Ind. E n g . C h e m . R e s . 1989,28, 1431-1437
major ions seen in these spectra as well as their various base peaks. There may be some way to distinguish between thermal and electron impact effects. However, additional information is required before any such distinction can be made. The chemical ionization of certain structurally related compounds provokes speculation that thermal effects are present. The presence of a marker for compounds capable of releasing formaldehyde was identified previously by thermal analyses and speculatively in mass spectrometry. The analyses of the fragmentation patterns reported here supported the assumption that the mlz 31 ion seen with N-methylol compounds was a reliable marker for use with mass spectrometric data. The full potential of the thermal and mass spectral markers to the textile industry remains to be explored. An unknown agent can be examined for the capacity to release formaldehyde, and the techniques could offer a means to monitor etherification reactions that are often used to reduce formaldehyde release in textile finishing formulations.
Acknowledgment The authors thank Elena Graves for performing a portion of the mass spectrometric analyses and Mary Patterson for lettering drawings for the figures. Presented in part in the Symposium on Textile Finishing at the 194th National Meeting, American Chemical Society New Orleans, Aug 1987, and the 39th Pittsburgh Conference and Exposition, New Orleans, Feb 1988. Names of companies or commercial products are given solely for providing scientific information and do not imply endorsement by the US.Department of Agriculture over others not mentioned.
1431
Nomenclature amu = atomic mass unit DHEU = 4,5-dihydroxyethyleneurea DMDHEU = N,N’-dimethylol-4,5-dihydroxyethyleneurea EU = ethyleneurea = 2-imidazolidinone M = molecular ion m / z = mass-to-charge ratio PU = propyleneurea = tetrahydro-2-(1H)-pyrimidinone RIC = reconstructed ion current chromatogram Registry No. EU, 120-93-4; PU, 1852-17-1;N,”-dimethyl-EU, 80-73-9; N,Nf-dimethyl-4,5-dihydroxy-EU, 3923-79-3; Nmethyl-4,5-dihydroxy-EU, 22322-62-9; 4,5-dihydroxy-EU, 372097-6; 4,5-dimethoxy-EU,3891-44-9;4,5-diethoxy-EU,24044-29-9; N,”-dimethylol-EU, 136-84-5;N,”-dimethylol-4,5-dhydroxy-EU, 1854-26-8; N,N’-dimethylol-4,5-dimethoxy-EU, 4211-44-3; N,N’-(dimethoxymethy1)-EU, 2669-72-9; N,N’-(dimethoxymethyl)-4,5-dimethoxy-EU, 4356-60-9; N,N’-dimethylol-PU, 3270-74-4; N,”-(dimethoxymethy1)-PU, 13747-15-4;urea, 57-13-6. Literature Cited Beck, K. R.; Springer, K.; Wood, K.; Wusik, M. GC/MS Analysis of Durable Press Agents. Text. Chem. Color. 1988, 20(3), 35. McLafferty, F. W. Interpretation of Mass Spectra, 3rd ed.; Turro, N. J., Ed.; University Science Books: Mill Valley, CA, 1980; Chapters 3, 4, and 8. Shrader, S. R. Introductory Mass Spectrometry; Allyn and Bacon: Boston, 1971, Chapter 3. Trask-Morrell, B. J.; Franklin, W. E.; Liu, R. H. Thermoanalytical and Mass Spectrometric Search for Formaldehyde Release Markers in DP Reagents. Book of Papers 1987 AATCC Internatl. Conf. & Exhibition, 1987, p 72. Trask-Morrell, B. J.; Franklin, W. E.; Liu, R. H. Thermoanalytical and Mass Spectrometric Search for Formaldehyde Release Markers in DP Reagents. Text. Chem. Color. 1988, 20(3),21. Trask-Morrell,B. J.; Kottes Andrews, B. A. Common Thermoanalytical Characteristics of Durable Press Reactants Based on Cyclic Ureas. J. Appl. Polym. Sci. 1988, 35(1), 229.
