat the feed solution. The flow was under natural circulation. The operability of the system was tested by using water as the working fluid.

Fig. 1: Setup of the process Results and Discussions After testing, the setup was run using actual solution of sodium hydroxide. Table 1 lists the data collected and calculated results in a summarized form. The feed rate was calculated using initial and final feed tank readings and intermediate charges. The difference in



36

flash tank levels (between initial and final) and the amount of solution fed was used to calculate the total water evaporated and the average evaporation rate. Table 2 gives a calculation of the cost savings for a typical textile factory producing 1000 kg of dilute depreciation neither does it include the cost saved for solution leaving mercerizing unit per day (this costs do

not include the cost of electricity, overhead and waste treatment that would have been required). As can be seen a textile factory involved in dyeing and finishing could save around Tk. 1000 for each 1000 kg of mercerizing effluent.

Table: 1: Data Collected and Calculated Results

Evaporator Preheater

Run Steam Press.,

psig

Run Time,

hr

Feed Rate, kg/hr

Water Evap. Rate, kg/hr

Total Steam Cond.,

kg

Cond. Rate, kg/hr

Overall Heat Transfer Coeff.,

W/m2.K

Steam Cond, kg/hr

Cond. Rate, kg/hr

Overall Heat Transfer Coeff.,

W/m2.K

Water evap/sq. ft

heat transfer surface

Ratio of water evap

to steam consumed

1 + 2 20 4.5+1 29 6 22 145.7 26.5 2195- 2425 24.65 5.5 362 5.99 0.83

3 + 4 20 2+3, for

flow 1.67+3

24 18.76 126.3 25.3 1875- 2072 17.9 3.85 319 5.11 0.74

Heat transfer calculation and data 2,4. Table 2: Cost calculation for a typical textile factory. Quantity Cost. TkFeed solution (4%) 1000 kg Sodium hydroxide saved 40 kg Market price of sodium hydroxide Tk 40/kg Cost of sodium hydroxide saved 1600 Water evaporated 800 kg Steam consumed (taking water evaporated to steam consumed ratio =0.8) 1000 kg Heat required 2.257 x 106 kJ Heat provided by NG (taking boiler efficiency = 0.8) 2.821 x 106 kJ Heating value of NG (source www titasgas org bd) 1050 Btu/SCF(1108 kJ/SCF) NG required 2546.2 SCF Price of NG (source www titasgas org bd) Tk 145.2/1000 SCF Cost of NG 370 Cost of daily labor 200 Cost saved 1030 Conclusion The recovery of caustic soda from the discarded effluent can be performed by using the system used in this work. This recovery would bring economic benefit to the industry and lead to resource recovery and reduction of treatment cost. Acknowledgement The authors are indebted to Dr. AKMA Quader, Professor of Chemical Engineering Department, BUET for his kind supervision of this project

References 1. Khan, Nymul E. Khan and Rahman, Md. Atikur,

Study of an Evaporation System for Sodium Hydroxide Solution, B.Sc. Engg. (Chemical) Thesis, Chem. Eng. Dept., BUET, November 2006.

2. Donald Q. Kern, Process Heat Transfer, Tata McGraw-Hill, New Delhi, 1997.

3. Alan S. Foust, Leonard A. Wenzel, Curtis W. Clump, Louis Maus and L. Bryce Andersen, Principles of Unit Operations (Second Edition), John Wiley & Sons, 1994.

4. Perry’s Chemical Engineers’ Handbook (Seventh Edition), Editors: Robert H. Perry (Late), Don W. Green and James O. Malony (Associate Editor), McGraw-Hill, 1997.


37

CORROSION CONTROL OF ELECTROLYZER, ANOLYTE TANK AND DECHLORINATION TOWER TANK OF A CHLOR-ALKALI PLANT BY

AN INNOVATIVE METHOD

Sazal Kumar Kundu* Global Heavy Chemicals Limited (GHCL), Dhaka, Bangladesh

Abstract Brine purification process of GHCL did not meet the specification of electrolyzer in the context of excess hydroxide ion (OH-). The electrolyzer, anolyte tank and dechlorination tower tank faced serious corrosion. This paper describes an innovative method adopted to meet the electrolyzer’s specification of excess OH-. This method consists of an innovative HCl dosing system added to purified brine tank. After adopting this method corrosion of electrolyzer, anolyte tank and dechlorination tower tank has been decreased in a noticeable rate. Also some chemical dosings have been reduced.

Introduction Global Heavy Chemicals Limited (GHCL), a private company, produces mainly caustic soda and chlorine. This plant is located on the southern part of Dhaka district in Hasnabad Union under Keranigonj Thana. Keranigonj is on the south bank of the river Buriganga. This plant is producing 35 TPD caustic soda. Also this plant is expanding and it is expected that this plant will produce 50 TPD caustic soda in 2007. There are three processes for producing elemental chlorine, caustic soda and elemental hydrogen by decomposing sodium chloride solution (brine) electrolytically. The processes are: mercury cell process, diaphragm cell process and membrane cell process. GHCL selected membrane cell process (Figure 1). An ion-selective membrane separates anodic reactions from cathodic reactions in membrane cell process. Only sodium ions and a little amount of water pass through the membrane from the anode to the cathode compartment. The main advantage of membrane cell process is the production of high purity caustic soda. But the disadvantage is the requirement of high quality brine. GHCL faced trouble to meet eletrolyzer’s specification of excess OH- from the beginning of commercial production. The author analyzed data of brine purification unit, examined several options and finally

solved the problem with a small change of process. This paper deals with how the problem was solved using an innovative idea. Brine Purification Process and the Problem The industrial grade salt used to prepare brine in GHCL is imported from India. This salt contains high quantity of impurities. The impurities are mainly calcium, magnesium and sulfate ions as shown in Table 1. So, the brine needs to be purified before using it for electrolysis. The brine purification process is shown in Figure 2. 30% NaCl solution enters the anode side of electrolyzer. After electrolysis about 22% brine solution leaves the electrolyzer. Hydrochloric acid is added to this brine at anolyte tank to decrease its pH below 2. This decrease in pH helps in mechanical dechlorination by a steam ejector. After mechanical dechlorination sodium hydroxide and sodium sulphite are added to the dechlorination unit to remove chlorine fully from brine. The brine is then send back to salt saturator where its concentration rises to 30% NaCl . While leaving salt saturator the brine also receives salts of calcium, magnesium and other metals. Cations other than sodium ions must be removed according to the specification of electrolyzer’s membrane. This brine then enters the brine purification reactor. Sodium carbonate and barium chloride are added to the reactor for removing calcium and sulfate ions successively. Sodium hydroxide and flocculant are added after brine



38

purification reactor. Sodium hydroxide removes magnesium ions from brine. After reaction total hardness of brine reduces to ppm level (below 10ppm). This brine is then sent to brine clarifier, anthracite filter and finally candle filter to remove suspended solids. After passing through these units chemical compositions of the brine remain unchanged. Then the brine enters ion-exchange columns where total hardness reduces to ppb level (below 20ppb). But excess OH- content remains unchanged. This is the purified brine for the electrolyzer. According to the electorlyzer’s specification, excess OH- should be less than 200 mg/liter. But excess OH- was more than 1200 mg/liter in the purified brine of GHCL. As a result, the electrolyzer, anolyte tank and dechlorination tower tank faced serious corrosion. And GHCL faced frequent shutdown. Options to Solve the Problem The author considered the following options to solve the problem: • Controlling NaOH dosing in dechlorination unit

and after brine purification reactor • Adding HCl to purified brine tank before sending

brine to electrolyzer The first option was not feasible. This option was tried to put but total hardness of brine before clarifier increased (above 10ppm). As a result, total hardness of brine after ion-exchange columns increased (above 40ppb). And the second option was finally selected to solve the problem. Implementing second option involved additional equipment and chemicals. The author was planning to do something very simple and cost-effective. The author found two ways to implement the second option. They are: • Online mixing of HCl and brine after ion-

exchange column • Mixing by agitation of falling liquids, HCl and

brine, through a hollow pipe from the top of the purified brine tank

The first way needs a pump, which is costly. So, the second way was chosen. One HCl tank is placed in GHCL dechlorination unit building at above 45 ft( 13.7m) height. This tank was connected with purified brine tank to add HCl with brine through potential energy using the arrangement shown in Figure 4. (Height of purified brine tank is 17 ft (5.2m).) Implementing the Scheme The schematic diagram for implementing the scheme is shown in Figure 4. One hollow pipe of 152mm ID has been used here. Another pipe of 25mm ID is passed through this hollow pipe. Brine is passing through the hollow pipe and HCl is passing through the narrow pipe with the help of a rotameter. At the bottom of the hollow pipe a good mixing takes place from agitation of falling liquids. One pH meter was installed from top of the purified brine tank. The pH meter is sensing at 70% level from the bottom of the tank. It could be mentioned that this tank is always maintained above 90% level. When the scheme was put into operation excess OH- of the purified brine met the specification of the electrolyzer. The data on HCl consumption at purified brine tank after operating with the new scheme are given below: • Concentration of HCl : 18%, w/w • Range of Brine Flow Rate : 10 – 15 m3/hr • Requirement of HCl : 60 – 80 liter/hr The plant is operating successfully with this modification. And GHCL has achieved some advantages after implementing the scheme. Achievements The frequent leakage of electrolyzer, anolyte tank and dechlorination tower tank has been stopped. Before implementing the scheme GHCL used to be shut down for serious corrosion of these units (electrolyzer, anolyte tank and dechlorination tower tank) once in a week. And after implementing the scheme GHCL


39

rarely shut down for corrosion problem of the above mentioned units and there is very little corrosion. Besides having the above improvements GHCL achieved some benefits from this modification. As can be seen from Table 2 the other benefits are: • Less consumption of sodium hydroxide in brine

dechlorination. • Less consumption of hydrochloric acid in anolyte

tank. • Less consumption of sodium sulfite in brine

dechlorination. • Less consumption of barium chloride in brine

purification unit. Barium chloride is used to decrease SO4

= content in brine. High content of SO4

= ions can affect the electrolysis process. • Less consumption of flocculant. • Sodium Chlorate (NaClO3) content of brine has

been decreased. NaClO3 is corrosive to metals. The decrease in content of this compound is

beneficial for plant operation.

Acknowledgements The author would like to thank Mr. Dipak Kumar Kundu (Project In-Charge of GHCL) for giving permission to carry out this work and providing helpful suggestions. The author also thanks all personnel of process area and QC of GHCL for their assistance. References

1. Plant Documents of Global Heavy Chemicals Limited.

2. Chlor-Alkali Process : <www.akerkvaerner.com/Internet/IndustriesAndServices/Pulping/BleachingChemicals/ChloralkaliProcess.htm>

Fig. 1: Membrane cell process to produce sodium hydroxide, hydrogen and chlorine.


