I

WSSR ORNL/MIT-300

Analysis of Barium Hydroxide and Calcium Hydroxide Slurry

Carbonation Reactors

K. D. Patch R. P. Hart W. A. Schumacher

:r,;r ;o uriimirta

ORNL/MIT-300

Contract No. W-7405-eng-26

EMPLOYEE RELATIONS DIVISION

ANALYSIS OF BARIUM HYDROXIDE AND CALCIUM HYDROXIDE SLURRY CARBONATION REACTORS

K.D. Patch R.P. Hart H.A. Schumacher

Consultants G.L. Haag, D.W. Holladay, and D.F. Green

Date Published - May 1980

Oak Ridge Station School of Chemical Engineering Practice Massachusetts Institute of Technology

K.J. Fallon, Director

Oak Ridge National Laboratory Oak Ridge, Tennessee 37830

Operated by Union Carbide Corporation

for the Department of Energy

•CUM*. t^mmmmmmmHIHW—WITIHWH' — uuwlnwoi • mi,

«W" » MIM. « M a ** <*» HKr * m n» i« M —mi p np n M M M * PJ •*rtH|f 0i&0f M M I npn> P M w MUH w jfip 4Ml"t(

m IIIW*I »• '»• « MMr at «—»». m WW , v kvio * * . UMM tnaMMM>ar«m«ni i .n i iMMi iH>> i ia iM a iw« iM>«>a «——n»»n^n—«« —umm»ii|>iMII Minr•>«»»» w l .

ABSTRACT The removal of CO2 from air was Investigated by using a continuous-

agitated-slurry carbonatlon reactor containing either barium hydroxide [Ba(0Ky or calcium hydroxide [Ca(0H) 2]. Such a process would be applied to scrub l 4C02 from stack gases at nuclear-fuel reprocessing plants. De­contamination factors were characterized for reactor conditions which could alter hydrodynamlc behavior. An attempt was made to characterize reactor performance with models assuming both plug flow and various degrees of backmlxlng In the gas phase. The Ba(0H) 2 slurry enabled Increased conversion, but apparently the process was controlled under some conditions by phenomena differing from those observed for car­bonatlon by Ca(0H)2. Overall reaction mechanisms are postulated.

V

Contents Page

1. Summary 1 2. Introduction i

2.1 Background 1 2.2 Theoretical Considerations 2

2.2.1 Overview 2 2.2.2 Integration of the Carbonatlon Rate Expression 5

3. Apparatus and Procedure 6 3.1 Apparatus 6 3.2 Procedure 8

4. Results and Discussion 8 4.1 Ca(0H) 2 Reactor 8 4.2 Ba(0H) 2 Reactor 13

5. Conclusions 17 6. Recommendations , 17 7. Acknowledgment 17 8. Appendix 18

8.1 Carbonatlon Rate and Interfaclal Area Expressions 18 8.2 Physical and Chemical Properties 19 8.3 D>ta and Computer Ana lysis 22 8.4 Location of Original Data 32 8.5 Nomenclature 32 8.6 Literature Referenced 33 8.7 Literature Surveyed 35

1

1. SlfKARY

Removal of CO? (330 ppm) from an air stream was studltd 1n a contin­uously sparged, agitated-slurry carbonatlon reactor. The C02 content of the outlet gas was measured for barium hydroxide [Ba(0H)2] and calciua hydroxide [Ca(0H)z] slurries at various operating conditions, and results were compared with those of Sheppard et al. Qj>), who investigated ta(0H)9 slurries. Decontamination factors (DFsTrahged from 3 to 1200 for Ca(0Hj2 and from 60 to 2100 for Ba(0H)2. For both slurries, lower values of OF were observed at higher gas flow rates and lower impeller speeds. On the other hand, the importance of backmixing for the high-conversion Ba(0H)2 system apparently caused the DF's to pass through an optimum at conditions toward the opposite extreme, whereas bactaixing had a smaller effect on conversion by Ca(0H)2, which was primarily controlled by the available gas-liquid interfacial area. Increased slurry loadings enhanced conversion for Ba(0H)2 slurries, In contrast to the opposite effect noted foi Ca(0H)2 slurries. A gas-solid reaction which competes with reactions in the liquid phase Is postulated for the Ba(0H)2 case.

An empirical relationship was developed for the Ca(0H)2 system, which accounts for a degree of backmixing of the gas phase intermediate to that inherent in the plug-flow and perfectly backmixed models. A nonlinear regression yielded the optimal correlations:

a = ( / . S x l O ^ N 0 - 9 7 ^ 1 ^ - 0 ' 1 ^ } - 1 cm 2/cm 3

n = (1.4 x 104) I f 0 - 5 4 U 0 ' 3 4 S-°' 4 3 d f 3 - 0

where a Is the gas-liquid interfacial area (cm^/cm^), n is the number of equal CSTR's (constant stirred tank reactors) in series, N is the Impeller speed (rps), U is the superficial gas velocity (cm/s), S is the weight fraction of solids, and dj Is the impeller diameter (cm). Predicted values for Interfacial area varied from 0.8 to 2.3 cm2/cm3, and values for the number of equal-volume CSTR's were between 3 and 15. No correlation was recommended for the Ba(OH)? system due to the lack of data obtained, the unrealistic values achieved for a and n, and the differing hydrodynamlc and chemical phenomena postulated.

2. INTRODUCTION

2.1 Background

Nuclear-fuel reprocessing plants emit stack gases that contain signifi­cant amounts of carbon-14 In the form of 1 4C02. which should be removed to prevent possible health hazards (5, 8). Carbon-14 has a 5730-yr half-Ufa,

2

and there Is some concern that It may be Incorporated into the food chain, possibly leading to mutagenesis. Essentially complete removal of CO2 from the gas stream can be accomplished by reaction with agitated alkaline slur­ries. The carbonate product is very stable and satisfies many long-term disposal requirements.

Agitation increases gas-liquid phase subdivision, as well as the degree of liquid-phase mixing. Phase subdivision produces relative motion between the phases and increases the gas-liquid interfacial area (2., 2, 16, U.); both effects contribute to a higher reaction rate by increasing the overall mass transfer. The interfacial area is the principle variable determining the capacity of an agitated gas-liquid reactor (2_lJ.

Previous workers (3, 4, 5_, 6, 8, 12, 15) have investigated calcium hydroxide [Ca(OH)?] slurries for removal of CO2. The carbonation reaction for barium hydroxide [Ba(0H)2], however, has not been investigated. Study­ing the significantly higher rate of reaction of Ba(0H)2, due to the much greater solubility of the hydroxide (5.6 g/100 g H2O vs 0.2 g/100 g H2O), should yield a better understanding of the overall carbonation process under slurry conditions.

The objective of this study was to develop a model for the performance of Ca(0H)2 and Ba(0K)2 slurry reactors by: (1) developing empirical rela­tionships for interfacial area and degree of mixing as a function of the hydrodynamic parameters of the reactor and (2) summarizing the results from both alkaline slurries to develop a model that can be extended to other systems.

2.2 Theoretical Considerations

2.2.1 Overview

Juvekar and Sharma (8) discuss the overall process for the absorption of CO2 Into an alkaline slurry as outlined below:

X(0H") 2(s) ^ X 2 + (aq) + 20H"(aq) (1)

C02(g) ^ C02(aq) (2)

C02(aq) • 0H"(aq) - • HCO3 * a q ) (3)

HCO^aq) + 0H"(aq) - * H20 + C0£"(aq) <*>

X 2 + (aq) * CO^'(aq) - %COJs) • (5)

3

where X= Ba, Ca Sections (4) and (5) are instantaneous, and thus the rate-controlling step is either the dissolution of the hydroxide or the absorption and subse­quent reaction of C0>. Reaction (1) is essentially at equilibrium due to the excess of X(0H)2(s) present and the relatively small amount of CO2 ab­sorbed from the gas. Combining the individual rate expressions for the transport of CO? through the gas film, transport of CO2 into the liquid, and reaction of CO2 with the hydroxy! ions yields the following rate ex­pression (see Appendix 8 . 1 ) :

where Ra = V W (6)

R = specific rate of CO2 absorption (gmol/s-cm 2) a = gas-liquid interfacial area (cm2/cm3)

K, = psueo first-order rate constant (gmol/cn^-s-kPa) P f l = average pressure of the gas in the contactor (kPa)

x = mole fraction of COg in the gas

The pseudo first-order rate constant in Eq. (6) is actually a function of several parameters, as given by Danckwerts 1 surface renewal theory (3):

H ^ C O K 2 [ O H ~ ] + K L K l a . _ ~ (7) HVW2^*T 1* 2 h

where D C 0 2

B diffusivity of C 0 2 in aqueous solution (cnrVs) H » Henry's coefficient of solubility (gmol/cnP-kPa)

Kg * second-order rate constant (cmfygmol-s) Kg • gas-s1de mass transfer coefficient (gmol/cm2-s-kPa) K, • I1qu1d-s1de mass transfer coefficient In the absence of chemical reaction (cm/s)

4

Several authors (2, 8, jS) consider the liquid-phase mass transfer coefficient to be essentially independent of the operating conditions such as gas flow rate, bubble diameter, and mixing intensity; however, there are conflicting opinions concerning this parameter. Danckwerts (3) reports that %i is constant at relatively low speeds of agitation for which the mean bubble diameter is greater than 2.5 mm. His values for K|_ then drop sharply as the speed of agitation is Increased and thereafter remain constant. He contends that K|_ decreases because bubbles behave hydrodynamlcally as rigid spheres, with a relatively low KL» when they are reduced to diameters less than 2.5 an. Miller Q l ) also reports that liquid-film-controlled mass transfer is dependent on mean bubble size. Bubble shape, motion, and any tendency for the interface to ripple, fluctuate, o- otherwise deform, might also influence mass transfer, yery little information is available in the literature on the gas-side mass transfer coefficient, KG, in mechanically agitated V2ssels (JO).

