ENGINEERING DEVELOPMENT OF



ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SCBR) TECHNOLOGY

CONTRACT NO. DE-FC-22-95 PC 95051

Monthly Report, Budget Year 6

Reporting Period: November 1-30, 2001

(For the 27th Quarterly Period: October 1 to December 31, 2001)

from

Chemical Reaction Engineering Laboratory (CREL), Washington University

TO: Dr. Bernard Toseland

DOE Contract Program Manager

Air Products and Chemicals, Inc.

P. O. Box 25780

Lehigh Valley, PA 18007

FROM: Dr. Milorad P. Dudukovic

The Laura and William Jens Professor and Chair

Director, Chemical Reaction Engineering Laboratory

Washington University

One Brookings Drive

Campus Box 1198

St. Louis, MO 63130

Cc: R. Klippstein, Air Products and Chemicals, Inc.

M. Phillips, Air Products and Chemicals, Inc.

L. S. Fan, Ohio State University

K. Shollenberger, Sandia National Laboratory

ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SCBR) TECHNOLOGY

ABSTRACT

During the month of November progress has been made in computational efforts to simulate bubble column flows and in development of an optical probe for measurement of bubble sizes and velocites. The following has been accomplished:

1. Two different bubble breakup models and one coalescence model have been implemented into the bubble population balance equation which is coupled with CFD simulation.

2. Evaluation of the wall effects, caused by the finite depth of a 2D bubble column, on its hydrodynamics has been initiated.

3. Sources of error in measurements of bubble rise-velocity and bubble chord length by four-point optical probe have been investigated.

Executive summary

• Two different breakup models and a coalescence model are implemented in CFD and compared. The implementation of breakup and coalescence model and bubble population balance equation eliminated the need for choosing an arbitrary “mean” bubble size via trial-and-error as done previously and routinely used by others.

• 3D simulations have been performed to study the effect of finite depth of a 2D bubble column (Mudde et al. 1997) on averaged flow characteristics. The simulations have been completed and results are being processed.

• A study has been initiated to evaluate the errors induced by the bubble deformation on the measurements by a four-point optical probe. It was found that due to the deformation, caused by bubble impact on the probe, the measured bubble velocity and bubble size might be underestimated by 15-20%.

In the following each of these topics are described briefly.

Experimental and Computational Design

1 Implementation of Breakup and Coalescence Models

into CFD of Bubble Column Flows

In this study, the Algebraic Slip Mixture Model (ASMM) is used in the framework of FLUENT (version 5.5). We have previously shown that the ASMM model for bubble column flows provides comparable results to those of the two-fluid Eulerian model (Sanyal et al. 1999). The ASMM is most convenient for incorporation of the bubble population balance equation. The principal assumptions in this formulation were explained previously (25th Quarterly Report (April-June, 2001)), details of the solver and numerical techniques used are available in the FLUENT manual.

The simulations were performed for 6 in. (14.0 cm i.d.), 8 in. (19.0 cm i.d.) and 18 in. (44.0 cm i.d.) air-water bubble columns operated in churn turbulent flow regime. Gas superficial velocities simulated were 12.0 cm s-1 for 6 and 8 inch columns and 10.0 cm s-1 for 18 inch column. The column contained a batch liquid with unexpanded height of 98.0 cm, 96.0 cm and 176.0 cm, respectively. The distributor used in the experiments was a perforated plate, with an open area of 0.05-0.077%. In the present simulations, the perforated plate has been modeled as a uniform surface source of the gas phase.

The numerical simulation was performed on a 300 (axial) ( 19 (radial) grid using a time step of 0.005 seconds. Inlet boundary conditions were assigned at the distributor, and outlet conditions at the free surface. No-slip conditions were applied at the wall, and symmetry conditions at the central axis of the column.

The gas phase is discretized into n (n = 9 in this simulation) subclasses, according to bubble size, and all classes are assumed to move with identical velocity relative to the liquid. The population balance equation for the ith bubble class can be written as

[pic] (1)

There is no reaction and phase change in the present work and the source term due to pressure change was neglected. Therefore, the source term is only due to breakup and coalescence of bubbles.

