Modeling the filtration process with a flat-type fabric filter

Modeling the filtration process with a flat-type fabric filter

Advanced Powder Technol., Vol. 17, No. 3, pp. 237– 256 (2006) © VSP and Society of Powder Technology, Japan 2006. Also available online - www.vsppub.c...

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Advanced Powder Technol., Vol. 17, No. 3, pp. 237– 256 (2006) © VSP and Society of Powder Technology, Japan 2006. Also available online - www.vsppub.com

Original paper Modeling the filtration process with a flat-type fabric filter NING MAO 1 , YOSHIO OTANI 1,∗ , YUPING YAO 1 and CHIKAO KANAOKA 2 1 Graduate

School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan 2 Ishikawa National College of Technology, Kitachujo, Tsubata, Kahoku-gun, Ishikawa 929-0392, Japan Received 7 July 2005; accepted 8 August 2005 Abstract—The fabric filtration process is divided into three stages, i.e. depth filtration, transition filtration and surface filtration. A new model is proposed to describe the three stages under both virgin and regeneration conditions. The concept of an interface dust layer is introduced to predict the transition from the depth filtration stage to the transition filtration stage. The transition filtration stage due to the non-uniform accumulation of residual dust on a filter is characterized by two parameters — the surface cleaning fraction, f , and the residual dust load on the uncleaned surface, Wu0 . It is found that f decreases and Wu0 increases with the number of filtration cycles. This result suggests that both the fraction of uncleaned surface and the thickness of dust cake on the uncleaned surface increase with the number of filtration cycles. The present model successfully describes the change in pressure drop during the filtration cycles using the parameters. Keywords: Depth filtration; transition filtration; surface filtration; fabric filter; pressure drop.

NOMENCLATURE

A, B, d C c0 df f K m N p ∗ To

coefficients in (12) dust concentration (kg/m3 ) inlet dust concentration (kg/m3 ) fiber diameter (m) surface cleaning fraction (—) specific resistance of accumulated dust on filter (m/kg) dust retention in unit volume of filter (kg/m3 ) number of filtration cycles (—) filter pressure drop (Pa)

whom correspondence should be addressed. E-mail: [email protected]

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Pj R t u W x

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pulse jet cleaning pressure (kPa) resistance of filter (l/m) filtration time (s) filtration velocity (m/s) dust load per unit surface area of filter (kg/m2 ) filter depth (m)

Greek α η λ μ ρp τ 

filter packing density (—) single fiber collection efficiency (—) collection efficiency raising factor (—) gas viscosity (Pa s) particle density (kg/m3 ) duration of depth filtration period (s) duration of transition and surface filtration periods (s)

Subscript 0 c d i in m max r s u τ

initial cleaned surface depth filtration stage number of filtration cycle inside filter dust loaded condition maximum residual transition and surface filtration stages uncleaned surface at the end of depth filtration

1. INTRODUCTION

There is a growing tendency to employ bag filters in various industrial processes because of their high particle collection efficiency at a low pressure drop. Since bag filters are operated in cycles of dust accumulation and cleaning, it is necessary to accurately predict the filtration performance during the cycles, especially the evolution of pressure drop under a wide range of operational conditions.

