Optical in-situ measurement of filter cake height during bag.pdf

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Optical in-situ measurement of filter cake height during bag

filter plant operation

Mahmood Saleem a,⁎, Gernot Krammer a, b

a Institute for Apparatus Design, Particle Technology, and Combustion, Graz University of Technology, Austria b Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway

Received 22 August 2006; received in revised form 12 September 2006; accepted 1 December 2006

Available online 15 December 2006

Abstract

A pilot scale jet pulsed bag filter test facility is operated at conditions similar to those of the industrial bag filters. The facility is equipped with a

stereo vision based optical system for in-situ cake height distribution measurements on the bag filter surface. Experimental data are presented and

data evaluation procedures are discussed to elaborate the features of the measuring system.

The results show that the cake height distribution becomes narrower towards the end of filtration cycles. A steep pressure drop rise is observed

at the start of a filtration cycle in the absence of re-attachment and a non-uniform bag cleaning, which may be attributed to different cake

properties. The specific cake resistance remains constant over the linear part of the pressure drop curve indicating a non-compressible cake

formation.

The analysis of residual cake patches shows a large number of small sized cake patches and a few large sized cake patches on the filter surface.

The cake patch size increases with the cake formation. The fractal analysis of patches boundary indicates preferential cake formation at the

boundary of the residual cake patches shortly after regeneration.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Cake height; Distribution; Bag filter; Gas cleaning; Optical measurement; Cake patch size; Experimental; Fractal dimension

1. Introduction

Bag filters, having excellent separation efficiency (N99.99%)

for coarse as well as fine particles, provide a very good choice

for process engineers to meet stringent solid emission levels.

The filter pressure drop (Δ P ) over time for the jet-pulse bag

filters commonly exhibits steep increase after jet pulse (JP)

cleaning for short duration. It is followed by a moderate and

linear rise over the rest of the filtration cycle. This phen omenon is commonl y related to in-complete cake

detachment or patchy cleaning. The patchy cleaning gives

rise to a non-uniform cake load distribution on the bag filter

and hence affect cake formation and its detachment.

Quantitative knowledge of cake height distributions, their

evolution, and the factors affecting them is important for

better understanding of the filter behavior.

The bag filter consists of cylindrical bags made of woven or

needle felt fabrics. The bags are supported on metal cage rods

and are hanging from a support plate inside the housing. The

bags might be arranged in rows, in one or more compartments.

The gas stream pervades the permeable filter media and the dust

is separated on the surface of the filter media and forms a dust

cake. The forming cake is a source of increasing flow resistance.The industrial units and hence the bag filters operate mostly at

constant gas flow; therefore, a fan at the discharge provides the

necessary head to compensate for increasing Δ P .

A filtration cycle starts at a lower Δ P as the dust laden gas

flows through the filter. The Δ P increases with the cake

formation on the filter medium. The end of the cycle is reached

as soon as the Δ P reaches a certain predefined upper limit

(Δ P max) or a predefined filtration time (t filt ) is elapsed [1]. There

the dust cake has to be detached to sustain filter operation. The

cake detachment is accomplished, most commonly, by reverse

JP. High pressure short duration gas injections in reverse

Powder Technology 173 (2007) 93–106

www.elsevier.com/locate/powtec

⁎ Corresponding author. Institute for Apparatus Design, Particle Technology,

and Combustion, Graz University of Technology, Austria. Tel.: +43

3168737486; fax: +43 3168737492.

E-mail address: [email protected] (M. Saleem).

0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2006.12.008

mailto:[email protected]

http://dx.doi.org/10.1016/j.powtec.2006.12.008

http://dx.doi.org/10.1016/j.powtec.2006.12.008

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direction blow the cake off the bag surface, which is collected in

the dust hopper located at the bottom of the filter housing. As

soon as the cake is removed, the Δ P is reduced and filtration

continues for another filtration cycle.

The JP cleaning process may be divided into three phases: (a)

acceleration of the filter medium towards outside, (b)

deceleration of the filter medium once it reaches a circular shape and (c) acceleration of the filter medium inwards towards

the cage after completion of the cleaning cycle and after the

decay of the cleaning pulse in the bag interior. The dust cake on

the surface of the bag is broken by the inflation of the filter

element. The acceleration from a concave to a convex shape

with sudden impact mechanically ejects the dust together with

particles that have penetrated the felt. The flowing air following

the pressure pulse flushes out the dust assisting cake removal

[1]. The reverse flow, in addition to acceleration, is reported

necessary for cake detachment in [2]. The cake removal is

improved at higher cake load in acceleration tests [3]. In

practice a fraction of filtration area is exposed to jet pulses and possibly only a fraction of the cake is removed from the jet

pulsed area [4] resulting in a non-uniform cake distribution

called patchy cleaning. Non-uniform filter cake distribution on

the bag surface is a natural outcome of patchy cleaning and

possesses many consequences like different residence times of

the cakes on the bag surface [5], distribution of gas velocities

across the filter surface as a result of the cake height distribution

[6], different cake characteristics depending on different

formation conditions [7], and as a consequence more frequent

bag cleaning is required.

Various theoretical and experimental studies are reported in

literature to provide understanding of underlying process of

cake formation and detachment which affect the Δ P . The Δ P isrelated to the operating parameters using regression analysis [1]

in one approach. Mostly, the Δ P within the filter media (Δ P m)

and the Δ P within the cake (Δ P c), are taken additive based on

the assumption that the resistances contributed by the filter

media and the cake act in series as reported in [1,5] for example.

Filtration process is simulated using one dimensional model in

[8] from its start-up, where a uniform cake is assumed to form

on a clean filter medium. At the end, JP removes a part of the

cake leaving a thin dust layer behind on the filter surface. The

second cycle starts with two model areas, one with the cake and

one regenerated and containing a thin dust layer. A Darcy

equation represents each model area but pressure drop is thesame across both areas. The fact that only a fraction of total area

may be subjected to jet pulses is not considered by [8].

Therefore, the characteristic property of cake detachment, a

fraction of cake of certain thickness removed on jet pulsing, is

not determined. The model presented in [9] deals with the case

of filtration at constant pressure drop. It also does not

distinguish between the fractions of the filter area that is

subjected to jet pulses. A model considering the fractional area

subjected to jet pulses is used for predicting operating points

from specific cake detachment experiments [10]. The model

parameters are estimated from the linear part of the pressure

drop curve ignoring the steep rise of the pressure drop curve.

The cake formation on non-uniformly covered filters may

influence the cake detachment due to highly non uniform gas

velocities, though the overall gas flow remains constant.

