Bubble Size and Frequency in Corrugated-Wall Bubbling Fluidized

Article pubs.acs.org/IECR

Bubble Size and Frequency in Corrugated-Wall Bubbling Fluidized BedsImage Analysis and Neural Network Correlations A. N. Khan Wardag, F. Larachi,* and B.P.A. Grandjean Department of Chemical Engineering, Laval University, Québec, Québec, G1 V 0A6, Canada S Supporting Information *

ABSTRACT: Digital image analysis was implemented to monitor bubbling dynamics in corrugated-wall bubbling fluidized beds (CWBFB) loaded with Geldart D particles. Various geometrical configurations were investigated in terms of corrugation angle, interwall clearance, and rest bed height and gas superficial velocity. Implementation of wall corrugation led to improved gas− solid fluidization quality with respect to flat-wall bubbling fluidized beds (FWBFB) as measured in terms of retreat of the onset of bubbling as a function of gas flow rate, of reduction of bubble sizes and rise velocities, and of increase of bubble frequency. Two artificial neural network correlations valid both for FWBFB and CWBFB were recommended for estimation of bubble frequency and size using a common set of independent variables, that is, gas superficial-minimum bubbling velocity ratio, bed rest height, corrugation angle, average clearance, and vertical location. The bubble frequency explicit correlation accounted additionally for interwall minimum clearance and distance between side wall and either neck or hip of front plate, at a given elevation, whereas bubble size correlation needed bubble frequency as a supplementary input variable. exchange and heat transfer performances.3 Fluidized beds were also filled with stationary, regular or irregular, and floating packings to break large bubbles for accomplishing even gas distribution. However, as compared to internals-free fluidized beds, their utilization is limited by undue pressure drops, channeling, and particles segregation.3 Design strategies to harness bubbling fluidization hydrodynamics as described in the literature do not lend themselves to easy adaptations to a multiple compartment fluidized bed geometry for controlling bubble size and dynamics in bubbling fluidization regimes.2 Therefore by considering the effect of walls on bubble growth and bed stability, we recently implemented corrugated plates as modified separating walls with the following outcomes: reduced minimum bubbling velocity, promoted bubbles breakup, increased bubble frequency, and decreased bubble rise velocity to improve gas distribution and stability of fluidization operation.6,7 In the present contribution, we strive to analyze the geometrical and hydrodynamic variables to identify those needed for developing a set of correlations relating quantitatively the impact of corrugation geometry and gas throughput to bubble size and frequency both in flat and corrugated bubbling fluidized beds. These latter properties were measured for various wall declinations (corrugation angle, interwall clearance, rest bed height) by means of a high-speed digital image analysis.

1. INTRODUCTION In traditional flat-walled parallelepipedic fluidized bed enclosures, wall effects are known to prompt slug flow due to narrow interwall clearance. Slugging, therefore, makes the requirement for stable, uniform, and homogeneous fluidization somewhat difficult to achieve. 1 We recently proposed a reactor configuration for biomass steam gasification in which slug formation is avoided in specially designed multicompartment bubbling fluidized beds.2 The concept consists of multiple intercalated parallelepipedic compartments with corrugated walls to keep away inception of slugging while enhancing unit heat integration and thermal efficiency by preventing contact between flue gas (combustion cells) and N2-free syngas (gasification cells). In the literature several strategies toward improving the efficiency of fluidized beds targeted renewal of the bubble surface to exchange fluid between bubbles and interstitial gas in the emulsion phase. Various researchers realized the significance of bubbles in gas−solid fluidized beds and employed various internals, e.g., baffles, tubes, packings, inserted bodies, and other configurations to generate evenly distributed smallerbubbles for improving the quality of fluidization. Their main features, advantages, and limitations were discussed by Jin et al.3 Most transverse baffles in fluidized beds effectively increase gas residence time and reduce solids entrainment. However, this was achieved at the expense of formation, at high gas velocities, of unwanted gas cushions underneath baffles.3,4 These dilute environments were reported to hinder solids motion thus prompting axial particles segregation and large pressure drops. Horizontal or vertical tube banks were used for bubble breakup and heat exchange purposes. While vertical arrangements promote better heat transfer, horizontal internals favor bubbles breakup. For an effective use, these must be placed closer to each other;5 despite closer spacing could promote channeling and gushing both deteriorating gas−solid © 2012 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Fluidization Setup. Flat-(FWBFB) and corrugated(CWBFB; θ = 120° and 90°) wall bubbling fluidized beds (see Figures A1a,b in the Supporting Information) were used for Received: Revised: Accepted: Published: 12107

March 23, 2012 July 18, 2012 August 24, 2012 August 24, 2012 dx.doi.org/10.1021/ie3007775 | Ind. Eng. Chem. Res. 2012, 51, 12107−12116