Many conflicting investigations of interfacial area have been published in the literature (Z\). Reith (_H) notes that experiments performed in vessels with the same dimensions, filled with the same liquid, and operated under Identical conditions, may lead to completely different interfacial areas when different measuring methods (such as light scattering, light reflection, and photography) are used. Calderbank (2)> by utilizing a light-scattering technique, showed that the interfaci&l area across a par­ticular radius of a 100-liter tank can vary from 0.7 to 1.08 cr.2/cm3. In addition, extreme variations with reactor depth (0 to 1.2 cm2/cm3) are pos­sible.

The expression most commonly cited for Interfacial areas is that de­rived by Calderbank (2), who correlates interfacial area with the power dissipated by the agitator:

a s ! 44 P 0 , 4 P°' 2 #JL)l/2 a 1'*4 0.6 \ }

a t

[(djNp/ji)0,7 (Ndj/U) 0 / 3 < 20,000]

where power dissipated per unit volume of liquid (hp/ft3) density of the liquid (g/cm3)

5 1

surface tension of the liquid (10 J/cm ) superficial gas velocity (cm/s) upward velocity of bubbles (typically 26.5 cm/s)

P »

P * a •

U «

Ut *

5

dj = impeller diameter (cm) N = frequency of impeller rotation (s" ) u = liquid viscosity (g/cm-s)

Because Eq. (8) refers to pure liquids rather than to a mixed phase, its usefulness in predicting interfacial areas in slurries is questionable. In addition, the Calderbank correlation relies on an accurate estimate of the power consumption which, for bubbling reactors, requires much empiricism. The complexity of factors influencing power consumption in this case have led some researchers to doubt the practicality of achieving universal rela­tionships to predict power consumption accurately, except for the cases of limited ranges of the relevant variables (18).

2.2.2 Integration of the Carbonation Rate Expression Equation (6) can be integrated assuming: (1) K|_a is constant throughout

the vessel, (2) the liquid is mixed well, and (3) the gas phase is in plug flow. It can then be shown that (see Appendix 8.1):

*n(DF) = a a (9) where

OF = decontamination factor - inlet C0 2 mole fraction/outlet CO? mole fraction

3 V. * aerated liquid volume (cm ) a ^air = m ° l e c u ^ a r weight of air (g/gmol)

Q » air flow rate at 21 °C and 101 kPa U/min)

P a 1 r * density of air at 2«°C and 101 kPa (g/cm3)

Equation (6) can also be Integrated after assuming that the gas phase can be modeled as n equal-volume CSTR's in series, which accounts for varying degrees of backmlxing In the gas phase (see Appendix 8.1);

6

OF (1 + M } n (10)

If n is unity, Eq. (10) models the behavior of the gas phase as being per­fectly backmixed. The limiting behavior as n approaches infinity is that of plug flow, as given by Eq. (9).

3. APPARATUS AND PROCEDURE

3.1 Apparatus

The experimental apparatus is shown in Fig. 1, and vessel specifica­tions are listed in Table 1. The impeller, a 6-bladed Rushton turbine, was driven through a 2:1 reduction gearbox by a compressed-air motor, while the speed was monitored with a stroboscope. Water flowing through cooling coils kept the temperature of the slurry at 292 K.

Table 1. Vessel Specifications

Tank diameter height

Baffles number width

Impeller type diameter position (above tank bottom)

Sparger type extension above tank bottom

27.3 cm 35.0 cm 4 2.7 on (1/10 tank diameter) 6-blade Rushton turbine 13.7 cm 11 cm (4/10 tank diameter) 0.95 cm open pipe 5.5 cm

The reactor was operated 1n semi-batch mode by continuously passing gas through a slurry. The air flow was measured by a calibrated rotameter and entered the reactor through and open-pipe sparger located directly under the Impeller. In all experiments the pressure above the slurry was held at 112 kPa.

BELLOWS PUMP

STROBOSCOPE

<©«K)

THERMOMETE!

KNOCKOUT BOTTLE?

TO VENT PRESSURE GAUGE

REACTOR

INLET GAS

EXIT GAS INFRARED A

DETECTOR

' i\ C ) ^ I 1 1 0 O ^ I 1 1

—. 0 ( J , 1 °' 1 I — VOLTMETER

CHART RECORDER

MASSACHUSETTS INSTITUTE OP T I C H N 0 L 0 6 Y SCHOOL OP CHEMICAL ENOINEERINO PRACTICE

AT OAK RIDGE NATIONAL LABORATORY

EXPERIMENTAL APPARATUS

DATE 10-11-79

DRAWN BY RPH

PILE NO. CEPS-X-3001

PIO.

8

The sample stream of effluent gas passed through a series of three knockout bottles to remove any entrained slurry or condensed water vapor. A bellows punp maintained a constant flow to a Wilkes-Foxboro Model 1-A Infrared Spectrometer set at a wavelength of 4260 ran. Exit CO, concen­trations were measured at a path length of 20.75 m, with the temperature and pressure kept at 320 K and 136 kPa respectively. The output was dis­played on both a digital voltmeter and a strip-chart recorder. A calibra­tion curve allowed conversion of measured voltages to CO2 concentrations.

3.2 Procedure

The reactor was charged with about 16 liters of slurry containing the desired Ba(0H) 2 solids concentration. The desired air (330 ppm CO2) flow rate was set, followed by the adjustment of the Impeller speed. The exit CO? concentration was continuously monitored on the strip-chart recorder, • and on reaching steady-state conditions, the agitated slurry height and exit CO2 concentration <*ere recorded. Care was taken to avoid any entrain-ment of slurry from the reactor; thus upper limits on the flow rate and impeller speed were established. The values of operating conditions are presented in Table 2. •

Table 2. Experimental Variables

Variable Values Impeller speed (rpm) 350, 450, 550, 650 Flow rate U/min) 10, C , 44 Weight % solids 12, 21 Slurry Ba(0H) 2 • 8H 20

4. RESULTS AND DISCUSSION

4.1 Ca(0H) 2 Reactor

Preliminary experiments conducted with BafOH)? slurries indicated severe blockage of the T-sparger located beneath trie impeller. It was postulated that the Increased rate of reaction, as compared with the ' Ca(0H)2 system, resulted In deposition of the carbonate onto the sparger. To circumvent this problem, the T-sparger was removed, leaving an open-pipe sparger. Experiments with Ca(0H)2 slurries were repeated and com­pared with results obtained previously Q 5 ) (F1g. 2).

£ o o

c o u *J c W c ©

100

50

20.

10-

2-

1-

250 —T" 350

A OPEN PIPE SPARGER O T-SPARGER

GAS FLOW RATE (Jt/min)

"\A

450 i 550 — r ~

650 Impeller Speed (rpm)

Temperature * 292 K

C0„ Inlet Concentration * 330 ppm

MASSACHUSETTS INSTITUTI Of TECHNOLOGY SCHOOL Of CHEMICAL ENGINEERING PRACTICE

AT OAK RIDGE NATIONAL LABORATORY

EXIT C 0 2 CONCENTRATION VS IMPELLER SPEED WT % CA(0H) 2 SLURRY

DATE OUAWK «Y IflLE NO.

IEPS-X-300 no.

10

Mesterterp (20) also round that the method of gas injection made little difference if gas were fed to the eye of the impeller. The results shown in Fig. 2 corroborate his observation, with the exception of the open-sparger run at a gas flow rate of 44 t/min. The inconsistently high exit CO2 concentration at this higher flow rate could be due to some by­passing of large gas bubbles around the impeller. The T-sparger previously used was placed 7.6 cm from the bottom of the tank, whereas the current opeh-pipe arrangement released the air 5.5 cm from the tank bottom. This effect should be investigated further if more tests are to be run at high gas flow rates with the current sparger arrangement.