Received f o r review September 26, 1988 Accepted June 5 , 1989
Absorption Kinetics and Mixing Studies in Pressure Response Cells Richard G. Rice,* John A. King, and Xiang Y. Wangt Department of Chemical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803
The recently popularized pressure response cell (PRC) allows direct physical measurements to deduce chemical rate parameters. Because of its batch nature, the PRC method is subject to serious problems owing to possible interfacial temperature rise following initial gas-liquid contact. Furthermore, if a PRC is not properly mixed, the effects of physical mass transfer can become significant. Conditions under which these two effects can be neglected are determined for the PRC. In addition, an improved cell design that can be used a t elevated gas pressures is described. T h e new cell is applied t o the industrially important dissolution of carbon dioxide in carbonate-bicarbonate solution. Rate parameters are determined t o be in good agreement with the literature values obtained with widely different methods. New results are also obtained which extend the rate parameters to elevated carbon dioxide partial pressures exceeding 3 atm, and it is shown the reaction order is unchanged a t these conditions. Recently, Rice and Benoit (1986) demonstrated how the pressure response cell (PRC) could be used to obtain not only reaction rate constants but also the reaction order. Several researchers have independently developed pressure response methods (Laddha and Danckwerts, 1981,1982; Blauwhoff et al., 1984) to find linear rate constants only. Owing to its physical simplicity, this method is becoming *To whom all correspondence should be sent.
‘Present address: Research Institute of Nanjing Chemical Industry Company, Nanjing, People’s Republic of China.
quite popular (Chakraborty et al., 1986; Versteeg et al., 1987, 1988; Kim et al., 1988). Because the method is a batch process, questions have arisen regarding the possibility of a local temperature rise at the gas-liquid interface. Since the pressure is measured only in the early time period (initial 15 min), it is important to determine if these primary data are in any way contaminated owing to the unwanted local temperature excess. In the present work, we use the PRC method to study C02 reaction-absorption in carbonate-bicarbonate buffer solutions a t higher pressures than heretofore obtained.
0888-5885/89/2628-1431~01.50/0 0 1989 American Chemical Society
1432 Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989
The possibility of a change in the reaction order for higher pressure, such as observed in sulfite oxidation, was uppermost in mind (Rice and Benoit, 1986). It is well-known (Astarita et al., 1983) that, when carbon dioxide is absorbed in potassium carbonate-bicarbonate buffer solutions, the following reactions occur: C 0 2 + HzO COS' COz
-
+ H+
+ OH-
COB=+ HzO
-
HC03- + H+
(1)
HC03-
(2)
HC03-
(3)
HC03- + OH-
(4)
-
(5)
In the buffer solution, equilibrium is attained quickly for the following:
KW
HzO
K2
HC03-
H+ + OH-
(6)
H+ + CO,'
(7)
So the hydroxyl concentration can be calculated with the equilibrium relation [OH-] = (Kw/KJ([C03=l/[HCO,-I)
(8)
Therefore, the rate can now be expressed as
The carbonate conversion, f,, can be defined (Tseng et al., 1988) as
fc
[HCO3-1 = 2[C03'] + [HC03-]
This allows eq 8 and 9 to be expressed in terms of conversion: [OH-] =
(KK:)l?jcfc -
-
Taking the hydroxyl concentration to be essentially invariant yields a linear rate expression for the dissolved gas: where kr depends on the conversion, f,, and the constants kOH,K,, and K2, are dependent on the ionic strength, I. Equilibrium constants K 2 and K , may be estimated with the relationships given by Tseng et al. (1988),which give the proper temperature dependencies. The expression for the overall reaction rate constant in terms of the order in a PRC was developed by Rice and Benoit (1986). For a pseudo-first-order reaction, the expression for the overall reaction rate constant k simplifies to (kO)1/2 =
KHe v, AR,T
Pco,(t)/Po = exp(-Kt)
(15)
provided 1/K < t,, where t, is the total contact time. This constraint is removed for first-order kinetics. Here, Po is the initial partial pressure of COz,and the carbon dioxide partial pressure, Pco2,was calculated as the total absolute pressure, PA,less the saturated water vapor pressure at the system temperature, so pC02
=
-pH~O
(16)