The breakup kernel as given by Martínez-Bazán et al. (1999) is used. Binary breakup was assumed and the breakup rate b((,di) for a given bubble of diameter di is given by

[pic] (2)

where b((,di) is the breakup rate (s-1), ( is the local dissipation rate (m2 s-3), di is the bubble diameter (m), ( is surface tension (N m-1), (c is continuous phase density

(kg m-3). The dimensionless constants ( = 8.2 and Kg = 0.25 were provided by Martínez-Bazán et al. (1999). The daughter bubble size probability density function (p.d.f.) is

[pic] (3)

where [pic] is the breakup probability of a parent bubble with diameter D0 (m) into a daughter bubble with diameter D1 (m). Furthermore, other quantities are defined as:

[pic]

Another breakup kernel as given by Luo and Svendsen (1996) for binary breakup is given by,

[pic] (4)

where [pic] is breakup rate per unit volume of continuous phase (m-3 s-1) of a parent bubble with volume v into a daughter bubble with volume vfBV, fBV is the volume fraction of one daughter bubble, cf is defined as the increase coefficient of surface area, that is [pic], ( = (/d, and ( is the arriving eddy size.

This model predicts the breakup rate for original bubbles of a given size at a given combination of the daughter bubble sizes and thus does not need a predefined daughter bubble size distribution. The daughter bubble size distribution is a result that can be calculated directly from the model.

The coalescence model is divided into two parts, the collision frequency and the coalescence efficiency. The collision rate of bubbles per unit volume (ij (m-3 s-1), as given by Saffman and Turner (1956), can be written as:

[pic] (5)

The coalescence efficiency (dimensionless) is given by Luo (1993) as:

[pic] (6)

where [pic]

The coalescence rate [pic] (m-3 s-1) then can be written as

(C = (ijPC(di,dj) (7)

The basic idea, in discretizating the above equations, is that bubbles in a size range, say Ri, are assigned to a pivotal size xi. However, breakup and coalescence processes may produce bubbles that are between such pivotal sizes (except in the case of a uniform linear grid, i.e., xi = ivmin) and must be reassigned to the pivots. The reassignment must be done carefully to preserve the accurate calculation of selected moments of the p.d.f.

Kumar and Ramkrishna(1996a) proposed the following way to preserve any selected moments. For xi ( v < xi+1, let the fraction of bubbles of size v assigned to xi be denoted by [pic], and a fraction of [pic] be assigned to size xi+1. The reassignment will preserve the rth moment provided:

[pic] for r = r1, r2 (8)

These two equations above (i.e. Eq. 8 for r = r1 and r = r2) yield a unique solution for the quantity [pic]. To preserve the mass balance and the number balance, we set r = 0 and 1, respectively. Then the source term for Equation 1 may be written as

[pic] (9)

Ni (m-3) is the number density of ith bubble class.

2 Effect of finite depth of a 2D-bubble column on its hydrodynamics

In the last quarter, we have evaluated the effect of different interfacial closures on the hydrodynamics of bubble column flows, using 2D simulations. It was found that the implicit assumption of zero-velocity gradient in the third direction in 2D simulations caused an over-prediction of averaged axial velocity in the centerline and in the back flow zones near the walls. In order to evaluate the effects due to the presence of walls in the third direction, 3D simulations of the bubble column, as studied by Mudde et al. (1997), have been completed and results are being processed.

Euler-Euler simulations are performed using the two-fluid model in the framework of the CFD code library CFDLIB (Los Alamos National Laboratory). The governing equations (i.e. the continuity and momentum equations) remain the same as reported in the 26th quarterly report (July 01- September 30, 2001). The interfacial momentum exchange terms appearing in the momentum equations are closed as follows:

1 Drag force:

[pic] (10)

In the above expression, [pic], [pic] and [pic], and where Rep and dp are respectively bubble Reynolds number and bubble diameter.

2 Virtual mass force:

[pic], with Cvm=0.5 (11)

3 Lift force:

[pic] , with CL=0.5 (12)

4 Turbulence:

Like 2D simulations reported in the last quarter, our 3D simulations as well assume that the turbulence is present in the liquid phase only and that it can be modeled by the standard k-ε model for single fluid flows.

3.2.5 Geometry and Mesh system:

The column (Figure 1) has the dimensions of 15.2x1.27x170 cm, and is operated at a superficial gas velocity of 1 cm/s. The gas is sparged into the column through three nozzles (each 0.2 x 1.27 cm, rectangular strip) situated at the bottom boundary.