40

Fig. 2: Block diagram of brine purification process and electrolysis including the modification

Fig. 3: Schematic diagram of purified brine tank (before the modification)

RETURN BRINE TANK

SALT SATURATOR

PURIFIED BRINE TANK

BRINE PURIFICATION

REACTOR

ION EXCHANGE COLUMNS

POLISHED BRINE TANK

ANODE

CANDLE FILTER

DECHLORINATION UNIT

ANOLYTE TANK

CATHODE

CATHOLYTE TANK DM WATER

32% NaOH PRODUCTION

NaCl

H2

CATHOLYTESEPARATOR

ANOLYTE SEPARATOR

Cl2

NaCO3 BaCl2 NaOH

HCl

Flocculant NaOH

BRINE CLARIFIER

CLARIFIED BRINE TANK

ANTHRACITEBRINE FILTER

FILTERED BRINE TANK

22% NaCl

30% NaCl

ELECTROLYZER

HCl

Na2SO3


41

Fig. 4: Schematic diagram of purified brine tank (after the modification) Table 1: Salt composition (imported from India)

Date of Test Ca++ Mg++ SO4= NaCl Moisture

23.04.05 0.211% 0.035% 0.411 % 95.28 % 3.23 %

01.06.05 0.18 % 0.022 % 0.361% 96.14 % 2.64 %

Source: QC, GHCL

Table 2: Improvement after implementing the new scheme Serial No. Parameter Before operating

with new scheme

(July 18, 2005)

After operating

with the new

scheme (August

06, 2005)

Source

1 NaOH (32%, w/w) Dosing to

Dechlorination Tower Tank

60 liter/hr 20 liter/hr

2 HCl (18%, w/w) Dosing to

Anolyte Tank

150 liter/hr 110 liter/hr

3 Sodium Sulfite Dosing 525 kg/ day 225 kg/day

4 Barium Chloride Dosing 860 kg/day 270 kg/day

5 Flocculant Dosing (0.07%, w/v) 57.6 liter/hr 36 liter/hr

Brine

Purification

Unit, GHCL

6 NaClO3, Purified Brine 11.50 gm/liter 7.80 gm/liter

7 SO4= content, Brine after Clarifier 8.00 gm/liter 5.6 gm/liter

QC, GHCL

N.B.: Brine purification process of GHCL has been operating with the new scheme from July19, 2005


42

EFFECT OF SPARK ADVANCE ON A GAS RUN AUTOMOTIVE SPARK IGNITION ENGINE

Md. Ehsan*

Department of Mechanical Engineering Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh

Abstract Petrol engines can run on natural gas, with little modification. The combustion characteristics of natural gas is different from that of petrol, which eventually affects the engine performance. The performance of a typical automotive engine was studied running on natural gas, firstly at a constant speed for various loads and then at a constant load for a range of speeds and results were compared with performance using petrol. Variation of the spark advance, consisting of centrifugal and vacuum advance mechanisms, was investigated. Results showed some reduction in power and slight fall of efficiency and higher exhaust temperature, for natural gas. The air-fuel ratio for optimum performance was higher for gas than for petrol. This variation in spark requirement is mainly due to the slower speed of flame propagation for natural gas. For both the cases, the best power spark advance for natural gas was found to have higher values than petrol. This issue needs to be addressed during retrofitting petrol engines for running on natural gas.

Introduction The sharp rise of conventional fossil fuel price is creating a huge effect on world economy. The issue of environmental pollution created by conventional fossil fuels is becoming more important, as we are getting more concern about the environment of our planet. These concerns as well as emission standards enforced by legislation, have led the research for the use of alternative fuels in different prime movers, including the extensively used internal combustion engines. Fuels, which have been studied for replacing petrol include - natural gas, compressed natural gas (CNG), liquefied petroleum gas (LPG), hydrogen, bio-gas etc 1 . Each of these has its merits and demerits for its use in different application. Among these alternative fuels, natural gas is attracting significant attention at present time. It is low in pollutants, high in calorific value, economical and available in abundance globally. Pollution level from the engine could be drastically reduced using natural gas 2. Unlike liquid petroleum reserves, natural gas is widely distributed around the world with substantially large reserves already discovered in most of the regions3. At the present time, the availability of natural gas, relative simplicity of engine conversion technology, economical and environmental benefits and in some cases strategic advantage makes it the preferred fuel4. CNG as an Alternative Fuel for Internal Combustion Engines Compressed Natural Gas (CNG) is one of the most promising alternatives to traditional fuel energy resources for internal combustion engines of various

types. Over two million natural gas vehicles (NGV) are in operation worldwide. Natural gas available in Bangladesh has very high methane content (94-98%). The Auto-ignition temperature, Octane rating and Calorific value of methane is much better for use in internal combustion engines compared to gasoline. Table 1 shows the comparison of some relevant properties of methane, gasoline and diesel1,5. Natural gas being a gaseous fuel at normal atmospheric conditions has the inherent advantage of high level of miscibility and diffusion with gaseous air, which is essential for good combustion. On the other hand lot of development of the engine fuel system have been dedicated to proper mixing of conventional liquid fuel with gaseous air in modern internal combustion engines. As a result use of CNG in more conventional engines like those using carburetor and older versions of electronic fuel injection system results drastic improvement in exhaust emissions. The emission improvements are less dramatic for engines with sophisticated closed loop fuel supply systems and post engine emission control devices. CNG conversion technology itself is also going through developments – from open loop without active gas flow towards close-loop active gas flow control and ultimately electronic control of gas injection. Although the emission control and environmental aspects of using CNG was the prime consideration of CNG application in internal combustion engines, especially inside big cities, in recent days with sharp increase in oil prices, the increasingly significant economic advantage of using CNG has become the real prime consideration for lot of new users. Table 1: Comparison of typical values of some related properties of three fuels.



43

Property Natural gas (Methane)

Gasoline Diesel

Formula CH4 C4-C12 C8-C25 H-Content %weight

25 12-15 13-16

Density kg/m3

(Ambient, 25°C) 0.66 730 840

Vapour density, compared to air

Lighter Heavier Heavier

Boiling point Temp °C, atmp

-162 27-225 188-343

Latent heat of vaporization kJ/kg (Ambient, 25°C)

- 349 233

Flash point temperature °C

-188 -43 74

Auto Ignition (SIT) temperature °C

540 257 316

Octane/Cetane Number

120 90-100 40 – 55

Flammability limit, Vol%

5 – 15 1.4 - 7.6 1 – 6

Flammability limit, AF ratio (mass)

34.3– 10.2 25 - 4 -

AF ratio, Stoichiometric (mass)

17.2 14.7 14.7

Flame propagation Speed m/s

0.43 0.5 -

Common Compression ratio

9 – 12 9 –12 16 – 24

Lower Heating value MJ/kg MJ/liter

50 0.033

44 32

42 36

CNG Technology Natural gas can be readily used in the spark ignition (SI) engines without major modification to the engine structure, retaining the option of easy switchability back to gasoline. So retrofitting/conversion of these engines are most suitable for use of NG/CNG and popular in automotive applications. For using CNG in automotive applications two pre-requisites have to be ensured. Firstly to convert/modify the existing engine so it can run with natural gas. This requires pressure reduction of high pressure CNG in cylinders in order to introduce it into the engine and control its flow with engine requirements. Secondly a fuel compressing, storing and dispensing system that will

allow transportation of the gas under high pressure to overcome the low power density of natural gas and allow it to be used in mobile applications. For stationary engines a more simple system using a line supply of natural gas may be used CNG Conversion Components A typical standard CNG conversion (retrofit) system essentially consists of the following5, the locations are indicated in fig. 1.

Fig. 1: CNG conversion components of a vehicle 1. The Cylinder is used to store CNG at a

working pressure of 200 bar. It is fitted with a shut-off valve and a safety burst disc. Cylinders may be of seamless steel structure or reinforced carbon fiber composite. 50, 60, 90 water liter size cylinders are commonly used. At a pressure of 200 bar and ambient temperature CNG is compressed to about 3.7 times of equivalent petrol volume5. Due to the cylindrical shape and wall thickness the packing efficiency is poor and the real car space blocked by the cylinders is much more. The shut-off valve with the cylinder may have overflow limiter facilities built-in.

2. The selector Switch is fitted at the dash board, enabling the driver to choose either the CNG mode or the petrol mode of operation. The electronics built in this unit also ensures safety by switching off the gas solenoid whenever the engine is switched off. It also indicates the quantity of CNG available in the cylinder.

3. The High Pressure Pipe connects the refueling valve to the CNG Cylinder and Pressure Regulator.

4. The Refueling Valve is used to refuel the CNG cylinder.

5. The Pressure Regulator has a solenoid valve to shut-off gas supply to the engine. The CNG stored at a high pressure in the cylinder, is reduced to just below atmospheric pressure by this unit. This negative pressure is also a safety


44

feature that will not allow gas to pass through when the engine is not running. Generally this is provided with a gas filter element.

6. The Gas- Air Mixer is a unique component, specially designed to suit each engine model. It precisely meters gas fed into the engine.

7. Petrol Solenoid valve is used to cut off petrol supply to the engine when it is run on CNG.

8. Fitted near the cylinder, the Vapour bag/enclosure is used to enclose the cylinder valve and the pipes connecting it and is vented out of the car.

In addition to these basic components the conversion system may have few more components, generally if the engine is equipped electronic fuel injection system and electronic control unit (ECU). These include the following:

Spark Timing Advance Processor (STAP/TAP): The slower flame propagation speed in methane-air mixture make it necessary to increase the spark advance for CNG operation of a petrol engine1,6. This unit allows optional spark advances (e.g. additional 6, 9, 12, 15° BTDC), generally during accelerating conditions. The processor modifies the spark advance signal to the electronic ignition system accordingly. Use of this improves the peak power and acceleration performance of the vehicle running on CNG, while retaining the performance with petrol.

Emulator/Simulator: The EFI injectors are generally kept non-functional at CNG operation. On the other hand, in some engines feedback signals from the fuel injectors operation is fed back to the electronic control units (ECU). Under CNG operation the emulator simulates dummy feedback signals to the ECU, maintaining its normal operation as with petrol. This component may not be necessary for all models of EFI engines.

Oxygen Sensors and Speed sensors: Often these are required in close-loop gas flow-control CNG conversion systems.

Active Mixing Valve : Controls the flow of gas into the mixing chamber according to engine requirements sensed.

Gas Injectors : These are used for conversion systems, where just like multipoint fuel injection system, individual gas injectors control gas flow into each cylinder controlled by a processor unit.

Fig. 2: CNG conversion components fitted on a typical automotive engine.

From the storage tank up to the pressure regulator the CNG conversion components are almost similar for all the systems. In the most conventional conversion systems, used with carburetor engines, the spark advance is manually adjusted to an optimum position for CNG but compromises performance running on petrol. In open-loop CNG systems the STAP/TAP is used making the manual adjustment of spark advance unnecessary. This improves the acceleration performance while retaining most of the performance while running with petrol. In both the category stated above the gas flow is not actively controlled with engine speed and load requirements, it changes indirectly through the variation of intake manifold vacuum and hence cannot be fully optimized for both the fuels. During CNG operation the petrol flow is cutoff by deactivating the fuel pump or signal to the injectors through relay switches. In more advanced conversion kits a closed loop system is used where sensors like oxygen/lambda sensors are used to actively control the gas flow rate according to the engine requirement. In conversions using gas injections the CNG gas flow is controlled by a system almost parallel to the existing EFI fuel supply system running for petrol.

CNG being an indigenous fuel, using it replaces imported petrol and diesel, saving lot of foreign currency and dependency on other countries. CNG being a clean gaseous fuel is capable of reducing engine emissions significantly if properly used. Bangladesh is correctly trying to make use of its indigenous fuel source in internal combustion engines of various categories. The world wide rise of oil prices has provided the very effective economic incentive to get this technology established. CNG being a technology dealing with high gaseous fluid pressure, the safety issues related to it is of prime public interest worldwide.


