Chemical reaction and effective interfacial areas in gas absorption

ChemicdEngincering Science, 1973, Vol. 28, pp. 453-46 1. PCQY~O~ Press.

Printed

in Great Britain

Chemical reaction and effective interfacial areas in gas absorption G. E. H. JOOSTENt and P. V. DANCKWERTS Department of Chemical Engineering, Pembroke Street, Cambridge,England (Received 1 June 1972) Abstract-Experiments have been carried out in a packed column to test the hypothesis that the interfacial area effective for gas absorption with chemical reaction depends on y, where ’ =

factor by which reaction increases capacity of absorbent factor by which reaction increases rate of absorption ’

For physical absorption, y = 1. For absorption into certain buffer solutions, y S=1, and the effective interfacial area is much larger than for physical absorption. For absorption with “instantaneous reaction”, y - 1 and the effective interfacial area is equal to that for physical absorption. Provided y exceeds a certain value, the effective interfacial area does not depend on y, so that values of the effective interfacial area determined by reactions with a sufficiently high y have a general signiticance. The experiments show that it is not simply the occurrence of a chemical reaction but the value of y to which it leads which determines the effective interfacial area. Values of the interfacial area determined with high y should not be used for the design of physical absorbers.

THERE

are numerous references in the literature to the fact that the e$ective area of interface between gas and liquid in an irrigated packed column depends on the transfer process occurring between gas and liquid. The subject is summarised by Danckwerts 111 (p. 2 17). In particular, investigators have sought to show that the area effective for the evaporation of the irrigating liquid is larger than the area effective for the physical absorption of a gas. It seems probable that the liquid running over the packing forms at some points very thin films and at other points stagnant pools in which the rate of tumover will be low. Such regions are as effective for evaporation as those covered by fast-moving liquid of adequate depth. However, in the case of physical absorption the thin regions will tend to become saturated and cease to contribute to the rate of absorption, and the exposed surfaces of the slow-moving pools will likewise become saturated. We may therefore suppose that less of the surface will be effective for physical gas absorption than for evaporation, and there is a

considerable body of evidence which suggests that this is the case. The present paper is concerned with the effective interfacial area when a gas is absorbed and reacts with a substance dissolved in the liquid. This is particularly important because a considerable number of determinations of interfacial areas have been made with the help of chemical reactions (e.g. Danckwerts and Rizvi [3]), and it is important to know whether the values obtained have any general significance or whether they are characteristic only of the particular reactions employed. Onda et al. [6] have shown that the area effective for evaporation is equal to that effective for the absorption of COZ into solutions of NaOH, but it seemed to us that the problem needed to be more clearly set out and more precisely investigated. When a reactant is added to an absorbing liquid, there are in general two effects. In the first place the quantity of gas which can be absorbed by unit volume of the liquid is increased by some factor C by virtue of the reaction, and

tPresent address: Koninklijke/Shell-Laboratorium, Amsterdam, The Netherlands.

453

G. E. H. JOOSTEN

and P. V. DANCKWERTS

thus it will take longer for thin and slow-moving patches of the liquid surface to become saturated; this effect therefore tends to increase the area which is effective for gas absorption. On the other hand, the reaction will increase the rate of absorption by some factor E (the enhancement factor), and this tends to have the opposite effect. The net effect of the reactant on the effective interfacial area may therefore be expected to depend on the quantity ‘y,which is

C Y’E’

technique consists of operating with the bottom of the packing flooded and with different heights of packing exposed, thus allowing end-effects to be virtually eliminated. The packing was initially cleaned with chromic acid solution, and was kept wet between experiments. The gas was pure COz at atmospheric pressure (thus there was no gasside resistance). The whole apparatus, and the other apparatus described below, were in a constant temperature room at 25°C.

factor by which reactant increases capacity of solution factor by which reactant increases rate of absorption .