Industrial & Engineering Chemistry Research

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fluidizing 1.2 mm glass beads with air at ambient conditions. The enclosures consisted of transparent polycarbonate sheets with dimensions as listed in Table A1 (Supporting Information). The vessel width for all the configurations was kept constant at W = 0.3 m. The CWBFB average clearances were estimated from neck, C1 (narrowest passage) and hip, C2 (largest passage) clearances, as (C1+C2)/2. Correspondingly, the FWBFB clearances, C, were adjusted to be equal to (C1+C2)/2 to allow comparisons between corrugated and flat walled geometries for the same gas superficial velocities. The onset of fluidization was determined experimentally for each configuration of FWBFB and CWBFB by using pressure drop− gas superficial velocity plots. For Geldart D particles, an increase in gas superficial velocity, Ug, albeit small, immediately prompts formation of rising bubbles after the onset of fluidization in cylindrical or flat-wall fluidized beds. This critical velocity was referred to as minimum bubbling velocity, Umb. Details on the operation of these corrugated and flat wall bubbling fluidized beds were provided elsewhere.6,7 2.2. Digital Image Analysis. Images from the widest frontside of the bed were captured while the bed backside was exposed to a powerful light source (2 kW total lighting power). The interrogated field of view was 0.3 m in width and 0.42 m in height (454 × 640 pixels). Up to 205 frames per second were captured during 30 s periods. Image processing steps were implemented in MATLAB to discriminate between bubble and emulsion phases to obtain maps of pixel (or gray scale level) intensity. The workflow algorithm for image processing consisted of background subtraction (see Figure A2 in the Supporting Information), filtering and smoothing morphological operations, thresholding and image binarization, edge detection for bubble properties, and determination of bubble projected area, bubble centroid, and bed free surface locations.6,7 Figure A3 (Supporting Information) illustrates tagging of bubbles to particular (Xi,Yj) lateral/axial location at two consecutive events. Area-weighted bubble equivalent diameter, Db, (eqs A1,A2, Table A2, Supporting Information) was obtained from the acquired images. Bubble frequency, f b, (eq A3, Table A2, Supporting Information) was estimated by counting the total number of bubbles crossing at a particular elevation during a period of 30 s. The NNfit software8 was employed to build artificial neural network (ANN) based correlations for bubble equivalent diameter and bubble frequency. These correlations are valid for the following geometrical and operating conditions in FWBFB and CWBFB: gas velocity ratio (Ug/Umb = 1.1−1.55), rest bed height (Hi = 0.15−0.3 m), clearance between walls (C = 0.028, C1 = 0.015−0.025 m), corrugation angle (θ = 90°, 120°, 180°). The neural regression methodology is detailed in Larachi et al.9 where the ANN parameters (weights) were fitted on a training data set (80% of the database) and ANN models were tested on a generalization data set with the remaining 20%.

Figure 1. Effect of walls, interwall clearance, and initial bed height on CW minimum bubbling velocity in FWBFB (UFW mb ) and CWBFB (Umb ).

The performances of the various designs of FWBFB and CWBFB were compared at a particular degree of fluidization captured via the Ug/Umb ratio (or gas velocity ratio). Figure 2 panels a and b depict the vertical variations of, respectively, frequency, f b, and area-weighted mean bubble equivalent diameter, Db, determined by digital image analysis at Ug/Umb = 1.4 in FWBFB (F_B, C = 0.028 m) and CWBFB (C120_D and C90_D, C1 = 0.015 m), see Table A1, Supporting Information.6 For illustration, the Hilligardt and Werther10 and the Lim et al.11 correlations for flat-wall bubble size evolutions are also shown (Figure 2b). The Lim et al.11 correlation yields predictions that are closer to our flat-wall bubble size evolutions. CWBFB geometry initiates very peculiar periodic oscillations in bubble size and frequency leading to noticeably reduced bubble sizes in comparison to FWBFB. This can be attributed to the network of converging−diverging zones (Figure A1b in the Supporting Information) which offers as many obstacles for bubble breakup and coalescence phenomena during their rise throughout the bed6 despite a growth in bubble sizes with bed elevation due to lateral and/or axial coalescence. Furthermore, since Umb in CWBFB is lower than FWBFB (Figure 1) so at given Ug/Umb lower values of Ug − Umb (Umb ≈ Umf in case of Geldart D particles)1 can also contribute to the generation of relatively smaller bubbles in CWBFB. 3.2. Rationale for Selection of Input Variables in Neural Network f b and Db Correlations. ANN correlations for bubble frequency and size in FWBFB and CWBFB were developed from 2870 data entries (having respective experimental f b > 0.03) of each obtained by digital image analysis (DIA) technique. In total, 10 geometrical and operating variables were identified to constitute numerous candidate sets of input variables for ANN correlations. Table 1 provides the details of cases (1−9) employing various input variables investigated in the developing phase of correlations. Axial location/elevation (Yj), corrugation angle (θ), gas velocity ratio (Ug/Umb), and initial rest height of bed (Hi) were common input variables in all these cases. Figure 3 gives a pictorial view to understand the various geometrical input variables (C, Hi, dX1, dX2, Zmin, and Zmax) considered in the developing phase of correlations (Table 1). For illustration, typical examples of F_A,B and C120_C,D are shown in this regard. Figure 3a shows the side view of the bed to demonstrate Yj, the average

