CARBON DIOXIDE ABSORPTION INTO AMINEPROMOTED POTASH SOLUTIONS A.
L. S H R I E R ' A N D P . V . D A N C K W E R T S
Department of Chemical Engineering, University of Cambridge, Cambridge, England Examination of equilibrium and rate data on amine-potash systems in terms of an absorption-reaction scheme suggested that rates of C 0 2 absorption into potash solutions could be significantly increased by addition of small amounts of selected amine promoters. To demonstrate the predicted effect, a brief experimental study was carried out using a stirred absorption cell. Cell characteristics were determined for physical absorption (CO2-H20), and the degree of rate enhancement was measured for a number of amines with absorption of saturated C 0 2 at 1 atm. Additional experimental results for the most effective of the amines tested, 2-ethylaminoethanol (EAE), at 25" C. and saturated COSpressures of 1 atm. and 75 mm. of Hg were in reasonable agreement with the proposed mechanism. Additional work is recommended to evaluate amine promotion further as a technique for improving commercial COZ absorption processes involving potash solutions.
ARBON DIOXIDE absorption processes are used throughout the process industries for purifying natural, refinery, and synthesis gases. Water was employed as an absorbent in early processes, but has been largely replaced by reagent solutions that react chemically with dissolved COS. This reduces COZ backpressure and increases mass transfer rates arid absorbent solution capacity. Potassium carbonate solutions are the most commonly employed chemical absorbents, especially for bulk COz removal, because of their low cost, large capacity, ease of handling, and relative ease of regeneration. In particular, hot carbonate processes (Benson et al., 1956; Eickmeyer, 1958; Xullowney, 1957) are widely used, notably in situations where decreased-pressure regeneration is practical-e.g., in ammonia synthesis plants. The over-all absorption rate of COZ in ordinary carbonate solutions is influenced by both chemical and physical processes (Danckwerts and Sharma, 1966). The dominant chemical reaction in this rase is
Under conditions of interest, the rate of Reaction 1 is relatively low because of the small hydroxyl ion concentration (typically to 10-5111). For orientation, using the value of k O H a t 25'C., -lo4 liters/mole-see. (Danckwerts and Sharma, 1966) the pseudo-first-order rate constant k o ~ C 0 H - l - lo-' to 10' see-'. The rate of reaction of C 0 2 in aqueous solutions can in general be increased by the addition of catalysts (Sharma and Danckwerts, 1963) which accelerate the normally slow hydration reaction
+ H20 S H&03 kw
COz
(2%1
In alkaline solutions, Equation 2a is followed by the rapid dissociation of carbonic acid H z C 0 3 e HC03-
+ H+
-
(2b 1
At 25' C., the first-order rate constant k , see.-' (Pinsent et al., 1956) and can be increased by two or more orders of magnitude upon the addition of hydration catalysts. I
Present address, Chemical Engineering Technology Division,
Esso Research and Engineering Co., Florham Park, N. J. 07932.
This approach is the basis for the Giammarco-Vetrocoke (G-V)process, which utilizes an arsenic catalyst in carbonate solution. Although the G-V process is commercially important, the use of arsenic compounds introduces certain complications in practice. The present work concerns a somewhat different technique for increasing COZ absorption rates in carbonate solutions: using amines as carriers of COz from the surface region into the bulk liquid. Previous work a t Cambridge and elsewhere (Danckwerts and Sharma, 1966; Sharma, 1965) has shown that for many primary and secondary amines the rate of the second-order reaction
coz+ RR'NH=
k Am
RR'KCOO-
+ H+
(3)
is fairly rapid, with typical second-order rate constants
hrn-lo4 liters/mole-see. at 25' (Sharma, 1965). Simple equilibrium considerations, described below, indicate that for selected amines a significant fraction of the amine present in amine-potash solutions exists in the free form (RR'NH). Thus, even small total amine concentrations (-O.lJI, or perhaps 1% by volume) should provide sufficient free amine (say 10-2M) t o produce more rapid COn reaction by Reaction 3 than by Reaction 1-Le., k*,[RR'NH]
-
10 to 1000 ko1rCOH-1 Subsequent re-establishment of equilibrium in the bulk liquid then regenerates free amine by Reaction 3 proceeding in the reverse direction, with COz consumed via Reaction 1. Furthermore, a sustained increase in the over-all absorption rate is obtained, provided that Reaction 1 in the bulk liquid proceeds a t a sufficiently rapid rate, as discussed below. A brief exploratory study was undertaken to verify the predicted enhancement of COZ absorption rate and obtain a measure of its magnitude. The results of screening runs with a number of amines amply demonstrate the effect. Additional data for the most effective amine tested, P-ethylaminoethanol (EAE), show that COz absorption rate can be substantially increased and that the results are reasonably consistent with the proposed absorption-reaction mechanism. The use of suitable amines for promoting carbonate scrubbing solutions appears to have potential merit for commercial VOL.