45

Effect of Spark Advance for Using Natural Gas in a Typical Automotive SI Engine The Experimental Setup A typical 4-stroke, 4-cylinder, Inline, Water cooled automotive engine was run with natural gas. The Carburetor car engine with 1600cc displacement volume, Mechanical Contact Breaker ignition and a Compression ratio of 9 had a rated power of 33 kW and speed range of 700-3600 rpm. The absence of electronic control on the fuel flow and spark timing allowed independent manual adjustment of these parameters. This research work involved a detailed study of effect of variation of spark advance on the performance of the engine run on natural gas. In the study two approaches were adopted. In the first approach the engine was tested at varying speeds (1025, 1200, 1500, 1700, 2000, 2200, 2500, and 2700 rev/min) keeping the load constant (15 kg) running on petrol. For petrol at each speed the variation of power was measured using the dynamometer and tachometer readings, at various spark advance settings. The variation of speed and load was controlled by the throttle valve control mechanism. The spark advance positions were changed manually. The spark advance position at which best power is attained, is known as the best power spark advance (bpsa). At each bpsa condition the fuel flow rate, exhaust temperature, cooling water temperature, manometer reading for air flow rate and intake manifold vacuum were recorded. The same procedure was followed for the engine when running with natural gas at various speeds (1025, 1200, 1500, 2000, 2500 rev/min, at load of 15kg). In this case the load and speed was controlled by the simultaneous adjustment of the gas flow control valve and the throttle position. For natural gas, a rotameter was used to measure the gas flow rate. The rotameter was calibrated prior to the experiment. In the second approach the speed was kept constant at 2500 rev/min. For petrol the readings similar to the first approach were taken, but this time at variable loads (at 18,19,20,21,22,23,24 and 25 kg) keeping the speed constant (2500 rev/min). Also for natural gas readings similar to the first approach were taken at the best power spark advance positions for variable loads (at 15, 17, 18, 19, 20, 21, 22, 23 and 24 kg loads at 2500 rev/min). Similar to the first approach natural gas needed simultaneous adjustment of gas flow control valve and throttle control mechanism. A water-brake type hydraulic dynamometer (model no. TFJ-250L) was used to measure the engine performance. Three separate metering systems were

used to measure the flow rates of air, petrol and natural gas. The acceleration paddle (throttle valve) control mechanism of the engine was replaced by linear motion of a spring-locked screw mechanism. An air drum fitted with a parabolic nozzle and inclined manometer was used for measuring the mass flow of the air entering the engine. A cross flow-mixing box was used to introduce line supply of natural gas in to the intake air7,8. Type-K thermocouples were used for temperature measurements of the cooling water, lubricating oil and engine exhaust. Relevant test results were de-rated as per BS5514. The spark advance measuring mechanism consisted of a high voltage electric bulb, cord connections and a light-reflecting marker. The high surge carrying electric cord from the distributor, which is aimed for no. 1 cylinder of the engine, was connected to the input cord of the special electric bulb. The output cord

Fig. 3: Photograph of the engine test bed. of the electric bulb was connected to the spark plug of the first cylinder (firing order 1-3-4-2). Each time a high voltage surge from the ignition coil passes through this connecting system, the bulb blinks. A light-reflecting marker was placed on the flywheel plate indicating the TDC of the first cylinder. A stationary scale was placed on the engine body (as in Fig. 4), which shows the angle in degrees before top dead center (btdc). Each time a high voltage surge passes through the circuit, the lamp blinks and the reflector becomes visible. The relative position of the reflector marker with respect to the stationary scale indicates the angle at which the spark occurs before the piston reaches the TDC. The mechanism used as shown in figure-4, is similar to a stroboscope in operation8. The spark advance positions were changed by manual adjustment of the distributor unit. In this process the position of the contact breaker plate was changed relative to the distributor casing, causing the spark advance to change with respect to the TDC.


46

Fig. 4: Photograph of the spark advance measurement system. Results and Discussion In the first approach the best spark advance was found for engine running at various load conditions, but at a constant speed with both fuels. Since the speed is constant (2500 rev/min), for both the fuels, the effect of the centrifugal advance mechanism is the same. Therefore the required variation of spark advance for best power has to be done with the vacuum advance mechanism. Fig. 5 shows the variation of air flow rate at various loads at 2500 rev/min, for both petrol and natural gas. At higher load the throttle opening is wider, more fuel enters the engine and more air is needed for its combustion. The curve for natural gas has higher values than that of petrol. This indicates that greater amount of air is needed for combustion of natural gas, than petrol fuel. So for natural gas the throttle position had to be opened more, even for the same load. At loads higher than 22 kg, for natural gas the airflow was almost constant, which indicates that the extreme limit of the throttle position for the petrol engine had been

reached. The spark advance needed for natural gas is much higher than that of petrol, while the vacuum effect created in the intake manifold is less for natural gas, so further increase of spark advance was done manually to get the best power with natural gas4,7,8. Fig.5 shows the variation of A/F ratio and variation of the intake manifold vacuum, which is weaker for NG as the gas occupies more volume. Because of limitation of air intake as gas occupies more volume the maximum engine power (17.9 kW) running with natural gas is less than when running with petrol fuel (19.7 kW). The minimum equivalent bsfc found for natural gas was found to be slightly higher (1.7 %) than the minimum bsfc for petrol fuel. This is mainly caused by the slower flame propagation speed of natural gas. The slower burning rate allows exit of a greater amount of unburned natural gas through the exhaust. In case of petrol, the fuel enters the carburetor in the form of fine liquid along with air. By the time the charge enters the cylinder the liquid particles become almost completely vaporized this increases the inlet pressure of the cycle. In case of natural gas, the fuel supplied is gaseous; hence such increase in inlet pressure is not present. These two factors most likely cause the slight rise of the bsfc (347 g/kW-h for petrol and 353 g/kW-h equivalent for natural gas, at rated load) and fall of brake thermal efficiency (23.6% for petrol and 23.1% for natural gas). Fig.6 shows the variation of exhaust temperatures with load for both petrol and natural gas. At all loads the exhaust temperature is higher for natural gas than petrol fuel. The flame speed of natural gas is less than that of petrol. Therefore, burning of the air gas mixture continues well in the expansion stroke, which causes the exhaust temperature to rise. The spark advance requirement for natural gas is 15-20 degrees more compared to petrol for best power9. In both cases as the throttle opens up at higher loads the advance requirement decreases. In the second approach the load was kept constant while the engine speed was varied. Similar experiments were carried out first using petrol and then natural gas as the fuel. Fig.7 shows the Air flow rate, AFratio and Intake manifold Vacuum at different speed varied between 100-2700 rpm at constant load. The centrifugal advance mechanism plays the main role in changing the spark advance at different speeds. Although load is unchanged for both the fuels, but since the throttle valve needs relatively larger opening and the intake manifold vacuum is weaker with gas some motion of vacuum advance mechanism occurs in parallel.


47

Fig. 5: Variation of Air flow, AF ratio and Intake

Manifold Vacuum for petrol and natural gas. Tests are carried out at variable loads and at a speed of 2500 rpm.

At speeds of 1000, 1250, 1500, 2000 and 2500 rev/min the spark advances were recorded along with fixed load for natural gas. At each of these speeds, spark advance and air-gas ratio were manually changed to get best possible power. The data recorded at various speeds, with different spark advances are shown in Fig. 8 the best power spark advances (bpsa) were determined. The requirement is almost linearly proportional to engine speed for both natural gas and petrol, but with different slopes. For the engine, spark advance needed for best power at any speed is higher (about 12-15 degrees BTDC) for gas compared to petrol fuel. This mainly is caused by the lower flame

Fig. 6: Variation of Exhaust temperature, Best

power Spark Advance and Equivalent Bsfc for both fuels

speed of natural gas compared to petrol10,11. The minimum equivalent bsfc with gas was better for low powers, but reaching only slight improvement to 406 g/kWh (about 21% efficient) compared to petrol (411 g/kWh), at higher power. The maximum power produced was limited to 11.4 kW with gas compared to 12.1 kW with petrol.


48

Fig.7: Variation of Air flow, AF ratio and Intake Manifold Vacuum for petrol and natural gas. Tests are carried out at constant load and at a speeds varying from 1000 to 2700 rpm. Conclusions For running a retrofitted petrol engine efficiently with natural gas, few limitations need to be recognized and a number features need to be incorporated in the conversion system. In case of a dedicated gas engine these probably would already have been addressed by the manufacturer. • The maximum automotive engine power

produced when running on natural gas will be lower (in the order of about 5-10%) compared to when running on petrol. This should not have very visible effect during normal cruise of a vehicle. However it may increase the time taken by the vehicle to accelerate when operating under full load conditions.

Fig. 8: Variation of Exhaust temperature, Best power Spark Advance and Equivalent Bsfc for both fuels

• The gas flow rate needs to be adjusted

according to the engine operating conditions to attain the required air-fuel ratio. It should be noted that the gas flow practically by-passes the carburetor details or the sophisticated electronic fuel injection system but being gaseous has the inherent advantage of far better miscibility with incoming air. Even an optimized passive flow control device will be altering gas flow close to the required level as the intake vacuum changes, under some operating conditions. For better performance through out the power range, active flow control devices (eg. close loop flow control using O2 sensor, electronically controlled Gas injection etc.) may be used.


49

• Many engines use intake manifold vacuum signal as an important parameter, for controlling different engine function (eg, vacuum advance of spark, throttle positioning, fuel enrichment etc.). In the same manifold structure when gaseous fuel is introduced it weakens the vacuum created by suction process (due to the larger volume occupied by gas) compared to petrol. If this is not taken into account, it may result in improper adjustment of the support features (eg. vacuum advance) of the engine hampering the engine performance. Producing same power requires more throttle opening.

• The speed dependent spark advance

(centrifugal) requirement is much higher for natural gas compared to petrol. The requirement also changes at a different rate with speed compared to petrol. In engines with ECU and electronic ignition system this can be addressed by using a spark advance processor (STAP/TAP), correcting the spark advancement signal when using natural gas especially during engine acceleration. More conventional engines go for a fixed manual advancement optimized for running on gas but have to compromise performance when running on petrol.

• The higher hydrogen contents allow the

maximum temperature of combustion to be higher in case of a gas run engine. On the other hand the temperature of exhaust gas is a function of power produced. As the peak power is a little bit limited, the maximum temperature attained may not be significantly higher in comparison to petrol operation, but at part loads the engine experiences higher temperature (in the order of 20-35°C in this case) in exhaust path. This also may cause some overheating specially in old vehicles where the cooling performance of the radiator was already limited.

Acknowledgement Department of Mechanical Engg, BUET provided the funding for the research work.

References 1. Goodger, E. M., “Alternative Fuel”, Macmillan

Press Ltd., ISBN-0-333-25813-4, U. K., 1980. 2. Karim, G. A. and Ali, A. I., “Combustion, Knock

and Emission Characteristics of a Natural Gas Fuelled Spark Ignition Engine with Particular Refference to Low Intake Temperature Conditions”, Proc. Mech. Engrs. Vol: 189, 24/75, 1975.

4. C R Stone, K J S Mendis, and M Daragheh, "Measurements and Modelling of a Lean Burn Gas Engine". Proc. I Mech E Vol 210 Part A6, pp 449-462, London, 1996.

5. Bechtold R. L., “Alternative Fuels Guide Book”, SAE International Publication, ISBN 0-7680-0052-1, Warrandale, PA, USA,1997.

6. Bell A., Stuart R., “Natural Gas as Transportation Fuel”, SAE Technical Paper No.931829, pp. 29-35, Warrendale PA, USA 1993.

7. Ehsan Md. and Alam M. S.B., “Effect of Independent Gas Flow Control on the Performance of a Fixed-Speed Gas Run SI Engine”, accepted paper No. JMED-128, ME 33, Journal of Mechanical Engineering, Institution of Engineers Bangladesh (IEB), pp. 1-11, June & Dec 2004 Vol. ME 33.