3. RESULTS AND DISCUSSION 3.1. Bubble Size and Frequency. It was observed that the gas flow rate required to achieve an incipient bubbling condition in CWBFB was lower as compared to that in FWBFB especially for the deeper beds (F_B vs C90_D and C120_D, Table A1 in the Supporting Information), see Figure 1.6 This can be attributed to the higher drag force in case of CWBFB by fluidizing medium on particles at the converging− diverging high pressure zones than at the corresponding lateral and axial (Xi,Yj) locations in FWBFB.6 12108

dx.doi.org/10.1021/ie3007775 | Ind. Eng. Chem. Res. 2012, 51, 12107−12116


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Figure 2. Vertical variation of bubble frequency, f b, (a) and area-weighted mean bubble equivalent diameter, Db, (b) in FWBFB (F_B, C = 0.028 m) and CWBFB (C120_D and C90_D, C1 = 0.015 m) at Ug/Umb = 1.4.

Table 1. Details of Various Geometrical Variables Investigated in the Developing Phase of ANN Correlations for Bubble Frequency and Equivalent Diameter in FWBFB and CWBFB along with the Statistics on the Global Databank variablesa (common Y (m), Ug/Umb, Hi (m), θ) cases

C (m)

Zmin (m)

Zmax (m)

dX1 (m)

dX2 (m)

f b (s−1)

AAREG (%) ( f b/Db)

CCG (%) ( f b/Db)

CDG (%) ( f b/Db)

case 1 case 2 case 3 case 4b case 5 case 6 case 7 case 8 case 9b

+ + + + + × + × +

× + + + × + + × ×

× + + × × × × × ×

× + + + + + × + ×

× + × × × × × × ×

× × × × × × × × +

42.3/12.4 26.2/11.5 27.2/11.7 28.1/12.1 28.8/12.2 30.4/12.7 31.6/11.8 77.9/17.9 NA/11

82.8/98.5 91.5/98.6 91.6/98.6 90/98.5 92.8/98.5 89.6/98.2 89.1/98.6 65.9/97.1 NA/98.8

66.8/97 83.4/97.3 83.5/97.2 80.7/96.9 85.5/97 80/96.4 79/97.1 40.6/94.3 NA/97.5

a Symbols ‘‘+’’ and ‘‘×’’, respectively, represent the variables included and excluded. bCases 4 and 9 were, respectively, selected to propose the final versions of bubble equivalent diameter and frequency correlations.

clearance between walls, that is, C (0.028 m (i.e., C1 = 0.015 m) and 0.038 m (i.e., C1 = 0.025 m)), and Hi (0.15 and 0.3 m). Figure 3b portrays the top view of the bed at various elevations, Yi, to show the axial variation in minimum (Zmin) and maximum (Zmax) lateral distance or clearance between parallel plates in the Z direction and the distance of nearest vertices (neck/hip) of front (dX1) and rear plates (dX2) from the side wall. In Figure 3b, filled and empty circle markers represent neck and hip locations, respectively. In the typical case of CWBFB (C120_C,D), at elevation Y = 0 (Figure 3a) the clearance between opposite plates at their neck (filled markers)/hip (empty markers) locations are minimum (Zmin = C1)/ maximum (Zmax = C2). Minimum and maximum clearances start to increase/decrease with an increase in elevation (Yj) reaching their respective extreme maximum/minimum values (Zmin = Zmax = C) at Y = 0.019 m (Figure 3a). Then, Zmin/Zmax start to decrease/increase with further increase in Yj until reaching their respective extreme minimum/maximum values (i.e., Zmin = C1 and Zmax = C2) at Y = 0.038 m (Figure 3a) completing one period. Such periodically varying behavior of Zmin and Zmax in CWBFB (C120_C,D) with elevation is plotted

in Figure A4a (Supporting Information). Similar trends were observed in the case of C90_C,D (results not shown). Obviously, Zmin and Zmax kept constant at a value of C (0.028 m and 0.038 m) in FWBFB (F_A,B). Figure 3b also highlighted another set of geometrical input variables for CWBFB, i.e., dx1 (distance between side wall and either neck or hip (whichever is nearest to side wall) of the f ront plate) and dx2 (distance between side wall and either neck or hip (whichever is nearest to side wall) of the rear plate). In the typical case of CWBFB (C120_C,D), at an axial location of Y = 0 (where Zmin = C1 and Zmax = C2) the nearest vertices to the given side wall in the front and rear plates are neck (filled marker) and hip (empty marker) locations, respectively, having dX1 = 0 and dX2 = 0.038 m. dX1 and dX2, respectively, start to increase/decrease with elevation and reach their respective extreme maximum/minimum values just before Y = 0.038 m (Figure 3a). At Y = 0.038 m (where Zmin = C1 and Zmax = C2), the nearest vertices to the side wall in the front and rear plates will be reversed, that is, hip (dX1 = 0) and neck (dX2 = 0.038 m) locations, respectively. Meanwhile, dX1 = dX2 = 0.019 m midway at Y = 0.019 m. With further increase in elevation, dX1/dX2 start 12109