We may expect the effective interfacial area to be greater than that for physical absorption of a nonreacting solute gas in the same solution if y > 1, smaller than that for the non-reacting gas if y < l,andthesameify= 1. In the experiments described below we have used three types of solution for the absorption of COe: (a) non-reacting solutions; (b) buffer solutions in which the absorbed COz underwent a pseudo-first order reaction and in which y % 1; (c) solutions in which the CO, underwent an “instantaneous” reaction, and y - 1. In view of the difficulty of separating a and kLowe have compared the values of (kLou)in the various solutions, the values being referred to as &OU),~~, (k~‘a)chemand (krP@i,t respectively. Since the physical properties of the solutions were similar, kLowas to a first approximation the same in each case (this is discussed further later on), and the ratio of the (kLou)values depended principally on the variation of a with y. Here, kLois the liquidfilm transfer coefficient for absorption without reaction and a the effective gas-liquid inter-

The luminur jet apparatus (Fig. 1). This was similar to that used by Kramers et al. [4], with certain modifications. It was surrounded by a water-jacket through which water at 25°C was circulated; this was found to be desirable in order to prevent fluctuations in temperature of the gas space (Schriider 181).The chamber was designed to minimise the effect of spilled liquid on the absorption rate (liquid spillage always occurred at the beginning of an experiment, when the liquid flow was started). Spilled liquid sank to the bottom of a pool of 1,3 di-isopropyl benzene

facial area per unit volume of packed space. EXPERIMENTAL

The packed column. This was 11 cm i.d. and

packed with 4 in. ceramic Raschig rings or Intalox saddles. The liquid was introduced by 64 separate nozzles fixed in a plate immediately above the packing. The column was operated by the socalled differential height technique, first described by Danckwerts and Kennedy[2]. This 454

(1)

separating

Fig. 1.

Chemical reaction and effective interfacial areas

(having low density and vapour pressure). The surface of the organic liquid was at the neck of the vessel. The organic liquid was saturated with COz before each experiment. The length of the jet could be varied stepwise by placing spacer-rings between the lid and the main body of the absorption chamber. The ancillary apparatus was as described by Danckwerts [l] (p. 84). The wetted-wall column. This was the same as that described by Roberts and Danckwerts [7] (see Danckwerts [ 11p. 73). Solutions used. Two different buffer solutions were used to determine (kLoa),,,; one consisted of 1 g mol KzC03+ 1 g mol KHC03 per l., the other of 1.69 g mol KzHPO + 0.26 g mol KH,PO ., per 1. In order to preserve dynamical similarity in the packed column, the solutions used to determine (kLoa),b,, and (kLoa)i,t were matched with the two buffer solutions with respect to viscosity and density. The compositions of the solutions used are shown in Table 1. CHARACTERISTICS

OF THE SOLUTIONS USED

The carbonate bufer. The overall reaction in

this case is COz+C03=+HzO

+ 2HC03-.

(2)

Conditions were such that dissolved COa underwent a pseudo-first order reaction in solution (for criteria for this see Danckwerts [l] p. 246) and

the concentration of CO, in the bulk was negligible. The reaction of COz in the buffer can be catalysed by the addition of potassium arsenite (Danckwerts[l] p. 244). The pseudo-first order rate constant, kl, depends on the concentration of arsenite. Values of k, with different concentrations of added arsenite were determined with the laminar jet apparatus, using a well-established technique (Danckwerts[ 11 p. 89). It was found that k1 = 1.2 + 538(KAs02) set-’

where (KAs02) is in gmol/l. The highest concentration of arsenite used was 0.04 g mol/l. Considering the packed column, and using the Danckwerts surface-renewal model, we have Ra = &Oa) cherd

(Ra)’ = ((t”&h&4*)z(

Matching the carbonate Matching the phosphate buffer buffer 1.16 1.24 137 2.29

272 92 1000

l+$)

(5)

where Ra is the observed rate of absorption per unit packed volume, A* the physical solubility of COz in the solution, and D the diffusivity of dissolved COz. Thus, if absorption rates (Ra) are measured at various values of kl, and (Ra)2 plotted against kl, a straight line should result with an intercept of ((kLoa),h,,A*)2 on the ordinate. Thus, if the value of A * is known, that of @Loa)e h em can be deduced. Methods for

“Instant“Instantaneously” aneously” Inert reacting Inert reacting solution (0.2OM NaOH) solution (0*18M NaOH) Sodium nitrate, g Sugar, g Sodium hydroxide, g Water, g

(4)

*J(1+%)

whence

Table 1.