Therefore ignoring the cake formation may lead to erroneous

results. Other models describing filter cake additionally

consider cohesive stresses between single patches of filter

cakes. However, the three dimensional structural information of

the filter cake needed by these sophisticated approaches is not easily available [11,12]. The size and thickness of single patch

in conjunction with the length of boundary to the neighbouring

patches are decisive for plausibility of the assumption of

rectilinear, parallel gas flow. The question whether the actual

size of patches observed in filter experiments allows the

assumption of rectilinear flow is not yet settled, although this

assumption is often used for the reasons of simplicity. Transient

growth of the filter cake is simulated using two-dimensional

model in [13]. Results revealed that the pressure drop after a

cleaning pulse with constant cake mass removed is higher or

lower depending on whether the removed patches are larger or

smaller respectively. In the fringe zone between thick and thincakes, gas enters sideways increasing the permeability of the

filter cake. However, discrepancies in the pressure drop curves

are small and restricted to the first 10% of the filter cycle only.

The Darcy's law with constant specific filter cake resistance (α)

is applicable to filter modelling at constant gas velocity if the

rise of Δ P versus time is linear. At changing velocity, the Δ P

coefficient of filter cake is intrinsically not constant [14,15].

Consideration of cake compaction for the modelling of patchily

regenerated filters could be made, when complex cake

formation models [16,17] are combined with a model

describing the distribution of solid cake over the filter area.

The specific resistance of filter medium ( R) may change over

time [18–20] due to changes in filter media resulting fromentrainment of fine dust particles and more generally filter

media aging. Moreover, if the residual cake mass (cake

remaining on the bag after jet pulse cleaning) is lumped to R

then R may have different values if the distribution of residual

cake mass (cake height and/or cake density) is locally different

[21]. The flow resistance through the filter cake may depend on

the cake porosity (dependent on particle size and shape

distribution) or density, permeability of the cake, and density

of the solid particles [1]. The conditions of the filter medium

after regeneration at the start of a filtration cycle may affect the

formation of the cake and its properties, porosity and strength

[22,23]. The cake detachment is dependent on the cake properties [22] e.g. strength, therefore, changes in the cake

properties affect the cake detachment and hence the formation

again [23]. Non-uniform distribution of residual cake is a result

of incomplete cake detachment, but may also be due to

reattachment of detached cake on the neighboring or the same

bag. The cake height distribution affects the filter medium as

well as the filter cake resistance parameters. The increased

resistance is responsible for shortening of filtration time which

may lead to unstable operation in extreme case [24].

In general the characterisation of dust cakes is difficult. The

cake properties, e.g. porosity can be estimated from semi

empirically derived equations, e.g. Karman–Kozney, Ergun's

or Rudnick and Happel, describing flow through porous media

94 M. Saleem, G. Krammer / Powder Technology 173 (2007) 93 – 106



[14]. Naturally the derivations of these equations are based on

assumptions and involve empirical constants. Alternatively, the

cake samples can be characterised by direct examination under

the microscope [23,25]. A large number of observations and

statistical methods provide good estimate of cake properties.

However, information about 3D structure is mostly inferred

from 2D examinations. The cake undergoes extensive prepara-tion steps before it is examined under the microscope.

Therefore, uncertainties are also there. Fractal dimension (FD)

is a property of self similar objects and is used to characterize

complex systems e.g. dust powders or cake structure. The

fractal analysis of dust cake structures from micrographs of cake

cross-section of prepared dust cake samples is reported in [23].

The limestone dust (mass mean diameter of 3.5 μm) cakes

prepared at 500, 1000, and 2000 Pa are analysed using Box

Counting Method. The FD are scattered in the range 1.62–1.66

and no dependency of cake structure on the studied parameters

is reported. The invasive techniques, for characterising filter

cake, are superior since the cake is examined in-situ on the filter surface with minimum disturbances if any.

Some in-situ measurement techniques for determining cake

height/mass distribution on gas filters are reported in literature.

A radiometric method based on beta ray absorption and laser

light reflection is reported in [26]. Three aerial dust density

profiles on polyester bag filter of 2.5 m length using X-ray

absorption are measured. Non uniform dust cake profiles along

the length of the bag and a higher dust load near the bottom of

the filter are observed.

In another method, beta mass probe is used for investigating

the cake formation and release on a flat filter felt [27]. The β-ray

source and the detector are moved together on opposite sides of

the dust laden bag for scanning the bag surface. The filter bag issupported on a rectangular frame of 6 in×11 in, divided in 1 in2.

Because of the interference of metal wires of the frame on

radiation, a continuous measurement of the cake load along the

length or width of the filter is not possible. Only point wise

measurements could be obtained. The system required calibration

under exactly the same condition as expected in operation using

sheets of known mass per unit area. Dust and gas flow are stopped

during scanning and cleaning is off-line. The dust is found

depositing non-uniformly on the filter surface. The reported

detachment mechanism is acceleration and deceleration.

A laser displacement system is reported in [14] to measure

the dust cake thickness and the amount of dust cakecompaction. Higher filtration velocity is found responsible for

irreversible dust cake compaction. The laser displacement

system works on the principle of reflection, thus it requires a

rigid surface.

Invent of high resolution digital cameras and improved

machine vision techniques has led to wide spread applications

of digital cameras for remote sensing and monitoring of objects

and processes. The approach is non hazardous and provides in-

situ measurements of a large surface from relatively long

distance. Use of CCD-colour vision camera for characterizing

the surface treatment of needle felts is reported in [28]. The

images are processed to compute the surface porosity and size

distribution of the pores. One variant of optical in-situ technique

is reported in [29] for measuring the cake thickness distributions

on rigid ceramic filters. The circular and flat filter element of

14 cm in diameter is used. The cake thickness distributions are

recorded by an image acquisition process with a lateral

resolution of about 280 μm and a vertical resolution of about

50 μm. The experiments are performed using quartz dust at high

temperature. The measuring principle is based on a projectedfringe technique and reconstruction of the surface is done using

shape from structured light technique. The technique revealed

useful information regarding cake load distributions on filter

surfaces; however, this technique cannot be employed for

flexible filter media where the hidden filter deforms due to

increased pressure drop during cake formation. Thus simply

reconstructing the surface from structured light technique will

not account for such deformation.

In this paper an optical system is presented for measuring the

cake height distributions in the course of cake formation and

after regeneration on flexible filter media. This includes a

description of the bag filter facility, and the optical system. Thedata evaluation procedures are outlined and exemplary results

are presented and discussed. The residual cake height measure-

ments are used for estimating the residual cake patch size

distribution. The fractal analysis of the residual and forming

cake patches is also discussed.

2. Experimental

2.1. Bag filter set-up

The experimental set-up consists of three rows of bags (two

bags per row at maximum) enclosed in a chamber, which

closely resembles the large scale bag filter, and providesinstrumentation for acquiring all important data simultaneously.