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Figure 3. Illustration of various geometrical input variables investigated in the developing phase of ANN correlations for f b and Db in FWBFB and CWBFB (Table 1). Typical examples of F_A,B and C120_C,D are reported here. Variables include: C, Hi in (a); dX1, dX2, and Zmin, Zmax in (b). In Figure 3b, filled and empty circles represent neck and hip locations, respectively.

regard, Figure 4 panels a−c correspond to f b and Figure 4 panels d−f to Db. For each case, results from training (80%), generalization (20%), and global (100%) databanks used for ANN correlation development are given separately. The criteria to select the final version of input variables for ANN correlations was based on lower values of AARE and higher correlation and determination coefficient values, with as minimum as possible number of hidden neurons to prevent overfitting. Initially ANN correlations were developed for f b and Db by using the operating and geometrical variables, that is, Yj, θ, Ug/ Umb, Hi, and C (case 1, Table 1). This set of variables led to large global AARE of 42.3% for f b (Figure 4a) but a reasonable value of 12.4% for Db (Figure 4d). The correlation (CC)/ determination (CD) coefficients in the case of Db were higher enough with values of 98.5/97% (Figure 4e,f); albeit significantly lower values of 82.8/66.8% (Figure 4b,c) were obtained in the case of f b. Furthermore, case 1 correlations were unable to capture the periodic behavior of axial variations of f b and Db in the case of CWBFB as showcased by experiments of Figures 2a,b. This can be sensed from Figure 5 panels a and b which depict the vertical variations of experimental and computed (case 1) values of f b (a) and Db (b) in FWBFB

to increase/decrease and at Y = 0.076 m (where Zmin = C1 and Zmax = C2) both front and rear plates retrieve periodicity, that is, neck (dX1 = 0) and hip (dX2 = 0.038 m), respectively, just as at Y = 0 (Figure 3b). Therefore, at any axial location whenever Zmin and Zmax will attain their respective extreme minimum and maximum values, the focal vertices (neck/hip locations) for front and rear plates will be swapped. A point of swap in designating the vertices to front and rear plates can also be seen in Figure A4b (Supporting Information). Similar behavior was observed in the case of other configurations of CWBFB (C90_C, D, results not shown). Since flat walls do not contain any neck/hip locations so a zero value was associated to dx1 and dx2 in the case of FWBFB. In addition to these geometrical input variables, the ANN correlation for Db was also tested for a variant with f b as input variable (case 9, Table 1). 3.3. Analysis of Input Variables. A thorough comparison of the cases summarized in Table 1 employing the aforementioned input variables was made on the basis of the average absolute relative error (AARE, eqs A4,5 Table A2, Supporting Information and Figure 4a,d), correlation coefficient (CC, eq A7 Table A2, Supporting Information and Figure 4b,e), and coefficient of determination (CD, eq A8 Table A2, Supporting Information and Figure 4c,f). In this 12110



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Figure 4. Comparison of various cases for the selection of final correlation in terms of averaged absolute relative error (AARE, %), correlation coefficient (CC, %), and coefficient of determination (CD, %) on the basis of training, generalization and global data sets: f b (a−c) and Db (d−f). Labeled data correspond to global values.

(F_B, C = 0.028 m) and CWBFB (C120_D and C90_D, C1 = 0.015 m) at Ug/Umb = 1.4. This led to further explorations regarding more meaningful geometrical features of CWBFB by introducing Zmin, Zmax, dX1, and dX2 (Figure 3b) as input variables for ANN correlations of f b and Db. Then, various combinations of these geometrical variables were tested. Case 2 among cases 1−8 (Table 1) provided the lowest value of global AARE for f b (26.2%, Figure 4a) and Db (11.5%, Figure 4d) and sufficiently high global CC/ CD values for f b (91.5/83.4%, Figure 4b,c) and Db (98.6/ 97.3%, Figure 4e,f). Case 2 captured the periodic trends unlike case 1. However, case 4 offered less overfitting problems and sufficient oscillations capturing ability with a reduced set of input variables by dropping the counterparts of Zmin (i.e., Zmax) and dX1 (i.e., dX2) at the expense of marginal inflation in global AARE (28.1% for f b and 12.1% for Db) and decrease in global CC/CD values (90/80.7% for f b and 98.5/96.9% for Db), see Figure 4. Case 4 for Db was further refined to case 9 (Table 1) with elimination of Zmin and dX1 and sole introduction of f b as input variable in addition to the common Yj, θ, Ug/Umb, Hi, and C variables. The difference between the two cases is that case 4 involves Zmin and dX1 explicitly while case 9 contains implicit information of Zmin and dX1 in the form of f b. This implicit embedding of Zmin and dX1 in the form of f b as an input variable improved the ANN model for Db with the global AARE, CC, and CD values of 11%, 98.8%, and 97.5%, respectively (Figure 4d−f). It was interesting to see that the quality of Db correlation, in terms of AARE, CC, and CD values, with the implicit embedding of only dX1 and Zmin (case 9) was found even better than case 2 which employed all the geometrical input variables (see, Figure 4d,e, Table 1). ANN correlations were also developed without C (cases 6,8) then, after it was