Density (g/cm3) Viscosity/g,,.

(3)

268 89 9.4 1000

455

405 169 1000

400 166 9.1 1000

G. E. H. JOOSTEN and P. V. DANCKWERTS

estimating A * are discussed in Appendix 1. (This method of determining (kLou),hemassumes that ache,,,is independent of R and hence of y. This question is discussed later.) The values of y for the carbonate buffer solutions ranged from 30 to 60, depending on the arsenite concentration. The phosphate lx&r. The overall reaction in this case is H,O+CO,+HPO;

(10) Here (OH-) is the bulk concentration of sodium hydroxide and Ei is the value which the enhancement factor E would have if the reaction were truly instantaneous. When

(11)

--, HCOI-+HzPOa-. (6)

(which was the case in our experiments), Ei is given to a close approximation by

The value of k, in this solution is so small (0.2 set-l) that the specific absorption rate is given by the limiting form of Eq. (3): Ra = ( kLou)chemA*

(7)

and it is only necessary to know A* to deduce (kLO&,emfrom the absorption rate. The value of y for this solution was about 16. In the case of both types of butfer it was verified by calculation that the rate of reaction was fast enough to maintain equilibrium in the bulk of the reactant and that the equilibrium concentration of COZ was in all circumstances much less than A* and hence could be neglected (Danckwerts [ 11p. 244). The solutions containing NaOH. These solutions were designed to give conditions approaching “instantaneous reaction”, i.e. the case where the rate of reaction is determined entirely by the diffusion of the CO 2and the reactant towards the reaction zone, and is independent of the kinetics of the reaction. The overall reaction in this case is CO2 + 20H- --* COa= + H,O.

(8)

The reaction is second-order, the rate per unit volume being given by k&OH -)(CO,).

(9)

The reaction can be considered “instantaneous” in the above sense when

E, =

(12)

where DOH is the effective diffusivity of OH-. Using the following estimated or actual values: D,,/D = 1.67, koH = 1041./g mol set, (OH-) = O-2g mol/l., kL = 5 X 10m3cmlsec, A * = 2 X 10e2 g mol/l., D = 1.4 X 10m5cm2/sec, condition (10) combined with Eq. (12) takes the form 34 S 7.5.

(13)

This indicates an error of only about 4 per cent in assuming E for the NaOH-containing solution to be equal to El. The factor C by which the reaction enhances the capacity of the solution for the absorption of CO, is

c= 1+$$$?

(14)

The enhancement factor, E, is given by Fq. (12) (since E = Et). Thus, using the values of &H/D and A * given above, we can calculate that the factoryhasavalueofabout0*8for0*2MNaOH, and more for a solution depleted by absorption of CO2 during its passage through the column. In order to interpret the results of absorption experiments in packed columns it was necessary to know EJ* as a function of the degree of conversion of NaOH to Na2C03, which increased progressively as the liquid passed

456

Chemical reaction and effective interfacial areas

through the column. Although this could be calculated, as above, in view of the uncertain values of some of the quantities involved it was decided to determine values of &A* experimentally, using the wetted-wall column, and solutions representing various amounts of absorbed COz. The method is described in Appendix 2. RESULTS

AND

I

I

I

I

DISCUSSION

Determination of (kLoa)pti. The absorption rate M gmol/sec in the column is determined with various heights, h, of packing exposed. The cross-sectional area of the column is X. Then dM = (kLoa)Phys(A* -A)Xdh

(1%

where A is the bulk concentration of COz at height h. But the liquid entering the column is free from CO,; thus A=MIL

-

dh

Carbonate Inert

X

Very rapidly

(16)

(kLoa),,,.