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Incomplete filter cleaning or patchy cleaning has a marked effect on the filtration performance of fabric filters where the dust cake is detached unevenly from the filter surface during the periodical filter cleaning process. The causes of patchy cleaning are various. Dust removed from a filter during cleaning with pulse jets may redeposit on the filter when the filtration is resumed [1, 2]. The variation in detachment force caused by pulse jets leads to non-uniform filter cleaning [3]. There are areas of the bag where the surface dust cake is completely removed and other areas where the dust cake is undisturbed. At the bottom of a bag, the inertia forces by pulse jets alone are not capable of removing the adhering dust layers and other mechanisms such as reverse air flow play a role in dust removing [4, 5]. A number of efforts have been made to model the filtration process with patchy cleaning. Although the overall fraction of cleaned areas on the filter surface may be measured or estimated, it is virtually impossible to predict the exact locations of the cleaned and uncleaned sites. Duo et al. proposed a probabilistic model based on the assumption that the cleaned sites are distributed randomly over the filter surface [6, 7]. Dittler et al. developed a two-dimensional quasi-stationary flow model, in which the surface of completely or patchily cleaned filter medium was divided into small sections to predict the pressure drops as a function of regeneration efficiencies and regeneration patterns [8]. These models may reflect the actual cleaning pattern of the filter surface, but they seem too complicated for practical use. Kanaoka and Yao experimentally studied the filtration phenomenon using a nonwoven fabric filter with pulse jet cleaning. They employed the type 1 filter testing rig specified in VDI/DIN 3926 to measure the development of the pressure drop during the filtration cycles and showed that the evolution of pressure drop of a flat-type fabric filter could be divided into three stages in a filtration cycle, where the increasing rate of pressure drop gradually increases in the first stage and then decreases in the second stage, and finally it is almost constant in the third stage, as shown in Fig. 1 [9]. Since most of the particle penetration from a bag filter occurs just after the filter cleaning in each filtration cycle, the modeling of the first and second stages in a filtration cycle is especially important for preventing particle penetration through bag filters as well as for the prediction of pressure drop evolution. The objective of present work is to propose a new filtration model, which can express the pressure drop development during the repeated filtration cycles, taking into account the patchy cleaning.

2. MODEL DESCRIPTION OF THE FABRIC FILTRATION PROCESS

Kanaoka and Yao explained the mechanisms of the three stages in a filtration cycle as follows: Stage 1 = depth filtration; Stage 2 = the self-equalizing mechanism for parallel path flows through unevenly distributed dust cake or the change in density of accumulated dust; Stage 3 = surface filtration with uniformly

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Figure 1. Increasing pressure drop rate of filter A.

distributed dust cake [9]. The present model assumes that the second stage of the transition stage occurs due to uneven dust cake distribution on the filter surface after cleaning. Figure 2 illustrates the three stages for fabric filters under the virgin condition (the first cycle) and the regeneration condition (the ith cycle). For a virgin filter, dust particles penetrate into filter and are collected inside the filter. As filtration proceeds, the dust load in the filter reaches a maximum and dust cake starts to build up on the filter surface. When the pressure drop reaches a prescribed value, the filter is cleaned. After filter cleaning, a part of the residual dust cake remains on the filter surface. However, on a part of the filter surface, not only is the dust cake completely removed, but also part of the dust inside the filter is also cleaned. Therefore, depth filtration takes place on the cleaned surface just after the filter cleaning until the dust load reaches the maximum retention in the filter. Since the filtration velocity through the cleaned surface is much higher than that through the uncleaned surface, we assume that there is air flow only through the cleaned surface. Once the dust begins to accumulate on the cleaned surface, which is the end of the depth filtration stage, the second stage of transition filtration stage begins. During the transition stage, the surface filtration on the uncleaned surface also plays a role for dust collection. The local filtration velocity varies over the filter surface because of the non-uniformity in the dust cake distribution. This leads to nonlinear pressure drop development of the filter. As time passes, the non-uniformity

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Figure 2. Model description of the first cycle and the ith cycle.

will gradually disappear because of the self-equalizing mechanism for parallel path flows. The difference in local filtration velocity will then diminish and this will lead to uniform deposition of filter cake, which is the beginning of the surface filtration stage. Moreover, the present model assumes that depth filtration takes place without surface filtration or, vice versa, surface filtration occurs without penetration of particles into the filter.

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Figure 2. (Continued).

2.1. Stage 1: depth filtration stage 2.1.1. Mathematical description of depth filtration. Since fibrous filters and fabric filters are similar in structure, one may apply the depth filtration theory for fibrous air filters to fabric filters. In fabric filtration, depth filtration takes place for virgin filters and also for the regenerated filter where the dust inside the filter is partially removed by filter cleaning. The depth filtration stage of fabric filters is expressed by the following set of partial differential equations: 1 4 α ∂C ηm C, = ∂x π 1 − αm df 1 ∂m ∂C =− , u ∂t ∂x



(1) (2)