The decontamination factors calculated from Fig. 2 range from about 3 to 1200. For both modes of gas introduction, the same qualitative be­havior is observed. Extent of reactor conversion increases with increasing impeller speed, but decreases with increasing gas flow rates. Increased agitation is expected to increase the gas-liquid interfacial area because bubbles will rupture and form ones of smaller diameter. This will enhance the extent of conversion if the overall reaction is controlled by mass trans­fer at the interface and If the increased backmixing associated with greater agitation produces a less significant effect.

Increasing gas flow rate will Increase both the mean bubble diameter and the gas holdup (11). The former effect will decrease the specific interfacial area whereas the latter will increase it, so that the overall reactor conversion is not obvious. In addition, greater gas flow rates also lead to shorter residence times and consequently to lower degrees of backmixing, which would tend to enhance reactor conversion. The results in Fig. 2 indicate that the change in mean bubble diameter is the dominating phenomenon under the conditions examined. For the purposes of hydrodynamic modeling, it generally appears that backmixing of the gas phase can be neglected as a first approximation.

By assuming the gas phase to be in plug flow, multiple linear regres­sion techniques were used to obtain the following correlation for inter-facial area from the data in Fig. 2 and the additional data of Sheppard et aj.. (lj>) for Ca(0H) 2 slurries (see Appendix 8.3):

a = 0.059 N 0 ' 6 3 U 0 ' 4 2 S " 0 - 1 1 6 d j 0 ' 4 4 cm 2/cm 3 (11)

where N Is the impeller speed (rps), U Is the superficial gas velocity (cm/s), S is the weight fraction of solids, and dj 1s the impeller diameter (cm). The correlation predicts the Interfacial area will Increase with in­creasing Impeller speed and gas flow rate, as was postulated above. Calcu­lated Interfacial areas ranged from 0.5 to 2.0 cm^/cm3, results which are within the range of reasonable values (8, W, 21). Interfacial areas were also calculated when assuming a backmlxed gas pfiase but those values, ranging from 1.5 to 150 cm^/cm3, seemed to be excessively large (see Appendix 8.3).

Many authors feel that the gas phase 1s best described by plug flow (7, 11, 12) especially at low speeds of agitation; however, there are

11

conflicting opinions as to whether a plug flow or backmixed model Is appro­priate. Calderbank (2) finds that his results correlate best when complete backmixing is assumed. Several authors Q i , 18, Jl) find that impeller-induced coalescence of recirculating bubbles is significant and, under many conditions, the gas bubbles leaving the impeller zone are composed mainly of recirculating gas. In addition, it has been demonstrated that gas bub­bles passing through the impeller region are much more likely to be coalesced in pockets above the impeller blades than to undergo simple rupturing that has been previously envisaged Q 9 ) . Thus, neither a simple plug-flow nor a perfectly backmixed model for the gas phase can be considered adequate.

The experimental data also exhibit the inadequacy of a plug-flow model. A comparison of measured decontamination factors with those predicted by the plug-flew irodel is presented in Fig. 3. Although the correlation seems to be acceptable a*, lower decontamination factors, reactor efficiency is overestimated at conditions procicing higher decontamination factors. Backmixing appears to significantly reduce the conversion efficiency if the reactor is operated at low flow rates and high impeller speeds.

In an attempt to account for different degrees of backmixin<j in the gas phase, the system was modeled as CSTR's in series. Simultaneous empirical relationships were obtained for the number of equal-volume CSTR's n and the interfacial areas a as functions of the measured hydrodynamic parameters of the reactor. Using nonlinear regression (see Appendix 3.1), power-law correlations of the following form result

n = (1.4 x 10 4) N-0.54 yO.34 s-0.43 ^-3.0 ( 1 2 )

a = (7.8 x N T 3 ) N 0 ' 9 7 U 0 * 1 3 S - 0 ' 1 1 d j 1 ' 1 (13)

The ir-odel predicts an increase In interfacial area with increases in impeller speed, gas flow rate, and impeller diameter, as expected. A de­crease in interfacial area is indicated for an increase in solids content, possibly due to bubble coalescence at the solid particles. A trend toward greater backmixing decreasing n) occurs with increasing impeller speed, impeller diameter, and solids content, whereas an increase in gas flow rate suggests an approach to plug-flow conditions. Values of Interfacial area generated from this model range from 0.8 to 2.3 cm2/cmJ, and the num­ber of equal-volume CSTR's varies between 3 and 15. ^lues of n greater than 10 can be shown to indicate essentially plug-flow behavior (9).

A measure of the applicability of this model is shown in Fig. 4, where measured and predicted decontamination factors are compared. In contrast to Fig. 3, the correlation appears to be an improved representation of the experimental data throughout the range studied.

#

12

8-

!

6 -

*- 4 -

c

2-

tn x0/Xr (experimental)

Temperature - 292 K

x * mole fraction CO-MASSACHUSETTS INSTfTUTK Of TKCHN0LO6Y

SCHOOL OP CHEMICAL ENGINEERINC PRACTICE AT

OAK RIDGE NATIONAL LABORATORY

PREOICTEO VS EXPERIMENTAL DECONTAMINATION FACTORS

FOR PLUG-FLOW MODEL |OATI

10-14-79 DRAWN BY

RPH PILE NO. CEPS-X-300

PIC.

13

4.2 Ba(OH) 9 Reactor

Initial studies involving Ba(0H) 2 indicated that foaming of the slurry was a significant problem which led to the entrainment and deposition of slurry in the sample line and the first knockout pot. The gas flow rates examined were consequently restricted to valuer less than 50 t/min.

The Ba(0H)2 slurries yielded substantially higher conversions than did the Ca(CH)2 cases investigated. From Figs. 5 and 6, decontamination factors for the former can be calculated as ranging from 60 to 2100. The different qualitative behavior of thase curves also suggests the possibility of other overall reaction mechanisms under these conditions.

Figure 5 illustrates the effect of flow rate on exit CO2 concentration as a function of impeller speed. Note that exit CO2 concentrations are an order of magnitude less than those obtained for Ca(0H)2 (Fig. 2). The Ba(0H)2 curves reach a CO2 concentration minimum at approximately 550 rpm, in contrast to the Ca(0H)2 slurries, for which the CO2 concentration steadily decreases with increasing impeller speed (Fig. 2). Apparently the increased backmixing at higher agitation speeds and lower gas flow rates is not bal­anced by a corresponding increase in interfacial area. Slight changes in the residence-time distribution at the high conversions of the Ba(0H)2 sys­tem (^99.9%) could significantly alter the extent of reactor conversion and lead to the effects observed.

The effect of solids content on CO2 conversion is shown in Fig. 6. The apparent trend indicates that CO2 removal efficiency improves with increasing solids content. The CafOH)? system manifests the opposite effect. The ex­planation may lie in competing effects between bubble coalescence and gas-solid reaction. As mentioned above (Sect. 4.1), increased solids concentra­tion may increase bubble coalescence and thus decrease interfacial area and conversion; however, it is also possible that a significant gas-solid reaction exists. If the gas-solid reaction effect were more pronounced than the coales­cence effect, one would expect the trend observed in Fig. 6. The literature does not elucidate this problem but only states that conversion is highly dependent on the system in question.

From the above discussion and attempted correlations using the experi­mental data, It is obvious that the simple plug-flow model above could not explain the observed behavior of the Ba(OH)? system. In addition, modeling the system as a series of stirred tanks yields results that are physically intractable. Since the optimal correlation predicts 0.1 CSTR In series and Interfacial areas on the order of IP 5 0 cn?/ca&f the re­sults are clearly unrealistic. Undoubtedly the poor correlation is also attributable to the lack of data; only 27 data points are available for the nonlinear-regression correlation of eight paraiwters (96 data points are used for the Ca(0H)2 correlation). Evidently a better knowledge of the residence-time distribution of the gas and the variation of mass transfer coefficients, as functions of the various hydrodynamic parameters, Is re­quired to predict the behavior of hydroxide slurry carbonation reactors operating at conversions exceeding 99%.

14

•

8 -

^r *

6 -

V o

t 3 4 - 9jr

* >• >••

9 JF

X • • > » . o X c

2 -

4 r #

0 1 0 2 i i i

4 6 8 in x / x . (experimental)

Temperature « 292 K

x * mole fraction C0»

Temperature « 292 K

x * mole fraction C0» MASSACHUSf TTS INSTITUTf Of T f CNNOLOCT

SCHOOL OF CHEMICAL EWONEEItlNO PRACTICE AT

OAK RIDGE NATIONAL LABORATORY

Temperature « 292 K

x * mole fraction C0»

PREDICTED VS EXPERIMENTAL DECONTAMINATION FACTORS

FOR n CSTR'S IN SERIES MODEL DATE lORADN IV 10-22-79 I RPH

FILE NO. CEPS-X-300

no. 4 1

1 15

!WS»

10.0-

5.0

a.