The operating conditions are selected in the range where

commercial bag filters are operated [1] and are listed in Table 1.

The basic experimental set up (Fig. 1) is presented in [30]

and is briefly described here. The two screw feeder (1) delivers

a controlled constant mass (variation ±1% at steady state) of

powder into the dispersion nozzle (3) through a vibrating chute

(2). Compressed, filtered and dried gas (air) meets the dust

tangentially in the dispersion nozzle. Ambient air is sucked in

and mixed with the dispersed dust to make the raw gas stream.

Table 1

Range of operating variables and the test conditions

Description Range Test conditions Unit

Dust concentration, c b1 to N50 7.17 g/m3

Total filtration area, A b= 4 2.03 m2

Upper pressure drop

limit, Δ P max

b2400 1200 Pa

Filtration velocity, u ∼16.6–200 20.5 mm/s

Pulse tank over pressure, P jet Up to 4 3.6 bar

Cleaning impulse, t impulse 10–100 50 ms

Time between consecutive

cleaning pulses, t interval

2–254 3 s

Dispersion air, P dis Up to 5 2 bar

Relative humidity – 54% at 26 °C




The raw gas flows into the bag filter (4) near the bottom. The

raw gas pipe is gradually expanded near the filter to reduce gas

velocity before entering the filter. The bags are arranged in threerows, each row containing one bag. The load cell and dust

collector (5) are enclosed in the housing (4) to allow online

measurement of settling as well as detached dust instanta-

neously. The gas flows through the filter bags (6) into the clean

gas header and then to the discharge fan (8).

The Δ P regulator monitors the Δ P across the filter. A pulse

of compressed air (9) enters the bag through an 8 mm hole in the

gas supply pipe (d =27 mm) trapping secondary gas from the

clean gas side. The JPs are issued in a cyclic order once the pre-

set Δ P max is reached. The pressure of the cleaning air ( P jet ),

time of cleaning impulse (t imp), and interval between consec-

utive pulses (t inter ) are up to 4 bar, 10–100 ms, and 2–450 s

respectively. The Δ P across the orifice plate (Δ P o), absoluteupstream pressure ( P abs) and temperature (T ) are recorded. The

gas flow (V ) is calculated by the Labview® software according

to DIN EN-ISO 5167-1: 1995 (large fan) and ISO 5167:2003

(small fan), depending on the fan in use, and recorded. The V is

calibrated using Pitot tube measurements.

The Δ P is transmitted at a time constant of less than 3 ms

which provides transient monitoring of the Δ P . As long as the

Δ P is a small fraction of the over all pressure drop (Δ P sys), the

V remains steady despite changes in the Δ P . However, if the

Δ P sys is comparable to the Δ P , the decrease in the Δ P on JP

cleaning makes the V to increase which is captured by the

frequency converter. The V is higher for short duration (15–30 s) just after JP, causing the transient Δ P to become higher

than the actual value corresponding to the steady state V . The

change in the Δ P due to temporarily increased V is corrected

according to Eq. (1):

D P corr ¼ D P t V set

V t : ð1Þ

V t is the transient gas flow, Δ P t is the transient filter pressure

drop, V set is the steady gas flow or set point, and Δ P corr is the

corrected filter pressure drop. The Δ P corr , in this document, is

the filter pressure drop (Δ P ) unless otherwise mentioned.

Additionally, the transient rate of dust feed (m), and the

transient mass of collected dust (m) are recorded at 1 s resolution

along with date and time. Relative humidity ( H r ) and dispersion

air pressure ( P disp) are recorded manually. Also the mass of dust

in the feeder hopper is recorded at the start and at the end of theexperiment. The dust concentration on clean gas side is found in

the range 2–4 mg/m3 using gravimetric methods. The overall

material balance is closed at less than ±1%.

The dust concentration relevant for filtration and the dust

fraction settling in the filter can be calculated because m and m

are known.

Limestone (OMYACARB 5 GU) with weight mean diameter

(d 50,3) of 5 μm and bulk density of 1200 kg/m3 is used as dust.

The filter bags are made of Polyimide (P84) and Polypheny-

lensulfide (PPS) needle felt. The felt has a specific weight of

624 g/m2 and 73.5 l/dm2 min permeability corresponding to

200 Pa pressure drop.

The facility incorporates an optical system for in-situ dust cake height measurement on the filter surface. The measure-

ment system is based on stereo vision and is called the optical

stereo set-up.

2.2. Optical stereo set-up

The principle of stereo vision is that if an object is viewed

from two angles, it is possible to reconstruct a 3D object from

the two images with known camera calibration. The stereo set-

up consists of two industrial CMOS cameras (11), 1.3 megapixel

resolution, mounted as a vertical stereo setup with a stereo angle

of approximately 50°. The filter bag is visible through a 6mmthick and large optical glass window. The window is manually

cleaned with double magnetic wipers as and when optical

measurement or bags inspection is required. A black and white

random pattern is projected on the target bag to generate surface

texture on the bag surface. The cameras observe a filter area of

nearly 40 mm×40 mm (this is the size of focused area, actual

image size is bigger than this) from a distance ( z -axis) of

550 mm through the glass window. The whole setup can be

moved vertically ( y-axis) along the filter bag to measure a set of

consecutive, partially overlapping surface patches that cover the

desired length of the bag to be examined or the entire length of

one filter bag (1800 mm). The movement of the stereo set-up

and image acquisition is automated through graphical user

Fig. 1. Process flow diagram of the bag filter test facility.




interface in Matlab® environment. The development of the

optical technique, its tailoring to meet the specific needs of our

system, and its boundary conditions are discussed in [31].

Land mark points on the filter surface are necessary for non

rigid alignment and registration. Wooden pearls of 4 mm outer

diameter and 1 mm hole are used for this purpose. The choice is

a compromise based on extensive experimental investigationsto meet the accuracy limits. Each marker is attached on a small

4 mm×4 mm piece of hard paper to provide a plane surface for

the marker to stay vertical to the filter surface. The paper blocks

the gas flow through the hole thus preventing dust particles

from entering and blocking the holes. The paper and marker's

outer surfaces are painted white while the inside of the hole and

bottom is painted black. Care has been taken to keep the holes

open and possibly uniform at the top of the markers for easy

detection. Marker to marker distance along width is nearly 1 cm

and along length of the bag is 3 cm. This distance is optimised

experimentally for target depth accuracy of 50 μm. Changing

this distance will affect the depth accuracy. The markers areglued to the filter bag using commercially available glue which

is found sufficient to hold the markers on the bag against jet

pulses up to 4 bar. The effect of markers on filter permeability is

studied and found insignificant. Variation in the height of the

marker top to the filter surface, due to the height tolerance of the

pearls, paper and glue, does not affect the cake height

measurement because the markers are rigidly fixed to the filter

surface and the cake height measurements are relative.