In eq 14, the Henry law constant (He)was calculated with (Danckwerts and Sharma, 1966)
The C02 reaction rate, R , can be written as
R = kH20[C021+ kOH[OH-l [c021
time constant) is easily obtained from the slope of a semilog plot of PcG(t)/Poversus time, since, for any order, Rice and Benoit deduced
(14)
This expression is valid only when the Hatta number Ha > 3. In eq 14, the parameter K (the inverse of the system
log (HH,o/HJ = -KJ
(17)
In this expression, HHlo is the pure water Henry's constant, I is the ionic strength of the solution, and K, is the sum of the contributions owing to ions and dissolved gas. The gas volume above the liquid is V,, and A denotes the interfacial area. The diffusivity, D, can be estimated by the following equation obtained from Ratcliff and Holdcroft (1963) at 25 O C and used by Savage et al. (1980) for temperatures from 40 to 110 OC:
D
= DH20(~H,o/~)0~637
(18)
Viscosity data for carbonate solutions have been reported by Bocard and Mayland (1962). In this work, three series of experiments are used to study this reaction: (i) the COz reaction order is ascertained to verify the existence of pseudo-first-order conditions; (ii) the influence of ionic strength, I , and conversion, f,, on reaction kinetics is examined; (iii) the temperature is varied in order to deduce the Arrhenius parameters. In addition, we make apparently the first accurate measurements of interfacial temperature rise in the initial period of COz absorption with reaction. The development of local temperature gradients during the initial time period is an inherent problem encountered in batch systems such as the PRC. The interfacial temperature rise, which is caused by the heat of solution and reaction, directly affects the physical properties and the interfacial concentration of the dissolved gas. The original chemical model (Rice and Benoit, 1986) is based on the assumption that the surface temperature is equal to the bulk temperature. Only a few studies have been made that measure the excess surface temperature directly, with the most recent work being that of Green and Chiang (1971) who used small junction thermocouples to measure the temperature rise following butane or propane absorption into decane solutions.
Design Details and Preliminary Tests A new cell was designed based on the principles of the Rice-Benoit prototype (1986), as shown in Figure 1. The improvements and modification are as follows. (i) The new cell was made to be stronger and more transparent by using Lexan for the cylindrical body and plates instead of Plexiglas. Lexan, a polycarbonate, resists brittle fracture and sustains excellent chemical resistance. (ii) Mixing uniformity in the region near the liquid surface was improved by using four baffles instead of two. In addition, the distance from the edges of the baffles to the wall of the cell was increased to 5 mm. (iii) The range of pressures under which the PRC could be operated was increased by implementing a new triple
Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989 1433
. .
14
.
‘i 0.6
.
1 4
I
0.4
0.2
-
A
.
4
O
’ 0
,
8
8
,
I
200
,
400
8
..” ,
,
600
,
800
,
I
I , 1000
, 1200
RPM
Figure 2. Effect of the concentration and stirring speed of the rate constant. The physical properties were calculated according to eq 17 and 18. Viscosity was taken from Bocard and Mayland (1962).
=dMP\NG
BOLTS
2
Figure 1. Schematic diagram showing the cross section of the pressure cell.
O-ring sealing arrangement. The new seals, depicted in Figure 1, were designed so that increasing the pressure tended to mechanically enhance the contact made by the O-rings. (iv) The water recirculation rate was increased by increasing the gap in the water jacket surrounding the cell to reduce the pressure drop. (v) Two standard thermistors (YSI 400 Series probes) were sealed in a stainless steel tube and inserted through the top of the cell. The sensors were arranged to contact gas and liquid separately. This permitted measurement of actual cell temperatures, rather than measuring the temperature of the external water bath. The response time of the sensors was less than 0.5 s. The meter itself could be set up to measure either a single temperature or a difference between gas and liquid temperatures. The latter arrangement was used to ensure the existence of vaporliquid equilibria. The internal volume of the cell including ancillary fittings (e.g., pressure relief valve, etc.) was carefully measured before experiments were