realized that its presence is imperative to develop a good model. After thorough analyses of various input variables, cases 4 and 9 were finally selected to develop the ANN correlations for f b and Db, respectively. Figure 5 panels a and b also compare the axial variations of experimental and computed values of f b (case 4) and Db (case 9) in a typical set of operating and geometrical configurations of FWBFB and CWBFB and show the effective strength of the explicit (for f b) or implicit (for Db in the form of f b) introduction of geometrical variables (Zmin and dX1) to capture the oscillating trends. The correlation in the entrance zone for case 4 led to an under-prediction of frequencies. It was however difficult to identify whether the reason was ascribable to imperfections in initial gas distribution, to the erratic nature of the developing entrance zone of the bed, or to biases in the bubble counting algorithms in the entrance zone (see also discussion in the next section). 3.4. Discussion on Final Correlations. The set of equations for the neural network correlations of f b (case 4, Table 1) and Db (case 9, Table 1) in FWBFB and CWBFB are reported in Tables 2 and 3. Tables A3, A4 (Supporting Information) provide the weights of the correlations in Tables 2, 3, respectively. Relatively higher values of AARE and lower values of correlation and determination coefficients in case of bubble frequency ( f b) were obtained as compared to bubble diameter (Db). This could be attributed to a more diversified pattern of whole data in FWBFB and CWBFB which was showing axially fluctuating trends only in the case of CWBFB. Parity plot of f b in Figure 6a compares the 2870 entries of experimental and ANN computed values obtained for various operating and geometrical configurations of FWBFB and CWBFB. The envelopes at ±2 AARE (AARE = 28.1% and σ = 37%, eq A6, Table A2, Supporting Information) are also 12111



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Figure 5. Vertical variations of experimental and computed values of f b (a) and Db (b) in FWBFB (F_B, C = 0.028 m) and CWBFB (C120_D and C90_D, C1 = 0.015 m) at Ug/Umb = 1.4. Explicit or implicit introduction of geometrical input variables (Zmin and dX1) improved ANN correlation predictions for f b (case 4) and Db (case 9) as compared to case 1.

12.2%, eq A6, Table A2, Supporting Information) are also shown. Figures 7a,b indicate that lower values of bubble equivalent diameter (Db < 0.02 m) offer high ARE values which decrease with increasing Db and then become almost constant at higher values (Db > 0.055 m). This can be attributed to the inherited limitations of digital image analysis technique at lower gas flow rates where sometimes the curtain effect of particles plays a detrimental role in hiding smaller bubbles from the camera on front side (especially in case of C = 0.038 m). A spread of data in the range of 0.004 to 0.145 m also overspills the lower number of smaller bubbles in the whole databank from the ±2 AARE envelopes. So, Db > 0.03 m seems to be well within the ±2 AARE envelopes. Figure 8 panels a−d present an analysis of ANN correlations developed for f b (case 4, Table 1) and Db (case 9, Table 1) in terms of AARE (%) and correlation coefficient (CC, %) for a given type of operating/geometrical configuration. Figure 8a shows that the AARE for f b and Db values in the case of CWBFB is slightly higher than for FWBFB. This can be attributed to the widespread data showing periodic behavior in

shown. Data used for training and generalization purposes during the ANN correlation building process are shown separately (training, circle marker; generalization, triangle marker). Figure 6b shows the effect of experimental values of f b on the individual absolute relative error (ARE, eq A4, Table A2, Supporting Information) values. Figure 6 panels a and b reveal that lower values of bubble frequency (f b < 1 s−1) are associated with higher ARE values which decrease as f b increases and then slightly increase at higher values (f b > 8 s−1). This can be attributed to the few number of data entries with high amplitude periodic trends of f b in the case of CWBFB (especially in the lower section of deep beds, C120_D, C90_D) as compared to FWBFB. Periodicity was also observed in the upper sections but with relatively lower amplitude (see Figures 2 and 5). Hence f b > 1 seems to be well within the ±2 AARE envelopes. Parity plot of Db in Figure 7a compares the experimental and correlation values for the same number of data entries as in f b obtained for the same locations, operating conditions, and geometrical configurations of FWBFB and CWBFB. The ±2 AARE envelopes (AARE = 11% and σ = 12112