2.3. Description of an exemplary experimental run including

optical measurements

Data is acquired from the filtration test at operatingconditions, listed in Table 1, with simultaneous but intermittent

optical cake height measurements during a filtration test. The

acquired data is presented in Fig. 2 for one filtration test from

the start of the filtration with jet pulsed filter bags which have

been in use. Among the measured parameters, only Δ P , V , and

m are presented versus t filt . To cope with the slight and short

duration variation of gas flow at jet pulsing, the Δ P is corrected

according to Eq. (1) before further use.

The bags are thoroughly cleaned at the start of the filtration

test. The gas flow is switched on and increased to obtain higher

Δ P across the filter. At steady Δ P , the reference measurement at point ‘a’ is made. Then the gas flow is reduced to the steady

operating value and another reference measurement is made at

point ‘ b’. This measurement is made to verify whether the

different reference pressure drop will affect the measurement

and to what extent? Since the two reference measurements only

differ in pressure drop, any difference in the measurement

results will be a measure of the error at these conditions. After

the reference measurement at steady gas flow, the filter is

operated without any changes for few minutes to determine the

clean bag resistance at the start of the filtration test.

The filtration starts by supplying dust to the gas and the Δ P

increases as filtration continues. The points‘c’,‘d’,‘e’

and‘f ’

refer to the measurements with cake on the bag surface and

hence represent cake height measurements at respective Δ P s.

After the measurement ‘f ’ the gas flow is stopped before starting

the jet pulses. This arrangement is adopted to eliminate the

influence of increased local dust concentration on the

subsequent filtration i.e. cake reattachment. Stopping gas flow

at JP cleaning is a special case adopted for the test requirement

and not a normal operation. Turning on the JP control cleans the

bags. The cleaning is actuated manually if the cake height

measurement is required at the end of the cycle. After the image

acquisition, the bag cleaning is started. Once the dust is settled

and the housing environment is clear, the gas flow is established

again along with dispersion air. At steady gas flow, the cakethickness measurement after jet pulsing is carried out at point

‘g’. Then the dust feed is turned on and the filtration test is

continued for further three cycles. It can be seen that four

measurements of cake thickness are obtained during the first

cycle. The only positions corresponding to further cake height

measurements for 2nd to 4th cycles are shown by arrows, where

the Δ P curve is constant at the points of measurements due to

shut off of the dust feed. In addition to transient Δ P , m and V are

also displayed in Fig. 2. The Δ P curve will be discussed later in

this paper.

3. Image data handling procedures

3.1. Image acquisition

During a filtration test the images are acquired which on

reconstruction reveal the cake height distributions. To build the

cake, a filtration test is carried out. The bags are cleaned

repeatedly by jet pulses prior to the filtration test. While the gas

is flowing through the filter without dust feed, the glass window

is cleaned and the reference surface is optically scanned i.e. the

jet-pulse cleaned reference bag (referred as clean bag in the

following discussion, the word ‘virgin’ is used for the new dust

free bag). In this process, the two cameras starting at the top

acquire a pair of images of the first patch at the same instant. The

Fig. 2. Transient data plot of the filtration test. The points ‘a’, ‘ b’, ‘c’, ‘d’, ‘e’, ‘f ’,

and ‘g’ refer to the cake height measurements. Points ‘a’ and ‘ b’ are the blank or

reference measurements. Dust feed is stopped for cake height measurement. Gas

flow is stopped too at jet-pulse cleaning. Gas flow is regulated constant during

the filtration cycle. Additional cake height measurement points are indicatedusing arrows for 2–4 cycles.




optical system moves to the next position (2 cm downwards),

stops for 10 s, acquires an image pair of the second patch, moves

to the next and so on until the desired length of the bag iscovered. The acquired images are saved automatically for post

processing. This serves as reference clean bag.

At any intermediate point during a filtration cycle or at the

end of the filtration cycle, the dust feed is stopped though gas

flow is maintained to avoid the fall of the dust cake and

deformation of the filter bag. Once the gas in the filter chamber

is free of dust (it takes two to three minutes), the glass window is

cleaned and the image acquisition is repeated (referred as

measurement of dust laden bag). The gas flow may be stopped

for jet pulse cleaning but must be switched on for cake height

measurements.

The points on each pair of images have one to one

correspondence. The region within the markers is facing thecameras while the edges are turning outwards due to cylindrical

shape of the bag and are out of focus. The principle surface on

which measurements are obtained is the region within the

markers excluding markers themselves. A large number of

images are processed according to the procedure described in

the next section using Matlab® routines to obtain the point wise

cake height measurements on the examined filter surface.

3.2. Post processing of image data

A number of distinct processing steps are necessary to

retrieve the desired thickness profile. First, single patches arereconstructed such that they are partially overlapping using

stereo reconstruction [31] which results in a dense point cloud.

The surface patches reconstructed in this step are all defined

within their own local camera coordinate system. Second, the

relative motion (rotation and translation) between neighbouring

patches is estimated. Afterwards the patches are aligned such

that a continuous bag surface is generated. From the control of

the mechanical motion platform, the relative motion of the

stereo setup is known fairly accurately. With this initial solution,

an Iterative Closest Point (ICP) algorithm [32] is used to refine

the alignment. Third, registration of reconstructed surfaces is

necessary because the filter cloth is flexible. During operation it

undergoes a deformation due to the increasing Δ P between the

dust side and clean side. Schematically Fig. 3 shows a part of a

filter bag cross-section. The thin dashed line represents the bag

surface while the continuous line represents the filter cake

surface. The bag behind the cake is pressed further inwards due

to a higher pressure difference. In order to calculate the relative

height difference between both surfaces and hence the cake

height, a non-rigid deformation transformation is estimatedwhich aligns both filter surfaces. Artificial landmark points

(markers) on the filter in combination with Thin Plate Spline

(TPS) interpolation are used for this task. The interpolation

requires the two optical measurements (the reference and the

cake height) should be close for zero alignment error [31].

Therefore, the reference surface measurement should be at the

expected Δ P later in the experiment. The Δ P in the experiment

is higher or lower depending on the cake on the bags at certain

operating condition. Optical measurement of the reference

surface at higher Δ P is not a practically viable solution. The

reference surface is measured, therefore, at a steady gas flow at

the start of the test before dust feed and used for measuring therelative cake height distribution. The measurement error as a

result of different Δ P of the two measurements is tackled in an

alternative way outlined in the next section. The measurement

error is separately measured at various Δ P s and deconvolved

from the height measurements.

3.3. Evaluation of cake thickness as a distribution

The alignment error is found to be a function of the Δ P [31].