8. Ehsan, M., “Study of the effect of Spark Advance on Gas run Petrol Engine.” M. Sc. Engg. Thesis, BUET, Dhaka Bangladesh, 1993.

9. Bell, S. R., Loper, G. A., Gupta, M., “Combustion Characteristics of a Natural Gas fuelled Spark Ignition Engine”, ASME Paper 93-ICE-17, 1993.

10. Maly, R., and Vogel, M., “Ignition and Propagation of Flame Fronts in Lean CH4-Air Mixture by three modes of Spark Ignition”, Proceedings of the 17th international Symposium on Combustion, pp. 821-831, The Combustion Institute, 1986.

11. A Spencer, R Stone, E P Lim and S Simonini, "Combustion Performance of Methane, Iso-octane, Toluene and Methanol in a Spark Ignition Engine", Journal of Institute of Energy, Vol 72, pp 157-164, Dec 1999.


50

TROUBLESHOOTING PLANTWIDE OSCILLATIONS USING NONLINEARITY INFORMATION

M. A. A. Shoukat Choudhury Department of Chemical Engineering

Bangladesh University of Engineering and Technology Abstract Plant-wide oscillations are common in many processes. Their effects propagate to many units and may impact the overall process performance. It is important to detect and diagnose the cause of such oscillations in order to rectify the situation and maintain the proper profitability of the plant. This paper proposes a new procedure to detect and diagnose plant-wide oscillations using routine operating data. The method has been developed based on the nonlinearity information in the process data. A new Total Nonlinearity Index (TNLI) has been defined to quantify nonlinearities. The method is based on the assumption that the nonlinearity is highest near the source and decreases as one moves away from the source. This assumption is true because chemical processes have the nature of low-pass filters and they filter out gradually higher order harmonics of the signals. Signals with higher order harmonics are generally more nonlinear. The proposed diagnostic method has already been successfully applied for troubleshooting many industrial plant-wide oscillation problems. Two of such case studies have been presented in this paper.

1 Introduction Oscillations are a common form of plant-wide disturbance. The presence of oscillations in control loops increases the variability of the process variables thus causing inferior quality products, larger rejection rates, increased energy consumption and reduced average throughput. The high level of energy integration in most modern plants facilitates the propagation of oscillations from one process unit to another. It is important to detect and diagnose the causes of oscillations in a chemical process because a plant running close to product quality limits or operating constraints is more profitable than a plant that has to back away due to the amplitude of the oscillations (Martin et al., 1991; Shunta, 1995). In this paper, we present a new method for the detection and diagnosis of plant-wide oscillations and demonstrate its efficacy through an application to a chemical process at Eastman Chemical Company, USA. In a control loop, oscillations may arise for various reasons including poorly tuned controllers, presence of oscillatory disturbances and nonlinearities. Bialkowski (1992) reported that about 30% of the loops are oscillatory due to control valve problems. In a recent industrial survey, Desborough and Miller (2002) found that control valve problems account for about a third of the 32% of controllers classified as “poor” or “fair”. The method presented here is quite general for finding the root cause of oscillations due to nonlinearities, which is known to be the key reason for oscillations in process industries (Bialkowski, 1992; Desborough and

Miller, 2002). The attraction of this method is that it primarily uses only regular operating data. No additional experimentation of the plant is required. The main contributions of this paper are: (1) Methods for automatic detection of multiple oscillations across an entire plant site. (2) Development of new indices based on higher order statistics for diagnosing root cause of plant-wide oscillations. (3) Demonstration of the potential of systematic use of signal processing techniques for solving industrial problems through case studies. 2 What is Plantwide Oscillation(s) When one or more oscillations is generated somewhere in the plant and propagates throughout a whole plant or some units of the plant, such oscillations are termed as plantwide or unitwide oscillation. Oscillation may propagate through many units of the process plants because of the tight heat and mass integration in the plant as well as the presence of recycle streams in the plant. Figure 1 shows an example of a plant-wide oscillation problem. The left panel shows the time trends of 37 variables representing a plant-wide oscillation problem in a refinery (courtesy of South-East Asia Refinery). The right panel shows the power spectrum of these variables. This clearly shows the presence of an oscillation with a frequency of 0.06 or approximately 17 samples/cycle in many of these variables. The presence of such plant-wide oscillation(s) take a huge toll on the plant economy.


51

Fig 1: Time trends and their power Spectra

3 Detection of Plantwide Oscillations Detection of plantwide oscillation may not be a difficult problem. Often times the plant operators

notice some oscillations in the plant, which leads to a deeper investigation of the problem and may cause the invention of a plantwide oscillation of a larger nature. However, it is difficult to find all variables oscillating together out of the hundreds or thousands of variables in a chemical plant. Before a full scale oscillation diagnosis exercise is undertaken, it is important to find all signals oscillating at the same frequency as the root cause generally lies within this set. In contrast to this, most of the available techniques for detection focus on a loop by loop analysis (Hagglund, 1995; Taha et al., 1996; Miao and Seborg, 1999). Recently, Thornhill and co-workers have presented some detection tools that consider the plant-wide nature of oscillations (Thornhill et al., 2003a). To detect oscillations in process measurements and identify signals with common oscillatory behavior, use of spectral principal component analysis (Thornhill et al., 2002) or autocorrelation functions (acf) (Thornhill et al., 2003a) is suggested. Over the last few years, some studies were carried out to detect plant-wide oscillations (Tangirala et al., 2005; Jiang et al., 2006) and to group the similar oscillations together. The following are the brief description of some the techniques that can be used for detecting plant-wide oscillation(s). 3.1 High Density Plot - An excellent Visualisation Tool This plot describes time series data and their spectra in a nice compact form in one plot. From this plot, one can easily visualize the nature of the data and the presence of common oscillation(s) in the data. However, this method cannot provide a list of the variables that oscillate together automatically. Figure 1 is an example of a high density plot. 3.2 Power Spectral Correlation Map (PSCMAP) The power spectral correlation index (PSCI) is defined as the correlation between the power spectra of two different measurements. It is a measure of the similarity of spectral shapes, i.e., measure of the commonness of frequencies of oscillations. The Discrete Fourier Transforms (DFT) that are used to calculate the spectrum are calculated after removal of means from the time-series data. However, the correlation used in the calculation of PSCI is calculated without the removal of mean of the spectra. The PSCI for any two spectra |Xi(ω)|2 and |Xj(ω)|2 is calculated as

44

2222

|)(||)(|

|)(||)(|)|)(|,|)((|

kjki

kjkiji

XX

XXXXncorrelatio k

ωω

ωωωω ω∑=

(1)


52

As a result, PSCI always lies between 0 and 1. The phase information is excluded due to taking the magnitude of the DFT of the measurements. In the detection of plant-wide oscillations, the objective is to collect variables with similar oscillatory behaviour. For multivariate processes, the PSCI is a matrix of size m × m, where m is the number of measured variables. In order to provide an effective interpretation of the PSCI, the matrix is plotted as a colour map, which is termed as the power spectral correlation map. The intensity as well as the type of colour in the map is assigned in proportion to the value of the correlation index. This mapping is performed according to the choice of colour and the number of shades in that colour. An important aspect of this colour map is its ability to automatically re-arrange and group variables together with similar shapes, i.e., variables, which oscillate at a common frequency and have therefore similar values of PSCI. For a detailed discussion on this method, refer to (Tangirala et al., 2005). This method provides a list of the variables that are oscillating together. 4 Diagnosis Techniques for Plant-wide Oscillations As described in the last section, the detection of plant-wide oscillation is relatively an easy problem compared to the diagnosis of its root-cause. Recently there appeared a few papers that described a few techniques to perform root-cause diagnosis of plant-wide oscillation (Zang and Howell, 2006; Zang and Howell, 2005; Thornhill et al., 2003b; Thornhill et al., 2001). Industrial processes generally deviate from Gaussianity and linearity and exhibit nonlinear behaviour. The distribution of signals from nonlinear processes is often skewed and non-normal. These processes can conveniently be studied using Higher Order Statistics (HOS) (Nikias and Petropulu, 1993). Among the various frequency domain HOS measures the bispectrum is the simplest. It is the frequency domain counterpart of the third order moments and defined as

(2) where, X(f) is the Fourier transformation of the data series x(t). Equation 2 shows that it is a complex quantity having both magnitude and phase. It can be plotted against two independent frequency variables, f1 and f2 in a three dimensional plot. Each point in the plot represents the bispectral energy content of the signal at the bifrequency, (f1, f2). In fact, the

bispectrum,B(f1, f2), at point (f1, f2) measures the nonlinear interaction between frequencies f1 and f2 (Nikias and Petropulu, 1993). This interaction between frequencies can be related to the nonlinearities present in the signal generating systems and therein lies the core of its usefulness in the detection and diagnosis of nonlinearities. The bispectrum is normalized in the following way to give a measure called bicoherence whose magnitude is bounded between 0 and 1:

(3)

where ‘bic’ is known as ‘bicoherence’ function. Equation 3 can be rewritten as

(4)

If Welch’s periodogram method is used to estimate the bicoherence, the expectation operator can be replaced with a summation operator over the number of data segments using the assumption of ergodicity:

(5)

The squared bicoherence is usually estimated using this equation. 4.1 Test of Gaussianity and Linearity of a Signal Two indices - Non-Gaussianity Index (NGI) and nonlinearity Index (NLI) – were developed in Choudhury et al. (2004) to test the Gaussianity and linearity of a signal or time series. The indices were developed based on the statistical hypothesis test on the average squared bicoherence in the principal domain (0 < f1 < 0.5, f2 < f1, and 2f1 + f2 < 1) of the bicoherence. The average bicohernce was used in the formulation of the indices because the estimation of bicoherence was not free from spurious peaks. The new estimation method described in (Choudhury et al., 2006a) allows us to modify the previously published indices. The modified indices have fewer cases of false positives and better capability of detecting nonlinearities. The following section describes the modification of the indices with a brief overview of the old indices.


53

A discrete ergodic stationary time series, x(k), is called linear if it can be represented by

(6) where e(k) is a sequence of independent identically distributed random variables with E[e(k)] = 0, σ2 = E[e2(k)], and µ3 = E[e3(k)]. For a linear time series, it can be shown that

(7)

Equation 7 shows that for any linear signal, x, the squared bicoherence will be independent of the bifrequencies, i.e., a constant in the bifrequency plane. If the squared bicoherence is zero, the signal x is Gaussian because the skewness or µ3 is also zero in such a case. To check whether the squared bicoherence is constant, two tests are required. One is to determine whether the squared bicoherence is zero, which would show that the signal is Gaussian and thereby the signal generating process is linear. The other is to test for a non-zero constant value of the squared bicoherence which would show that the signal is non-Gaussian but the signal generating process is linear. 4.1.1 Modified Non-Gaussianity Index (NGImodified) It is well established in the HOS literature that bicoherence is a complex normal variable, i.e., both estimates of real and imaginary parts of the bicoherence are normally distributed (Hinich, 1982) and asymptotically independent, i.e., the estimate at a particular bifrequency is independent of the estimates of its neighboring bifrequencies. Therefore, the squared bicoherence at each bifrequency is a non-central chi-squared (χ2(m)) distributed variable with 2 degrees of freedom and mean, m. The following statistical test can be applied to check for the significance of bicoherence magnitude at each individual bifrequency:

(8)

or,

(9)

where K is the number of data segments used in

bicoherence estimation, 2χ

αc is the critical value calculated from the central χ2 distribution table for a

significance level of α at degrees of freedom 2. For

example, at α = 0.05, the value of 2

05.0χc is 5.99.