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where C, u, α and df are, respectively, the dust concentration, filtration velocity, filter packing density and fiber diameter. The subscripts ‘m’ stands for the condition with dust load. αm and ηm are, respectively, the filter packing density and the single fiber collection efficiency under the dust-loaded condition. Substituting (2) into (1), the increasing rate of dust load is expressed by the following differential equation: 4 α 1 ∂m ηm Cu. = ∂t π 1 − αm df

(3)

The single-fiber collection efficiency with dust load can be expressed by the following equation [10]: ηm = η0 (1 + λm),

(4)

where λ is the collection efficiency raising factor and η0 is the single-fiber collection efficiency without dust load. The packing density of dust-loaded fiber is a function of the dust load, m, and the particle density, ρp , and is given by: m αm = α + . (5) ρp Substitution of (4) and (5) into (3) yields: 4Cuρp αη0 1 + λm ∂m = . ∂t π df ρp − ρp α − m

(6)

Equation (6) can be used to predict the dust load, m, at an arbitrary filter depth, x, and time, t. 2.1.2. Transition from the depth filtration stage to the transition filtration stage. In order to find the transition from the depth filtration stage to the transition filtration stage in each filtration cycle, we introduce a new concept of the interface dust layer on the filter surface. The interface dust layer is a hypothesized surface layer at x = 0. When the deposited dust fully occupies the voids of this layer or when the dust load reaches the maximum in this layer, the dust particles would not penetrate into the filter and start accumulating on the filter surface. Using the interface dust layer, we can predict the transition from depth filtration to transition filtration without solving (6) for the whole filter depth. Now, we apply (6) to the interface dust layer. We assume that the interface dust layer consists of the uncleaned surface and cleaned surface with the surface cleaning fraction, f , and that the flow passes through only the cleaned surface at the filtration velocity, u/fi−1 , during the ith filtration cycle. Supposing that the depth filtration ends at τi for the ith filtration cycle as the dust accumulation increases from mi to the maximum, mmax , the integration of (6) gives:  mmax  τi ρp − ρp α − m 4c0 uρp αη0 dt, i = 1, 2, . . . , n, (7) dm = 1 + λm π df fi−1 mi 0

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where c0 is the dust concentration at the filter inlet. The solution for (7) is:    ρp − ρp α π df 1 1 τi = fi−1 + 2 ln(1 + λmmax ) − mmax λ λ λ 4c0 uρp αη0    ρp − ρp α π df 1 1 − fi−1 . + 2 ln(1 + λmi ) − mi λ λ λ 4c0 uρp αη0 Since m1 = 0 and f0 = 1, we have the following equation for i = 1:    ρp − ρp α π df 1 1 = τ1 . + 2 ln(1 + λmmax ) − mmax λ λ λ 4c0 uρp αη0 Substitution of (9) into (8) gives:    ρp − ρp α π df 1 1 fi−1 . + 2 ln(1 + λmi ) − mi τi = τ1 fi−1 − λ λ λ 4c0 uρp αη0

(8)

(9)

(10)

One may assume that the dust retention per unit volume in the interface dust layer after filter cleaning, mi , is proportional to the total residual dust load, Wr , and that the coefficient of proportionality is invariant for two consecutive filtration cycles. Now, for i > 2, τi is expressed as:      ρp − ρp α Wr,i Wr,i 1 1 − mi−1 + 2 ln 1 + λmi−1 τi = τ1 fi−1 − λ λ Wr,i−1 λ Wr,i−1 π df fi−1 . (11) × 4c0 uρp αη0 m2 can be determined from the experimental result of τ2 using (10). Wr,i is obtained experimentally by weighing the filter after cleaning. Since (11) is a recurrence formulae, τi for i > 2 is successively determined from mi−1 , Wr,i−1 and Wr,i . 2.1.3. Pressure drop development during the depth filtration stage. To predict the pressure drop development during the depth filtration stage, an empirical equation is used [11]: pd = (A + BW d )u,

(12)

where A, B and d are the empirical constants, and W is the dust load per unit filter area given by W = c0 ut for t  τi . 2.2. Transition filtration stage and surface filtration stage 2.2.1. Stage 2: transition filtration stage. The transition filtration, which is an unstable filtration process with uneven filtration velocity distribution, is caused by a non-uniformity in the filter surface. When the non-uniformity is caused by such surface treatment as calendar, the transition filtration process could occur for a