[pic]

Figure 1 Schematic description of geometry

To simulate the inlet nozzles, the entire width of the column is divided into 7 sections. There are 38 mesh points along the column width (x-direction) of 15.2 cm. These points are distributed over 7 segments as follows: 6, 2, 10, 2, 10, 2, 6 points over the segments of length 2.4, 0.2, 4.9, 0.2, 4.9, 0.2, and 2.4 cm, respectively. The depth of the column (y-direction) contains 6 mesh points, which are uniformly distributed over the length of 1.27 cm. Similarly the column height (z-direction) contains 170 mesh points, which are uniformly distributed as well over entire column height (170 cm).

The working fluids are air/water where water is in batch mode having the initial static height of 152 cm (L/D=10). At start up instant (t=0), air starts entering the column through inlet nozzles. After initial transient hydrodynamics (40 seconds), a quasi-steady state develops. Once the quasi-steady state is reached (t=40 seconds), different flow variables like velocities, holdup and turbulent kinetic energy, are sampled with a sampling rate of 10 Hz for statistical averaging. The results are being processed and will be reported in the upcoming monthly report.

3 Bubble dynamic measurement with a four-point optical probe

In the monthly report of October 2001, the comparison of bubble rise velocity measured by four-point optical probe against that measured by CCD camera was reported and it was noticed that the relative error can be as high as 50%. It was found that, among other error sources, the bubble shape fluctuation might cause considerable errors in the measurements by the probe. In the following, this fact is elaborated briefly. The sketch in Figure 2 describes the physical situation.

[pic] [pic]

Figure 2 Schematic of the Bubble Chord length Measurement. Legend: D1 - Bubble chord length when the leading edge hits the central tip; D2 - Bubble chord length when the leading edge hits the side tips; D3 - Bubble chord length when the trailing edge hits the central tip.

The bubble velocity in the probe axial direction obtained by the probe is:

[pic] (13)

Where L is the axial distance between the central tip and peripheral tips of the probe (see Figure 2); (t is the time interval between the time when the bubble leading edge hits the central tip and the time when the leading edge hits peripheral tips.

The real bubble velocities in the probe axial direction referred to the centroid of the bubble (see Figure 2) is:

[pic] (14)

Then the relative error in the bubble rise velocity measurement due to bubble size fluctuation is:

[pic] (15)

The bubble vertical chordal length pierced by the probe is:

[pic] (16)

However, the real bubble vertical chord length when the bubble leading edge hits the probe is:

[pic] (17)

Then the relative error in the bubble chord length measurement due to the bubble fluctuation is:

[pic] (18)

RESULTS AND DISCUSSION

1 Bubble Population Balance and CFD

During the last few months we simulated three bubble columns of different size operating in the churn turbulent flow regime. They are 6 inch diameter column with gas superficial velocity at 12 cm/sec, 8 inch diameter column with gas superficial velocity at 12 cm/sec, and 18 inch diameter column with gas superficial velocity at 10 cm/sec. 2D axi-symmetric simulation was used. Either the breakup model of Martínez-Bazán et al. (1999) or of Luo and Svendsen (1996) and the coalescence model of Luo (1993) were used.

Table 1 shows the comparison of the computed radial averaged gas holdup and the experimental results obtain from Computed Tomography (CT). Both simulations with breakup and coalescence closures predict the gas holdup well, with relative error within 20 percent. It seems that the predicted radial averaged gas holdup without breakup and coalescence model is better (within 10 percent) when we tune the mean bubble size parameter (dmean = 10 mm). One should keep in mind that the models containing the bubble population balance have not been tuned.