conducted. The difference between the total internal volume of the cell and the volume of the liquid added is the effective gas volume, Vr The measured cell volume was 1030.6 cm3 and the interfacial area was 52.7 cm2. The standard liquid aliquot for all experiments in the new cell was fixed at 850 cm3, so the gas volume was invariant a t 180.6 cm3. Mixing Uniformity Tests. Comparative mixing performance of the redesigned cell was evaluated with flow visualization techniques in a side-by-side comparison with the original Rice-Benoit cell. A VCR was used to record the mixing process following the addition of a drop of phenolphthalein to potassium carbonate solutions. The stirring speed was varied over a range from 200 to 1100 rpm with a feedback controlled stirrer (IKAMAG REO, manufactured by Drehzahl Electronics, West Germany). The mixing time could be easily determined using the VCR. In addition, the uniformity and stability of the
mixing conditions throughout the cell could be evaluated. Based on these visual tests on the two cells, the following improvements were noted. (i) Mixing was more uniform and steady than previously obtainable. The older cell operated with only two baffles, and when stirring speed exceeded 800 rpm, the liquid interface would become unstable. Worse still, at 900 rpm, the stirring bar would jump out of its stirring groove. With the new cell, even when the stirring speed was set a t the maximum rate (1100 rpm), the stirring bar remained stable. Also, the horizontal interface remained completely smooth for the new design. (ii) The “well-mixed”time was about 7 s for the old cell design with 750-cm3solution at 700 rpm. By comparison, it took only about 3 s for the new cell with 850-cm3solution a t 900 rpm. (iii) It was seen that mixing was most rapid in a region near the center of the flat interface for the older cell. This was a consequence of the placement of the two baffles very close to the cell wall. The new cell had a more uniformly distributed region of rapid mixing. Thus, the modifications mentioned earlier ensure that the interface is more uniformly accessible in the new cell design and mass transfer is independent of radial position. Well-Mixed Criteria. In order to verify that mixing was sufficiently vigorous to satisfy the Hatta criterion, experiments were made to determine a threshold stirring speed, such that increasing the stirring rate did not affect the rate of gas uptake. The rate of reaction is then independent of the stirring speed as long as the stirring speed is held above this critical threshold speed. Experiments were performed for C 0 2absorbed by 850 cm3 of carbonate solution. The initial pressure was consistently maintained a t 3.04 atm (30 psig), and the concentrations of the solutions for the respective tests were 0.3, 0.6, and 0.9 M. The stirring speed was varied from 200 to 1000 rpm. The rate constants k were calculated with eq 14 and are shown in Figure 2. From these plots, it can be seen that the rate of absorption becomes independent of the stirring speed in the range 700-800 rpm. Accordingly, a stirring speed of 900 rpm was used for all subsequent experiments. As an additional test, to allow the Hatta number to be calculated with precision, we measured the pressure response to saturated COz absorbing into pure, degassed water, which was also stirred a t 900 rpm. Figure 3 shows the normalized response. The slope of the line (-kLoARg/( V g H ~ , o )yielded ) a value of the physical mass-transfer coefficient equal to 0.955 X cm/s.
Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989
1434
. . ... .
o t - -
_-
35 __-
-
~
8
1,
-
a
..0
%
-01 -
0
E
I
o_
.
.
a
-0.2
..
.
t-Upper Curve 5 Sec injection I
30
a ?
_1
i
-
,>+Lower
Curve 15 sec injection
a
22 026 200
800
600
400
1000
Time (secj
Figure 3. Absorption in reboiled pure water for estimating the cm/s. physical mass-transfer coefficient; k~~ = 0.955 X 5-p
-____
~
p
-
-
___
-
7 -
0 20 40 Time From C02 Valve Closure (secj
-20 0
_-
n"
60
Figure 5. Interfacial temperature: effect of gas injection rate. 2, _ _ _ _ ~
-
--
_--
a No Mixing I
26
4
0 6 degree excess
-_
I!
23-
1
1
22
~-20
I T _
' 2 U z r j
Gc=3
__--
0 3 degree excess
,
0 20 40 60 Time From C 0 2 Valve Closure (sec)
80
-100
Figure 6. Interfacial temperature: effect of mixing rate.
--. 0
01
03
02 Time (sec)
04
-
Figure 4. Precision thermistor response characterization: hot-water plunge. Least-squares fit slope = 11.874 5-l T = 0.084 s.