(17)

The value of (kLoa),,, at a particular flow-rate is determined from the slope of a plot of log,, X (1 -M/LA*) against h. Values of (kLoa),,h, for the two inert solutions at various flow-rates are shown in Figs. 2-4. Determination of (kLoa),h,,. As regards the carbonate buffer,

buffer

solution

(ktalchem (k~o)p,y,

reacting

solution (k?ah

Liquid

viscosity

Liquid

density

I 0.2

Id31 01

where L is the liquid flow-rate. Thus Eq. (15) becomes

!!!ZEE2 =-&

o A

Liquid

superficial

: I .57 I.169

:

I 0.4 velocity

x II npO /cm3 1 06

,v ,

I1 0.6

IO

cm/set

Fig. 2.4 in. Raschii rings. Comparison of (kLoa),hysr (kLon),hem and (k”&ut.

the estimated value of A *, according to Eq. (7). Values of (kLoa),he, are shown in Figs. 24 for various liquid flow-rates. Determination of (kLoa)m,t. The differential equation relating the absorption rate to the height of packing exposed is dM = ( kLoa)instA*EiXdh

(19)

(18) and from a material balance (for the solution matching the carbonate buffer): so that (Ra) can be determined from a plot of M against h. (kLoa),,,,,, is determined as described above, by altering the arsenite concentration and plotting (Ra)2 against k,. Some plots of this kind are shown in Fig. 5. As regards the phosphate buffer, (kLoa),,,,, is found simply by determining Ra and dividing by

(OH-) = O-20X 10m3- 2$gmol/cm3

(20)

where (OH-) is the concentration (gmol/cm3) of NaOH unconverted to carbonate. A *Et is related to (OH-) (for the solution matching the car-

457

G. E. I-L JOOSTEN and P. V. DANCKWERTS I

I

I

I

6

Corbonote

Very

buffer

ropidly

reacting

viscosity Liquiddensity

o-I

:

0.2 Liquid

superficial

(k fo),,,

: ,

solution (k?ahn.,

T,, o I.16 g/cm 23 I

Inert

solution

x

Very

rapidly

1.57~

0.6

04 velocity

A

,

V

,

,

-

O-6

(k~a)p,,v, reacting

,.. L,quld

vlscoslty

: 2.29

Liquid

density:

I.24

0.2

0.1

Liquid

cm/set

superficial

velocity

x qHzo g/cm3

I

I

I

0.4

06

06

I I.0

solution (kga),,,,,

,

V,

I.0

cm/set

Fig. 3. tin. Intalox saddles. Comparison of (ktoa),hys,(kLoa),,,em and &“a),,,.

Fig.

bonate buffer) by Eq. (26) (Appendix 2). Hence

rate. The fact that these latter two are so nearly equal is a matter of some surprise, since y < 1 for the case of (kLou)rnst.However, this fact may be compensated for by the fact that the reaction was not quite within the “instantaneous” regime, a circumstance which tends to increase y somewhat. However, the results show clearly that (kLoa) is larger when y S 1 than it is when y = 1, and that it is the value of y and not simply the presence or absence of a chemical reaction which determines (kLou). Figure 6 shows the ratio (k~“u),~,,/(k~“u),~~. Tire ratio is almost the same for the carbonate buffer as it is for the phosphate buffer, despite the very different values of y. The results suggest that even in the case of the phosphate buffer, the value of y is large enough to render effective the whole of the available wetted surface (for the concept of availability, see later). In practice this

-din

(3.4 X 10e5 +(OH-))

= +LOa),“.,Xdh (21)

where (OH-) is determined from Eq. (20) and is in gmol/cm3. Thus, for a given value of L, M is determined as a function of h, and In (3.4 x lo-“+(OH-)) plotted against h. From the slope of the plot, (k,,“u)instis determined. The solutions matching the phosphate btier are treated similarly. Values of (krP~&,,~~ for the two solutions are shown in Figs. 2-4 for various liquid flowrates. DISCUSSION

As can be seen from Figs. 2-4, (kLou),hemis larger than &OU),~, and (/rLou)inst,the latter two quantities being almost equal at any given flow-

458

4. t in. Raschig rings. Comparison of (kLOa),h, (kr,%),~em and (k~%~)~

Chemical reaction and effective interfacial areas ,9

2

r

I

I

I

I

0.4

O-6

0.0

0

1600

6

-

o Y = 0.16

cm/set

1

-I

O-I

0

4

16

12

6 k (,

20

24

0.2

V.