CM o o

c 01 u c o o

2.0

1.0

0.5

0.2

0.1 150

/ 44 t/mln

24 t/min o / l 0 t/uin

X X 250 350 450 550

Impeller Speed (rpm) 550

Temperature - 292 K Inlet concentration of CO, 330 ppm

MASSACHUSf TTS INSTITUTE Of TCCNN0LO6T SCHOOL 0^ CHEMICAL OfOMECUfNO MACTICI

AT OAK RIDGC MATIO-AL LASORATOftT

EXIT C 0 2 CONCENTRATION VS IMPELLER SPEED FOR 21 WT X B a ( 0 H ) 2 SLURRY

DATE MAIN tY

ML-Hit NO,

(-3Qol i.

16

5.0

CM o

c o

01 o c o o

2.0

1.0

0.5

0.2

0.1 J.

24 t/nin gas flow rate Ba(0H)_ slurries

12 wt X

wt X

_L -L 1 150 250 350 450 550

Impeller Speed (rpm) 650

Temperature * 292 K Inlet concentration of C0 2 * 330 ppm

MASSACNUSf TTS INSTITUTE 0 * TECHNOLOGY SCHOOL OF CHEMICAL ENGINEERING PRACTICE

AT OAK RIDGE NATIONAL LABORATORY

EXIT C0 2 CONCENTRATION VS TMP&IER SPEED FOR DIFFERENT SOLIDS LOADINGS

OATf 10-22-79

DRAWN BY RPH

FILE NO. DEPS-X-300

Fie.

17

5. Conclusions

1. Ba(OH) 2 has a much greater C0 2 removal efficiency than Ca(CH) 2-2. It Is possible to model Ca(0H) 2 slurries by accounting for both the Interfaclal area and degree of mixing as functions of the hydrodynamlc

parameters. 3. Ba(OH)? slurries cannot be characterized by using simple plug-flow

or backmixed models. 4. Ba(0H) 2 slurries produce an Increase In COg removal efficiency with Increasing solids concentration, wherecs the opposite behavior Is

noted for Ca(0H) 2 slurries.

6. Recomnendatlons

1. A better knowledge of residence-time distributions of the gas phase in the agitated contactor is necessary when attempting to correlate interfacial areas in slurry reactors.

2. Additional Ba(0H) 2 data are needed to better characterize system behavior. 3. Relationships for mass transfer coefficients as functions of hydro-

dynamic parameters of the reactor are needed to improve modeling of slurry systems.

4. Improvements in the reactor design could be made by placing the sparger closer to the impeller to avoid gas bypassing and Increasing dead height above the slurry surface to reduce entrainment of Ba(OH). foam.

7. Acknowledgment

The authors thank their consultants, 6.L. Haag, D.U. Holladay, and O.F. Green, for their guidance and Inspiration, who always gave generously of their time, assistance, and moral support.

18

8. APPENDIX

8.1 Carbonation Rate and Interfacial Area Expressions

The rate of reaction of C0 2 in the liquid film is given by Dankwerts1

surface renewal theory (3):

Ra = Kp a Pj (14) where

KR = H ^Dco ^ [ O H M + K * R - specific rate of absorption of CO2, gmol/cnP-s a = interfacial area, cm^/cm* H - Henry's coefficient of solubility, gmol/cm^-kPa

Dco 2 = diffusivity of CO2 in aqueous solution, cm2/s K2 = second order rate constant, cmtygmol-s

[0H~] = hydroxide concentration, gmol/cm3

Kf_ s liquid side mass transfer coefficient, cm/s Pj * partial pressure of C0 2 at the gas/liquid interface, kPa

The rate of reaction In the liquid must be balanced by the rate of trans­port of CO2 through the gas film at steady state (8):

Ra - Kga (P 6 - P,) (15)

where Kg Is the gas side mass transfer coefficient (gmol/cnl-kPa) and Pg 1s the partial pressure of CO2 in the gas stream (kPa). Eliminating Pi from Eqs. (14) and (15) gives:

to * [1 • ( V K 6 ) 3 8 PG "" Kl 3 P6 ( 1 6 )

19

where Kj is a pseudo first-order rate constant, gmol/c«2-kPa-s. The par­tial pressure of CO2 can be related to the total pressure by

PG - * P a v g 07)

where x is the mole fraction of CO2 in the air stream and P is the average pressure in the contactor, kPa. Combining Eqs. (KT and (17) we obtain:

R a = Kl a Pavg x { 6 )

Under the assumptions that the liquid phase is well-mixed and that the gas travels through the contactor in essentially plug flow, we can write the following differential mass balance on CO2:

-6 dx = RaA dz (18)

where G is the molar gas flow rate (gmol/s), A is the contactor cross-sectional area (cm2), and z is the vertical height in the reactor (cm). Combining Eqs. (6) and (18) and integrating between initial and final conditions yields the equation given previously:

1n(£) = aa (9)

Treating the gas phase as n equal-volume CSTR's in series [as opposed to an infinite number which is implicit in the development of Eq. (9)], one can easily obtain:

rf • " + i r > " <"»

8.2 Physical and Chemical Properties

8.2.1 Henry's Law Constant At 20°C the solubility of Ba(OH) 2 in water is 5.6 g/100 g water;

therefore, the concentration of the OH" ions is 0.355 M. The Henry's Law solubility constant for CO2 in pure water (H 0) at 20°C is 3.9 x 10-7 gmol/cm3-kPa (3_). The correction for the effect of ionic strength or Henry's constant is (3):

20

log({{-) - -h I (19)

where h is the sun of contributions referring to the species of positive and negative ions present, and I is the ionic strength of the solution defined as:

I - \ I C t Z* (20)

where Cj is the concentration of ions of valence Zj. Using these values for h from DanckMerts (4), h = 0.115 and I = 0.532, and substituting into Eq. (19), H was found to equal 3.4 x 10-7 gmo1/cm3-kPa,

8.2.2 Rate Constant (IU)

The reaction between CO2 and OH" is

C0 2 + OH" - ^ > HCOJ (21)

and the rate expression is

R * K2[C02]C0H"3 (22)

At infinite dilution the rate constant in pure water K2 is 5900 i/gmol-s at 20°C (4). A correction must be made for the ionic strength of the solu­tion, using Fig. 6 in Oanckwerts and Sharma (4):

Kg = KJ + 3200 I (23)

where I is the Ionic strength. Therefore, the corrected rate constants are:

Ba(0H) 2: K 2 * 7600 A/gnol

Ca(0H) 2: K 2 * 6050 A/gmol

21

8.2.3 Diffusivity

The diffusivity of C0 2 in water at 20°C when the viscosity is 1.1 x 10~ z g/cro-s was found to be (13):

Dco 2 = 1.4 x 10" 5 cm 2/s

8.2.4 Mass Transfer Coefficients

The liquid-side mass transfer coefficient for CO2, K L, was estimated byJuvekarand Sharma (.7) to be:

K L = 6.5 x 10" 2 cm/s

This value was constant over the. range of experimental conditions considered. The gas-side mass transfer coefficient for CO2, KQ, was estimated from measured values of Kga, where a is the interfacial area. Values of this product are approximately 10~6 gmol/cm3-s-kPa (_7). I f the interfacial area is assumed to be 2 cmZ/cnr.the value of KQ is aboit 5 x 10-7 gmol/cmZ-kPa-s.

8.2.5 Viscosity and Density The slurry densities were measured by making up the appropriate

solution vol unethically and weighing the solution. Viscosities at 20°C were measured with a Brookfield viscometer fitted with an ultfa-viscosity spindle Which rotated at 60 rpm. The results are shown in Table 3.

Table 3. Viscosities and Densities Solution % Solids Dens ity (g/cm3) Vi­scosity (10-2 g/cm-s)

0.5 M Ca(0H) 2 3.64 1.018 1.099 1.0 M Ca(0H) 2 7.14 1.038 1.210 1.5 M Ca(0H) 2 10.56 1.056 1.484 0.4 M Ba(0H) 2 11.86 1.064 1.150 0.75 M Ba(0H)o 21.11 1.121 1.200

Tc

8.3 Data and Computer Analysis

Three computer programs were written to analyze the data. Two were statistical analyses programs, while the third placed the data into a form convenient for analysis. The first program listed was the program used to calculate interfacial areas and decontamination factors (DF). Data were read in free fonnat from a data file, in this case F0R21.DAT. Calculations of interfacial area and DF were stored along with the initial data in a new data file, F0R22 DAT, which was compatible with the statis­tical programs. Separate versions of the program were made for the barium hydroxide data, the 1979 calcium hydroxide data from this study, and the calcium hydroxide study of Sheppard et al. (15), along with separate sets of data files. The original data and the calculated inter­facial areas obtained by using ideal reactor models are tabulated in Table 4.