Often the principal domain of the bicoherence plot contains more than a hundred bifrequencies. The hypothesis test results for this large number of bifrequencies can be conveniently summarized into the following modified Non-Gaussianity Index (NGImodified)

(10)

where bic2significant are those bicoherence which fail the

hypothesis test in Equation (9), i.e., bic2(f1, f2) > Κ2

2χαc

,

and L is the number of bic2significant. Therefore, the

following rule-based decision is suggested: • if NGImodified ≤ α the signal is GAUSSIAN • if NGImodified > α, the signal is NON-GAUSSIAN Thus, a signal is non-skewed or Gaussian at a confidence level of α if theNGImodified is less than or equal to zero. This index has been defined to facilitate the automation of this decision. 4.1.2 Modified Nonlinearity Index (NLImodified) If a signal is found to be Gaussian, the signal generating process is assumed to be linear (Rao and Gabr, 1980). In the case of a non-Gaussian signal, the signal generating process should be tested for its linearity. As shown in Equation 7, if the signal is non-Gaussian and linear, the magnitude of the squared bicoherence should be a non-zero constant at all bifrequencies in the principal domain because µ is a non-zero constant. A simple way to confirm the constancy of squared bicoherence is to have a look at the 3-D squared bicoherence plot and observe the flatness of the plot. If the squared bicoherence is of a constant magnitude at all bifrequencies in the principal domain, the variance of the estimated bicoherence should be zero. To check the flatness of the plot or the constancy of the squared bicoherence, Choudhury et al. (2004) developed a nonlinearity index by comparing the maximum squared bicoherence with the average squared bicoherence plus two times the standard deviation of the estimated squared bicoherence. The disadvantage of using this index is that the presence of a few large peaks significantly bias the standard deviation and mean of the estimated bicoherence, which leads to some false negatives. The other problem with this index is that it cannot give an indication of the extent


54

of nonlinearity because with the increase of peak sizes, the mean and the standard deviation also increase. In order to avoid these limitations, the index can be modified as:

(11)

where 2^

robustcib and robustcib ,2

^α are the robust mean

and the robust standard deviation of the estimated squared bicoherence. They are calculated by excluding the largest and smallest Q% of the bicoherence. A good value of Q may be chosen as 10. There is a similar concept used in statistics to calculate robust mean called ‘trimmed mean’. The users may choose a different value of Q. Therefore, it can be concluded that: • if NLImodified≤· 0, the signal generating process is

LINEAR • if NLImodified > 0, the signal generating process is

NONLINEAR Since the squared bicoherence is bounded between 0 and 1, the Nonlinearity Index (NLI) is also bounded between -1 and 1. 4.1.3 Total Nonlinearity Index (TNLI) It is important to measure nonlinearity in terms of a metric especially when there is a need to compare the extent of nonlinearities in various time series. If a time series is detected as nonlinear by the above-mentioned NGImodified and NLImodified indices, then the total nonlinearity present in the time series can be quantified using the following new index:

(12)

where, TNLI is Total Nonlinearity Index, bic2significant

are those bicoherence which fail the hypothesis test in

Equation (8), i.e., 2K bic2(f1, f2) > 2χ

αc . The TNLI is bounded between 0 and L, where L is the number of bic2

significant. 4.1.4 Illustrative Example 1 The purpose of this example is to demonstrate the efficacy of the proposed indices in the presence of varying noise and extent of nonlinearity of a signal. Let a signal be generated as follows:

(13) where, f1 = 0.12, f2 = 0.30, φ1 = π/3, φ2 = π/8, nl is a multiplication factor employed to represent the contribution of the nonlinear component of the signal, and d(k) is a white noise sequence. Again, frequencies are normalized such that the sampling frequency is 1. The quadratic term in Equation 16 will introduce phase coupled nonlinearity in the output signal, y. The quadratically phase coupled nonlinearities arise due to the interactions between any two of the signal components at frequencies f1, f2, 2f1, 2f2, f2 - f1, and f1 +f2. For details refer to (Choudhury, 2004).

Figure 2 shows the modified Non-Gaussianity Index (NGImodified) and the modified Nonlinearity Index (NLImodified) plotted against nl for varying cases of signal to noise (SNR) ratio. The dotted lines represent the modified NGI and the solid lines show the modified NLI. It is clear from the figure that both


55

indices increase with the increase of nonlinearity in the signal. The total nonlinearity index shown in Figure 3 represents the extent of nonlinearity in the signal. For nl = 0, there is no nonlinearity. Therefore, TNLI = 0. With increase of nl, the TNLI also increases. The amount of noise influences the calculation of all indices because the denominator of the bicoherence is affected by the noise. 5. Investigating nonlinearity of a Continuously Stirred Tank Reactor (CSTR) In this section, the nonlinearity of a non-isothermal continuously stirred tank reactor (CSTR) is measured around the operating point used for Case 1 in Marlin (1995).The schematic of the CSTR process is shown in Figure 4.

A simple first order irreversible exothermic reaction of the form A B is considered here. Assuming a perfect mixing in the reactor and the jacket, the CSTR model can be described by the following differential equations:

(14)

The notation and the parameters for simulation are given in Table 1. The simulation of the CSTR with the above mentioned parameters results in a steady state value of 0.2645 kmole=m3 for CA and 393.9 K for the reactor temperature, T. Sinusoids with varying amplitudes and frequencies were used to excite the process and the subsequent nonlinearity was quantified for each case. The results are shown in Figure 5. The figure clearly shows that total nonlinearity increases with the increase of the amplitude of the excitation

signal. Also, an increase in frequency of the input excitation causes an increase in nonlinearity.

6 Industrial Case Study 1 - Eastman Chemical Plant An industrial data set was provided by the Advance Controls Technology group of Eastman Chemical Company. Figure 6 shows the process schematic of the plant, which contains three distillation columns, two decanters and several recycle streams. There are 15 control loops and 15 indicators on the schematic. There are eight flow controllers. Six of them are in cascade configuration. The Advanced Controls Technology group had identified a need for diagnosis of a common disturbance with an oscillation period of about 2 hours. Thornhill et al. (2003b) had found out and confirmed that the root cause was a control valve problem. In this section, the newly proposed procedure is applied to this data set to demonstrate its efficacy in the detection and diagnosis of the plant-wide disturbance.


56

6.1 Data Description Uncompressed plant data were collected at a sampling period of 20 s for the period of two days. Therefore, there are 8640 samples for each tag. The data set contains 48 variables: 14 process variables (pv’s), 14 controller outputs (op’s), 15 indicator variables and 5 cascade loop setpoints (sp’s). 6.2 High Density Plots Figure 7 shows the time trends and power spectra of the first 15 variables which are pv’s.

The power spectra shows the presence of oscillation at the frequency of 0.003 cycles/sample (or about 333 samples/cycle, nearly a period of 2 hours). This oscillation had propagated through out the adjacent units and affected many variables in the process. Figure 8 show the time trends of controller output signals and the indicator variables with their spectra,

respectively. These figures also show that there is a dominant oscillation with frequency 0.003 cycles/sample which affects many of the variables.

6.3 Reduction of the problem size Thornhill et al. (2003b) performed nonlinearity analysis using surrogate data method on all 48 variables. In order to troubleshoot an oscillation, it is better to investigate the control error signals for the possible presence of oscillations in them. Figure 9 shows the time trends and power spectra of the control error signal for the 15 control loops. This figure clearly shows that only four loops namely LC1, TC1, LC2 and TC2 have oscillations at a frequency of 0.003 cycles/sample (or about 333 samples/cycle, nearly a period of 2 hours). Therefore, as a first attempt to diagnose the root-cause of this oscillation, only these four control loops were examined for performing a nonlinearity test.


57

6.4 Detection of Plantwide Oscillation by PSCMAP Figure 10 shows the PSCMAP of the 15 error variables. It is again clear from this figure that only LC1, TC1, LC2 and TC2 loops have similar oscillation.

6.5 Nonlinearity analysis using bicoherence based indices Nonlinearity analysis has been performed on the error signals of the four control loops. In order to exclude any effect from oscillations other than the frequency of 0.003 cycles/sample (or about 333 samples/cycle, nearly a period of 2 hours), the data was filtered using a band-pass Wiener filter with boundaries of [0.001 to 0.1] cycles/sample. Then, the filtered data were down-sampled by a factor of 10 in order to make them suitable to use with the parameters of the bicoherence estimation algorithm. The direct method of bicoherence estimation using an approach similar to Welch’s average periodogram estimation was used where a 128 point FFT was implemented using 128 samples for each data segment. For details, refer to (Choudhury, 2004). Downsampling the data by a factor of 10 reduces the oscillation period to approximately 34 samples/cycle. Therefore, a 128 samples segment of the data contains enough number of cycles of oscillation to perform a bicoherence estimation. The results of this analysis are shown in Table 2.

The table clearly shows that TNLI is highest for loop LC2, i.e., this loop has the maximum nonlinearity. This is also the loop that was identified as a root-cause in a previous analysis performed by (Thornhill et al., 2003b). Therefore, it can be concluded that the Total Nonlinearity Index (TNLI) can correctly identify the root cause of plantwide Oscillation problems caused by nonlinearity related faults. 6.6 Diagnosis of the problem in Loop LC2 Once a nonlinearity is detected using higher order statistical method, the pv-op plot is used to diagnose its cause. It is well known (Hagglund, 1995; Rengaswamy et al., 2001; Choudhury et al., 2005; Choudhury, 2004) that the presence of stiction in control valve in a control loop produces limit cycles in the controlled variable (pv) and the controller output (op). For such a case, the pv-op plot shows elliptical cyclic patterns, which are taken as a signature of valve stiction. If no such patterns are observed, it is concluded that there may be valve problems other than stiction. Note that for the cases of tightly tuned controller or a process with time delay, the pv-op plot may also exhibit elliptical patterns. But they do not add nonlinearity in a control loop. Therefore, these cases do not pass the nonlinearity test. The pv-op plot is investigated only after a successful nonlinearity detection in the loop. That is why the pv-op plot should not be used alone to detect stiction. This must be used in conjunction with the nonlinearity test. For a detailed discussion on these issues, refer to Choudhury et al. (2004),Choudhury et al. (2006).

Figure 11 shows the diagnostic plots for this loop. Figure 11(a) shows that there are significantly large peaks in the bicoherence plot indicating a nonlinear loop. The values of NGI and NLI for this loop are 0.15 and 0.42, respectively, which clearly indicates that the loop exhibits nonlinearity. Once a loop nonlinearity is detected, it should be checked whether this is due to stiction or other process nonlinearity. Figure 11(b) shows the pv-op plot for this loop. The plot clearly shows an elliptic pattern indicating the presence of stiction in the control valve. The apparent stiction is


58

quantified to be approximately 3% using the method described in Choudhury et al. (2006). Similar results of root cause diagnosis were also discussed in Thornhill et al. (2003b). It was reported that the control valve of loop LC2 suffered from a high static friction or stiction problem (Thornhill et al., 2003b). It has been confirmed that the control valve caused control variable LC2.pv to oscillate, and the oscillation passed through the feedback controller and made the controller output LC.op also to oscillate. After that, the oscillations propagated to the temperature control loop TC1 in the second distillation column and caused the temperature to oscillate. This is the reason why temperature indicator TI4.pv and control variable TC1.pv had oscillations too. For more information, refer to Thornhill et al. (2003b). 7 Industrial Case Study 2 - SE Asia Refinery This case study describes the method applied to a refinery data set, courtesy of a SE Asian Refinery. A simplified schematic of the refinery process is shown in Fig 12.