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virgin filter during the first cycle. For the regenerated filter, the transition filtration is caused by the non-uniform residual dust distribution after filter cleaning. In order to express the non-uniformity of residual dust cake distribution after filter cleaning in a simpler manner, the present model introduces two parameters, i.e. the surface cleaning fraction, f , which is the ratio of cleaned surface area to the total surface area of a filter, and the residual dust load on the uncleaned surface after cleaning, Wu0 . Here, ‘cleaned’ implies that the accumulated dust cake on the filter is completely removed and yet the dust inside the filter is also partially cleaned up. The residual dust distributes homogenously on the uncleaned surface. Both Wu0 and f change with the number of filtration cycles. On the cleaned surface, depth filtration takes place before the dust accumulation reaches the maximum and then surface filtration until the cake resistance becomes the same as that through the uncleaned filter surface. 2.2.2. Stage 3: surface filtration stage. The surface filtration process is a stable filtration process with a constant filtration velocity all over the filter surface. The pressure drop increases linearly with the filtration time. 2.2.3. Pressure drop development during the transition and surface filtration stages. In order to predict the pressure drop development during the transition and surface filtration stages, we need to express the resistances of the cleaned and the uncleaned surfaces, Rc and Ru , as a function of f , Wu0 and t. Since the cleaned and uncleaned surfaces give the resistance to air flow in parallel, the following holds: ps = uc Rc μ = uu Ru μ = uRμ,

(13)

where R and u are the average resistance and the average filtration velocity, respectively. u is related to the filtration velocities through the cleaned and uncleaned surfaces, uc and uu , by: u = uc fi−1 + uu (1 − fi−1 ).

(14)

Combining (13) and (14): fi−1 1 − fi−1 1 + = . Rc Ru R

(15)

Rc and Ru vary with filtration time, and are given by (16) and (17) respectively:  t uc dt, (16) Rc = Rcτ,i + Kc0 τi  t Ru = Ruτ,i + Kc0 uu dt, (17) τi

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Rcτ,i and Ruτ,i are the resistances of the cleaned and uncleaned surfaces at the start of transition filtration in the ith filtration cycle, K is the specific resistance, and c0 the inlet dust concentration. Differentiation of (16) and (17) with respect to t gives: dRc = Kc0 uc , dt dRu Ru = = Kc0 uu . dt Eliminating R in (13) by (15): Rc =

uc =

u uRu 1 = . fi−1 1 − fi−1 Rc (1 − fi−1 )Rc + fi−1 Ru + Rc Ru

(18) (19)

(20)

Substitution of (20) into (18) yields: Rc =

Kc0 uRu . (1 − fi−1 )Rc + fi−1 Ru

(21)

Now we want to eliminate Ru in (21) in order to find the solution for Rc . From (14), we have: uu =

u fi−1 − uc . 1 − fi−1 1 − fi−1

(22)

Substituting (22) into (17) followed by the integration: Ru = Ruτ,i +

Kc0 u fi−1 (t − τi ) − (Rc − Rcτ,i ), 1 − fi−1 1 − fi−1

(23)

Ruτ,i is the sum of resistance due to the dust load on the uncleaned surface at the end of depth filtration, Wuτ,i is equal to the residual dust load on the uncleaned surface, Wu0,i−1 , and the resistance of the cleaned surface at the end of the depth filtration in the ith cycle (see Fig. 2). It is expressed as: Ruτ,i = Rcτ,i + KWu0,i−1 .

(24)

Substituting (24) to (23): Ru = Rcτ,i + KWu0,i−1 +

Kc0 u fi−1 (t − τi ) − (Rc − Rcτ,i ). 1 − fi−1 1 − fi−1

(25)

Substituting (25) into (21), the following equation is obtained:   Kc0 u fi−1 (t − τi ) − (Rc − Rcτ,i ) Kc0 u Rcτ,i + KWu0,i−1 + 1 − fi−1 1 − fi−1  . Rc = Kc0 u fi−1 (1 − fi−1 )Rc + fi−1 Rcτ,i + KWu0,i−1 + (t − τi ) − (Rc − Rcτ,i ) 1 − fi−1 1 − fi−1

(26)