The other programs were written to use the Statistical Analysis System (1_) package available on the IBM 360 computer at ORNL. The second program listed attempted to correlate interfacial area using a General Linear Models Procedure (GLM). The GLM program used a multiple linear regression to fit the data to the specified model. In addition, a step­wise regression procedure was used to find the collection of independent variables that best fit the data. The third program used a nonlinear regression procedure to fit the data to a n-CSTR's-in-series model. The program produces least-squares estimates of the parameters of the non­linear model specified.

23

1. Program 1

TYPE CALCBA.F0R OOIOO OOPOO 00300 00400 00500 00*00 00700 00800 00900 01000 0 1 100 01 POO 0 1300 0 1 4 0 0 0 1 5 0 0 0 1 * 0 0 0 1 700 01R00 0 1900 OPOOO 0P100 02200 OP.100 0P350 OP 400 0P500 0 2 * 0 0 0P700 OPROO 0PR50 02900 0 3000 0 3 1 0 0 0 3P00 0 3 3 0 0 03350 0 3 4 0 0 0 3500 0 3600 0 3700 0 3R00 03900 0 4000

04100 04P00 0 4300 04400 04500 0 4 * 0 0 0 4 f 2 0

C*** C*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** r,*** c*** c*** C*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c*** c***

THIS PR0GRAM CALCllLATFS INTFRFACIAL ARFAS CI.A.'S) F0R BA(0H)2 SLURRIES BASF!) UP0N TV0 M0DELSS

1. PFRFFCT BACRMIXING ( 0NF CSTR) P. PFRFFCT PLUG FL0<J

THF THF0RETICAL DEVELOPMENT IS DFTAIl FD IN CFPS-X-^OO THF VARIABLES AIRDEN AIRPT ALPHA AMIX = APLHG = C0PIN = C0P0HT = DC0? = DIMP = FL0I-' HEIT = HEITC = HENRYS =

USFD ARF: DFNSITY 0F AIR CG/CC) M0LECULAR VEIGHT 0F AIR CG/G-M0I.) A RATI0 0F RFACTI0N RATF T0 GAS FL0<-' RATF. (CM)

BACKMIXED IN1FRFACIAL AREA {CMP/CM3) PLUG FL0V 1NTERFACIAL ARFA (CMP/CM3) INLET C0P C0NCENTRATT0N CPPR) 0IITLFT C0? C0NCFN1RATI0N (PPR) DIEFUSIVITY 0F C0P IN AOUE0IIS S0LIITI0N (CMP/S)

IMPELLrR DIAMFRFR (CM) V0LUMETRIC FL0V RATF Cl./MIN) AERATED HEIGHT IN C0NTACT0R CC*»> UNAGITATED SLURRY HFIGHT (CM) HFNRY'S C0EFFICIFNT 0F S0L1IBILITY

CG-M0! /CC-ATM)

(/MIN)

(G-M0I /CD

C***

IDF = DEC0NTAMINATI0N FACT0R IRPM = RFV0LUTI0NS PFR MINUTF 0F THF

AGITAT0R IRIIN = DATA P0INT NUMBER NPTS = NUMBFR 0F DATA P0INTS 0H = CONCENTRATION 0F HYDR0XIDF PERS0L = PERCENT S0LIDS IN SLURRY S0LHTI0N PIN = INLFT CAS PRESSURE CPSIG) PAV = AVERAGE GAS PRESSURF IN RFACT0R (ATM) •S = CR0SS-SFC7I0NAL AREA 0F C0NTACT0RCCM?) SLUfcY = SLURY "PSFUD0 MOLARITY" (M0L/1 ) VA = AERATED V0LIIMF (CO VISC = VISC0SITY 0F SLURRY S0LUTI0N (CP) XKG s GAS SIDE MASS TRANSFER COEFFICIENT

0F C0P (G-M0L/CMP-S-AT*) XKL = LI GUID SIDE MASS TRANSFFR

C0EFFICIFN1 0F C0P (CM/^y XKR S A LUMPED RFACTI0N C0NSTANT (G-W0L/CMP-S-ATW) XK1 = PSFUD0 FIRST 0RDFR KATE C0NSTANT

(G-M0LA:MP-R-ATM> XX? = SEC0ND 0RDFR RATF CONSTANT (CC/G-M0L-S)

DATA A I R r F . N / ' . O O l ? O 5 / # A I R 1 ' , T / ? R . 9 * 4 / , C 0 P I N / 3 . 3 F 5 / # ! D C 0 ? / 1 . 4 E - 5 / , H F N R Y S / 3 . 4 O F - S / , 0 W / 3 . 5 5 F - < 4 / ' , S / 5 R S . / , ? X K r , / 5 . E - 5 / > X K L / * . 5 F - ? / , X K ? / 7 . * F * /

XKR = HENRYS * SORT( DC0? * XKP * OH • XKL* *? ) XKJ = XKR / ().") * XKR/XKG)

N0TF» PRFSSURF AH0VE C0NTACT0R MAINTAINFP AT 1.5 PSIG

24

0 * 6 4 0 C*** ME ASSUME PRESSURE T0 BF DUE T0 0NLY THF HYDR0STATIC 0 4 6 * 0 C*** HEAD 0F VATER IN THE C0NTACT0R. 0 * 6 8 0 PAV = N I 15 0 4 7 0 0 READ ( P N 1 0 ) NPTS 0 4 R 0 0 10 FORMAT C I ) 0 4 9 0 0 D0 1 0 0 J a N N P T S 0 5 0 0 C READ < ? 1 , P 0 ) I R U N , DIWP, IRPM, SLURY. P I N . FL0V, H F I T , 0 5 1 0 0 1HE1TC, C0P0UT 0 5 P 0 0 ? 0 F0RMAT C I » E , I , 6 E ) 0 S 4 0 0 VA = S * HFIT 0 5 5 0 0 ALPHA = 0 . 0 6 * XKI • PAW * VA * AIR^T/CFI 0«-» * AIRPEN) 0 5 6 0 0 C*** CALCULATE INTFRFACIAL AREA F0R PLl'G FL0V M0PFL 0 5 7 0 0 APLUG = AL0G(COPIN/C0P0I>T)/ALPHA 0 5 B 0 0 C # * * CALCULATE INTFRFACIAL ARFA FOR RACKMIXFD M0PFL 0 5 9 0 0 AMIX = CC0PIN/COP0UT - NO) /ALPHA 0 5 9 3 0 IF (SLURY . E O . 0 . 7 5 > RH0 = N 1 P 1 0 5 9 6 0 IF (SLURY . E O . 0 . 4 0 ) RHM = 1 . 0 6 4 0 6 0 0 0 IF (SLURY . F O . 0 . 7 5 ) PERS0L = 0 . P 1 1 1 0 6 1 0 0 IF (SLl !RY .EO. 0 . 4 ) PFRS0L = 0 . 1 1 R 6 0 6 P 0 0 IF (• SLURY .EG. 0 . 7 5 ) VISC = NPOO 0 6 3 0 0 IF (SLURY . E G . 0 . 4 ) VISC = N 1 5 0 0 6 4 0 0 C * * * CALCULATE DECONTAMINATION FACTOR 0 6 5 0 0 IDF = C0PIN/COP0UT • 0 . 5 0 6 6 0 0 C * * * ST0RF DATA IN F0RPP.DAT FOR ANALYSIS BY SAS F-R0GRA* 0 6 7 0 0 V'RITF(PP. 3 0 ) I R U N , IRPM, FLO'*, DIMP. RHO, PFRS0L. V I S C , 06«*00 IHEITC. H F I T . I D E , ALPHA, API UG, AMIX 0 6 9 0 0 3 0 F 0 R M A T ( I 3 , I 4 , F 5 . N F S . | » F 6 . 3 , F 6 . 4 , F 6 . 3 . P F 5 . I . I 5 . F R . 4 . 0 6 9 5 0 I F 5 . P . F 7 . P ) 0 7000 100 CONTINUE 0 7 1 0 0 ST0P 0 7 P 0 0 END

2. Program 2

4 1 7 ) , f B I N P . K . P . PATCH* / / • C L A S S CPU9N40S ,PRINT=*>0 ,CARPS=99 , 1 0 = 3 / • R 0 U 1 E PRINT LOCAL / / EXEC SAS76 / / S T F P L I B DP DSN=A.F . IN1o307 .SAS.LIBRARY.PISP-SHR / / S A S . S Y S I N PD • * • * THIS PROGRAM CORRELATES HY0ROPYNAMIC PARAMFTFRS *'ITH