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Table 2. Set of Equations for Bubble Frequency (f b) Correlation by ANN Technique in FWBFB and CWBFB (Case 4, Table 1) S=

Table 3. Set of Equations for Bubble Equivalent Diameter (Db) Correlation by ANN Technique in FWBFB and CWBFB (case 9, Table 1)

1 J+1

1 + exp[− ∑j = 1 ωjHj]

1 Hj = I+1 1 + exp[− ∑i = 1 ωijUi ]

S=

(1) (2)

U1 =

S1 =

(3)

Y − 0.0305 0.2695 − 0.0305

(4)

U2 =

θ − 90 180 − 90

U3 =

Hi − 0.15 0.30 − 0.15

U4 =

C − 0.028 0.038 − 0.028

U5 =

(5)

Zmin − 0.015 U6 = 0.0399 − 0.015

U7 =

U3 =

(6)

dX1 0.0374

U8 = 1 H17 = 1

(7)

(3)

U6 =

(9)

θ − 90 180 − 90

(5)a

(6) (7) (8)

(Ug /Umb) − 1.1

U7 = 1 H15 = 1

(10)

(4)

1.3939 + 1.4664

C − 0.028 U5 = 0.038 − 0.028

(8)

1.55 − 1.1

(9)

(10) (11)

a

f b (in U2, eq 5) must be calculated from Tables 2 and A3 (Supporting Information) at the same operating and geometrical configurations. A user friendly spread sheet is also available on our website12.

(11) (12)

⎛ θ⎞ Zmin = α − β × cos⎜(γ × Yj) ⎟ ⎝ 2⎠

(2)

fb + 1.4664

Hi − 0.15 U4 = 0.30 − 0.15

(Ug /Umb) − 1.1 1.55 − 1.1

log(D b) + 2.4412 − 0.8397 + 2.4412

Y − 0.0305 U1 = 0.2695 − 0.0305

,

U2 =

(1)

Bubble Equivalent Diameter(Db) I = 6, J = 14

log(fb ) + 1.4664 1.3939 + 1.4664

J+1

1 Hj = I+1 1 + exp[− ∑i = 1 ωijUi ]

Bubble Frequency ( f b) I = 7, J = 16

S1 =

1 1 + exp[− ∑j = 1 ωjHj]

(13)

increase in clearance between plates (C). For any design of bed, a significant decrease in AARE for f b and Db can be seen with the increase in gas flow rate (i.e., Ug/Umb) or excess gas (Ug − Umb). Since excess gas is mainly responsible in the generation of bubbles in gas−solid fluidized beds1, this leads to a databank with relatively less diversified larger bubbles throughout the FWBFB/CWBFB.

where for θ = 90° and 120°, α = 0.0225 (C1 = 0.015 m) and 0.0325 (C1 = 0.025 m), β = 0.0075, γ = 372.09 (θ = 90°), and 157.89 (θ = 120°) for θ = 180°, α = 0.028 (C = 0.028 m) and 0.038 m (C = 0.038 m) ⎛ Y ⎞ d j dX1 = Yj − n Y × Integer_part⎜ d ⎟ ⎜ nY ⎟ 4 ⎝ 2 ⎠ (14)a

4. CONCLUSION Corrugated walls were successfully mounted in slim beds to improve the quality of gas−solid fluidization of Geldart D particles. An incipient bubbling condition was achieved at lower gas flow rates in corrugated-wall bubbling fluidized bed (CWBFB) due to high drag force at the neck (minimum clearance) locations as compared to flat-wall bubbling fluidized bed (FWBFB). CWBFB offered peculiar periodic trends in bubble size (equivalent diameter) and frequency. CWBFB generated smaller bubbles than FWBFB due to continuous bubble breakup phenomena at the necks and lower excess gas (this corrugation artifice would be equally valid in circular fluidization vessels). In this regard, a high-speed digital image analysis technique was employed to estimate the aforementioned bubble properties. Neural network correlations were developed to estimate the area-weighted mean bubble equivalent diameter (Db) and bubble frequency ( f b) in flat (FWBFB)- and corrugated (CWBFB)- wall bubbling fluidized beds under different operational and geometrical configurations. Various combinations of input variables were under investigation in the developing phase of correlations which include gas superficial-minimum bubbling velocity ratio (Ug/ Umb), bed rest height (Hi), corrugation angle (θ), average

where dnY = 0.043 (θ = 90°); 0.076 (θ = 120°); dX1 = 0 (θ = 180°) a

Integer_part means to consider quotient of Yj/(dnY/2), e.g., at Yj = 0.15 m and θ = 90°; Integer_part = 6. A user friendly spread sheet is also available on our website.12