The data set consisting of 512 samples of 37 measurements sampled at 1 min interval. It comprises measurements of temperature, flow, pressure and level loop along with some composition measurements from the gas analyzers. The process contains a recycle loop from the PSA unit to the reformer unit. Controller errors (SPPV) are analyzed for control loop measurements. The time trends of the controller errors and their corresponding power spectrum are already presented in Figure 1. It is clear from both figures that there is very dominant oscillation at the frequency of 0.06 or approximately 17 samples/cycle. This particular oscillation was all over the plant and affected the plant operation a lot.

7.1 Oscillation Detection by PSCMAP The rearranged spectral correlation colour maps is shown in Figure 13. This clearly identifies that the tags 2, 3, 4, 8, 9, 10, 11, 13, 15, 16, 19, 20, 24, 25, 28, 33 and 34 have similar spectral shape and are affected with the above-mentioned oscillation.

7.2 Oscillation Diagnosis The power spectral correlation map finds that tags 2, 3, 4, 8, 9, 10, 11, 13, 15, 16, 19, 20, 24, 25, 28, 33 and 34 are oscillating with the frequency 0.06. The total nonlinearity test was applied to only these tags to trou-


59

-bleshoot this oscillation. Table 3 shows the results of this analysis. It is clear from the figure that the tag 34 is the most nonlinear tag because the total nonlinearity index (TNLI) is highest for this tag. Therefore, the tag 34 can be treated as the potential root-cause of this plantwide oscillation problem. This finding is in agreement with other previous studies performed on this data set (Thornhill et al., 2001). 8 Conclusions This paper presents a systematic method to diagnose the root-cause of a plant-wide oscillation problem. The plant-wide oscillation can be detected using high density plot or spectral correlation color map. Then the variables oscillating together are tested for possible presence of nonlinearity in them. The variable or the control loop that has the highest amount of nonlinearity should be treated first as a possible candidate for the cause of the plant-wide oscillation. A list for priority maintenance can be prepared based on the Total Nonlinearity Index (TNLI). The pv-op plot can be used to diagnose the fault of a control loop. The proposed method has successfully been applied on simulated as well as industrial data sets. Acknowledgements The author gratefully acknowledges Eastman Chemical Company and SE Asia Refinery for their help and permission to publish the results. References 1. Bialkowski,W. L. (1992). Dreams vs. reality: A

view from both sides of the gap. In: Control Systems. Whistler, BC, Canada. pp. 283–294.

2. Choudhury, M. A. A. S. (2004). Detection and Diagnosis of Control Loop Nonlinearities, Valve Stiction and Data Compression. PhD thesis.

3. Choudhury, M. A. A. S., N. F. Thornhill and S. L. Shah (2005). Modelling valve stiction. Control Engineering Practice 13, 641–658.

4. Choudhury, M. A. A. S., S. L. Shah and N. F. Thornhill (2004). Diagnosis of poor control loop performance using higher order statistics. Automatica 40(10), 1719–1728.

5. Choudhury, M. A. A. S., S. L. Shah, N. F. Thornhill and D. Shook (2006). Automatic detection and quantification of stiction in control valves. Control Engineering Practice 14, 1395–1412.

6. Collis, W.B., P.R. White and J.K. Hammond (1998). Higher-order spectra: The bispectrum and trispectrum. Mechanical Systems and Signal Processing 12, 375–394.

7. Desborough, L. and R. Miller (2002). Increasing customer value of industrial control performance monitoring - honeywell’s experience. In: Preprint of Chemical Process Control, CPC-6. Tucson, Arizona. pp. 153–186.

8. Hagglund, T. (1995). A control loop performance monitor. Control Engg. Practice 3(11), 1543–1551.

9. Helbig, A., W. Marquardt and F. Allg¨ower (2000). Nonlinearity measure: definition, computation and applications. Journal of Process Control 10, 113123.

10. Hinich, M. J. (1982). Testing for gaussianity and linearity of a stationary time series. Journal of time series analysis 3, 169–176.

11. Jiang, H., M.A.A.S. Choudhury, S.L. Shah, J.W. Cox and M. A. Paulonis (2006). Detection and diagnosis of plant-wide oscillations via the spectral envelope method. In: In the proceedings of ADCHEM 2006. Gramado, Brazil. pp. 1139–1144.

12. Marlin, T. E. (1995). Process Control: Designing Processes and Control Systems for Dynamic Performance. McGraw Hill. New York.

13. Martin, G. D., L.E. Turpin and R. P. Cline (1991). Estimating control function benefits. Hydrocarbon Processing pp. 68–73.

14. Miao, T. and D. E. Seborg (1999). Automatic detection of excessively oscillatory control loops. In: Proceedings of the 1999 IEEE International Conference on Control Applications. Kohala Coast-Island of Hawai’i, Hawai’i, USA.

15. Nikias, C. L. and A. P. Petropulu (1993). Higher-Order Spectra: A nonlinear signal processing frame work. Prentice Hall. New Jeresy.

16. Rao, T. S. and M. M. Gabr (1980). A test for linearity and stationarity of time series. Journal of time series analysis 1(1), 145–158.

17. Rengaswamy, R., T. Hagglund and V. Venkatasubramanian (2001). A qualitative shape analysis formalism for monitoring control loop performance.. Engng. Appl. Artificial Intell. 14, 23–33.

18. Shunta, J. P. (1995). Achieving world class manufacturing through process control. Prentice-Hall. NJ, USA.

19. Taha, O., G. A. Dumont and M. S. Davies (1996). Detection and diagnosis of oscillations in control loops. In: Proceedings of the 35th conference on Decision and Control. Kobe, Japan.

20. Tangirala, A.K., S.L. Shah and N.F. Thornhill (2005). Pscmap: A new tool for plant-wide oscillation detection. Journal of Process Control 15, 931941.

21. Thornhill, N. F., B. Huang and H. Zhang (2003a). Detection of multiple oscillations in control loops. Journal of Process Control 13, 91–100.


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22. Thornhill, N. F., F. Cox and M. Paulonis (2003b). Diagnosis of plant-wide oscillation through data-driven analysis and process understanding. Control Engng. Prac. 11(12), 1481–1490.

23. Thornhill, N. F., S. L. Shah and B. Huang (2001). Detection of distributed oscillations and root-cause diagnosis. In: Preprints of CHEMFAS-4 IFAC. Korea. pp. 167–172.

24. Thornhill, N. F., S. L. Shah, B. Huang and A. Vishnubhalota (2002). Spectral principal component analysis of dynamic process data. Control Engng. Prac. 10, 833–846.

25. Zang, X. and J. Howell (2005). Isolating the root cause of propagated oscillations in process plants..

International Journal of Adaptive Control Signal Processing 19, 247–265.

26. Zang, X. and J. Howell (2006). Isolating the source of whole-plant oscillations through bi-amplitude ratio analysis. Control Engineering Practice, 2005, In Press, corrected proof, available online 5 June 2006.


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MONITORING AND TREND ANALYSIS OF AIR-BORNE PARTICULATE MATTER (PM10 AND PM2.5) AT MAJOR HOT-SPOT AREAS:

MOHAKHALI AND FARMGATE IN DHAKA CITY

Md. Mominur Rahman*, Feroz Kabir Department of Chemical Engineering, Bangladesh University of Engineering and Technology

Bilkis Ara Begum, Swapan Kumar Biswas Atomic Energy Centre, Dhaka

Abstract The objectives of this work were to monitor and quantify the airborne particles (PM10 and PM2.5) and to predict the influence of human and natural activities on their ambient concentrations. Samples of Air-borne Particulate Matter (APM) in the size range 0-2.5 µm (PM2.5) and 0-10 µm (PM10) were collected simultaneously using two MiniVol portable air samplers at Mohakhali and Farmgate area in Dhaka city. At Mohakhali effective sampling duration was from May 16 to May 23, 2004 and at Farmgate from June 6 to June 13, 2004. Continuous seven day monitoring was carried out to find the effect of meteorology, traffic load and other anthropogenic activities on ambient Particulate Matter (PM) pollution level. Weekday and weekend average traffic number was evaluated by field technicians at both sampling sites. These sites are regarded heavily polluted because of the proximity of major roadways. Daily and weekly average concentrations of PM10 and PM2.5 at Mohakhali were found higher than USEPA and Bangladesh 24-hrs average guideline values but at Farmgate the concentrations were within the guideline values. Average proportions of PM2.5 in PM10 were found higher at Farmgate than that at Mohakhali.

1. Introduction The particulate matters are classified into two groups: fine micro particles (≤ 2.5 µm) PM2.5 and large micro particles (≤ 10 µm) PM10. Through respiration fine micro particles get into blood stream and dissolve into it [Biswas et al., 2003]. The number of motor vehicles in Dhaka up to the registration year 2003 was 3,29,644 among which 26,429 were two stroke three-wheeler auto rickshaws and auto tempos [BRTA, 2004]. The total number of vehicles in the city is not large relative to the population. However, high traffic congestion due to poor traffic management and poor vehicle maintenance (using impure fuel, high-sulfur diesel) has resulted in the transport sector being a major contributor to air pollution in Dhaka [ICTP, 2001]. Particulate Emissions calculated for different vehicles in 1998 by World Bank revealed that two-stroke three-wheeler was the main polluter vehicles with respect to particulate pollution in Dhaka city [WB, 1998].

Follow the observation and pressure from social and environmental organizations the government banned two-stroke three wheelers for Dhaka by December 31, 2002. In January 2003, after the complete phase-out of two-stroke three-wheelers, a step decrease in ambient levels of particulate matter was observed [Fabian, 2004].

Before banning two-stroke three wheeler (during 2001-2002), the average concentrations of PM2.5 and PM10 were 67.2 and 147 µg/m3 respectively in Dhaka city. In the following year (2003) these concentrations were 47.4 and 125 µg/m3 respectively [Begum et al., 2006]. Even after this significant reduction, the average concentrations of PM10 and PM2.5 in 2003 were much higher than the US EPA standards as well as the yearly average standards of PM10 (50 µg/m3) and PM2.5 (15 µg/m3) for Bangladesh. Currently it is believed that along with vehicular emission, building and road construction, soil dust, biomass burning and other industrial sources also contribute to particulate emission levels [Begum et al., 2005]. It has already been understood from the ambient air quality measurements by different initiatives that the main air quality related health problem in Dhaka city is associated with the airborne particulate matters (PM10 and PM2.5) [Akhtar, 2004]. The impact of airborne particles on human health has been observed [Dockery et al., 1993]. Severity of damage on human health is related with the size, composition and concentration of the particulate matter [Seinfeld, 1975]. Estimation of economic loss due to health impact of PM10 in Dhaka city has revealed a huge loss of about 124,184 million taka per year, an equivalent of 3-4% of GDP [Azad et al., 2003].