In Figure 3 the computed time-averaged liquid axial velocity profiles are compared against the time-averaged velocity profiles obtained by CARPT. The mean bubble size parameter is adjusted to 10 mm for all the three cases without breakup and coalescence models. All the breakup and coalescence model parameters are kept the same. The general shape of the velocity profile is well captured and the discrepancy in the model predicted and CARPT-measured time-averaged axial liquid velocity diminishes as one moves radially outwards in the column. The computed liquid velocity from the crossover point to the wall is well predicted while there is some difference in the core region for the liquid velocity prediction. As the mean bubble size parameter for the simulation without breakup and coalescence models is tuned to fit the small-sized columns (the 6 inch and 8 inch columns), the discrepancy in simulated liquid velocity profile and CARPT data is not pronounced and the liquid axial velocity in the centerline is well predicted. However, the crossover point prediction without breakup and coalescence is not satisfactory compared to the simulation with breakup and coalescence. The experimental data indicate the velocity cross-over point at around r/R = 0.68-0.69, the simulation with the breakup and coalescence model places it around r/R = 0.71, while the simulation without the breakup and coalescence model yields around r/R = 0.73-0.74. Moreover, as mentioned before, the mean bubble size for the simulation without breakup and coalescence model has been tuned for the small column. When we try to predict the liquid axial velocity in the larger column (18 inch column) while keeping the bubble diameter parameter tuned for small diameter columns, the accuracy of our prediction deteriorates. In contrast, the simulation with breakup and coalescence predicts the liquid axial velocity well in all columns.

Table 1 Comparison of computed radial averaged gas holdup

|  |CT |Martinez-Bazan |Error |Luo and Svendsen |Error |No B/C |Error |

| | |(1999) | |(1996) | |dmean= 10mm | |

|6” Column, |0.213 |0.177 |-16.9 % |0.190 |-10.8% |0.199 |-6.57% |

|Ug = 12 cm/sec | | | | | | | |

|8” Column, |0.202 |0.175 |-13.4% |0.191 |-5.45% |0.195 |-3.47% |

|Ug = 12 cm/sec | | | | | | | |

|18” Column, |0.170 |0.142 |-16.5% |0.156 |-8.24% |0.155 |8.82% |

|Ug = 10 cm/sec | | | | | | | |

[pic]

[pic]

[pic]

Figure 3 Comparison of Time Averaged Liquid Axial Velocity

1 Summary

Incorporation of the bubble population balance and breakup-coalescence models into the CFD of bubble column flows eliminates the need to assign the bubble size which is now computed by the model. The computed time averaged liquid axial velocity is not sensitive to the breakup closures, and axial liquid velocity profile is predicted quite well in different diameter columns operating in the churn turbulent flow regime. 2D axi-symmetric simulation predicts liquid axial velocity reasonably well.

2 3D Computations of “2D” Column

As stated earlier the results are being processed and should be reported next month.

3 Four-point optical probe measurements

Tables 2 and 3 display the estimated measurement errors due to bubble fluctuation, calculated with Equations (15) and (18) presented earlier.

Table 2 Relative Error (%) of Bubble Rise Velocity Measurement

|f |0.99 |0.98 |0.97 |0.96 |0.95 |0.9 |

|D1=3.0mm |-1.0 |-1.9 |-2.8 |-3.7 |-4.6 |-8.8 |

|D1=4.0mm |-1.3 |-2.5 |-3.8 |-5.0 |-6.1 |-11.5 |

|D1=5.0mm |-1.6 |-3.2 |-4.7 |-6.1 |-7.6 |-14.1 |

|D1=0.6mm |-1.9 |-3.8 |-5.6 |-7.3 |-9.0 |-16.5 |

* Assumptions: L=1.5mm, f=D2/D1

Table 3 Relative Error (%) of Bubble Chord Length Measurement

|f |0.99 |0.98 |0.97 |0.96 |0.95 |0.9 |

|D1=3.0mm |-1.5 |-2.9 |-4.3 |-5.7 |-7.0 |-13.4 |

|D1=4.0mm |-1.8 |-3.5 |-5.2 |-6.9 |-8.5 |-16.0 |

|D1=5.0mm |-2.1 |-4.1 |-6.1 |-8.0 |-9.9 |-18.4 |

|D1=0.6mm |-2.4 |-4.8 |-7.0 |-9.2 |-11.2 |-20.6 |

• Assumptions: L = 1.5mm, f = D2/D1=D3/D1

|[pic]a) |[pic]b) |

|[pic]c) |Bubble Chord Length Pierced by the Tip a) |

| |D2= 4.94mm = 0.925D1 |

| |b) D1= 5.33mm= |

| |c) D3= 4.84mm= 0.907D1 |

Figure 4 Bubble Fluctuation During Measurement (Bubble rise velocity: 21.1 cm/s; Field of View: 10mm(10mm; Resolution: 0.0398 mm/pixel)

Figure 4 shows an example of the bubble fluctuation during measurement. In this case the error in the bubble rise velocity measurement by the probe due to the bubble fluctuation is –10.3% according to equation (15), the error in the bubble chord length measurement by the probe due to the bubble fluctuation is -14.4% according to equation (18). Because big bubbles fluctuate more violently, the measurement error for these bubbles can be even larger.