INTFRFACIAL ARFA AND PLOTS THF RFSULTS. IT ALSO ATTEMPTS TO FIT THF PATA TO THF BFST EMPIRICAL MODEL.I

*** THE BULK 0F THF PROGRAM CONTAINS MISCFLLANF0US CORRELATIONS FRO* CFPS-X-PR1 (197R)I

DATA IHTFPi *••

25

RFAD VARIABLFS FROM Di TA F I l . F : FXPFRIMFNTAL RUN. SPFFD CRPM>; GASFI.0W RATF C L / M I N ) , IMPFLLFR DIAMFTFR C O W RM0 <G/CC)» FRACTIONAL PFRCFNT SOLIDS I N SLURRY* SLURRY VISCOSITY CCP>» 'UNAGITATFD SLURRY HEIGHT CCM), AFRATFD SLURRY HFIGHT fCM>» DECONTAMINATION FACTOR, ALPHA CC.M), PLUG FLO* INTFRFACIA1. ARFA CCMP/CO* BACKMIX INTFRFACIAL ARFA ( W / C C ) t

INPUT RUN 1-3 RPM * - 7 GASFLOI-' R - I P I^PPIAM 13 -17 RH0 1B-P3 PF.RS0L 9*-?9 V ISC 3 0 - 3 S 0FFMT 3 * - 4 0 AFRHT i» l -^S PF Af-SO ALPHA 51-SB APLUG S 9 - * 3 AMIX * 4 - 7 0 t AGF = l ; I F -N«* > 9 * THFN AGF = 9\

*** t»F ARE GOING T0 F I T A LINFAR M0PFL T0 THF FXPFRIMFNTAL

DATA USING AN FOUATI0N 0F THF FORM: LNCIARFA) = A LNtRPM) • B LNfGASFL0W) . . . ;

* * * C0NVFRT GAS FL0*«' RATF T0 SUPFRFICIAL VELOCITY CCM/S>» FL0K = GASFLO*'! It = GASFLO* * . 0 ? R 4 9 ! * * * CAl CULATF THF RFYN0LDR NUMBER! RFYN=IMP3IAM*IMPPIAM*RPM*RH0/VISr /*O» * * * CALCULATF THF FR0UDF NUMBFRj FR0UPF= IMPPIAM*RPM*RPM/3A00/9R0» * # * C0NVFRT RPM T0 REVOLUTIONS PFR SFC0NPJ RPS=RPH/fiO* * * *

CREATE A PIMENSI0NLFSS VARIARI.Ff NPSV = IMPPIAM*RPS/Ui * * * TAKF LOGARITHMS 0F THF V'ARIABI.FS T0 BF CORRFI ATFP» * * * IMPFLLFR SPFFDl LNRPS=L0GCRPS)» * * * IMPELLFR DIAMFTFRl L N DIAM=L0G<IMPDIAM) | * * * SUPFRFICIAL VELOCITY! LNOG=L0G(U)I * * * INTFRFACIAL AREA F0R PLUG FL0V MODEL! LNAPLHGsL0GCAPLUG)» **# INTFRFACIAL ARFA, RACKMIX ASSUMPTION! LNAMIXeLOG(AMIX)! * * * REYNOLDS NUMBER! LNRFYN=L0G<REYN>! * * * V ISCOSITY! LNVISC«LOGCVISC>! * # *

26

NF.P DIMENM0NLFSS VARIABl.Fl LNNDSV=L0G(NDSV)I * * * FR0MPE NUMBERS LNFRs L0G<ER0UDE)t * * * PFR CENT S 0 L I D 5 I LNPFRS0L=L0G<PF.R50L> I * * * DFC0NTAMINATI0N FACTOR! LNPF = L0G(PE) f * * * RFAP I N DATA I CARDSl =F0R1P.DAT*

• * * PFRF0RH THF LINFAR M0PELS PR0CEDUREI FR0C GLW PATA= IHTFPl

H0DEL LNDF LNAPLUG LNA*IX=LNRPS LNOG LNDIAM LNPPRS0L t eiiTPirr 0UT= RESULTS PRFDICTFD= CDF CAPLUG CAHTX RESIDUAL* RDF RPLUG RMIXl TITLE PL'SCELa" C0RRFLATI0NI

* * * PRINT THF RESULTS* PR0C PRINT; * * * MAKE SUBSETS 0F THF RESULTS F0R PLOTTING* * * * KAKF PL0TS 0F RESULTS* PR0C PL0T DATA = RFSIILTS I

PL0T LNAPLUC*CAPLIIG=RP* LNAPLUG*CAPLMGsFI 0M l.NAPLUG*CAPI UG=AGFt T I T L f l PL0T 0F L0G INTFRFACIAL ARFA (PLUG GASFL0f) VS . C0RRFI ATI0N*

PR0C PL0T DATA = RESULTSI PL0T LNDF*CDE=RPH LNDF*CDF=FL0<-' LNDF*CDF = AGFt T I T L F l PL0T 0F L0G DFC0NTAMINATI0N FACT0R VS. C0RREI ATI0N»

PR0C PL0T DATA * RESULTS1 PL0T LNAf IX*CAHIX=RP* LNA*IX*CA*MX=FI.0V LNA»MX*CA»*IX = AGEl T I T L F l PL0T 0F 1.0G INTFRFACIAL ARFA CBACKMIX) VS. C0RRELATI0N> PL0T RPF*RP*=FL0' ' RPLIJG*RPM=FL0w RWIX*RPf*=FL0' r» T I T L F l PL0T 0F RFSIDHAL VS. RPH BY FL0V RATFSl

* * * I FR0C GLW DATA* IHTFPl

H0DEL LNAPLUG* LNFR LNNPSV LNPFRS0L/PI 0IITPUT 0UT = INT PREDICTED* CAPLUG RESIDUAL-- RFSIDl TITLE PLUGEL0*-' C0RRFLATI0NI

PR0C PL0T DATA* INTf PL0T LNAPLUG*CAPLUG=RP*I T I T L E I PL0T 0F L0G INTERFACIAL AREA VS. C0RRFLATI0NI T ITLE? INTERCEPT INCLUDED IN C0RRELATI0NJ

* * * I PR0C GLf* DATA* IHTEPl

H0DEL LNAPLUG* l.NRPS LNOG LNPFRS0L LNPIAM/Pi 0UTPIIT 0UT* N01NT PREDICTED* CAPl.UG RESIDUAL* RFSTDl TITLE PLUGEL0'-' C0RRFLATI0NI

27

PR0C PL0T DATA= N0INTI PL0T LNAPLIIG*CAPLUG=RPMJ TITLEl PL0T 0F L0G INTERFACIAL AREA VS. C0RREATI0NI TITLE? INTERCEPT WAS N0T INCLUDED IN CORRELATION!

*** i PR0C GLM DATA= IHTFP» MODEL LNAPLUG= LNRPS LNOG LNPERS0L / N0INT Pl TITLE PLMGFL0W C0RRELATI0N»

*** t PR0C GLM DATA= IHTFP; MODEL LNAPLUG= LNFR LNRFYN LNNDSV LNPERSOL/Pl TITLF PLUGFL0H C0RRFLATI0N. DIMFNSI0NLFSS VARIABLES*

* * * f PR0C GLM DATA* IHTFPi

M0DEL LNAPL!I6= LNREYN LNNPSV LNPERSOL/Pl TITLE PLUGFL0W CORRELATION. REYNOLDS N0.» SMPF' ICIAI GAS VFL. . AND PERCFNT SOLIDS.*

* * * USE THE STEPWISE PROCEDURE T0 FIND THE RES M PR0C STEPWISE DATA= IHTFPI

M0DEL LNAPLUG= LNRPS LNGG LNDIAM LNPFRS0I. / MAXRi M0DEL LNAPLUG= LNRFYN LNFR I.NOG / MAXRl

/ * / / F.NDINPUT

3. Program 3

TYPE NLBA../CL / / f A S 3 J0B d * 4 | 7 ) , ' R I N P» K . D . PATCH' / / • C L A S S C P U 9 I = * M , I 0 = P /•ROUTE PRINT L0CAL / / EXEC SAS7* / / S T F P L I B DD PSN=A.EjN10.107.SAS.LIBRARY>DISP=SHR / / S A S . S Y S I N DD * * * * PR0GRAM T0 CORRELATE INTERFACIAL AREAS AND DEGREE 0F MIXEDNESS FOR 1979 RA(0H>2 DATA • • •

VARIABLE DESCRIPTION UNITS

A INTERFACIAL AREA (CMP/CM.1) AlftFLOf AIR FL0*'RATE AT STP (L/MIN> ALPHA A RATIO OF REACTION RATE

T0 GAS FLOW RATE (CM) OF DECONTAMINATION FACTOR HEIT AGITATED SLURRY HFIGHT (CM) IMPDIAM IMPELLER DIAMETER CCM) N N0. 0F CSTR'S IN SFRIES PERS0L PERCENT SOLIDS RPM AGITATOR SPEED (RPM) RUN RUN NO. U SUPERFICIAL VELOCITY (CM/S)