* e-mail: [email protected]


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2. Materials and Methods 2.1. PM Sampling Set-up and Sampling Preparation Two MiniVol Portable Air Samplers (Model no. Ver. 4.2, AirMetrics, U.S.A) were used to collect particulate matters (PM10 and PM2.5) from ambient air. Prior to sampling, the filters were conditioned (for 24 hrs at a constant room temperature and relative humidity of 25oC and 55% respectively) in conditioning room at Atomic Energy Centre (AEC), Dhaka. After conditioning, the filters were weighed in a microbalance. Filters were charged neutralized before each weighing by an electrostatic charge eliminator (Po-210; alpha emitter electrostatic charge eliminator, STATICMASTER). Airflow through the sampler was calibrated prior to each sampling. “O”-ring supported Teflon filter (Pall Corp., Gelman Lab., Zelfluor, 2 µm pore size, 47 mm diameter) was used for sampling ambient PM [AirMetrics, 1998]. 2.2. Site Selection and Sampling Protocol The objective of the project was to understand the air quality of Dhaka city, in particular the most densely polluted areas. Apparently it seems that the vehicles in Dhaka are the major polluters. This is why the samplers were placed near the busiest traffic intersections. At Mohaklhali, the sampler was kept in a box but the air inlet line was kept outside. With the support and cooperation of the police department, the sampler was setup within the police station compound, which was guarded by the police round the clock. At Farmgate, the samplers were placed over the flat roof of the guardhouse of Bangladesh Agricultural Research Council (BARC). The sampling location and the intersections of major roadways are shown in Figures 2.1 and 2.2. The sampler was positioned with the intake upward and located at an unobstructed area (at least 30 cm from any obstacle to air flow) and the sampler inlet was placed at a height of 3.5 m above ground level for Farmgate area and 2.5 m for Mohakhali area following US guideline (40 CFR, part 58, Appendix-6). The intake nozzle of the sampler at Farmgate location was about 5 m away from roadside whereas at Mohakhali it was about 3 m. Particulate fractions (PM10 and PM2.5) were collected simultaneously for 24 hours at every sampling station by two samplers. The sampling was continued for seven consecutive days at each site (for Mohakhali it was from midday of May 16 to midday of May 23, 2004 and for Farmgate it was from midday of June 6 to midday of June 13, 2004).

Fig. 2.1. Sampling site at Mohakhali

Fig. 2.2. Sampling site at Farmgate Preconditioned filters were placed to respective filter holder assembly of the sampler at the laboratory of AEC, Dhaka and were carried to sampling station in separate clean polyethylene bags at each sampling day. After sampling, filter holder assemblies (keeping the exposed filters inside) were brought back to the laboratory of AEC, Dhaka in separate clean polyethylene bags for conditioning prior to weigh and PM retrieval. A field blank was also used to make necessary correction in PM weight.


63

2.3. Meteorological Condition The meteorological data (Temperature: Max and Min, Percentage of Relative Humidity (%RH), Rainfall, Wind speed and Direction shown in Table 2.1 and Figures 2.3 and 2.4) in this study were obtained from meteorological station which is about 3 km at north-north-west of Farmgate sampling station and at west of Mohakhali sampling station. Table 2.1: Temperature, rainfall and relative humidity data collected from local meteorological center for the period- May 16 to 23 and June 06 to 13, 2004

Max. and Min. temperature

(oC)

Relative Humidity

Rainfall

Date

Max. (oC)

Min. (oC)

(%)

(mm)

For Mohakhali May 16 35.5 29 66.55 00 May 17 36 29 68.00 00 May 18 35.6 27.6 64.33 00 May 19 36.2 27.8 62.67 00 May 20 35.2 27.6 66.55 00 May 21 31.5 21.2 72.33 39 May 22 32.3 22.9 77.22 16 May 23 25.9 20.2 66.55 48

For Farmgate June 06 32.9 27.5 83.80 00 June 07 33.3 23.2 71.50 29 June 08 35.2 26.7 69.22 00 June 09 33.7 27.6 71.90 00 June 10 34.4 27.4 78.00 00 June 11 31.6 23 77.00 01 June 12 33.4 23.7 77.60 29 June 13 30.3 25.3 83.80 06

Source: Local Meteorological Centre, Agargaon, Dhaka

Fig. 2.3. Wind velocity from May 16 to May 23, 2004 during sampling at Mohakhali

Fig. 2.4. Wind velocity from June 06 to June 13, 2004 during sampling at Farmgate 2.4. Traffic Volume Measurement Traffic volume (Figure 2.5) was determined during weekdays and weekends at Mohakhali and Farmgate by manual counter round the clock to study the effect of vehicular emission on ambient air pollution. Suitable observatory points were selected by the incoming traffic route toward the sampling stations which are shown in Figures 2.1 and 2.2.

020000

4000060000

80000100000120000

140000160000

180000200000

Farmgate MohakhaliLocation

Ave

rage

veh

icle

num

ber Week-days

Week-end

Fig 2.5 Average traffic volume at Mohakhali and Farmgate during weekdays and weekends 2.5. Particulate Mass Measurements The masses of blank conditioned filters along with the collected particulate samples (PM2.5 and PM10) and filters (conditioned) were weighed at AEC as described in section 2.2. From the weight differences the PM masses were obtained. 3. Results and Discussions Particulate Matters (PM10 and PM2.5) at Mokhali and Farmgate were collected over a week (seven

1,50

,061

1,05

,957

1,82

,147

1,67

,932


64

consecutive days including weekends, at Mohakhali samples were collected from May 16-23 and at Farmgate from June 06-13, 2004) which picks up the impact of traffic on the ambient air quality of the city. Sampling started at midday and terminated at the same time next day (24 hours of sampling). Weekly average concentrations of PM10 and PM2.5 at Mohakhali were recorded much higher than amended Bangladesh national ambient air quality standards and USEPA standards (24-h average) for PM10 and PM2.5, which were set as 150 and 65µg/m3 respectively. However, the PM concentrations at Farmgate were recorded below the standard values. Results show that weekly average concentrations of PM10 at Mohakhali and Farmgate were 312.52 and 102.84 µg/std.m3 and concentrations of PM2.5 at Mohakhali and Farmgate were 87.45 µg/std.m3 and 54.66 µg/std.m3 respectively (Figure 3.1). It was found that average weekly proportion of PM2.5 in PM10 mass was 28% at Mohakhali, which was 53% at Farmgate (Figure 3.2).

0

50

100

150

200

250

300

350

PM10 PM2.5PM Fractions

MohakhaliFarmgate

0 10 20 30 40 50 60

Mohakhali

Farmgate

Loc

atio

ns

%(PM2.5/PM10)

FarmgateMohakhali

Higher PM concentrations at Mohakhali were due to the fact that the number of motor vehicles was higher at Mohakhali than that at Farmgate. Even the weekend average number of the vehicles at Mohakhali was higher than the weekday average vehicles number at Farmgate (Figure 2.5). Particulates emit into

atmosphere due to incomplete combustion and soil dusts are resuspended as vehicles run on the street. During sampling at Mohakhali massive construction work of Mohakhali flyover was going on. At Mohakhali, sampling was performed at the end of pre-monsoon period whereas sampling at Farmgate was performed at the beginning of the monsoon period. Several brik kilns were in operation at the periphery of Dhaka city up to the end of pre-monsoon period. These might be the possible reasons behind higher PM concentrations at Mohakhali. Lower proportion of PM2.5 in PM10 at Mohakhali compared to Farmgate might be due to presence of higher amount of coarse particles (PM2.5-10) in ambient PM10 at Mohakhali. It is believed that ambient PM concentration decreases as the horizontal wind speed increases. But this correlation was not observed completely during sampling at Mohakhali (Figure 3.3). This correlation held good from mid of sampling day Mon-Tue to mid of Tue-Wed (i.e., Tuesday), from mid of Wed-Thu to mid of Thu-Fri (i.e., Thursday) and mid of Fri-Sat to mid of Sat-Sun (i.e., Saturday). In the weekend, on Friday (from mid of Thu-Fri to mid of Fri-Sat) PM10 and PM2.5 concentration profiles reached the minimum. This relates to the lower volume of vehicular emission and other anthropogenic activities, which were lower during weekends. In the weekend the traffic volume was 92.2% of weekdays at Mohakhali (Figure 2.5). There was about 39 mm rainfall on that day (Table 2.1). Combined effect of these effects offset the effect of decreasing wind speed that might otherwise increase ambient PM levels. Tendency of increasing PM was observed during Fri-Sat to Sat-Sun.

0

50

100

150

200

250

300

350

400

Sun-Mon Mon-Tue Tue-Wed Wed-Thu Thu-Fri Fri-Sat Sat-Sun0

0.5

1

1.5

2

2.5

3

PM10 PM2.5 EPA (PM10)EPA (PM2.5) Wind Speed

24 hr. avg. EPA std. For PM10

24 hr. avg. EPA std. For PM2.5

This is because; each sampling was started at midday

PM C

once

ntra

tion

(µ

g/st

d.m

3 )

Fig 3.1. Weekly average concentrations of PM10 and PM2.5 at Mohakhali and Farmgate

Fig 3.2. Weekly average percent ratio of PM2.5 and PM10 at Mohakhali and Farmgate

Win

d Sp

eed

(m/s

)

Fig 3.3. Average concentrations (daily) of respirable particulate matter (PM10) and fine particulate matter (PM2.5) and the impact of wind speed on PM concentration at Mohakhali (samples collected between May 16 and May 23, 2004)

PM C

once

ntra

tion

(µ

g/st

d.m

3 )


65

and was terminated at about the same time next day. Thus, during sampling through Thursday (12.25 PM)-Friday (12.25 PM), samples were collected during heavy traffic load in the afternoon and evening of Thursday. Low traffic volume was recorded during morning through noon of Friday. Higher traffic volume was recorded during Friday afternoon through evening. During this time city dwellers usually go out for recreation, shopping, visiting relatives and friends. From the evening of Friday and by the morning of Saturday (beginning of working week) people return to work from distant places by various types of vehicles. As a result, greater traffic load within Friday evening is observed. The traffic load during Saturday morning becomes heavier than that of on Friday evening because of weekly routine activities. Thus, an increasing tendency of PM concentrations in the air was marked from Fri-Sat through Sat-Sun instead of occasional rain on Saturday and Sunday (May 22 and 23, 2004). Figure 3.3 shows that during Monday (from mid of Sun-Mon to mid of Mon-Tue), PM concentrations decreased though the average wind speed was low. Figure 2.3 shows that during May 17, 2004 (Monday), air was stagnant (zero wind speed) for about 15 hours. Maximum and minimum temperatures were recorded as 36-29oC during May 17 of 2004 (Table 2.1). And the day was recorded sunny. During this sampling period the average (24 hours) relative humidity was approximately 68% (Table 2.1). These conditions were favorable for the city atmosphere to become unstable. In this situation, vertical ventilation (dilution) of the pollutant predominates. The earth surface rapidly absorbs heat and transfers that to the surface air layer. So, this hot air parcel rises vertically and the cooler air falls to replace it. In this way vertical movements in both directions might be enhanced [Core, J., 2004]. On Wednesday (mid of sampling day Tue-Wed to Wed-Thu) PM concentration increased in spite of increasing wind speed. During this time wind blew predominantly from east, north-east and north-northeast (Figure 2.3). In these directions there are major traffic corridors where huge traffic congestion is a usual phenomenon (Figure 2.1). Wind also occasionally blew from north-northwest (Figure 2.3) part of the sampling point where massive civil construction of Mohakhali flyover was going on (Figure 2.1). Daily average concentrations of PM10 and PM2.5 at Farmgate were much lower than that at Mohakhali (Figure 3.1). Normally during weekdays PM levels show higher value than that of weekends due to higher traffic volume and other anthropogenic activities. However, during this sampling session meteorological effects offset traffic load effect and contribution from other anthropogenic activities. Synoptic southerly wind

from Bay of Bengal was predominant during this sampling session (Figure 2.4), which had to travel a shorter distance over the land compared to easterly or westerly wind. Average relative humidity was higher but ambient temperature (29.3oC) was lower (Table 2.1).

