**3.1 Upward flow profile**

734 Mass Transfer - Advanced Aspects

of 1, 2 and 3. The wall flow was separated from the bulk flow in the packing by an annular ring on the inside wall of the column at the packing support level and collected in a separate container so that it did not interference with the local liquid flow through the packing to the

In order to quantify liquid distribution in the packed bed, a liquid distribution factor was

1 <sup>1</sup> <sup>1</sup> *<sup>n</sup> <sup>i</sup>*

where MF is the liquid distribution factor, n is the number of liquid collecting tubes, Vi is the

6(a)

6(b)

Fig. 6. Tomographic images of the conductivity at various planes for upward flow

*<sup>V</sup> <sup>M</sup> n V* <sup>=</sup> ⎛ ⎞ <sup>=</sup> ⎜ ⎟ <sup>−</sup>

liquid velocity to individual collecting tubes and VAVG is the averaged liquid velocity

*F i*

2

⎝ ⎠ <sup>∑</sup> (1)

*AVG*

liquid collector described above.

used and defined as below (Dang-Vu et al., 2006b):

For the upward flow mode, the high conductivity tracer moved upward with the bulk flow and passed plane 1 to plane 6, consecutively, after the tracer injection. The advancement of the tracer upward through the column can be seen in the tomograms in Figures 6(a) and 6(b). The shade of a region in a tomogram indicates the conductivity of that region in accordance with the conductivity scale in mS/cm as shown below the tomograms.

Some time after the tracer injection, the high conductivity solution reached planes 1 and 2 as indicated by the light spots in the tomograms for P1 and P2 in Figure 6(a). The tomograms at planes 3 to 6 still have a dark shade indicating a low conductivity of the bulk water stream since the tracer solution didn't reach to those planes yet. As time went by, the tracer solution moved farther upward to P4, P5 and P6 as can be seen by the high conductivity regions (light shade) in Figure 6(b) while the conductivities at P1, P2 and P3 decreased (dark shade at those planes) since the tracer solution had moved out of those regions.

Using the mean conductivity data across a plane, conductivity peaks can be identified when the tracer has reached successive planes as shown in Figure 7. The distance between the peaks represent the time for the tracer to move between the planes. From the conductivity peaks and the time elapsed between two peaks, the liquid velocity from one plane to the next one was determined. It was noted that in the upward flow mode, a steady flow and a more even distribution of conductivity across a plane were obtained. The velocities at different planes are comparable to one another and the average velocity throughout the packed bed. This might be due to the fact that the liquid almost moved up the column in a plug flow pattern. The flow pattern wasn't distorted by liquid hold-up or liquid channelling. The ERT measurements of the liquid velocity were within 5% with the interstitial velocities calculated from the averaged liquid flowrate measured by a flowmeter and the bed porosity (Figure 8).

Fig. 7. Mean conductivity at various planes for the upward flow

Measurement of Liquid Velocity and Liquid Distribution

capturing the real flow distribution in the packed bed.

in a Packed Bed Using Electrical Resistance Tomography 737

times those predicted from the ERT data. It appeared that the deviation between the two residence times increased with liquid flow rate. The theoretical residence time based on the volumetric flow rate measurement and the bed void volume was unable to account for the effect of the liquid hold–up, the liquid channelling and the wall flow in the packed bed. In addition, it is relevant to note that the theoretical residence time was based on the whole void space, and the liquid was assumed to fill all the void space in the packed bed before eluting out at the bottom of the column. As a result, the residence time tended to be long. On the other hand, the actual liquid flow might have channelled through the packed bed; hence, by-passed some of the void space resulting in a shorter residence time as shown by the ERT measurement. This might be considered as an advantage of the ERT system in

9(a)

9(b)

Fig. 9. Tomographic images of the conductivity at various planes for trickle flow

Fig. 8. Comparison of liquid velocity measured by the ERT and the flowmeter

#### **3.2 Trickle flow profile**

Tomograms for the trickle flow mode are shown in Figures 9(a) and 9(b). In addition, the variations of the mean conductivities at individual planes with time are presented in two separate graphs, for clarity, in Figures 10(a) and (b). Tomographic images were recorded at six different heights downstream from the top of the column. The high conductivity tracer moved from plane 6 (P6) downwards to plane 1 (P1) after injection, as indicated by the high conductivity regions of light shade in the tomograms in Figures 9(a) and 9(b). When the column is operated in the trickle flow mode, the advancement of the high conductivity plane was not as clear as those obtained with the upward flow. The tomograms show successive increases in conductivity from plane 6 (P6) at the top of the bed to plane 1 (P1) at the bottom of the bed. However, the high conductivity liquid remains at a plane for a period longer than that observed with the upward flow mode. At times, high conductivity profiles of multiple planes overlapped since the high conductivity front didn't move from one plane to another in pulses, i.e. no distinctive peaks at individual planes at different time steps. Less pronounced and broader mean conductivity distribution was observed as shown in Figures 10(a) and (b). This might be due to liquid hold-up in the packed bed under the trickle flow mode. Liquid tends to linger in the void space of the packing before moving downward the column.