There is no direct measurement to verify the optical in-situ cake

height measurements. Therefore, blank (with no cake) optical

measurements of the filter bag are taken repeatedly at various

Δ P levels. The clean bags are subjected to increasing Δ P bymanipulating the gas flow for the measurements. The blank

measurements with reference to the starting Δ P yield a criterion

to judge the magnitude of error in the actual measurements. The

arithmetic mean (μ) and standard deviation (σ) of blank error

measurements are plotted versus Δ P in Fig. 4. The μ and σ

change with the Δ P . For the reference measurement of a clean

filter bag at many Δ P levels, one finds the following statistical

Fig. 3. Deformation of the filter bag during cake formation and the alignment of

the reference bag surface with the dust laden bag surface using TPS

interpolation.

Fig. 4. Variation of arithmetic mean (μ) and standard deviation (σ) of themeasurement error (Y ) with increasing Δ P .




model: Each measurement i of a single true thickness value k is

affected by an error yi and the measured value z i results

according to Eq. (2).

z i ¼ k þ yi ð2Þ

The known true value k equals zero for all reference

measurements, since the clean filter bag is measured. Thus the

reference measurements directly yield the error variations yi by

measuring z i.

When the actual cake height is measured, it does not have a

single value but each measurement i has an underlying true

value xi, and the distribution model can be extended to Eq. (3).

z i ¼ xi þ yi ð3Þ

Let the random variables Z , Y , and X represent the measured

cake height, the measurement error, and the true cake height

respectively. According to the statistical theory, the density

function of the measured variable is the convolution integral of

the density functions of true cake height and the distributed

error.

The underlying true distribution is obtained by deconvolu-

tion of the measured cake height ( Z ) and the measured error (Y )

using Fast Fourier Transformation. A cake height measurement

at 1200 Pa, the measurement error at the corresponding Δ P , the

deconvolved true cake height distribution, and the true cake

height distribution after truncating the oscillations on tails are

shown in Fig. 5. The negative values of deconvolved density

function are results of the sensitivity of the method on noise in

input data and do not convey physical meaning. Therefore,

starting at the maximum of the ϕ x, both tails are set to zero

beyond the points the density function first becomes negative.This truncation eliminates the oscillations but requires rescaling

to satisfy the condition that the area under the distribution curve

equals 1. See Fig. 5 for slight flattening of the distribution

function at tails after truncation and rescaling. The detailed

discussion about the deconvolution can be found in [33,34].

3.4. Patch size distribution

The resulting data from the optical measurement technique is

in the form of a matrix Z ( xx, yy), where Z is the relative cake

height and ( xx, yy) is the position on the measured surface in

terms of camera coordinates. The cake height data can be

displayed as intensity images where the intensity of each pixelrepresents the cake height. Image processing techniques provide

tools where digital images can be processed fairly accurately

and information about the objects in the images can be

extracted. For the determination of the patch size distribution,

the image is transformed into black and white to express the

cake patches versus the background. This transformation

requires a threshold value to be decided for the cake height.

The threshold for the regenerated bag is taken zero

corresponding to no cake or a clean area because the cake

height is measured relative to a jet-pulse cleaned reference bag.

The pixels with values at or below the threshold are assigned a

zero value (black) and the pixels above the threshold areassigned a value one (white). The resulting image has the cake

patches as white and the background as black. Using the

transformed image, the cake patches area and equivalent

diameter of all the cake patches are measured using the

developed Matlab® routines. The routines are tested with

objects of various shapes of known size for accuracy estimation

and the percentage error is found to be in the range of ± 0.5% of

the area of the objects. The retrieved data is then transformed to

a cumulative area distribution. It should be pointed out that the

landmarks on the measured filter bag are located nearly 3 cm

apart; therefore, the measured surface should be analysed using

sample area of 2 cm× 4 cm. Many samples can be taken,

analysed and results could be combined to obtain the over all behaviour of the filter bag.

3.5. Fractal analysis of the residual cake patch

The fractal dimension provides a means to characterize

complex systems like dust cake structure and the cake patches

[35,36]. The Box method is used here. The box-counting

dimension is defined as:

D ¼logð N Þ

logðr Þð4Þ

where N is the number of boxes of side length r covering the

fractal object and D is the box dimension.

To perform fractal analysis, a section of nearly 2 cm×4 cm

is selected in a way that the rows of markers are not included.

The data is transformed into an intensity image and patch

boundaries are detected and labelled as white pixels in

the background of black. The resulting image is used for

computing the fractal dimension of the cake patches boundary.

To calculate the box-counting dimension, a grid with a side

length of each grid element r =1/(width of grid) is defined. The

number of boxes that contain any part of the object is counted

as N (r ). The same process is repeated with a new grid size. The

grid size changes from 2 to 315 pixels in 30 steps. The grid is

Fig. 5. Deconvolution of the measurement error of the cake height distribution.

Cumulative area distributions of the measured cake height ( Z ), the measurement

error (Y ), and the deconvolved cake height ( X ) along with the truncated andscaled final cake height distribution.




subjected to 1000 random offsets and computations are per-

formed to get an average value for a single grid size. A plot of log( N ) versus log(r ) is generated. The slope of the linear fit of

the data points leads to the box counting dimension ( D). An

exemplary image is included in Fig. 12 along with the computed

fractal dimension results.

4. Results and discussion

In Fig. 6, the exemplary point wise cake height distribution at

the end of a filtration cycle (Δ P =1200 Pa) and after regen-

eration (Δ P =130 Pa), as measured by the optical system, is

displayed as 2D images on nearly 30 cm long and 6 cm wide

bag surface. A mask is defined to identify the surface pointsoutside the rows of the markers and the markers themselves.

The black areas in the image are the masked pixels. The cake

height is scaled from 0 to 1 mm on grey scale. The cake

distribution is obvious from comparison of the two measure-

ments. On the regenerated bag, the dust free and dust laden

areas can be seen. The height of residual cake patches is small

however. Some areas are cleaned more (dark grey) than the

others (light grey) and cake patches of varying heights and sizes

are observed.

Fig. 7 displays the actual cake height ( X ) distributions

obtained after deconvolution for the test (see Fig. 2) which

reveal the development of cake formation during filtration andafter regeneration. All measurements are relative to jet-pulse

cleaned reference surface corresponding to point ‘ b’. Each curve

corresponds to one measurement at a certain operating point

designated by the filter Δ P . The measurements at around 400 Pa

Fig. 6. 2D presentation of the distribution of the measured cake height on the bag

surface at the end of a filtration cycle (up) and after regeneration (below). The

section length is approximately 30 cm and width 6 cm. The gray scale represents

cake height in mm. The black strips are the masked regions.