8
NO.
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AUGUST
1 9 6 9
415
applications in both new and existing hot carbonate plants. For developing a practical process, however, additional largescale testing under representative conditions is required.
This scheme neglects un-ionized carbonic and carbamic acids. Based on an amine mass balance and the above equilibria, the fraction of total amine present in the free amine form is given by
Previous Work
[RR’NH]
I t has long been recognized that the rate of C02 absorption in carbonate solutions can be increased through the use of various additives, including amines and hydration catalysts. Referring to earlier work by Riou and Cartier (1927, 1928), Killeffer (1937) suggested that for COSabsorption in sodium carbonate-bicarbonate solutions the effects of formaldehyde, methanol, phenol, soap, sodium lactate, and ethanolamines were attributable to surface tension depression. More recently, Jeffreys and Bull (1964) studied the effect of adding glycine to sodium carbonate solutions and concluded that COS absorption is enhanced as a result of both favorable chemical equilibria and the tendency of surface-active glycinate ions, NH2CH2COO-, to concentrate at the surface, where they react rapidly with dissolved COS. McNeil and Danckwerts (1964) questioned this interpretation and proposed instead a somewhat different explanation also based on simultaneous chemical equilibria. The present work demonstrates that a number of amines can be used to promote C02 absorption in potash buffers; the results are discussed in terms of simultaneous chemical equilibria and familiar models of mass transfer with chemical reaction, as reviewed by Danckwerts and Sharma (1966). COZ absorption in amine-potash mixtures (“mixed lye”) was studied by Ellis (1960), who compared his results with theoretical predictions. Danckwerts and McNeil (1967a) described the effects of a hydration catalyst, sodium arsenite, on COn absorption in mixed amine-potash solutions. In both investigations, the solutions contained relatively high concentrations of amine (> 1M) and, from a practical point of view, such solutions could not be used conveniently in conventional carbonate processes. The use of small amounts of suitable amines as promoters avoids both the problems associated with handling concentrated amine solutions and the high regeneration heat duties required in amine scrubbing processes. In the present study, selection of amine promoters for potash solutions was based on the data tabulated by Sharma (1965), who measured second-order rate constants hrn by several methods. The experimental technique used to obtain absorption rates was developed by Danckwerts et al. (1967a, b).
+ co32- Kz H 2 O e H+ + OHK, RR’NH + C O z e R R NCOO- + H+ RR’NH + H+= RR’NH2+ 1/& IhEC
FUNDAMENTALS
+ +
(7 )
[RR’NHl0 1 [Am]
+
1
+ (KS/Kb)ro+ (Kc/KI)~o[CO~~-]O(8)
Subscript o refers to initial conditions, before any C02 absorption (for the present example, r, and [C032-], also refer to the reagent concentrations used to prepare the buffer solution). Using the ion-product constants in Table I, the fraction of free amine can be estimated for ammonia, MEA, and DEA a t 18’ C. as 0.18, 0.023, and 0.13, respectively. The variation in free amine concentration for small degrees of COSabsorption is also of interest for interpreting the data collected in the present study. In terms of the “fractional
0.9
0.8 0
z
-
2
0.7
z
z
0-
s
0.6
U
0.5
0.3 I
-130
0.1
0.2 0.3 FRACTIONAL SATURATION, CC
(41 (5 )
K,
(3) (6 )
0.4
Figure 1. Absorption of C02 into amine-promoted potash buffer solution Change in concentration of various species Initial Free Amine Concentration [RR‘NHIo
(21
K1
HCO3-e H+
416
4- CHCO3-1 (K,/Kd
where the K’s are ion-product constant and brackets, [ 1, denote molar concentrations. [Am] is the total amine con[RR’NCOO-] [RR’NH2+]. centration, [RR’NH] Consider a potash buffer solution of molarity p 2 1M (where p = [HC03-], [C032-]o) with 8 < pH < 11, to which is added a small amount of amine, [Am] < 0 . 1 ~ . At equilibrium, the following concentrations are neglected relative to [C032-]: [H+], [OH-], [CO,], [RR’NCOO-1, and [RR’NH2+]. Then the fraction of the total amine present in free form can be expressed in terms of the buffer ratio r,{ = [HC03-],/[CO~-],} and [C03S-]o by:
DEA
Approximate expressions for the rate of C02 absorption in amine-promoted potash solutions can be derived using equilibrium relationships and simple mass transfer models. The degree of enhancement obtainable can then be estimated where physicochemical data are available-e.g., ammonia, monoethanolamine (ME.4), and diethanolamine (DEA). For chemical equilibrium in the bulk of an amine-potash solution, the following reactions are considered (Danckwerts and McNeil, 1967a) :
+ H 2 0 e H+ + Hco3-
1 4- { [H+]/&}
[Am1
0.4
Theoretical Considerations
COS
1
-
Amine “3
MEA DEA [HCOa-I = 1M [COs2-] = 1M t = 18” C.