Furthermore, there are additional factors that may cause errors to the measurements by the four-point probe, for example the deviation of the bubble movement from the probe axial direction. The study of these factors is in progress.

SUMMARY AND FUTURE WORK PLAN

Successful implementation of the bubble population balance model and appropriate breakup and coalescence models allows us to eliminate the unknown bubble size as parameter in CFD simulations. Further extensions and studies of this new CFD model are planned. We need to investigate the effect of different closures and to perform 3D simulations. We will also attempt to incorporate the coalescence re-dispersion models into the Euler-Euler CFD simulations. We will also attempt to identify the experiments needed for validation of the combined CFD-bubble population balance models.

Our study of the effect of closures on bubble column flows will continue after we had interpreted the results of the effect of the walls in the third dimension on computed velocity and holdup fields.

Investigation of the four point optical probe continue in order to fully quantify the various error sources and develop a probe and measurement protocol for more reliable identification of the bubble size population.

The work also continues in processing CARPT, CT data at high gas velocities and elevated pressure.

Work on tracer data interpretation is also in progress.

References

Kumar, S. and Ramkrishna D., 1996, “On the Solution of Population Balance Equations-I. A Fixed Pivot Technique,” Chem. Eng. Sci., 51, 1311.

Luo, H., 1993, “Coalescence, Breakup and Liquid Circulation in Bubble Column Reactors,” Ph.D. Thesis, Norwegian Institute of Technology.

Martínez-Bazán, C., Montañés and Lasheras, J. C., 1999, “On the Breakup of an Air Bubble Injected into a Fully Developed Turbulent Flow. Part 1. Breakup Frequency,” J. Fluid Mech., 401, 157.

Martínez-Bazán, C., Montañés and Lasheras, J. C., 1999, “On the Breakup of an Air Bubble Injected into a Fully Developed Turbulent Flow. Part 2. Size PDF of the Resulting Daughter Bubbles,” J. Fluid Mech., 401, 183.

Mudde R. F., Lee D. J., Reese J. and Fan L, -S, 1997, “Role of coherent structures on Reynolds stresses in a 2-D bubble column”, AIChe. J., 43.

Sanyal J., Vasquez S., Roy S. and Dudukovic M. P., 1999, “Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactor”, Chem. Eng. Sci., 54, 5071-5083.

List of Acronyms and Abbreviations

2D Two Dimensional

3D Three Dimensional

ASMM Algebraic Slip Mixture Model

CARPT Computer Automated Radioactive Particle Tracking

CREL Chemical Reaction Engineering Laboratory

CFD Computational Fluid Dynamics

CT Computed Tomography

Nomenclature

d, dp Bubble diameter, m

d the real bubble vertical chord length when the bubble leading edge hits the probe

dp the bubble vertical chord length pierced by the probe, m

D column diameter, m

g breakup frequency, s-1

g gravity, m2 s-1

L the axial distance between peripheral tips and the central tip of the probe, m

k turbulent kinetic energy, m2s-2

Kg Constant in Equation 2, dimensionless

ni number density of ith bubble class

p pressure, Pa

PC Coalescence efficiency, dimensionless

R Radial position, m

S Source term, s-1

u Velocity, m/s

v, v’ Volume, m3

v the real bubble velocity referred to the centroid of the bubble, m/s

v’ bubble rise velocity in the probe axial direction measured by the probe, m/s

t Time, s

(t time interval between the time when the bubble leading edge hits the central tip and the time when the leading edge hits the peripheral tips, s

We Webber Number, dimensionless

z elevation, m

Greek symbols

( Gas void fraction, dimensionless

( Constant in Equation 2, dimensionless

( Fraction that to be reassigned to nearby bubble classes, dimensionless

( Dissipation rate, m2/s3

( eddy size, m

( Density, kg/m3

( Surface Tension, kg s-2

( Dynamic viscosity, kg m-1 s-1

( di/dj, dimensionless

Subscripts

b Bubble

c Continuous phase

d Dispersed Phase

i ith bubble class

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