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Equation (26) is numerically integrated to obtain Rc with the initial condition:  fi−1 pτ,i Rc t=τ = Rcτ,i = . μu

(27)

Finally, eliminating uc in (13) using (26) and (18), we have:   Kc0 u fi−1 (t − τi ) − (Rc − Rcτ,i ) μuRc Rcτ,i + KWu0,i−1 + 1 − fi−1 1 − fi−1  . ps = Kc0 u fi−1 (1 − fi−1 )Rc + fi−1 Rcτ,i + KWu0,i−1 + (t − τi ) − (Rc − Rcτ,i ) 1 − fi−1 1 − fi−1

(28) Equation (28) gives ps in the ith cycle as a function of fi−1 , Wu0,i−1 and t. In order to obtain the surface cleaning fraction, fi−1 , and the residual dust load on the uncleaned surface after cleaning, Wu0,i−1 , two points on the experimental curve of ps at t (t = τi and t = τi +ψi ) are substituted into (28), where ψi is the duration of transition and surface filtration periods for the ith cycle. At t = τi , (28) is reduced to (29) with the assumption of Ruτ,i  Rcτ,i : pτ,i = μ

u fi−1

(29)

Rcτ,i .

At t = τi + ψi , (28) becomes: pmax = μu(Rcτ,i + K(1 − fi−1 )Wu0,i−1 + Kc0 uψi ).

(30)

If we assume that (29) holds for a short time period, t, at the beginning of transition filtration, then we have:   u u Rcτ,i + Kc0 t , (31) pτ +t,i = μ fi−1 fi−1 where the second term in the brackets is the increase in resistance due to the particles accumulated on the cleaned surface. Subtracting (29) from (31), and letting t → 0, we have:   μKc0 u2 pτ +t,i − pτ,i dp = . (32) lim = 2 t→0 t dt τ,i fi−1 Since [ dp ] = [ dp ] , fi−1 can be calculated by: dt τ,i dt max,i  fi−1 = μKc0 u

2

 dp  dt

1/2 . max,i

(33)

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Now we have fi−1 , Wu0,i−1 can be calculated by (30):

Wu0,i−1

pmax − fi−1 pτ,i − Kc0 uψi μu = . K(1 − fi−1 )

(34)

2.3. Filter cleaning Filter cleaning is carried out when the filter pressure reaches a prescribed value. The pressure drop after filter cleaning is referred to as the residual pressure drop, which is a function of the residual dust load on a filter. Although the residual dust load consists of particles both in a filter and on the filter surface due to patchy cleaning, we assume that the residual pressure drop is determined only by the residual dust in the filter since most of the air flow passes through the cleaned surface of filter. Since the dust accumulated in a filter during the depth filtration stage decreases exponentially with filter depth, we assumed that the residual dust in the filter exists only in a very thin layer of thickness, L, in the vicinity of the filter surface (see Fig. 3). As shown in Fig. 3, the air flow passes through the thin layer of the cleaned surface at a velocity of u/fi and then spreads over the filter surface giving the air flow velocity of u because of high flow resistance of filter. Equation (12) of the pressure drop of the filter with dust load consists of two terms, i.e. the first term of the filter media contribution and the second term of the accumulated particle contribution. Consequently, one may assume that the contribution of filter media may be neglected in the thin layer with densely packed particles, whereas there is no contribution of accumulated particles in the deeper layer of the filter. Therefore, the residual pressure drop in the ith cycle may be expressed by: d pr,i = Au + BWin,i u/fi ,

Figure 3. Calculation of residual pressure drop.

(35)

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where Win,i is the residual dust in the filter, which is the difference between the total residual dust and the residual dust on the filter surface: Win,i = Wr,i − Wu0,i (1 − fi ).

(36)

3. EXPERIMENTAL SETUP

The filtration–cleaning cycle is performed repeatedly at a given filtration velocity using the experimental setup shown in Fig. 4. Test dust of fly ash fed by a screw dust feeder is dispersed by an ejector. The dust-laden gas is introduced into the top of the vertical duct and the dust in the gas is collected on the testing filter. The filter pressure is recorded by a pressure transducer (Valcom; VPRN-A4). When the filter pressure reaches a prescribed value (1000 Pa in the present work), filter cleaning is carried out by compressed air of 500 kPa-gauge through a solenoid valve connected

Figure 4. Schematic diagram of the experimental setup.