[Am1
0.179
0.023 0.130
Table 1.
Potash buffer solutions, I Kf = 1.25 X lo-’’
Ka K i / K , ( = KeQ)
In the case of amine-promoted potash solutions, the corresponding groups are
Values of ton-Product Constants (18’ C.) (McNeil, 1965) =
3
NHI
MEA
DEA
1.16 X lo-’’ 0.285
6.53 X lo-” 0.025
3 . 2 X 10-l’ =
the concentration of free amine relative to that initially present in the free form is given by
This is shown in Figure 1 for dilute solutions (say < 0.2M) of ammonia, MEA, and DEA in a 1M HC03-: 1 J I cos-’ buffer solution a t HOC. The concentrations of hydroxyl and carbonate ions are also included for reference. Figure 1 indicates that the free amine concentration decreases relatively slightly for small values of CY (< 10% for a < 0.05, with the given potash solution), which applies to most of the data below; also, the relative decrease in free amine concentration is rather insensitive to the individual values of Kb and K , for the individual amines. Moreover, the concentration of free amine is not greatly reduced even when C02 absorbed is equivalent to several times the amine present, because the bulk of the C02 ultimately reacts with c03’-. For practical purposes, then, it can be inferred from these calculations that the predicted effects of added amine in potash solutions will persist after considerable C02 absorption, unlike the situation with ordinary amine solutions wherein free amine is progressively converted to unreactive forms. The appropriate expression for the rate of absorption depends on the absorption regime under the given circumstances. For unmodified potash solutions, the regime is determined by comparing the magnitudes of the two groups (Danckwerts and Sharma, 1966)
and
where C* and Dco2 are, respectively, the solubility and diffusivity of C02 in the liquid phase and k~ is the physical mass transfer coefficient. Under the conditions of interest here, I >> 11, so that the over-all liquid-phase process is controlled by chemical reaction and the absorption rate is given by k L a C * d m
dn-z
(14)
Equation 13 assumes that [RR’NH]> ko~cOH-1. Then, for the two extremes of the inequality between I’ and 11’, the ab,sorption rate is given by
moles of C02 absorbed/liter
=
(13)
C*
0.158
saturation”
Na
[RR’NH]
I’= 1 +
(12)
where N is the molal flux and a is the specific area. [Following Danckwerts and Sharma (1966), the inequality is taken to hold when I 2 211.1
(Reaction)
(Na)’ = k L a C * d l
+ @ A ~ ( I>>’ 11’)
(15)
or (Diffusion)
(16) As a rough guide, for the experimental work described below Equation 15 or 16 applies depending on whether the gas-phase partial pressure of C02, Pco2, was low (> 11' (roughly) and
These very approximate calculations suggest that significant increases in absorption rate are obtainable with aminepromoted potash solutions under the assumed conditions, especially for reaction-controlled absorption (low Pco~), provided that the amines possess suitable characteristics-high reactivity with COZand significant equilibrium concentration of free amine in potash buffer solutions. These indications were considered sufficiently encouraging to warrant the brief experimental program described next.
0 RPM
Figure 2.
The physical absorption runs demonstrated the importance of stirrer positioning for obtaining reproducible results. With 100 ml. of water in the cell, sizable variations in values of k ~ a(&20y0) were noted, depending on whether the 0.5-cm. high cruciform stirrer was barely through the surface from above, about halfway immersed, or just below the surface. The first of these stirrer positions was selected for the work described below. Subsequently, it was noticed that even small differences in apparatus alignment produced significant run-to-run variations and the experimental procedure was appropriately modified (see below). Replicate runs made without disturbing the apparatus arrangement give reproducible results-e.g., Figure 2, 139 and 178 r.p.m. Three potash buffer solutions were used for the chemical absorption work; compositions and relevant properties are presented in Table 11. Measured absorption rates tended to level out about 2 to 5 minutes after beginning COz flow to the initially evacuated cell, and decreased only slowly thereafter. The relatively constant rate of absorption observed after the damping period is consistent with calculations based on applying the model discussed above to a buffer solution in a batch system. Even with the highest rates of COZ absorption encountered in this work, the absorption rates measured 5 minutes or so after the start of a run closely approximated initial rates for the given buffer solutions. For example, with solution TI the highest rate observed was 1.2 X mole/liter-sec. (18', 1 atm., 105 r,p.m.); in this case 9 0.4, and the sbsorption rate after 5 minutes should be only about 3% lower than the true initial rate.
-
418.
I&EC
FUNDAMENTALS
&La
COZ into water 18" C., 1 atm. Stirrer just in surface
Experimental Procedure
Absorption rates were measured by a stirred-cell technique previously employed by Danckwerts et al. (1967a, b ) ; the apparatus used was essentially identical to that used by Danckwerts and McNeil (1967b). Saturated CO2 was metered into the absorption cell, which was thereby maintained a t constant pressure in the course of a run. The COz saturator and the cell were immersed in a constant temperature bath. Some preliminary runs were carried out with water as the absorbent, to determine the characteristics of the cell and to obtain physical mass transfer coefficients. For these runs, values of k ~ acould be calculated from a semilogarithmic plot of the instantaneous volumetric absorption rate us. time, as discussed by Danckwerts and McNeil.