For the trickle flow, the conductivity peaks were not very distinctive from one plane to another. Therefore, liquid residence time in the column was used as an indicator for the liquid flow. A theoretical residence time was also calculated using the interstitial liquid velocity, which was determined from the average flow rate measured by a flowmeter and the void fraction of the bed. The ERT-measured residence time was shorter at a higher flow rate, as expected. The residence time determined from the ERT data also followed a trend similar to that of the theoretical residence time, as shown in Figure 11. For varied liquid flowrates from 5.05 – 7.57×10-4 m3.s-1, the theoretical residence times were about 1.5 -2.0

0.030 0.035 0.040 0.045 0.050 0.055 0.060 Interstitial velocity (m.s-1)

Tomograms for the trickle flow mode are shown in Figures 9(a) and 9(b). In addition, the variations of the mean conductivities at individual planes with time are presented in two separate graphs, for clarity, in Figures 10(a) and (b). Tomographic images were recorded at six different heights downstream from the top of the column. The high conductivity tracer moved from plane 6 (P6) downwards to plane 1 (P1) after injection, as indicated by the high conductivity regions of light shade in the tomograms in Figures 9(a) and 9(b). When the column is operated in the trickle flow mode, the advancement of the high conductivity plane was not as clear as those obtained with the upward flow. The tomograms show successive increases in conductivity from plane 6 (P6) at the top of the bed to plane 1 (P1) at the bottom of the bed. However, the high conductivity liquid remains at a plane for a period longer than that observed with the upward flow mode. At times, high conductivity profiles of multiple planes overlapped since the high conductivity front didn't move from one plane to another in pulses, i.e. no distinctive peaks at individual planes at different time steps. Less pronounced and broader mean conductivity distribution was observed as shown in Figures 10(a) and (b). This might be due to liquid hold-up in the packed bed under the trickle flow mode. Liquid tends to linger in the void space of the packing before moving

For the trickle flow, the conductivity peaks were not very distinctive from one plane to another. Therefore, liquid residence time in the column was used as an indicator for the liquid flow. A theoretical residence time was also calculated using the interstitial liquid velocity, which was determined from the average flow rate measured by a flowmeter and the void fraction of the bed. The ERT-measured residence time was shorter at a higher flow rate, as expected. The residence time determined from the ERT data also followed a trend similar to that of the theoretical residence time, as shown in Figure 11. For varied liquid flowrates from 5.05 – 7.57×10-4 m3.s-1, the theoretical residence times were about 1.5 -2.0

Fig. 8. Comparison of liquid velocity measured by the ERT and the flowmeter

0.030

0.035

0.040

0.045

ERT measurement (m.s-1)

**3.2 Trickle flow profile** 

downward the column.

0.050

0.055

0.060

times those predicted from the ERT data. It appeared that the deviation between the two residence times increased with liquid flow rate. The theoretical residence time based on the volumetric flow rate measurement and the bed void volume was unable to account for the effect of the liquid hold–up, the liquid channelling and the wall flow in the packed bed. In addition, it is relevant to note that the theoretical residence time was based on the whole void space, and the liquid was assumed to fill all the void space in the packed bed before eluting out at the bottom of the column. As a result, the residence time tended to be long. On the other hand, the actual liquid flow might have channelled through the packed bed; hence, by-passed some of the void space resulting in a shorter residence time as shown by the ERT measurement. This might be considered as an advantage of the ERT system in capturing the real flow distribution in the packed bed.