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Table 1. Test conditions Fabric filter material structure dimension Dust particle material median diameter density dust concentration Testing conditions filtration velocity pulse jet pressure filter pressure before cleaning

(—) (—) (mm)

PPS felt square (300 × 300)

(—) (μm) (kg/m3 ) (g/m3 )

fly ash (JIS Z8901 no. 10) 4.84 2300 5

(m/s) (kPa-gauge) (Pa)

0.033 500 1000

to a 2.5-l compressed air reservoir. The downstream dust concentration is measured by a photometer (laboratory made) as well as sampling the test particles with HEPA filters. Table 1 shows the testing conditions.

4. RESULTS AND DISCUSSIONS

4.1. Particle penetration after filter cleaning The relationship between dust penetration (or downstream dust concentration) and the pressure drop is shown in Fig. 5 for the initial nine filtration cycles. Figure 5 shows that most of the particle penetration from bag filters occurs in the virgin filter and the regenerated filter immediately after the cleaning. The filter pressure increases non-linearly during this period. From the viewpoint of particle penetration, it is important to predict the pressure drop development in the initial stages of each filtration cycle. 4.2. Surface cleaning fraction and residual dust load on the uncleaned surface after cleaning The experimental results of pressure drop development for the first, fifth and 30th filtration cycles are shown in Fig. 6, and the increasing rates of pressure drop calculated from Fig. 6 are plotted in Fig. 7. It is seen from Fig. 7 that the peak of pressure drop increasing rate is higher for a larger number of filtration cycle and that the transition stage starts at 47 and 29 s, respectively, for the fifth and 30th filtration cycle. The surface filtration ends at 1005 and 821 s, respectively, for the fifth and 30th filtration cycle. fi and Wu0,i are calculated using (33) and (34), and are plotted in Figs 8 and 9, respectively. In Fig. 8, f1 is 0.56 for the first filtration cycle and gradually decreases with the number of filtration cycles, indicating that the fraction of uncleaned surface

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Figure 5. Relationship between dust penetration and pressure drop.

Figure 6. Time dependency of filter pressure drop.

is about a half after the first cycle and then increases with the filtration cycles. In Fig. 9, Wu0,i increases with the number of filtration cycles, suggesting that the layer of dust cake on the uncleaned surface becomes thicker with the number of filtration cycles.

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Figure 7. Time dependency of increasing pressure drop rate.

Figure 8. Relationship between surface cleaning fraction and number of filtration cycles.

4.3. Residual pressure drop The pressure drop increases with the dust load and the filter is cleaned when the pressure drop reaches 1000 Pa in the present work. Immediately after the filter cleaning, the filter was removed and weighed to obtain the total residual dust load of the filter. The relationship between the residual pressure drop and the total residual

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Figure 9. Relationship between residual dust load on the uncleaned surface and number of filtration cycles.

Figure 10. Constitution of residual dust load.

dust load is plotted by solid diamond symbols in Fig. 10. In Fig. 10, the residual dust on filter surface, which is calculated from fi (see Fig. 8) and Wu0,i (see Fig. 9), is also plotted by hollow triangle symbols together with the residual dust in the filter, which is calculated as the difference between the measured total residual dust load and the calculated residual dust on filter surface. Figure 10 shows that there is a slight increase in the residual dust in the filter, but a significant increase in the

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Figure 11. Relationship between residual pressure drop and number of filtration cycles.