Effect of stirrer speed on
Table II. Composition and Properties of Potash Buffer Solutions
Solution I
Buffer ratio, TO = [HC03-],/CO~z-]o 1 Ionic strength, Z 4 9.86 PH(20") Density, g./ml. (20") 1.16 Relative viscosity 1.57 18" 25" 1.58 COz solubility, C* mole/La (satd. vapor, 1 atm.) 0.0226 18" 25" 0.0187 a
Estimated according t o
Nysing
and Kramers
I1
111
1 2 9.78 1.10
0.25 4.16 10.54 1.16
1.24 1.27
1.54 1.57
0.0304 0.0250
0,0222 0,0183
(1958) ( extrapolated
to higher values of I ) .
Rates of absorption into amine-promoted potash solutions a t first were measured separately and compared with previously determined rates for the unmodified buffer (solution I only). The procedure was altered, however, when the sensitivity of k L a to apparatus alignment was detected. With the revised procedure, the cell was set up and charged with 100 ml. of unmodified buffer solution, and the absorption rate was determined as before; then the cell was evacuated, the desired amount of amine was added (typically -1 ml.) taking care not to disturb the apparatus, and the rate was again determined. The ratio of the two rates was then taken t o be e. The net increase in solution height in the cell was slight: 10 a t 25' c.).
As a check, several amines were selected from among those with high k~~ and low Kb (pyrrolidine) and with low k ~ , and high Kb (ammonia, DEA). Experimental values of e for all the amines screened in this work (at 1-atm. total pressure and 18’ C.) are given in Table 111. No simple relationship was apparent among e , k ~ and~ Kb., An additional series of experiments was carried out with potash buffers promoted by 2-ethylaminoethanol (EAE), which produced the greatest increase in absorption rate of the amines tested. The effects of adding EAE to potash buffer solutions were studied for several amine concentrations and a t atmospheric and reduced pressures (Table V). Discussion of Results
To examine the chemical absorption results in terms of the absorption-reaction scheme referred to above, values of k~ are required in addition to physicochemical data. The physical absorption work indicated that k~ could not be simply predicted from cell geometry, stirring speed, and system properties. Accordingly, values of k L for the chemical absorption runs were estimated from the physical absorption results as described below. With the bottom edge of the stirrer barely immersed, the water surface appeared flat a t low stirrer speeds, with disturbances becoming increasingly evident at higher speeds. Therefore, ~ L ’ S at lower stirrer speeds ( 5 1 0 5 r.p.m. for 100 ml. of water in the cell) were calculated from experimentally determined values of k ~ a using the geometrical area of the flat water surface with allowance for the presence of the cruciform stirrer; for 100 ml. in the cell, a = 0.613 cm,’ The rate of “surface sweep,” [4 (r.p.m./60)] set.-', was not in general equal to the surface renewal parameter s = ~ L ~ / D C O ~ . A simple empirical relationship between k ~ and a r.p.m. existed a t the lower stirrer speeds. Figure 2, for 100 ml. of water in the cell a t 18’ C. and a total pressure ( P = Pcoa PH~O of )1 atm., shows that k L a a (r.p.m.)” with n- 1.5 for stirrer speeds below about 105 r.p.m. For estimates of k~ and k ~ for a potash solutions at higher stirrer speeds (runs with EAE at reduced pressures), the deviation a t higher stirrer speeds was attributed to surface distortion (increased
+
~~
Table 111.
Absorption of COZinto Amine-Promoted Potash Solutions Buffer ratio, [HC03-],/[,C032-]o. 1 Total amine concentration. 0.1M Stirrer speed. 105 r.p.m. System pressure. 1 atm. (saturated Cot) Temperature. 18” C.
Buffer Solution I
I1
Amine 2-Ethylaminoethanol (EAE) BMethylaminoethanol (MAE) Pyrrolidine Morpholine Ammonia 2,G-Dimethylmorpholine (DMM) Monoethanolamine (MEA) Monoisopropanolamine (MIPA) Ethylenediamine Hydrazine EAE MAE DEA MEA Benzylamine Glycine
e
=
(Na)’/(Na)
1.93 1.46” 1.37 1.28” 1.25” 1.22 1.2@ 1.11 1.09a 1.03a 1.84 1.59 1.25 1.20 1.16 1.09
a e based on average rate for unmodifled potash absorption and results subject to uncertainty estimated t o be &lo %.