28

• * • RFAD VARIARl.FS FROM PATA F1I.F« OATAl INPUT R«W l - . l RI'K * - 7 A IRF I .0 ' ' R - l ^ IPPPIAH 1 3 - 1 7 PFPSBL J>*-?9 MFIT Jk\-A<\ PF a * -SO ALPHA S I - S R i # * * IISF. I N BF DFC0NTAKINATI0N FACTOR FOR CORRFI.AT tONl LNDF = L8CCPF)« * • * CALCW.A1F SHPFRFICIAI VFLOCITt F R 0 * AIRFLOW AND CONTACTOR CR0SS-SFCTI0NAL ARFA CSFS C*P> » H = A I k F L 0 y * O . O ? R 4 9 l • • * CONVFRT RPM TO RFSl RPS = RPM/*O.Ol CARDS! =FPR??.PAT» t *** TANKS IN SFRIFS K0DFI.:

P0ST»iLATF C0NTACT0R CAN RF M0PFI FO AS N-CSTR'S I N SFRIFS . CORRFLATF ' N * AND 'A* AS F A C T I O N S 0F THF HYPR0PYNAKIC VARIAPLFS. I

* * • N 0 1 F : THF IKPFLI.FR PIAMFTFR VAS NOT VARIFO AND I S THFRFF0RF NOT INC1.HPFD I N THF M0PFI 1 I R 0 C N L I N ITFR=SPO fFTH0D=KARRHARPT1 PARA*F1FRS A 0 = I . B F 9

A l = * . . 1 A ? = - ? . 0 A.1=0.9SP NO=0..1??S N I = - O . R S 9 N ? = - C ? P S N T r - p . | 4 t

R0IINDS AO>0 NP>Pl * # * P0S1MLA.1F EMPIRICAL RFLATI0NSHIPS AS F0l.l.0>-'Sf A = AP*CRfT.»*An*CH»*A5>>*(PFRS0J * * A 3 > I N = N O * r N r S * * N I ) * < H # * N ? ) * f f'FRSOl • *N.1> » GAMMA = ALPHA«A/NI GAMMAPI = GAMMA • I .O» DFRA = (ALPHA/GAMMAIM)*At PERN = (LOGCGAMMAPI) - fAMMA/GAMMAP1>*Nl M0PFI. LNPF = N»L0G<CAMMAPl>» DFK.AP=OFRA/APl PFR.AlxPFRA*L0GCRPS)( DER.A?*DFRA*l .0f <ll> I DFK.A:UDFRA«L0G< PERSBL)t DER.NO=DEKN/N0» nFR.NIxPFRN*L0C<RPS)l DER.N? = DERN*I OGCH) » DFR .N.1spERN«L0GC PERS0L ) I ei lTMIT 0HT«CSTR PKEPICTEP=LNPFl KFSIP'IAI. = RFSI 0

PARMS*M-f 'Hf DATA RESULTS! SET CSTRl ARFA»» ' l *CKPS** r '? ) *< l '« * r .1>*CPFRS0L«*PA>l N C S T R * r S * C M ' S » * f ' * > * O l * * p 7 > * < r F R f . 0 l . « * P R > l PR0C PRINT DATA»RESMLTSi I'ROC PLOT DATA«PFSHl.TS»

PI.0T LNnE*LNDEI»RPSl I.Aflfl I.NPE»L0G DECONTAMINATION FACTOR

LNPE|»L0G DECONTAMINATION FACTOR (PREDICTED) I T I 1 L F I.OC DECONTAMINATION FACTOR ACTUAL US. PREDICTED! T I T L E ? N - C S T P " S I N SFRIFS MODEI 1979 PA(OH>f> DATA!

I ROC PLOT 0ATA«RFSIII.T5l PLOT RESID*I NPFlsRPS RFSI D*LNDF l»AIRFI .0 ' '»

/ * // ENPINrnT

55255 3s55= sees* s*s8e JBSSSS SXCSS- JCCKSS s«i*e «SSI;K sscs;= P?

ssSSs ggggg ggggg ggggg ggggg ggggg ssssg SSSgg ggggg ggssg Sf|

22222 gasae s s s tit 22 22:ae ?! # W W —-—* — — »J ** *w •>* *» * * ^ W W W %»—»—•—•-* w .* O O O O t ^ t/« W v< 0* 4T» « 0> O O O O O O O O - w — '*><BQ»a»b OOOV>W< tf****^*-*^- ' — » » < * » feffs

k l i 2. ft

F « * ( -O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O ) 2 w C *"* 0BCV999 o*o*w»^o* o t ^ f r w ^ 0*0*90000 ootttDccff OB as o» oo OD oftflpQBtpoB ffSSSfi S f i v f i S S 5 5 $ 5 t *y* ..**

ooooo ooooo ooooo ooooo ooooo ooooo ooooo ooooo ooooo ooooo oo ooooo ooooo ooooo ooooo ooooo ooobb

? s * sm% s£s*s nm ggg** mu *mt g»t2 52525 55555 55555

!i-| * > » Z.

mn mn mn Htn m i l sisif iisis ssssi Ssssi sssss ^fj

SSasi? 3S3SS "<*»?? S S S ^ |2|5»2S SS2SS oSSS^ SSSSg S » " * 5 »?S2S t c f c t i u M o a b i n v w - i o c » ' » t - » b o « i > w b a ' o v i n i>'s'a*>» '.->"ou>"oU w b i r w o N N O ' O O U w b u u

* - 5??SS

Mil J

iiili iiiii sfiit lilil Islii illil fills isili Hill iiiii tt ft — *•

o o —— — o ———o -- — © o o o o o * » ~ — — — — — — — — — o o o o o - —-* — — — —o — — o o o o o o lg£ » *

sssss sss=* sk iss SSJ582 Vssss s'sksis ssij's's i i ' sks essss ssssi: |2ss

< a » u » ' « « m o » « » ~ o A ^ s u i w » ^ a « . N S W B * ! ° £ a v j.>o--t*.». w « , ~ - ~ * * > S S S > . I f f j * * * S S S 8 Swiss's SSSSS SSSbs 8SSSS SSJRS^ 5"S"='2S 8 2 * 2 3 sbizkit S k s s k % | * : |

62

223*22 g§3»g ~22S= ggg«« a«=se S55SJ? Stcns SSKSS 55=25 l*f £

SoSgoS SoSoo gggois goSoS SoisSo SSoSS SSoSg ggggg SSoog Ifff f

3333** **22S rPPPP fS?3?* ***jS8 8800© ????? So!??? r"-?p *O<0*0«4rut Vttft^i^t^i ^ O N » ^ « K *0«e«P«fi>iD « ' « ' « ' 0 0 O O f V ^ N rs*'— — —'_- tiv*v>0>O O O O * *

(Iff J

kit i

iiiili iiiii iiiii iiiii iiiii iiiii §H§§ iiiii iHH Iff o o o o o o o o o o o o o o o o o o o o o o o p o o o o o o o o p o o o p o o o o p p o o o ssgggg isISi gggss 5552= J5555 55555 ;*£** ***** 2SH2

* * * * * * * * * * * * * * * * ro *V *> *•> *•> •VN'J'VM IS) <s» »s* •-.» fM *t> O O O O O O O O O O O O O O S S S S S S S S S S S S S S S S o o o o o o o o o o o o o o o o«<o*o<0 « « « « « *ow>«.»lS

t*?« tf> O O O O O O O O t * * lf»*4

ssSStiS 33833 -SSSp rr*?r P P * - * 5 ?S883 •8288 S83S2 pSSSS |gf f~

% . u ^ <.o.S^= . 5 5 s S . » , . : =.o.£2 5-XSS Si--—- 2C=^S S^sSS H I

iiliil iiiii mi llllllilll iiiii iiiii IIIII iiiii Ef -o —— o o o o o o —— — — — — — — — — — o o o o o —— — — — — — — — — — o o o :sbb:s s's'sss si'sxs V s s s s s'ssss s'ss'si: side's: sb's'ss i'l

HI M A I U O U U O O O » * » * 0 t *>K»*>Uf — U M O B t J * * —' *W — . * J M « ^ - s l 5 m * M V > U N * ( » * > « • — - 4 — * D B S " ^ O W W

» Q B * * > 0 ^ * t f «

n y w * «

0£

i

*S SSSiS 28RKS SCSSt £*S*S 55SSW . s sis sssss ssYis sssss sssss sissies

* 0 » 9 V W U U W W W t X V * «f*l/»0»9><F> ff> tn «/> <\t-/* W W O U» *

o* u» Z u » ? S w S <£ES w

SSS SSSSS SSSSS

I?? B

P? 2

?2t£ -4 — * 0 » V O D a O D S f ^ t ^ ^ f ^ f ^ i i S f " -

W W W W W W W W W W W U l W V# •«« ^rf -s^ -«J *«* « J -W * * - « * * * - * - *

s i !

sg SSSSS SSSSS SS5~ •St *W *V *V *V *V *V *V *N* *V 222 ggggg ggggg : ? 2

S i ?