Fig. 9. Tomographic images of the conductivity at various planes for trickle flow

Measurement of Liquid Velocity and Liquid Distribution

ERT Average flow

0.000

technique

0.020

0.040

0.060

0.080

Maldistribution coefficient, Mf

0.100

0.120

0.140

0.160

Trickle flow

values from the average flowrate measured by a flowmeter

ERT-12gpm LCM-12gpm ERT-8gpm LCM-8gpm

Liquid residence time in the measuring zone (s)

measure the aggregated liquid distribution at one bed height at a time.

in a Packed Bed Using Electrical Resistance Tomography 739

distances concurrently. This is an advantage over the liquid collecting method, which can only

0.00050 0.00055 0.00060 0.00065 0.00070 0.00075 0.00080 Liquid flow rate (m3

0 0.5 1 1.5 2 2.5 3 3.5 Packing height, x/D

Fig. 12. Liquid distribution factor obtained by the liquid collecting method and the ERT

Fig. 11. Liquid residence times estimated from the ERT measurements and the calculated

.s-1)

Fig. 10. Mean conductivity at various planes for the trickle flow

Liquid distribution factors estimated by Equation (1) using the liquid velocities obtained by the liquid collecting method and the ERT method at two liquid flowrates are plotted in Figure 12. As can be seen in Figure 12, the liquid distribution factor obtained from the ERT technique follows a similar trend of that obtained from the liquid collecting method. This indicates that the ERT method was suitable for the measurement of liquid distribution in a packed column. Moreover, the ERT method allows for measurements of liquid distribution at multiple axial

13:56:21 13:56:38 13:56:56 13:57:13 13:57:30 13:57:48 13:58:05 13:58:22 Time

13:56:21 13:56:38 13:56:56 13:57:13 13:57:30 13:57:48 13:58:05 13:58:22 Time

10(b)

Liquid distribution factors estimated by Equation (1) using the liquid velocities obtained by the liquid collecting method and the ERT method at two liquid flowrates are plotted in Figure 12. As can be seen in Figure 12, the liquid distribution factor obtained from the ERT technique follows a similar trend of that obtained from the liquid collecting method. This indicates that the ERT method was suitable for the measurement of liquid distribution in a packed column. Moreover, the ERT method allows for measurements of liquid distribution at multiple axial

10(a)

0.80

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30

Mean Conductivity (mS/cm)

0.85

0.90

0.95

1.00

1.05

Mean Conductivity (mS/cm)

1.10

1.15

1.20

P1

P3

P5

P2

P4

P6

Fig. 10. Mean conductivity at various planes for the trickle flow

1.25

distances concurrently. This is an advantage over the liquid collecting method, which can only measure the aggregated liquid distribution at one bed height at a time.

Fig. 11. Liquid residence times estimated from the ERT measurements and the calculated values from the average flowrate measured by a flowmeter

Fig. 12. Liquid distribution factor obtained by the liquid collecting method and the ERT technique

Measurement of Liquid Velocity and Liquid Distribution

A

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

down the column from top plane)

**5. Acknowledgement** 

**6. References** 

Normalized conductivity

liquid distribution in the packed bed, which doesn't exist in reality.

B

Direction

structured packings. *Chem. Eng. Sci.* Vol. 58, pp. 4037 – 4053.

C

Financial support from the National Science and Engineering Research Council of Canada (NSERC) for the purchase of the ERT system used in this project is highly appreciated. In addition, we would like to thank T. Vu and A. Nguyen for their assistance in the laboratory.

Aroonwilas, A.; Chakma, A.; Tontiwachwuthikul, P. & Veawab, A. (2003). Mathematical

modeling of mass transfer and hydrodynamics in CO2 absorbers packed with

Fig. 14. Distribution of the conductivity across the column area at plane 4 (or P4 at 60 cm

D

1

2 3 4

Direction

in a Packed Bed Using Electrical Resistance Tomography 741

In the upward flow mode, the liquid velocity and flow rate measured by the ERT system agreed to the velocity measured independently by a flow meter within 5%. A qualitative view of the images generated by the ERT system also provides information on the distribution within each plane. In addition, the ERT system could be used to capture radial and axial liquid maldistribution as well as liquid channelling in a trickle flow mode. For the trickle flow mode, the liquid residence time measured by the ERT method followed a similar trend of that calculated from the interstitial liquid velocity, which was determined from the liquid flowrate to the column and the packed bed characteristics. However, the calculated liquid residence time was about 1.5 – 2 times higher than that measured by the ERT method. This indicates the capability of the ERT method to capture the effect of liquid channelling, liquid hold-up and the wall flow on the actual liquid flow in a packed bed. The calculated superficial velocity is inaccurate since it is only true under an ideal condition with a perfect

As can be seen in Figure 12, the liquid distribution factor decreased with the bed height and liquid flowrate, as expected. This is in agreement with the results obtained and reported by other researchers (Hoek et al., 1986; Kouri and Sohlo, 1996; Dang-Vu et al., 2006b). At both liquid flowrates, the liquid distribution factors obtained by the ERT method are higher than those obtained by the liquid collecting method. This might be due to the fact that the number pixels used in the ERT method was 316, i.e. the cross-sectional area of the column was divided into 316 segments, while the number of liquid collecting tubes was only 39. The liquid streams collected in the collecting tubes covered a significant portion of the cross-sectional area of the column as compared with the local velocities obtained by the ERT method. Therefore, the liquid streams collected in the liquid collecting method were averaged out resulting in a more even liquid distribution as indicated by the lower liquid distribution factor.