Fig. 7. Deconvolved cake height distributions showing cake formation during the progress of filtration cycles.




are at points where steep Δ P rise is just to end and a moderate

and linear rise is going to start (Fig. 9). The results show that the

mean cake height in 1st cycle is slightly higher than in the other

three cycles because the Δ P is higher (445 Pa) and the others are

lower (400 or 420). The mean and the range of distribution in

2nd–4th cycles are similar. The Δ P at the start of the filtration

cycle increases rapidly and therefore the dust cake mass

deposited on the bags is small at around 400 Pa. However, the

distributions at 400 Pa and 130 Pa in 2nd cycle and distributions

at 130 Pa and 420 Pa in 3rd cycle are only slightly different. The

distributions at 400 or 420 Pa are slightly narrower than the

distributions at 130 Pa on left tail indicating preferential cake

formation on some areas than others at the start of each filtrationcycle after regeneration. The two curves at 130 Pa represent

residual cake distributions in 2nd and 3rd cycles. The two

distributions are symmetric and range from −0.03 mm (30 μm)

to 0.12 mm (120 μm) approximately. The measurements agree

well because the residual Δ P is also the same in both cases. The

distributions at the end of the filtration cycles become narrower

but the difference is not high. The mean cake height is higher in

the 1st cycle and decreases gradually in 2nd, 3rd and 4th cycles.

Slight variation is attributed to slightly different Δ P at the end

of the cycle.

The ratio of X 0.9 to X 0.1 is plotted against X 0.5 in Fig. 8 for

four filtration cycles. The ratio decreases very quickly at the beginning of the filtration cycle and then slowly reaching a

steady value indicating that the cake height distributions are

narrower on cake formation. It should be pointed out that the

X 0.10 values of some measurements are zero which makes the

ratio to infinity. Thus the values are taken as 0.01 mm instead of

zero for some of the measurements at 130 Pa and 400 Pa.

The transient Δ P curves at the start of the filtration cycles

(on-set of dust feed) are shown in Fig. 9. After the lag time

(∼20–30 s) where the dust concentration, relevant for filtration,

reaches a steady state value, the Δ P exhibits two distinct trends.

A steep increase initially followed by a moderate linear increase

later on during the cycle. The steeper part is relatively short

(∼150 s) as compared to the overall cycle time. A gradual

transition from steep to the moderate linear increase can be

observed. The Δ P across the filter is normally the sum of two

contributions [1], one of the filter media, and the second of the

deposited cake. Under the conditions of constant A, c, u and T ,

the Δ P should increase linearly if the cake height changes

linearly for an incompressible cake. However this increase is

not always linear as can be seen in Figs. 2 and 9. At lowmechanical stability cake compaction is considered as one of the

reasons for non-linear i.e. convex Δ P increase which results in

shorter cleaning intervals [23]. A steep increase of Δ P shortly

after regeneration followed by a more moderate increase i.e.

concave Δ P increase is often related to particle re-entrainment

and/or patchy cleaning [37]. Patchy cleaning results in a locally

higher filtration velocity leading to a fast build-up of the dust

cake in the regenerated areas [5]. Also patchy cleaning results in

a steep increase of the overall Δ P i.e. concave shape which

takes place when only a fraction of total filter area is cleaned at

the end of filtration cycle which is pointed out and simulated by

[5]. Since all bags are jet pulsed, there is no fraction of jet pulsedarea responsible for non uniform rise of Δ P . Also the gas flow is

stopped during jet pulse cleaning; therefore, reattachment is

excluded. Therefore, one can state that the fractional cleaning or

reattachment is not a reason for the observed steep Δ P rise. The

equivalent diameter (4⁎Area/ π)0.5 computed from the identi-

fied residual patches size analysis reveals that mostly the filter

area is covered by a thin layer (large patch) and many small

patches in the size range of 1–5 mm and few up to 15 mm in

diameter (see Fig. 11). The naked eye examination revealed that

the cleaning conditions are such that the cake is removed

leaving behind only a thin layer. The residual layer is observed

as comprised of a large number of small cake structures. The

height measurements reveal that the maximum height on theregenerated surface is less than 120 μm.

The jet-pulse cleaning may result into a regenerated surface

with large number of cavities due to patchy cleaning or flushing

effect of the cleaning air flowing counter currently for a short

duration [1,28]. On the start of the next filtration cycle, the small

cavities on dust side of the filter medium provide the easiest

Fig. 8. The ratio of X 0.90 to X 0.10, corresponding to the cake height distributions

in Fig. 7, is plotted versus the median cake height ( X 0.50) during the four

filtration cycles.

Fig. 9. The transient Δ P at the start of four filtration cycles. A cycle starts with

the start of the dust feed. The data is skipped when the dust feed is stopped for

cake height measurement. Data shown is only a fraction of the complete cycles.A trend line is added to one data set.




passage for the gas and are filled by the dust. Thus a distribution

of resistance may exist on the regenerated filter surface. A

fraction of the area can be regarded possessing low resistance as

compared to the others. Therefore, at the onset of the dust feed,

the filtration is preferential and thus cake growth at some

fraction of area is higher than the others for the same mass of

dust reaching the bags. As the filtration continues, the cavitiesare gradually levelled off, and as a result the rate of growth

slows down at some places and increases at others. Which may

finally lead to a uniform rate of increase of the cake height on

the surface and consequently a moderate and linear Δ P rise is

observed. Since the relative volume of such cavities is small, the

observed steep Δ P rise is of short duration. This is equivalent to

the deposition of initial cake layer thick enough to equilibrate

the resistance of the bag. The similar trend can be expected if the

regenerated filter surface consisted of cake laden and clean

(cake free) patches. The gas might be flowing preferentially

through the low resistance area (clean patches) resulting into a

higher local filtration velocity and higher cake growth and alower filtration velocity and a slower growth of cake at high

resistance areas. As the smaller clean patches get levelled off

gradually, more gas flows through the thicker cake patches, and

a moderate and linear increase of Δ P is observed. The Δ P curve

in Fig. 2 at the on-set of dust feed at points ‘c’, ‘d’, or ‘e’ shows a

linear rise, which supports the hypothesis of linear cake growth.

The above phenomenon is observed at the start of every

filtration cycle in the test and can be seen in Fig. 9. It is striking

that at any time t, the Δ P for the 1st cycle is lower than the Δ P

of other three filtration cycles. It is to be noted that the residual

Δ P s are nearly similar and all other operating conditions are

also the same.

Based on theΔ P evolution, one expects a narrow cake height distribution on cake formation. The cake height distribution at

400 Pa is narrower than the one at 130 Pa in cycle 3 in Fig. 7.

The same is true for the measurements at the end of the cycles.