a ) and it was assumed that a was the same for water and potash solutions. The results obtained at 25’show the Fame trend, with ( k ~ a ) %( /k ~ a ) l= s 1.18. (Slightly different values of n were found for the data obtained with 75 and 133 ml. in cell, although TZ > 1 in all cases.) Evidence of convection effects not due to stirring was obtained by carrying out absorption with the stirrer in place but static. With 100 ml. of water in the thermostated cell, the observed absorption rates were consistent with a model of mass transfer by convection rather than by molecular diffusion into a stagnant medium, with k ~ values a of 0.4 X set.-' at 18’ and 1.3 X set.-' a t 25’. Values of parameter for chemical absorption runs were estimated by assuming that k~ a p-’I2 and Dco2 a p-’, where p is the solution viscosity. This permitted using the same ~ and potash solutions. values of D c o ~ / ~forL water Absorption into Unmodified Potash Buffers. The criteria discussed above predict that pseudo-first-order conditions prevail for all the conditions studied. Thus, for a series of runs with the same buffer solution a t different os. ( k ~ a should ) ~ be linear stirrer speeds, a plot of (Equation 12). The slope and intercept of such a plot can be equated to (c*)’and ( u C * ) ~ & O ~ ~ O H [ O Hrespectively. -], Parameter +OH a t a given stirrer speed is then given by
+
(intercept) +OH
=
(19)
(slope)
where k ~ refers a to the given r.p.m. This method was used to calculate “experimental” values of +OH for solutions I and I1 a t 18’ and for solution I11 a t 25’ (Table IV). For comparison, “predicted” values of +OH were calculated using the Nysing and Kramers (1958) relationship to estimate k o ~ [ o H - ] . Nysing and Kramers found that for various carbonate-bicarbonate buffers a t 20°,
independent of the ionic strength, 1. An over-all activation energy of 10 kcal. per mole was used to estimate k o ~ [ O H - l a t 18’ and 25’. I n all cases, the “experimental” +OH values were greater than the “predicted” values. The ratio of the “experimental” to “predicted” +OH was 2.8 for Solution I (Bo),2.6 for Solution I1 (Bo),and 1.9 for Solution I11 (25’). The experimental values were used for interpreting the data for amine-promoted absorption. Absorption into Amine-Promoted Potash Solutions. The results presented in Table I11 confirm the expected increase in absorption rate and indicate the relative effectiveness of various amines under the experimental conditions. To demonstrate that the observed effect was persistent and
Table IV.
COz Absorption into Potash Solutions
Solution and Conditionsa 1/18’/1 atm. *
R.P.M.
kLa, Set.-*
&JH
105 78
4.0 X 2.6
0.40 0.99
11/18’/1 atm.
105 78 55 38
4.5 X 2.9 1.68 0.97
0.37 0.92 2.7 8.0
III/25”/1 atm.
105 78 55
4 . 7 X 10+ 3.0 1.76
a
1 atm.
=
P
=
1.52 3.6 10.9
PCo2+ pHzo,
VOL.
8
NO.
3
AUGUST
1969
419
32 28
e-N
24
5
8
20
2
$
16
2
P I-
L
3
12
4
8
4
0 TIME, min.
Figure 3.
Chemical absorption of
COz
Temperature 18' C. System pressure 1 atm. Stirrer speed 105 r.p.m.
0
Saln. I (1M HCOI-: 1M C0z2-) Soln. I -I-0.1M MEA Ir, 0.1 M MEA in water
30
25
,d
e
N
8
20
w'
5
15
2
P In. 0 e
3
10
5 1 *553 Conversion
00
25
Figure 4.
50
75
TIME, 100mln.
125
150
175
;
0
COSabsorption into potash solutions
Temperature 25' C. System pressure 1 a h . Stirrer speed 105 r.p.m.