Figures 13 and 14 show the distribution of liquid conductivity over the whole cross-section of the column at the top plane (P6) and at P4 that was at 60 cm downward the column from P6. The axes labelled as direction are the two directions enclosing the cross-section of the column with the column center being at the center of the bar graph. As can be seen in these figures, liquid conductivity was more even at plane 4, indicating a better liquid distribution at this plane. When the tracer was introduced into the top of the column, it trickled down the column with the main liquid flow. There was some level of liquid mal-distribution at the top section of the packed bed. Therefore, the liquid distribution was less even, as indicated by a higher level of variation of the liquid conductivity at top plane (P6) with a standard deviation of 0.149 as compared with the value of 0.062 at P4. Moreover, this also indicates that the liquid conductivity measured by the ERT method could be used as an indicator for liquid distribution at various axial distances along the packed bed

Fig. 13. Distribution of the conductivity across the column area at top plane (or P6)

#### **4. Conclusion**

In the present study, the ERT system was successfully applied to measure liquid flow distribution at varied axial distances along a packed bed without disturbing the flow profile.

As can be seen in Figure 12, the liquid distribution factor decreased with the bed height and liquid flowrate, as expected. This is in agreement with the results obtained and reported by other researchers (Hoek et al., 1986; Kouri and Sohlo, 1996; Dang-Vu et al., 2006b). At both liquid flowrates, the liquid distribution factors obtained by the ERT method are higher than those obtained by the liquid collecting method. This might be due to the fact that the number pixels used in the ERT method was 316, i.e. the cross-sectional area of the column was divided into 316 segments, while the number of liquid collecting tubes was only 39. The liquid streams collected in the collecting tubes covered a significant portion of the cross-sectional area of the column as compared with the local velocities obtained by the ERT method. Therefore, the liquid streams collected in the liquid collecting method were averaged out resulting in a more

Figures 13 and 14 show the distribution of liquid conductivity over the whole cross-section of the column at the top plane (P6) and at P4 that was at 60 cm downward the column from P6. The axes labelled as direction are the two directions enclosing the cross-section of the column with the column center being at the center of the bar graph. As can be seen in these figures, liquid conductivity was more even at plane 4, indicating a better liquid distribution at this plane. When the tracer was introduced into the top of the column, it trickled down the column with the main liquid flow. There was some level of liquid mal-distribution at the top section of the packed bed. Therefore, the liquid distribution was less even, as indicated by a higher level of variation of the liquid conductivity at top plane (P6) with a standard deviation of 0.149 as compared with the value of 0.062 at P4. Moreover, this also indicates that the liquid conductivity measured by the ERT method could be used as an indicator for

even liquid distribution as indicated by the lower liquid distribution factor.

liquid distribution at various axial distances along the packed bed

<sup>A</sup> <sup>C</sup>

Direction

Fig. 13. Distribution of the conductivity across the column area at top plane (or P6)

In the present study, the ERT system was successfully applied to measure liquid flow distribution at varied axial distances along a packed bed without disturbing the flow profile.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized conductivity

**4. Conclusion** 

<sup>C</sup> <sup>D</sup>

Direction

In the upward flow mode, the liquid velocity and flow rate measured by the ERT system agreed to the velocity measured independently by a flow meter within 5%. A qualitative view of the images generated by the ERT system also provides information on the distribution within each plane. In addition, the ERT system could be used to capture radial and axial liquid maldistribution as well as liquid channelling in a trickle flow mode. For the trickle flow mode, the liquid residence time measured by the ERT method followed a similar trend of that calculated from the interstitial liquid velocity, which was determined from the liquid flowrate to the column and the packed bed characteristics. However, the calculated liquid residence time was about 1.5 – 2 times higher than that measured by the ERT method. This indicates the capability of the ERT method to capture the effect of liquid channelling, liquid hold-up and the wall flow on the actual liquid flow in a packed bed. The calculated superficial velocity is inaccurate since it is only true under an ideal condition with a perfect liquid distribution in the packed bed, which doesn't exist in reality.

Fig. 14. Distribution of the conductivity across the column area at plane 4 (or P4 at 60 cm down the column from top plane)