Once a certain dust mass has initially deposited on the surface of

the filter which initially had a distribution of resistance, the

formed cake may possess different characteristics (e.g. specific

cake resistance and porosity). Thus the overall resistance

offered by the medium and the filter cake to the gas flow is

equilibrated. The gas flow and the cake growth become

uniform; leading to steady and linear Δ P increase. The steady

rate of cake growth is supported by the linear and moderate rise

of Δ P . The visual examination of dust laden bags revealed the presence of relatively small and localised loosely adhering

structures on the cake surface. They are visible only after a

certain layer of dust cake is formed and their number increased

over time until the end of the cycle at which jet-pulses removed

the cake. They are probably dendrites of the growing cake

because no coarse particles of such a size can be expected in the

system reaching the bags with a dust of 5 μm weight mean

diameter. However, in this work no attempt is made to

characterise these individual formations on the surface of the

cake.

In Fig. 10 the specific cake resistance (α) is plotted versus the

cake area load (w). The specific cake resistance is calculated

from the slope of the Δ P curve averaged over time Δt , w, u, η,

and A, according to Darcy's law and represents the mean valueover the interval Δt . The specific resistance of filter cake, α, is

higher at the beginning of the filtration cycle (steep Δ P rise),

and lower for the rest of the cycle where Δ P rise remains

moderate and linear. The dust load is calculated from the ccor , V

and the t filt . The cake area load decreases from 300 g/m2 at the

end of 1st cycle to 230 g/m2 at the end of 4th cycle. The

decreased cake area load at the end of cycle from the 1st to the

2nd cycles is more pronounced as compared to the 2nd, 3rd or

4th. Since the gas flow and dust concentration are constant, the

change of the dust load is due to reduced filtration time which

may be associated with the reduced filter permeability. The

residual pressure drop (Δ P res) at the start of each filtration cycle

is found in the range 130± 5 Pa which indicates that the residual permeability of the bags is not changed although small amount

of the residual cake is distributed on the surface. Thus the higher

Δ P for the same dust area load (w) in 2nd to 4th cycles as

compared to 1st cycle (see Fig. 9) is due to the modified cake

characteristic which is formed on the regenerated surface

possibly under locally differing flow conditions. The analysis

revealed that the transition of the Δ P curve took place at nearly

250 Pa in the 1st cycle whereas the transition is observed at

nearly 350± 20 Pa in the 2nd to 4th cycles. This transition took

place although the time until this transition occurred is in the

range 70± 10 s including the lag time which is constant at

approximately 20 s. Thus a difference of nearly 100 Pa exists at nearly the same dust area load. The reduction of cycle time

might be attributed to high resistance of the initial layers of

forming cake, since the specific cake resistance after the initial

transition cake formation phase remains nearly constant (see

Fig. 10). As a result the Δ P rises faster and the time of filtration

is reduced from 2nd to 4th filtration cycles at nearly the same

upper and lower Δ P limits.

The size analysis of cake patches can be carried out on

relatively small sections (20 mm × 40 mm) of the measured

surfaces using image processing techniques. The results of one

section are shown in Fig. 11. In the following discussion, the

term ‘cake patch’ means the filter area covered with the dust

cake and the term ‘clean patch’ means the filter area free of the

Fig. 10. Specific cake resistance versus cake area load; the specific cake

resistance is high at the start of the cycle and quickly decreases to a nearly

constant value for the rest of the cycle.




dust cake. The cumulative area of cake patches (percent of

measured area) is plotted against the equivalent diameter of the

cake patches for 6 measurements. From the start of the filtration,

after passing through the short duration steep Δ P rise, the

surface holds almost 99% dust covered surface (one big cake

patch) and few very small sized clean patches. Aft er

regeneration at the end of the 1st cycle, the cake patches area

on the regenerated surfaces makes up to approximately 75% of

the total area. A large cake patch and many small cake patches

are identified. As the filtration continues for the 2nd cycle, the

size of the cake patches increases. One large cake patch growsup to approximately 90% of the total area. The smaller cake

patches merge earlier or afterwards depending on their size and

distribution. However, in all measurements at higher Δ P only

one cake patch is identified (those measurements are not shown

here as there is only one patch of 100% cake area). The increase

in the size of large cake patch and disappearance of smaller

patches indicates the preferred dust deposition on the boundary

of the cake patches. In cycle 2, the cake patches area grows from

78% at 130 Pa to 93% at 400 Pa. In cycle 3 it grows from 76% at

130 Pa to 99% at 420 Pa. The measurement in cycle 4 at 420 Pa

shows a cake patches area of 98%.If one assumes that the dust deposits on the clean patches

preferentially, one should not see any clean patches once the

filter has been exposed to some dust after regeneration. But one

can observe a gradual reduction of the clean patches and an

increasing size of larger cake patches over a short time period

(nearly 150–250 s from the start of the dust feed). Few small

clean patches are still identified at 445, 400 or 420 Pa as can be

seen in Fig. 11. The boundary grows fast and in the short time

the clean patches disappear although the cake height has not

been equalized everywhere.

The comparison of the cake height distributions of

regenerated (130 Pa) and dust laden bag (400–

445 Pa) inFig. 7 revealed that the maximum cake height on the

regenerated bag and the dust laden bag does not increase unless

the cake patch area approaches 100% (Fig. 11).

The fractal dimensions of the dust laden bag surface at

different operating points are shown in Fig. 12. The fractal

dimension is computed after applying a threshold which

expresses the patch boundaries (equivalent to slicing the 3D

cake surface and looking at the edge boundaries between the

cake and the clean bag). The threshold is varied within the range

of present cake height. The variation of the batch boundary at

different positions from the bag surface reveals the uniformity

of the cake height. The FD of two measurements for residual

cake patches (130 Pa), two measurements of formed cakeimmediately after regeneration (400 and 420 Pa), and two

measurements at the end of the filtration cycle (1200 and

1250 Pa) are shown versus the threshold (mm). The FD of the

residual patches is around 1.35 at zero threshold. It increases to

Fig. 11. Cumulative cake patches area (%) of total sampled surface area versus

the equivalent diameter of the cake patch. On cake formation the size and

cumulative area of the cake patches increase whereas the total number of the

patches may or may not decrease over short time but decreases over longer

duration.