residual dust on the filter surface. This is probably because the residual dust in the filter greatly changes the sticking property of the filter to the accumulated dust cake on the filter. The residual pressure drop predicted by (35) is shown in Fig. 11 together with the experimental data. Although the predicted residual pressure drop is slightly higher than the experimental data, the predicted curve well expresses the tendency of the experimental data. 4.4. Filtration cycle time The filtration cycle time for each cycle is the sum of the duration of the depth filtration period, τi , and the duration of the transition and surface periods, ψi . Using (11) with fi and Wr,i given in Figs 8 and 10, respectively, τi is calculated and plotted in Fig. 12 for i > 2 and the filtration cycle time is shown in Fig. 13. In Fig. 12, the duration of depth filtration abruptly decreases from 191 to 79 s for the first and second filtration cycles, and then gradually decreases to 29 s for the 30th filtration cycle. Similar to Fig. 12, Fig. 13 shows that the filtration cycle time decreases rapidly for the first two filtration cycles from 1163 to 1088 s, and then declines gradually to 821 s for the 30th filtration cycle. From Figs 12 and 13, it is clear that the initial rapid decrease in filtration cycle time is mainly due to the sharp shortening of the depth filtration period and the later gradual decrease in the filtration cycle time is due to the reduction in the transition and surface filtration periods.

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Figure 12. Duration of depth filtration period.

Figure 13. Relationship between filtration cycle time and number of filtration cycles.

5. CONCLUSIONS

A new model is proposed for the prediction of the fabric filtration process, dividing a filtration cycle into three stages, i.e. the depth filtration stage, the transition filtration stage and the surface filtration stage. The major conclusions obtained in the present work are as follows:

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(i) A new concept of a hypothetical interface dust layer is useful for predicting the transition from the depth filtration stage to the transition filtration stage. (ii) The transition filtration is attributed to the non-uniform residual dust distribution due to patchy cleaning. The non-uniformity can be represented by two parameters — the surface cleaning fraction, f , and the residual dust load on the uncleaned surface after cleaning, Wu0 . (iii) The surface cleaning fraction, f , decreases with the number of filtration cycles, indicating that the fraction of uncleaned surface is increasing with the number of filtration cycles. (iv) The residual dust load on the uncleaned surface after cleaning, Wu0 , increases with the number of filtration cycles, suggesting that the layer of dust cake on the uncleaned surface becomes thicker with the number of filtration cycles. (v) The initial rapid decrease in the filtration cycle time is due to shortening of the depth filtration period, and the later gradual decrease is due to reduction in the transition and surface filtration periods. (vi) The model not only successfully describes the time evolution of the filter pressure drop during filtration cycles, but also quantitative evaluation of filter cleaning performance becomes possible.

REFERENCES 1. M. J. Ellenbecker and D. Leith, Theory for dust deposit retention in a pulse-jet fabric filter, Filtrat. Separat. (Nov./Dec.), 624–629 (1979). 2. M. J. Ellenbecker and D. Leith, Dust removal characteristics of fabrics used in pulse-jet filters, Powder Technol. 36, 13–19 (1983). 3. W. Humphries and J. J. Madden, Fabric filtration for coal-fired boilers: dust dislodgement in pulse jet filters, Filtrat. Separat. (Jan./Feb.), 40–44 (1983). 4. F. Löffler and J. Sievert, Cleaning mechanism in pulse-jet fabric filters, Filtrat. Separat. (Mar./Apr.), 110–113 (1987). 5. J. Sievert and F. Löffler, Dust cake release from non-woven fabrics, Filtrat. Separat. (Nov./Dec.), 424–427 (1987). 6. W. Duo, N. F. Kirkby, J. P. K. Seville and R. Clift, Patchy cleaning of rigid gas fitlers — I. A probabilistic model, Chem. Engng Sci. 52, 141–151 (1997). 7. W. Duo, J. P. K. Seville, N. F. Kirkby, H. Buchele and C. K. Cheung, Patchy cleaning of rigid gas filters — II. Experiments and model validation, Chem. Engng Sci. 52, 153–164 (1997). 8. A. Dittler and G. Kasper, Simulation of operational behavior of patchily regenerated, rigid gas cleaning filter media, Chem. Engng Process. 38, 321–327 (1999). 9. C. Kanaoka and Y. P. Yao, Time dependency of the pressure drop in a flat type pulse jet fabric filter, Kagaku Kogaku Ronbunshu 29, 267–271 (2003) (in Japanese). 10. T. Myojo, C. Kanaoka and H. Emi, Experimental observation of collection efficiency of a dust loaded fiber, J. Aerosol Sci. 15, 483–490 (1984). 11. K. Iinoya and K. Makino, Performance of Dust Collection Device. Industrial Technique Center, Tokyo (1976).