CWBFB. For other values of operating and geometrical variables, in the case of f b it follows an increasing trend with the decrease in corrugation angle (θ); however, in the case of Db the trend is not obvious. In Figure 8b, higher values of AARE for f b and Db in shallow beds (Hi = 0.5 m) were observed as compared to deep beds (Hi = 0.3 m). This could be possibly due to two main reasons, (i) the curtain effect of particles on smaller bubbles because Umb was lower in shallow beds (see Figure 1) and (ii) the gas or bubble flow was not well developed in the bed. This led to lower event number of relatively smaller bubbles representing shallow beds in the whole databank which was relatively enriched with bigger bubblesdue to high Umb, and more developed flow captured in the both lower (Yj < 0.15 m, shallow beds) and upper (0.15 < Yj < 0.3 m, deep beds) sections resulting in high values of global AARE in shallow beds than deep beds. Figure 8c shows a slight increase in AARE for f b and Db with the 12113



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Figure 6. Parity plot comparing experimental and computed values of f b (case 4, Table 1) with ±2 AARE envelopes in FWBFB and CWBFB (a); effect of experimental f b values on their respective absolute relative errors (b).

Figure 7. Parity plot comparing experimental and computed values of Db (case 9, Table 1) with ±2 AARE envelopes in FWBFB and CWBFB (a); effect of experimental Db values on their respective absolute relative errors (b).

combination failed to sufficiently capture the peculiar oscillating trends especially regarding f b. The explicit introduction of dX1, dX2, Zmin, and Zmax significantly improved the correlation with relatively lower/higher values of global AARE/CC (f b, 26.2/ 91.5%; Db, 11.5/98.6%) and much better ability to capture the periodic behavior of f b and Db trends. In the final version of correlations, the counterparts of dX1 (i.e., dX2) and Zmin (i.e., Zmax) were dropped at the expense of a marginal increase in global AARE (f b/Db = 28.1/12.1%) and decrease in CC (f b/Db = 90/98.5%) values to minimize the overfitting problems without damaging the ability to capture the correlation periodic trends. The correlation for Db was further refined with elimination of Zmin and dX1 and sole introduction of f b as input variable in addition to the common Yj, θ, Ug/Umb, Hi, and C variables. This implicit embedding of Zmin and dX1 in the form

clearance (C), vertical/axial location (Y), axially varying clearance between corrugated plates at neck (minimum clearance, Zmin) and hip (maximum clearance, Zmax) locations and axially varying distance between vertices (necks or hips whichever is nearest) of front (dX1) and rear (dX2) corrugated plates. In the case of FWBFB, dX1 and dX2 were set to zero, while Zmin = Zmax = C. The criteria to select the final version of input variables for ANN correlations were based on lower values of AARE, higher correlation and determination of coefficient values, with as minimum as possible number of hidden neurons to prevent overfitting. Initially the correlations for f b and Db were developed with a combination of input variables such as Ug/Umb, Hi, θ, Y, and C which offered the higher/lower values of global AARE/CC in the case of f b (42.3/82.8%) and reasonable values for Db (12.4/98.5%). This 12114



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Figure 8. Analysis of ANN correlations developed for f b (case 4, Table 1) and Db (case 9, Table 1) in terms of AARE (%) for a given type of operating/geometrical configuration. (a) θ = 180°, 120°, 90°; (b) Hi = 0.15 and 0.3 m; (c) C = 0.028 and 0.038 m; (d) Ug/Umb = 1.1, 1.25, 1.4, 1.55.

Chair “Green processes for cleaner and sustainable energy” are gratefully acknowledged for their financial support.

of f b as an input variable improved the ANN model for Db with the global AARE/CC values of 11/98.8%. Although it was not our aim in this present cold-flow study to optimize the corrugation geometry to achieve the required capacity of actual processing plants, it is perhaps demonstrative of the potential influence of hydrodynamics on reaction performance. This point however needs both hot flow and reaction data together to arrive at a final verdict whereby the use of a correlation such as the one proposed in this study could prove useful. Some of the issues related to hot flow implementation of corrugated bubbling fluidized beds were discussed elsewhere.7

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ASSOCIATED CONTENT

S Supporting Information *

Figures A1 to A4 and Tables A1 to A4 as discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].. Tel.: (418) 656-2131 ext. 3566. Fax: (418) 656-5993. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Natural Sciences and Engineering Research Council of Canada Strategic Grant Program and the Canada Research 12115