0 0 1.5M KzCOa (initial) 1.5M KzCOa (initial) f 0.08M EAE EAE added after 1 2-min. absorption into unmodified KzC03
that free amine was regenerated, 20-minute runs were carried out with unmodified potash buffer, with buffer promoted with 0.1M MEA, and with 0.1M MEA in water (Figure 3 ) . Thus, while the rate of COz absorption into aqueous MEA exhibits a marked decrease as MEA is converted to carbamate, the rate of absorption into MEA-promoted buffer solution 420
I 6 E C
FUNDAMENTALS
decreases only slightly because of the high capacity of the buffer for absorbed COP (released by Equation 3 proceeding in the reverse direction). Additional evidence of the persistence of enhanced CO2 absorption rates in the presence of amine is provided in Figure 4, which presents the data for two runs with 1.5M
potassium carbonate solutions. As shown, the addition of 0.08M EAE produced significantly higher absorption rates over a wide range of conversions of carbonate to bicarbonate. Of the amines tested, EAE was the most effective and was therefore selected for more detailed evaluation. Table V presents experimental results obtained for various EAE concentrations at 25' and system pressures of 1 atm. and 75 mm. of Hg. The reduced pressure runs were made to illustrate the substantial enhancement in rate obtained under conditions approaching pseudo-first-order behavior, as discussed below. Application of the simplified regime criteria presented above (Equations 13 and 14), with reasonable values of the physical parameters, suggests that absorption into the aminepronioted potash solutions might occur in a mixed regime a t 105 r.p.ni. but would approach diffusion-controlled behavior a t lower r.p.ni. This was supported by the observation that the absorption rates for the amine-potash systems in Table I11 did not vary with the 1.5 power of r.p.m. with stirrer speeds between 55 and 105 r.p.m. On the average, the rate at 105 r.p.m. was 42y0 greater than at 78 r.p.m., which in turn was 3Oy0 greater than at 55 r.p.m. When diffusion-controlled conditions exist, a direct proportionality between absorption rate and k ~ isa predicted by Equation 16. These results are not conclusive, however, and may reflect variations in a or a kLa-r.p.m. relationship for amine-potash solutions different from that found for water. Several screening runs carried out a t 25' demonstrated increased enhancement at the higher temperature for solutions promoted by EAE, hydrazine, and pyrrolidine, and decreased enhancement with benzylamine and MAE. Determination of equilibrium surface tension values for a few amine-promoted potash solutions indicated relatively small surface activity by the amines. For a 1 to 1 buffer with 0.1M amine, the potash surface tension was reduced by 8% with MAE, 16% with EAE, 11% with pyrrolidine, and < 1% by morpholine. No attempt was made to investigate the importance of interfacial turbulence during absorption in the course of this work. Absorption into EAE-Promoted Potash Solutions. An approximate quantitative interpretation of the results presented in Table V can be made if it is assumed that a diffusion model (Equation 16) describes absorption a t 1 atm., and that absorption a t the reduced pressure can be represented by a pseudo-first-order reaction model (Equation 15). The enhancement, e , for the two cases is then given by Table V.
Equations 17 and 18, respectively. Absorption into unmodified potash solutions occurs under pseudo-first-order reaction conditions for both pressures. Accordingly, straight lines are drawn through the 1-atm. data plotted as e us. [Am] in Figure 5. From Equation 17, the slopes and intercepts of these lines can be used to calculate D C O J D Aand ~ [RR'NH],/[Am]. Using experimentally determined values of t # t ) ~ ~(Table IV) and C* = 1.83 X lo-' mole per liter (Table 11), the 1-atm. results indicate that D c o ~ / D A ~ - 'and ~ [RR'NH],/[Am]-0.37 for the EAEpromoted potash solutions a t 25'. The calculated amine ratio suggests that a substantial portion of the total amine in this system is available for reaction with C02 (although, as noted following Equation 16, the estimated quantity may actually represent [RR'NH], [RR'NHzf],, both of which are available for reaction). Similarly, for the 75-mm. runs, values of karn can be calculated from the slopes of the straight lines shown in Figure 6, which were drawn to intercept the vertical axis a t e = 1 in accordance with Equation 18. Using the value of [RR'NH],/[Am] derived from the 1-atm. data and appropri-
+
0
Figure 5. solutions
0.05 0.10 0.15 TOTAL AMINE CONCENTRATION, [Am], mole/l,
0.20
COz absorption into EAE-promoted potash P = 1 atm. f = 25" C.
COn Absorption into EAE-Promoted Potash Solutions
System Pressurea
1 atm.
[Am], Mole/L.
0.047 0.092 0.139 0.185
75 mm.
0.047 0.092 0.139 0.185
R.P.M.
e
E
(Nu)'/(Na)
105 78 105 78 105 78 105 78
1.39 1.20 2.00 1.45 2.02 1.65 2.36 1.82
105 127 105 127 105 127 105 127
3.26 4.24 4.62 5.88 5.43 7.15 6.63 8.85
TOTAL AMINE CONCENTRATION, [Am], mole/l.
Figure 6. solutions
COz absorption into WE-promoted potash P = 75 mm. Hg t = 25" C.
VOL.
8
NO.
3
AUGUST
1969
421
ate values of D ~ o d k ~(from ' physical absorption results) and +OH (from unmodified potash solution results), an average value of kAm- 1 X lo4 liters/mole-sec. is calculated. This is in reasonable agreement with the value given by Sharma ~ -X 10' (1965) for the COz-EAE reaction a t 25' C., k ~ 1.45 liters/mole-sec. The above discussion is only approximate, since it is possible that mixed-regime mass transfer occurred during the 1-atm. runs and that surface distortion was significant in the reduced-pressure runs a t 127 r.p.m. At a given EAE concentration, the absorption rate a t 1 atm. and 25' was on the average higher by -40% for 105 us. 78 r.p.m. and by -15% for 78 us. 55 r.p.m. (cf. average values for various amines a t 1 atm. and 18' given above). Under diffusion-controlled , expected values conditions and with k ~ 0:a ( r . ~ . m . ) l . ~the would be 57 and 69y0, respectively. For the reduced-pressure runs, a pseudo-first-order reaction model predicts no de~> l ) pendence of absorption rate on stirrer speed (with + A > whereas in fact an average increase of 7y0 was found for 127 us. 105 r.p.m. This, however, may be attributed to surface distortion rather than to the effect of a mixed absorption regime. In any case, the results demonstrate a dramatic increase in absorption rate a t low COSpressures and thereby tend to support the proposed mechanism of enhancement via reaction with free amine in promoted potash buffers.