Fig. 12. (Up) An example of detected patch boundaries between the cake patches and the clean patches, the black area is either a cake patch or a clean patch; (down)

fractal dimension versus threshold cake height for some of the cake height measurements after regeneration and during cake formation. Higher FD at 400 or 420 Pa is

indicative of complex cake patches boundary on cake formation. The changing fractal dimension with threshold demonstrates the non uniform cake height. It alsodepicts the range of cake height on the filter cake surface.




a maximum (1.45) at 0.05 mm threshold, indicating more

complex patch boundaries near the patch peaks. The results are

similar for the situation shortly after regeneration. Just before

regeneration the trend is the same, i.e. at the base of the cake

patches, the FD is lower and increases with increasing cake

height. The FD at the base of the patches decreases significantly

compared with the situation at the regenerated bags. But the FDat the peaks is only slightly increased compared with the

regenerated bags. This gives rise to the hypothesis that cake

growth occurs simultaneously in two different directions. This

favours our argument of dust deposition on patch boundaries of

residual cakes and growing cake patches at least preserving the

boundary shape if not becoming more complex. If it is believed

that the dust deposits only on the clean patches preferably, then

shortly after regeneration the clean patches should have

disappeared and the FD of the cake patches boundary must

have reduced significantly due to a single dust laden patch being

identified at the same threshold. Further the smoothening of the

cake patches boundary should also have reduced the FD whichis not observed in this case. For the measurements at 400 and

420, the FD should be close to zero if the dust were deposited on

the whole surface, which is not the case here. This again favours

our argument that the cake formation takes place at the cake

patches boundary which progresses quickly and the clean

patches are covered by a dust layer in a short duration.

5. Conclusions and outlook

In connection with the measurement of cake height

distribution on bag surface, experimental results are presented

using a filter test facility. The test facility is provided with

necessary instrumentation for acquiring transient Δ P , V , m, m, P jet , and T . The facility incorporates an optical system based on

stereo vision for in-situ cake height distribution measurements.

The cake height distributions are measured at different Δ P

levels during filtration and after regenerations for few filtration

cycles. The features of the test facility, the optical measurement

system, and the data processing are described.

The cake height distribution are measured on flexible and

deforming filter surface during filtration and after regeneration

using the optical measurement technique at depth accuracy of

100 μm and planner resolution of 0.5 mm2. The measured cake

height distributions are affected by the measurement error and

must be deconvolved using the measured error distributions.The deconvolved cake height distributions do not change

significantly shortly after regeneration but grow uniformly later

on and become slightly narrower towards the end of filtration.

The measured cake height distributions reveal the cake growth

during the filtration and trends are similar over the filtration

cycles. The residual cake height distributions are similar for the

presented results indicating good reproducibility of results.

At the end of the cycles, all bags are subjected to jet pulses

while the gas flow is turned off. This arrangement ensures that

no cake is reattached on the bag surface during cleaning.

However, a steep Δ P rise is observed at the onset of the dust

feed at the start of every cycle. The modified cake formation at

locally altered flow conditions might be responsible for this

observation. The modified cake formation is possibly a result of

residual cake patches distribution coupled with the distribution

of filter media resistance.

The specific cake resistance is relatively constant for the

linear rise of Δ P indicating a non-compressible cake formation.

The cake patch size analysis is carried out on a section

(2 cm×4 cm) of the measured surfaces using image processingtechniques. The patch size analysis shows a large patch (∼70%)

and many smaller but varying sized patches. The larger patches

grow in size during cake formation. However the height of the

patches is small. While the residual cake patches grow in size,

the number may or may not decrease over a short period as

filtration continues after regeneration. However, over longer

duration the number of identified patches certainly decreases

and above 450 Pa only one cake patch is actually identified. The

cake height is not the same everywhere on the surface. Based on

the observation that cake formation takes place at cake patches

boundary, one may expect the residual cake patches being

thicker would lead to pronounced deviation from rectilinear assumption of gas flow on patchily cleaned surface. It should be

noted that the cake height distribution as well as patch size

distribution is likely to be different at different locations on the

bag as can be seen in Fig. 6, therefore, the analysis has to be

carried out at various locations to obtain a representative

behaviour of the filter. In future work the patch size evolution

during cake formation will be carried out at various locations on

the filter bag and under different filtration conditions using

different types of filter media.

The fractal dimension of the residual as well as forming cake

patches boundary is computed using the Box method. The FD

of cake patches decreases shortly after regeneration at zero

threshold but is higher at higher threshold. The FD at the base of the patches decreases significantly compared with the situation

at the regenerated bags. But the FD at the peaks is only slightly

increased compared with the regenerated bags. This gives rise to

the hypothesis that cake growth occurs simultaneously in two

different directions; at the base of existing patches and thereby

reduces patch boundary complexity, i.e. decreasing FD; and

also on top of existing patches where patch complexity i.e. FD,

is basically preserved. Future work will address the fractal

analysis of growing cake patches under different filtering

conditions at different locations of the filter bag on different

types of filter media.

The presented results demonstrate the capabilities of the filtration set-up and the optical measurement set-up

(Figs. 6,7,10,11 and 12). Further data will be provided in line

with the data evaluation procedures described here. The

influence of the operating parameters (filtration velocity and

Δ P max) on the cake height distributions will also follow.

Notations

A filtration area, m2

c dust concentration, g m−3

d diameter, m

D fractal dimension, –

k arbitrary measurement, m

m collected dust mass, g




m mass flow rate, g s−1

N number of grid boxes, –

P pressure, Pa

R specific bag resistance, m−1

t time, s

T temperature, °C

u filtration velocity, m s−1

V gas flow, m3 h−1

w cake area load or aerial density, kg m−2

X true cake height, mm

x single measurement of X , mm

xx position in the horizontal plane, mm

Y measurement error, mm

y single measurement of Y , mm

yy position in the vertical plane, mm

Z measured cake height, mm

z single measurement of Z , mm

Greek/Latin letters

α specific cake resistance, m kg−1

Δ P pressure drop, Pa

Δt time interval, s

η gas viscosity, Pa s

ϕ probability density function, m−1

μ distribution mean, mm

σ standard deviation, mm

Abbreviations

3D three dimensional

CMOS complementary metal oxide semiconductor FD fractal dimension

ICP iterative closest point

JP jet pulse

LOGO brand name of PLC from Siemens

OMYACARB 5 GU trade name for the limestone dust

produced by OMYA

pdf probability density function

PLC programmable logic controller

P84 trademark for polyimide

PPS trade mark for polyphenylensulfide

TPS thin plate spline

Subscripts

abs absolute

c cake

corr corrected

dis dispersion

f filter

filt filtration

imp impulse

inter interval

jet jet air

m filter medium

max maximum

min minimum

o orifice

r residual

set desired value

t transient

Acknowledgements

The research project is funded by Austrian Science

Foundation (FWF) project P 16313-No. 7. The support of

Higher Education Commission, Pakistan is acknowledged. The

authors are grateful to M/s Inspec Fibers (Lenzing, Austria) for

supplying the filter bags and to M/s Alicona Imaging (Graz,

Austria) for the use of their Microscope for filter bag surface

analysis. The authors are also thankful for the valuable

discussions with Michael Koch, Norwegian University of

Science and Technology, Trondheim, Norway.

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