0

cm/see

Fig. 6. Ratio (kLoa),he,,,/(kLoa)p as a function of the super. ficial liquid velocity, U.

set’

Fig. 5. The square of the specific absorption rate plotted against the pseudo-first order rate constant k, in the solution. Packing: 4 in. Raschig rings; carbonate buffer solution.

means that when interfacial areas are determined by the chemical method the values of a found will be independent of the value of y, providing this exceeds some minimum value (which depends, presumably, on the packing and flow-rate). Thus, these values of (&, have a general significance and are not specific to the particular reaction used. Danckwerts and Rizvi [3] have shown that values of a determined by dissimilar chemical reactions are in good agreement. It is possible, from the plots of (Ru)~ against k, in the case of the carbonate buffers, to determine the actual value of (&em, the effective specific interfacial area (Danckwerts [ 1I p. 2 10). The value of (u)~,,~,,,depends on the flow-rate, but even at the highest flow-rate used (O-62 cm/set) its value was somewhat less than half the total

geometrical area in the case of both Raschig rings and Intalox saddles. On the other hand, visual observation suggested that the entire surface of the packing was wetted by the liquid. In an irrigated packing, therefore, the situation appears to be as follows: only a fraction of the surface is “available” for mass transfer, and the fraction of the “available” surface which is effective for mass transfer depends on the value of y. The “unavailable” part of the surface is covered by an absolutely stationary film of liquid which is never renewed and thus does not contribute towards mass transfer when the stationary state is reached, even when y % 1. In experiments in which liquid is evaporated from the packing, the “unavailable” parts of the surface will be dried, and thus in the stationary state the “available” surface is the same as the wetted surface. This accounts for the findings of Onda et uZ.[6] that the area effective for evaporation of the liquid It may be noted that was equal to (&,,.

459

G. E. H. JOOSTEN and P. V. DANCKWERTS

Danckwerts and Rizvi[3] showed that with larger packings and high liquid flow-rates (&hem may become equal to the geometrical surface area of the packing (and in fact may slightly exceed it, perhaps because of the formation of drops). The fact that (~&‘a),~~~is independent of y provided this exceeds a certain value validates the method described above for determining for the carbonate buffer, in which (kt’&, (kL”u),h, was assumed to be independent of kl, and explains why there is no systematic curvature in the plots shown in Fig. 5. The ratio (k~“&~,,/(k~oa),ti, is probably not simply equal to the ratio of the effective interfacial areas, (~)~~~~/(a)~~~. Although the physical properties of the liquids were the same, it is probable that the mass transfer coefficients were different. The part of &O)ei,emand (kLO)pr,us the surface which is effective in the physical case consists of liquid in brisk motion, whereas in the chemical case comparatively sluggish regimes are also included. Thus we should expect (kL”),h,, < (kbo)pavs, nd the ratio of the effective interfacial areas would then be even larger than the ratio of the (kLou)values. Clearly, values of a or (kLou) determined by the chemical method with y % 1 should not be used for the design of physical absorbers.

NOTATION

A* U

c D d E Ei h Z k, kL” kOH L M R4 t X

solubility of COZ at 1 atm, 25°C gmol/cm3 effective inter-facial area for gas absorption per unit volume of packed space factor by which chemical reaction increases capacity of liquid for absorbing gas dfisivity of COZ in solution diameter of wetted-wall column factor by which chemical reaction enhances rate of absorption of gas value of E when chemical reaction is instantaneous height of packing exposed to gas; or height of wetted-wall column ionic strength first-order reaction-rate constant mass transfer coefficient in absence of reaction second-order rate constant for reactions of CO, with OHliquid flow-rate to packed column absorption rate in packed column absorption rate on wetted-wall column rate of absorption per unit effective interfacial area in packed column time of exposure of liquid to gas in wetted-wall column cross-sectional area of packed column

Subscripts Acknowkdgement- G. E. H. J. wishes to thank the managing directors of the Koninklijke/Shell-Laboratorium Amsterdam for their support during his stay in Cambridge.