mixed amine-potash solutions has been described by Danckwerts and McNeil (1967s). Increasing the rate of mass transfer in the liquid phase may also produce situations in which gas-phase mass transfer controls (especially with lean gas streams), thus limiting the extent of rate improvement obtainable with amine promoters which affect only liquidphase mass transfer rates. Several other factors are also relevant in developing a COZ absorption process utilizing amine promoters. Desorption characteristics must be checked to evaluate the over-all process benefits properly. More importantly, the suitability of a particular amine under consideration must be established under process conditions-i.e., upon consideration of amine vapor pressure; stability; corrosion, fouling, and foaming tendencies; toxicity; and inactivation through reaction with other components present in the gas stream (H& HCN, CSe, COS, etc.). And finally, the optimum amine concentration for a given application will depend on the improvements obtained and the associated chemical costs. Further investigation of the proposed technique would be worth while in view of the sizable incentives for developing improved C02 absorption processes. Nomenclature = specific interfacial area for mass transfer,
cm.-l = total amine present in system, [Am] = [RR'NH] -I- [RR'NCOO-]
Conclusions
The limited experimental data presented above demonstrate the substantial increase in rates of C02 absorption into potash solutions produced by the addition of small amounts of selected amines. The results can be explained approximately in terms of the reaction of COz with free amine according to well-known absorption-reaction models. Although interfacial turbulence can play a significant role in absorption systems, this effect is believed to be small for the EAE systems studied, in view of the marked difference in enhancement observed a t high and low Pco2. The concentration of free amine at the interface through surface adsorption is also a possibility, although this may be of secondary importance in view of the relatively low surface activity exhibited by the few amines for which surface tension measurements were made. In any case, additional physicochemical data (especially for amine-carbonate equilibria) are needed to establish a satisfactory mechanism adequately. For commercial applications of amine-promoted COz absorption into potash solutions, additional experimental work is needed to demonstrate the technique and to obtain process data under practical conditions (especially higher temperatures) and in representative equipment (packed or plate towers). -4vailable data (McNeil, 1965) suggest that for MEA more free amine would be available for reaction with COS a t higher temperatures-i.e., a fourfold increase in K,, between 18' and 50'. On the other hand, the stirred cell used in the present work gave a relatively low value of a, which facilitated the regeneration of free amine in the bulk solution by dissociation of carbonate (Reaction 3) followed by Reaction 1. In commercial equipment with higher values of a, the reaction of C02 with OH- in the bulk can become controlling (especially for high Pco2),thus reducing the benefit derived from the increased rate of C02 reaction with free amine a t the surface. If this occurs, however, the bulk reaction of COz with OH- can be accelerated by including a hydration catalyst in the promoter formulation; the effect of a hydration catalyst on COP absorption into 422
l&EC
FUNDAMENTALS
+
[RR'NH2+], moles/liter = solubility of solute (COz), moles/liter or mole/c c . = diffusivity of C02 and amine, respectively, sq. cm./sec. = enhancement factor 3 [ ( N u ) ' / (Nu)] = ionic strength, moles/liter = second-order rate constant for COZf OH(Equation 1) and C02 RR'NH (Equation 3), respectively, liter/mole-sec. = pseudo-first-order constant for COz 4-H2O (Equation 2a), sec-I. = liquid-phase physical mass transfer coefficient, cm./sec. = first and second ion-product constants for carbonic acid (Equations 2 and 4), moles/liter = ion-product constant for water (Equation 5), moles/liter = ion-product constant for RR'NH-RR'NCOO- equilibrium (Equation 3) = ion-product constant for RR'NH-RR'NH2+ equilibrium (Equation 6), moles/liter = Kl/K,, moles/liter = absorption rate per volume of solution for water or unmodified potash solution, moles/liter-sec., or moles/cc.-sec. = absorption rate per volume of solution for amine-promoted potash solution, moles/ liter-sec. or moles/cc.-sec. P , Pco2, P H ~ = O total pressure, partial pressure of COZ and partial pressure of HzO, respectively, atm. or mm. Hg T = bicarbonate-carbonate buffer ratio, [HCO3-]/[C03*I
+
GREEKLETTERS = fractional saturation for carbonate solu-
tions
Danckwerts, P. V., Sharma, M. M., Chem. Engr. 44, No. 202, CE244CE280 (October 1966). Eickmeyer, A. G.,‘ Chem. Eng. d6, 113-16 (Aug. 25, 1958). Ellis, J. E . , Trans. Inst. Chem. Engrs. 38, 216-24 (1960). Jeffrevs, G. V., Bull, A. F., Trans. Inst. Chem. Enqrs. 42, T118-25
-~ - (moles COS absorbed per liter) [C032-10
I.(
= solution viscosity, cp.