NOTATION Ab = projected are of bubble obtained by DIA technique, m2 C = clearance between walls in FWBFB and CWBFB = (C1+ C2)/2, m C1 = neck clearance in CWBFB, m C2 = hip clearance in CWBFB, m db = equivalent diameter of bubble based on projected area obtained by DIA technique, m dX1 = distance between side wall and either neck or hip (whichever is nearest to side wall) of front plate, m dX2 = distance between side wall and either neck or hip (whichever is nearest to side wall) of rear plate, m Db = area weighted mean bubble equivalent diameter estimated over a period of 30 s dc = corrugation depth, m dn = neck-to-neck vertical distance, m dp = particle diameter, mm f b = bubble frequency, s−1 fps = frames per second, Hz Hi = initial height of the bed, m N = total number of data entries to develop ANN correlations for f b and Db (2870 of each in the current study) m = number of lateral locations at Yj for DIA technique Nb = total number of bubbles at a particular elevation over a period of 30 s p = number of pictures/frames captured in digital image analysis technique dx.doi.org/10.1021/ie3007775 | Ind. Eng. Chem. Res. 2012, 51, 12107−12116


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(8) Cloutier, P.; Tibirna, C.; Grandjean, B. P. A.; Thibault, J. NNfit, logiciel de régression utilisant les réseaux à couches. http://www.gch. ulaval.ca/nnfit 1996. (9) Larachi, F; Belfares, L.; Iliuta, I.; Grandjean, B. P. A. Heat and mass transfer in cocurrent gas-liquid packed beds: Analysis, recommendations, and new correlations. Ind. Eng. Chem. Res. 2003, 42, 222−242. (10) Hilligardt, K.; Werther, J. Local bubble gas hold-up and expansion of gas/solid fluidized beds. Ger. Chem. Eng. 1986, 9, 215− 221. (11) Lim, K. S.; Gururajan, V. S.; Agrawal, P. K. Mixing of homogeneous solid in bubbling fluidized beds: Theoretical modeling and experimental investigation using digital image analysis. Chem. Eng. Sci. 1993, 48, 2251−2265. (12) Faiç̈ al Larachi, Universite Laval. http://www.gch.ulaval.ca/ flarachi.

tK = time, s Ug = gas superficial velocity determined over the bed cross section W × C, m/s Umb = minimum bubbling velocity in FWBFB and CWBFB, m/s UFW mb = minimum bubbling velocity in FWBFB, m/s UCW mb = minimum bubbling velocity in CWBFB, m/s W = width of fluidized bed, 0.3 m X, Y, Z = Cartesian coordinates corresponding to lateral location, vertical elevation, and clearance between walls, m Zmin = minimum lateral distance or clearance between the parallel plates in Z direction at any elevation, m Zmax = maximum lateral distance or clearance between the parallel plates in Z direction at any elevation, m Greek Letters

θ = corrugation angle (90° and 120°) τe = exposure time of camera (= 0.2 ms) Δ = change in properties or time σ = standard deviation in f b (s−1) and Db (m) Subscript

G = AARE, CC, CD of global f b and Db data bank i,j = to represent the local values Superscript

C = corrugated wall bubbling fluidized bed F = flat wall bubbling fluidized bed Abbreviation

ARE = absolute relative error AARE = averaged absolute relative error FWBFB = flat wall bubbling fluidized bed CWBFB = corrugated walled bubbling fluidized bed CC = coefficient of correlation for f b, and Db data bank CD = coefficient of determination for f b and Db data bank Cor = the values of Db (m) and f b (s−1) obtained from their respective ANN correlations DIA = digital image analysis Exp = experimental values of Db (m) and f b (s−1) NA = not applicable

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REFERENCES

(1) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd ed; Butterworth-Heinemann Series in Chemical Engineering: Newton, MA, USA, 1991. (2) Iliuta, I.; Leclerc, A.; Larachi, F. Allothermal steam gasification of biomass in cyclic multi-compartment bubbling fluidized bed gasifier/ combustornew reactor concept. Bioresour. Technol. 2010, 101, 3194−3208. (3) Jin, Y., Wei; F., Wang, Y. Effect of internal tubes and baffles. In Handbook of Fluidization and Fluid-particle Systems; Yang, W. C. Ed.; Marcel Dekker: New York, Chapter 7, 2003. (4) Zhang, Y.; Grace, J. R.; Bi, X.; Lu, C.; Shi, M. Effect of louver baffles on hydrodynamics and gas mixing in a fluidized bed of FCC particles. Chem. Eng. Sci. 2009, 64, 3270-3281. (5) Yates, J. G.; Ruiz-Martinez, R. S. Interaction between horizontal tubes and gas bubbles in a fluidized bed. Chem. Eng. Commun. 1987, 62, 67−78. (6) Khan Wardag, A. N.; Larachi, F. Bubble behavior in corrugatedwall bubbling fluidized bedsExperiments and CFD simulations. AIChE J. 2012, 58, 2045−2057. (7) Khan Wardag, A. N.; Larachi, F. Stability analysis of flat- and corrugated-wall bubbling fluidized beds: Differential pressure, heat transfer coefficient, digital image analysis and CFD simulations. Chem. Eng. J. 2012, 179, 349−362. 12116


Bubble Size and Frequency in Corrugated-Wall Bubbling Fluidized

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