[l] [2] [3] [4] [5] [6] [7] [8]

them phys inst

referring to buffer solutions referring to inert solutions referring to solutions containing NaOH

REFERENCES DANCKWERTS P. V., Gas-Liquid Reactions McGraw-Hill, New York 1970. DANCKWERTS P. V. and KENNEDY A. M., C&m. EngngSci. 1958 8201. DANCKWERTS P. V. and RIZVI S. F., Trans. Instn Chem. Engrs 197149 124. KRAMERS H.,.BLIND M. P. P. and SNOECK E., Chem. Engng Sci. 196114 115. MARKHAM A. E. and KOBE K. A., J. Am. Chem. Sot. 194163449. ONDA K. E., SADA E. and TAKEUCHI H., J. Chem. Engng Japan 1968 162. ROBERTS D. and DANCKWERTS P. V., Chem. Engng Sci. 1962 17 961. SCHRODER W., Compt. Rend. 36e Congres Int. Chimie Industrielle, p. 248, Brussels 1967.

APPENDIX 1 The solubility of CO, in the buffer solutions As explained above, it is necessary to know A* (the solubility of CO1 at 1 atm and 25°C) for the two buffer solutions in order to determine &%I),~,,. Three methods were used to determine A * :

(a) The van Krevelen-Hoftijzer method extended to mixed electrolytes (Dan&wet% [l] p. 20). This is not applicable to the phosphate butfer as the required parameters have not been determined. (b) The NpO method. According to the principles of the van Krevelen-Hoftijzer method and the parameters for the two gases (Danckwerts [l] p. 20), the solubilities of COe and

460

Chemical reaction and effective interfacial areas N1O in a given electrolyte solution are related by log,.>

= 0.019 x I

(22)

NIO

where I is the ionic strength of the solution (Bionll.). The solubility of NzO in the two solutions was measured by the method of Markham and Kobe[5] and the solubility of CO* deduced. (c)The laminar jet method. By absorbing COz into a laminar jet of the solution, the value of A *dD can be determined (Danckwerts[l] p. 89). The value of D was determined by the N20 method described in Appendix 2 (Eq. 25), and hence A * deduced. The solubilities predicted by the various methods are shown in Table 2.

hence A*dD is determined. A* can be found by the method of Markham and Kobe [5] for determining solubilities, and so D is found. The second method was to assume that the solutes have the same effect on the diffusivity of N,O as they do on that of COe. Using the wetted-wall column, DN,o was determined as above for pure water and the solution. D for COz in pure water is well-known. We then put

Table 2. Estimates of the solubility of carbon dioxide in the buffer solutions at 25”c, 760 mm Hg. (gmol/cm3) Carbonate buffer Predicted by method (a) Predicted by method(b) Predicted by method (c) Used in this work

Phosphate buffer

l-68 X 10e5

where q is the total absorption rate into the wetted column, d is the diameter and h the height of the column, and t the time of exposure of the falling liquid to the gas; the latter is easily calculated if the flow-rate, density and viscosity of the li uid are known (Danckwerts[l] p. 73), and thus a*E, 9 D is found. This was done for solutions representing different degrees of carbonation of the original OH- solution. Two methods were used to determine D in the solutions. Firstly the presence of NaOH and Na,C03 in the solutions was ignored, in view of the large excess of other solutes, and the diisivity of CO* in a similar solution free of NaOH was determined, using the wetted-wall column. The rate of physical absorption is

-

l-51 X lows

0.95 X 10m5

1.50 X lo+

0.92 X 10e5

1.51 x 10-S

0.94 x 10-S

and hence find Dmln. The results within 5 per cent, and the average The values of E,A* found for carbonate buffer were found to be

of the two methods agreed value was used. the solutions matching the given by

E,A* = 2.12 x 10++0.62[0H-]

APPENDIX

2

J

$

(26)

and those for the solutions matching the phosphate by

Determination of E,A* as function of absorbed CO2 Provided certain conditions are fullilled IDanckwerts111 p. 44) the absorption of COe into the sodium hydroxi& solutions on the wetted-wall column proceeds in the “instantaneous reaction” regime. These conditions were fulfilled in our experiments. Then q = 2mhdA*E,

gmole/cm3

E,A* = 1.10 x 10-S+0+4[OH-]

g mole/cm3

(27)

where [OH-] is the concentration (g mol/cm3) of NaOH unconverted to carbonate. The value of y in these solutions varies with the degree of carbonation, having a minimum value of about 0.8 in the uncarbonated solutions and a maximum value of about 0.9 at the bottom of the absorption column.

461