@OH, @Am
= parameter for absorption with reaction,
Dconkos[OH-I/k2 and DCO~[RR’KH]/~L~, respectively
(1964).
Killeffer, D. H., I d . Eng. Chem. 29, 1293 (1937). hlcNeil, K. M., Ph.D. dissertation, University of Cambridge, 196.5.
McNeil, K. M., Danckwerts, P. V., Trans, Inst. Chem. Engrs. 42. T294-7. ( 1 9fi4). __,
SUBSCRIPT
_ _ I -
= initial value, before COZ absorption
0
~
Pvlullowney, J. F., Petrol. Refiner. 36 (12), 149-52 (1957). Nysing, R. A. T. O., Kramers, H., Chem. Eng. Sci8,Sl-9 (1958). Pinsent. E. R., Pearson, L.. Roughton, F. J. W.. Trans. Faraday SOC.62. 1512-20 (1956).’ - ’ Kiou, P., Cartier, P., Compt. Rend. 184, 325-6 (1927); 196,
literature Cited
1727-8 (1928).
Astarita, G., lIarrucri, G , Gioia, F., Chem. Eng. Sci. 19, 95-103
Sharma, M. &I., Trans. Faraday SOC.61, 681-8 (1965). Sharma, hl. bl., Danckwerts, P. V., Chem. Eng. Sci. 18, 729-35 (1963); Trans. Faraday SOC.69, 386-95 (1963).
(1964).
Benson, 13. E., Field, J. H., Hayes, W. P., Chem. Eng. Progr.
RECEIVED for review July 22, 1968. ACCEPTED January 10, 1969.
62 110). 433-8 (1956).
Ilanckwe;ts, P. Y., Gillham, A. J., Trans. Inst. Chem. Engrs. 44 (2), T42-T49 (1967).
Danrkwerts, P. Y., IIcNeil, K. >I., Chem. Eng. Sei. 22, 925-30 (1067) ,-. /. Danckwerts, P. V., McNeil, K. X,, Trans. Inst. Chem. Engrs. .I.
46 ( I ) , T32-T49 (1067).
Work carried out during 1965-66, while A. L. Shrier was a rstdoctoral visitor in the Department of Chemical Engineering, niversity of Cambridge, on leave from Esso Research and Engineering Coo
ESTIMATING RATE CONSTANTS An, Improvement on the Time-Elimination Procedure NORMAN R. DRAPER AND
HIROMITSU KANEMASU
Department of Statistics, University of Wisconsin, itfadison, was. 53706
RElJl
MEZAKI
Department of Engineering and Applied Science, Yale University, New Haven, Conn. 06520 In certain complex chemical systems, the exact starting time of the reaction i s not known. One method sug. gested for treating such situations is to eliminate reaction time from the differential equatiohs which describe the system, and estimate the parameters in the models which result. The deficiencies o f this method are first illustrated by two constructed examples. An alternative method of tackling the problem is then presented, and i s applied to the same two examples to demonstrate its superior properties.
N RECENT years great progress has been made in the
I development of systematic procedures for determining rate constants in complex reaction systems. The development and application of these procedures have been documented and extensively discussed (hmes, 1960, 1962; Ark, 1964; Ball and Groenweghe, 1966; Himmelblau et al., 1967; Lapidus, 1961; Wei, 1962, 1963, 1965). The modeling process typically involves the following sequence of steps: -4. Postulation of plausible reaction models based upon experimental findings and setting up of rate equations which represent the principal features of the models. B. Estimation of the rate parameters involved in the rate equations, utilizing experimental observations. C. Examination of the adequacy of the fitted models via statistical methods such as examination of residuals and analysis of variance, and physical and chemical interpretation of the parameter estimates. To provide (for step A ) a mathematical representation of complex chemical systems, it is a common practice to postu-
late differential rate equations which describe the concentration changes of all existing major components with respect to reaction time. The analytical or numerical solution of these equations is usually possible but is often not easy, particularly with a complex system which involves many reaction components and, consequently, many unknown rate parameters. The use of a “steady-state approximation” may considerably simplify the situation. However, in many problems, such an approximation obviously fails and leads to an erroneous interpretation of rate data (Bowen et d.,1963). The elimination of an independent variable, frequently reaction time, has been suggested as an alternative procedure to obtain a simplified rate expression (Benson, 1960). The elimination can usually be performed readily by dividing all but one of a series of differential equations by the remaining equation. This suggestion appears, a t first sight, attractive, particularly when the starting time of the reaction is not known. Such a situation is often encountered, for example, when a recycling catalytic reactor is used for a kinetic experiVOL.
8
NO.
3 AUGUST
1969
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