o o o o o o o o o o o o o o o o o o o o o o o o o o o SS SSSSS SSSSS SS:

O Q O O O O O O O O O O O o o o o o o o o o'o'o'o'o g=*

—• —* — — ^ — — — - w - . . ^ . . —•-~fWf\)«U I M M M M ^ »W*»A»*W»*»

SS SSSSS SSSSS SS888 88888 88888 «\*ru*» IS* IS* f\» KJ «S» <\» <\> <\» <\> i\> l a O O O O O O O O O O O O O j n

#

o » ^ ^ o o o o oot»a>o» *=-xn*

o«a *««««• •» **aia»ou» t ^ « v o i « A Q O B N U * O O * J O

O 0 * O OE»O<0<0*B 0 « t P C B t S SB w t*» W B O N O W t * O O

X V»<D

N»»» — —

£ sssss S*Sss ISSiS sgSSs sssgs ;=~ -ssss Sssss ^ - ^ PM

— — —* —• w w w *•* &»•*•**•** t >

I'll lli'll III'II« rr r?PP? ????? ?9rrr r???p PPPPP rrr ?rr?? PPPP? SS 3322* SSSSS SSS^K SS^SS SSSSS

SS*2 R2~2£ =SSSS SXXSSE » ::s«ss ssx's's i ssss s'rissg — —. ow«»gt<o — « o * » ^ - *

«O<0 - s * » t » 0 a t - » O C » M * > I«

le

32

8.4 Location of Original Data

The original data are found in ORNL Databook A-9177-G, pp. 1-31, on file at the MIT School of Chemical Engineering Practice, Bldg. 1505, ORNL.

8.5 Nomenclature

a gas-liquid interfacial area, cm^/cm3

A contactor cross-sectional area, cm 2

[C0 2] concentration of C 0 2 in liquid, gmol/cm3

Deo- diffusivity of COp in aqueous solution, cm2/s DF decontamination factor [x /xf)

dj impeller diameter, cm G molar gas flow rate, gmol/s h sum of contributions effecting ionic strength [Eq. (19)]

3 H Henry's coefficient of solubility, gmol/cm -kPa H Henry's coefficient of solubility of C0 2 in pure water, gmol/cn^-kPa I ionic strength of the solution K, pseudo-first-order rate constant, gmol/cm^-kPa-s

3 K 2 second-order rate constant, cm /gmol-s Kg gas-side mass transfer coefficient, 9 --kPa K, liquid-side mass transfer coefficient, cm/s K- a 1< wiped reaction constant, gmol/cnr^-s-kPa K° second-order rate constant in pure water M W * molecular weight of air, g/gmol n number of equal-volume CSTR's in series N impeller speed, rps [OH'l hydroxide concentration, gmol/cm

33

P power dissipated per volume of liquid, hp/ft3

P_ average pressure in contactor, kPa avg P- partial pressure of CO- in gas, kPa P. partial pressure of CO- at gas/liquid interface, kPa Q air flow rate at STP, i/min

3 R specific rate of absorption of CO-, gmol/cm -s S weight fraction solids U superficial gas velocity, cm/s U. velocity rise of bubbles, cm/s

3 V a aerated volume in contactor, cm Q

x mole fraction COg in gas stream x f mole fraction CO- at contactor outlet x A mole fraction CO- at contactor inlet o 2 z height in contactor, cm Z. valence Greek Symbols

° ' 0 6 x Kl Pavg Va " a l r ^ 'air' c m

v liquid viscosity, 10" 2 g/cm-s 3 p liquid density, g/cm

3 p f t i r air density, g/cm S 2

a surface tension, 10 J/cm or g/s

8.6 l i t e r a t u r e Referenced

1. Barr, A.J., J.H. Goodnight, J.P. Sail, and J.T. Heiwig, "SAS Users Guide," SAS Ir^Mtute, Raleigh, N.C. (1979).

2. Calderbank, P.H., "Physical Rate Processes in Industrial Fermenta­tion, Part I: The Interfacial Area in Gas-Liquid Contacting with Mechanical Agitation," Trans. Instn. Chem. Engrs.. 36, 443 (1958).

34

3. Danckwerts, P.V., Gas-Liquid Reactions, McGraw-Hill, New York, 1970.

4. Oc»nckwerts, P.V., and M.M. Sharma, "The Absorption of Carbon Dioxide into Solutions of Alkalis and Amines (With Some Notes on Hydrogen Sulphide and Carbonyl Sulphides)," Chem. Engr. (London). October, 244 (1966).

5. Holladay, D.W., "Experiments with a Lime Slurry in a Stirred Tank for the Fixation of Carbcn-14 Contaminated COo from Simulated HTGR Fuel Reprocessing Off-Gas," 0RNL/TM-5757 (1978).

6. Holladay, D.W., and G.L. Haag, "Removal of ^-Contaminated CO? from Simulated LWR Fuel Reprocessing O^f-Gas by Utilizing the Reaction Between CO2 and Alkaline Hydroxides in Either Slurry or Solid Form," 15th DOE Nuclear Air Cleaning Conference, p. 30 (1978).

7. Juvekar, V.A., and M.M. Sharma, "Some Aspects of Process Design of Gas/Liquid Reactors," Trans. Instn. Chem. Engrs., j>5, 77 (1977).

3. Juvekar, V.A., and M.M. Sharma, "Absorption of COo in a Suspension of Lime," Chem. Eng. Sci. ; 28, 825 (1973).

9. Levenspiel, 0., Chemical Reaction Engineering, 2nd ed., Wiley, New York, 1972.

10. Mehta, V.D., and M.M. Sharma "Mass Transfer in Mechanically Agi­tated Gas-Liquid Contactors," Chem. E.g. Sci., 26, 461 ',1971).

11. Miller, D.N., "Scale-up of Agitated Vessels Gas-Liquid Mass Transfer," AIChE Journal, 20, 445 (1974).

12. Morris, R.M., and E.T. Woodburn, "Testing of Certain Design Equa-tiors for Predicting the Performance of a Calcium Hydroxide Carbonation Reactor, Part I: Gas Bubble Dynamics and Interfacial Areas in a Stirred Reactor," S.A. Chemical Processing, June-July, 88 (1967).

13. Perry, R.H., and C.H. Chilton, Chemical Engineers' Handbook, 5th ed., McGraw-Hill, New York, 1973.

14. Reith, T., "Interfacial Area and Scaling-Up of Gas-Liquid Contac­tors," Brit. Chem. Eng.. 11(12), 1559 (1970).

15. Sheppard, N.F., R.C. Rizo-Patron, and W.H. Sun, "Analysis of Stirred-Tank Carbonation Reactors," ORNL/MIT-281, 0RNL (1978).

16. Sidemon, S., 0. Hortacsu, and J.W. Fulton, "Mass Transfer in Gas-Liquid Contacting Systems," Ind. Eng. Chem., 58, 32 (1966).

17. Valentin, F.H.H., Absorption in Gas-Liquid Dispersions: Some Aspects of Bubble Technology, E. & F.N. Spon, London, 1967.

35

18. Van't Riet, K., J.M. Boom, and J.M. Smith, "Power Consumption, Impeller Coalescence and Recirculation in Aerated Vessels," Trans. Jnstn. Chem. Engrs., 54, 124 (1976).

19. Van't Riet, K., and J.M. Smith, "The Behavior of Gas-Liquid Mix­tures near Rushton Turbine Blades," Cherc. Eng. Sci., 28, 1031 (1973).

20. Westerterp, K.R., "Design of Agitators for Gas-Liquid Contacting," Chem. Eng. Sci., 18, 495 (1963).

21. Westerterp, K.R., L.L. van Dierendonck, and J.A. de Kraa, "Inter facial Areas in Agitated Gas-Liquid Contactors," Chem. Eng. Sci., 18, 157 (1963).

8.7 Literature Surveyed

1. Bates, R.L., P.L. Fondy, and R.R. Corpstein, "An Examination of Some Geometric Parameters of Impeller Power," I&EC Proc. Pes. Dev., 1(4), 310 (1963).

2. Froment, G.F., and K.B. Bischoff, Chemical Reactor Analysis and Design, Wiley, New York, 1979.

3. Gambill, W.R., "How to Estimate Mixture Viscosities," Chem. Eng., March, 151 (1959).

4. Luong, H.T., and B. Valesky, "Mechanical Power Requirements of Gas-Liquid Agitated Systems," AIChE. Journal, 25, 893 (1979).

5. Reid, R.C> J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and Liquids, 3rd ed., McGraw-Hill, New York, 1977.

6. Rushton, J.H., E.W. Costich, and H.J. Everett, "Power Character­istics of Mixing Impellers," Chem. Eng. Progr., 46_(8), Part I, p. 395, and 46(9), Part II, p. 4J7 (1950).

7. Weast, R.C., ed., Handbook of Chemistry and Physics, 56th ed., C.R.C. Press, Cleveland, 1976.