0

20

40

60

80

100

120

140

160

180

200

Sun-Mon Mon-Tue Tue-Wed Wed-Thu Thu-Fri Fri-Sat Sat-SunSampling Day

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

PM10 PM2.5EPA (PM10) EPA(PM2.5)Wind Speed

24 hr. avg. EPA std. For PM10

24 hr. avg. EPA std. For PM2.5

As the wind speed goes high pollutant concentration level in air decreases. This phenomenon was well correlated during the sampling session at Farmgate (Figure 3.4). During second and third sampling day PM concentrations were observed minimum. But normally these concentrations should be higher than the weekends due to traffic load since average traffic volume during weekdays was about 30% higher than that of weekends (Figure 2.5). Rain induced washout effects (Table 2.1) offset the traffic effect and contribution from other anthropogenic activities during these sampling days. During second sampling day wind directions were predominantly from south and south-west having high speed accompanying with occasional rainfall. In third sampling day PM concentrations were observed almost unaffected although there was no rainfall. This was probably due to clean air resulted from rains in the previous day that might prolong concentration build up of pollutants in air. During this sampling day wind directions were predominantly from south and north-east. Wind from north-east and east-northeast directions might contribute to PM load at Farmgate since in these directions heavy traffic congested area of Mohakhali and Tejgaon industrial area are located. Moreover, at Mohakhali massive construction work of Mohakhali flyover was continuing. At South of the sampling station there are several traffic intersections within 200 m of the sampling station (Figure 2.2). This might contribute to PM level at this station. The fourth

Win

d Sp

eed

(m/s

)

Fig 3.4. Average concentrations (daily) of respirable particulate matter (PM10) and fine particulate matter (PM2.5) and the impact of wind speed on PM concentration at Farmgate (samples collected between June 06 and June 13, 2004)

PM C

once

ntra

tion

(µ

g/st

d.m

3 )


66

sampling day was also rainless and sunny (Table 2.1) and the average wind speed was low (Figure 3.4). So an increasing trend in PM concentrations was observed due to gradual pollutant build-up in the air. Highest level of PM concentrations was observed on Thursday (from Wed-Thu through Thu-Fri sampling day). This was due to stagnant atmosphere (zero wind speed) for most of the time (Figure 2.4) and rainless and sunny weather conditions (Table 2.1). Moreover this was also the day before weekend when heavy traffic is observed. Again a decreasing PM trend concentration was observed during Friday (from Thu-Fri through Fri-Sat sampling day). This was due to high wind, rain washout and lower traffic volume on the weekend. During these sampling days predominant wind directions were from north-northeast, north and north-east (Figure 2.4). Low wind from Mohakhali and Tejgaon industrial area might contribute to the PM concentrations at Farmgate. Stagnant atmosphere (zero wind speed) for most of the time (Figure 2.4) might also help to build up PM levels in the air. This was why average PM levels during Thu-Fri through Fri-Sat sampling days were higher than that during Mon-Tue through Tue-Wed sampling days. Further decreasing trend in PM concentrations was observed during Saturday (from Fri-Sat through Sat-Sun sampling days). This was due to maximum average wind speed during this sampling session, rain induced washout effect irrespective of weekday heavy traffic volume and predominant wind from Tejgaon industrial area, heavy traffic congested Mohakhali area and major traffic intersections at Farmgate. 4. Conclusion Air quality of Dhaka city is poor in terms of particulate matter (PM10 and PM2.5) as measured at Mohakhali, the PM fractions were measured lower at Farmgate compared to that at Mohakhali which was due to lower traffic volume, termination of brick kiln activity and monsoon period when synoptic southerly prevailed from Bay of Bengal that carries less pollutant. Weekly average PM concentrations (both fine and respirable particulate matters) at Mohakhali were much higher than USEPA 24-hrs average standard values of150 µg/m3 for PM10 and 65 µg/m3 for PM2.5. It has been found that the contribution of fine particles with aerodynamic diameter less than 2.5 µm to PM10 at Mohakhali was about 28% and at Farmgate it was about 53%, which are mainly of anthropogenic origin and predominately from incomplete combustion sources. Vehicular and brick kiln emission has significant effect on particulate pollution. Positive correlation between vehicular and brick kiln emission and ambient particulate concentrations was identified. Particulate

concentration shows decreasing trend as the number of vehicles goes down during weekends and with termination of brick kiln operation. It was observed that the particulate concentration reduces as the wind speed increases. However, some discrepancy was observed at Mohakhali due to wind directions. High-speed wind even increases particulate concentrations if it is directed towards sampling location from polluting sources and vice versa. References 1. AirMetrics, (1998). Mannual of Mini-volume

Portable Air Sampler, Model-Ver 4.2, U.S.A. 2. Akhtar, H. B. (December 6-8, 2004). Reducing

Air Pollution by Awareness Programmes in Bangladesh. Better Air Quality (BAQ), Agra, India.

3. Azad, A.K., Sultana, J. and Jahan, S. (2003). An

Economic Evaluation of Air Pollution in Dhaka City, International Conference on Chemical Engineering, Dhaka, Bangladesh, paper no. 017, pp: 83-87.

4. Begum, B.A., Biswas, S.K., Kim, E., Hopke, K.

and Khaliquzzaman, M. (2005). Investigation of Sources of Atmospheric Aerosol at a Hot Spot Area in Dhaka, Bangladesh, Journal of. Air & Waste Manage. Association, vol. 55, pp: 227-240.

5. Begum, B.A., Biswas, S.K. and Hopke, P.K.

(2006). Temporal Variations and Spatial Distribution of Ambient PM2.2 and PM2.2-10 Concentrations in Dhaka, Bangladesh, Journal of Science of the Total Env., vol. 358, pp: 36-45.

6. Biswas, S.K., Tarafdar, S.A, Islam, A.,

Khaliquzzaman, M., Tervahattu, H. and Kupiainen, K. (2003). Impact of Unleaded Gasoline Introduction on the Concentration of Lead in the Air of Dhaka, Bangladesh, Journal of Air & Waste Manage. Association, vol. 53, pp: 1355-1362.

7. BRTA (Bangladesh Roads and Transport

Authority), (2004). Dhaka, Bangladesh.(Personal Communication)

8. Core, J. (August 29-September 2, 2004).

Technical Training Programme on Air Quality Management, Jointly Organized by Department of Environment, Ministry of Environment and Forests, Bangladesh and Asian Development Bank under ADB TA RETA 6159-South Asia Subregional Economic Cooperation (SASEC) for


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Regional Air Quality Management, Dhaka, Bangladesh.

9. Dockery, D.W., Pope, C.A., Xu, X.P., Spengler,

JD., Ware, J.H., Fay, M.E., Ferris, B.G. and Speizer, F.E. (1993). An Association between Air-pollution and Mortality in Six United States Cities, New England Journal of Medicine, vol. 329, pp: 1753-1759.

10. Fabian, H.G. (February 2004). Clean Air Initiative

for Asian Cities, Benchmarking Stage II, Version 0.2, ADB, Manila. http://www.cleanairnet.org/caiasia

11. ICTP (Intercontinental Consultants and Technocrats Pvt., India), (September, 2001). Urban Transport and Environment Improvement Study, Summary Final Report for ADB TA 3297-BAN.

12. Seinfeld, J.H. (1975). Air Pollution Physical and

Chemical Fundamentals, McGraw-Hill, Inc., New York, pp: 1-9.

13. WB (World Bank), (August 5, 1998). Air

Pollution in Dhaka, Bangladesh, A Draft Report, The World Bank Group, South Asia Environmental Unit, Washington D.C.

JOURNAL OF CHEMICAL ENGINEERING

The Institution of Engineers, Bangladesh GUIDE TO AUTHORS

The JCE paper should be clear, concise, and complete, with assumptions plainly identified and data presented with precise logic, and with actual accomplishments of the work clearly stated and honestly appraised. ELEMENTS OF THE PAPER The elements of the paper are listed below in the order in which they should appear: title, author names and affiliations, abstract, nomenclature, body of paper, figures and tables, acknowledgments, references, appendices, etc. Title: The title of the paper should be concise and definitive. Author Names and Affiliations: All those who have participated significantly in the technical aspects of a paper be recognized as co-authors or cited in the acknowledgments. Abstract: A short abstract (150 words maximum) should open the paper to give a clear indication of the objective, scope, and results of the paper so that readers may determine whether the full text will be of particular interest to them. . Nomenclature: The nomenclature list should be in alphabetical order (capital letters first, followed by lowercase letters, Greek symbols, subscripts and superscripts) identified with headings. BODY OF THE PAPER The text should be organized into logical parts or sections. The purpose of the paper, or the author's aim, should be stated at the beginning so that the reader will have a clear concept of the paper's objective. This should be followed by a description of the problem, the means of solution, and any other information necessary to properly qualify the results presented and the conclusions. Finally, the results should be presented in an orderly form, followed by the author's conclusions. Only original contributions to the engineering literature, not previously published, are accepted for publication. Under certain circumstances, reviews, or analyses of information previously published may be acceptable. SI Units should be used. When other customary units are given preference, the SI equivalent should be provided in parentheses. Mathematics: Equations should be numbered consecutively beginning with (1) to the end of the paper, including any appendices. The number should be enclosed in parentheses (as shown above) and right adjusted on the same line as the equation. Equations should be referenced within the text as "Eq. (x)." When the reference to an equation begins a sentence, it should be spelled out, e.g., "Equation (x)." Figures: Figures (graphs, line drawings, photographs, etc.) should be numbered consecutively and have a caption consisting of the figure number and a brief title of the figure. Figures should be referenced within the text as "Fig. 1." When

the reference to a figure begins a sentence, the abbreviation "Fig." should be spelled out, e.g., "Figure 1." Figures may be inserted as part of the text as close as possible to its first reference. Tables: Tables should be numbered consecutively and have a caption consisting of the table number and a brief title. Tables may be inserted as part of the text as close as possible to its first reference. Acknowledgments: Acknowledgments may be made to individuals or institutions not mentioned elsewhere in the paper who have made an important contribution. References: Within the text, references should be cited in numerical order according to their order of appearance. The numbered reference citation should be enclosed in superscripts. Example: It was shown by Prusa1 that the width of the plume decreases under these conditions. In the case of two citations, the numbers should be separated by a comma1,2. In the case of more than two reference citations, the numbers should be separated by a dash5-7. References to original sources for cited material should be listed together at the end of the paper. References should be arranged in numerical order according to their order of appearance within the text. Sample References: 1. Kwon, O. K., and Pletcher, R. H., Prediction of the Incompressible Flow Over a Rearward-Facing Step, Technical Report HTL-26, CFD-4, Iowa State Univ., Ames, IA, 1981. 2. Lee, Y., Korpela, S. A., and Horne, R. N., Structure of Multi-Cellular Natural Convection in a Tall Vertical Annulus, Proc., 7th International Heat Transfer Conference, U. Grigul et al., eds., Hemisphere Publishing Corp., Washington, D.C., 2:221-226, 1982. 3. Sparrow, E. M., Fluid-to-Fluid Conjugate Heat Transfer for a Vertical Pipe — Internal Forced Convection and External Natural Convection, ASME J. of Heat Transfer, 102: 402–407, 1980. 4. Sparrow, E. M., Forced-Convection Heat Transfer in a Duct Having Spanwise-Periodic Rectangular Protuberances, Numerical Heat Transfer, 3: 149–167, 1980. 5. Tung, C. Y., Evaporative Heat Transfer in the Contact Line of a Mixture, Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY, 1982. 6. Amon, A., Jr., Electronic Packaging, John Wiley and Sons, New York, 1995. SUBMISSION OF MANUSCRIPT Two sets of original hard copies along with one soft copy (preferably in CD) of the manuscript should be sent to the following address. Submission through email is also accepted.

EDITOR

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