Measurement of Interfacial Temperature. In order to address the concerns regarding incorrect parameter estimation owing to interfacial temperature rise, a number of experiments were conducted during which the transient surface temperature was monitored with a separate, very precise temperature measurement system that was equipped for more rapid acquisition of temperature data using a microcomputer dedicated to this purpose. During a series of experiments, the surface temperature and bulk temperature were monitored (as well as the pressure decrease with time) after introducing pure COz into an aqueous solution of 1 M K2C03at room temperature and various mixing speeds. The temperature measurement system used in these experiments was comprised of a Zenith ZlOO microcomputer, a Tecmar AD 212 12-bit A/D board, and thermistor-type temperature sensors. The A/D board was interfaced through a Tecmar DT201 Screw Terminal Junction board which incorporated custom circuitry, providing a steady excitation voltage to the thermistors. The epoxy-coated temperature sensors (Thermometrics Type BR16AB6C8) had a diameter of 0.041 cm and were designed by the manufacturer for fast response and full immersibility in conductive fluids. As shown in Figure 4,the thermal time constant (m,C,/hA,) was found by a stillwater plunge to be about 0.084 s. The accuracy of the measurements was f O . l "C with a precision/repeatability of fO.O1 "C. Data acquisition routines were set up to sample temperatures at a rate of approximate 1Hz until t = 10 s. After 10 s, the C 0 2 was introduced into the cell and the sampling rate was increased to approximately 16 Hz for the period from 10 to 75 s. The sampling rate was
then returned to 1 Hz for the remainder of the experimental period (up to 20 min). Figures 5 and 6 serve to effectively demonstrate the key results of the temperature experiments. The data shown in these figures encompass the typical range of behavior that was observed for the interfacial temperature rise under a variety of conditions. The traces shown were obtained by drawing a line connecting all of the data points collected. In general, when the interface is initially met with pure C 0 2 ,the absorption rate is great and the heat liberated results in a maximal temperature rise (as high as 11 "C). This heat is then rapidly dissipated downward into the bulk fluid, resulting in a smooth exponential decay of the excess temperature. In Figure 5, two experiments that contrast the results obtained by varying the length of time for C 0 2 injection are shown. For the upper curve, the C 0 2 injection time was -5 s, while the lower curve had a COz injection time of -15 s. In both cases, the temperature sensor was positioned, as precisely as possible, directly in the surface at the gas-liquid interface. It had been separately verified that the bulk temperature remained essentially invariant over the time scale shown here. The maximum temperature rise observed, as mentioned previously, was 11 "C and occurred when COP was injected most rapidly. As can be seen, the interfacial spike was broadened and lowered by injecting the COz into the cell more slowly. In addition, the excess surface temperature rises and decays more slowly when the cell is subjected to a slower COP injection rate. However, if the experimental period is considered to start in both cases at the instant when the COz valve is closed, then, within about 30 s, there is little discernible difference between the temperatures obtained after fast or slow C 0 2 injection. Thus, although the injection speed strongly influences the magnitude of the observed interfacial temperature rise, these effects are no longer measurable within 30 s after the injection valve has
Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989 1435 been closed and can be safely ignored thereafter. Another pair of experiments is shown in Figure 6, this time showing the variation resulting from altering the mixing rate. The lower curve in Figure 6 is for the wellmixed case, while the upper curve is from the data collected with no mixing in the cell. These data were collected with the sensor placed at a depth of -0.5 mm below the surface, and the peak heights observed are significantly lower than in Figure 5 as a result. Although a complete discussion of the interfacial dynamics is beyond the scope of this paper, it is worth mentioning, as an aside, that effects from the surface temperature disturbance could be detected only to a depth of 2.0 mm in the well-mixed pressure response cell. The temperature rise for the experiments shown in Figure 6 was about 3.5 "C in the well-mixed case and about 4.5 "C in the case of no mixing. Within 30 s, this heat had been largely dissipated by a combination of conduction and convection, and the temperature excess was about 0.3 "C in the well-mixed cell or 0.6 "C in the unmixed cell. The temperature excess continued to decrease over time and, in the well-mixed case, declined to less than 0.1 "C within 120 s. In the absence of mixing, however, it can be seen that the temperature excess appeared to stabilize and was maintained at a level of 0.3-0.4 "C for the remainder of the sampling period. Other data sets that are not shown here confirmed that this temperature excess was sustained for 20 min or longer when there was no mixing. These results clearly illustrate the critical importance of good mixing in the pressure response cell. In passing, we note that the pressure decreased more sharply in the first 10-15 s for the well-mixed case, before settling into a smooth exponential decay. It appears likely that this behavior is related to the interfacial temperature spike discussed above, suggesting that care should be taken in evaluating this initial portion of the pressure data. However, because the decay of the initial temperature spike is rapid, it should be possible to neglect any further temperature effects after about 30 s as long as the stirring speed is fast enough to provide vigorous mixing. In summary, the temperature data presented suggest that a pause of 30 s at the beginning of an experiment be consistently enforced before accepting data. Under these conditions, with the present cell design and mixing rates of at least 900 rpm, the analysis can be treated as an isothermal operation.
Determination of Reaction Order and Rate Constants The measurement of pressure in the vapor space above the reacting liquid is the essential primary data necessary to deduce the reaction order and rate constant in the liquid. This primary data base, along with the precedence ordering described by Rice and Benoit (19861, can be used to find liquid reactant as well as dissolved gas orders. Applied to the present case for an assumed nth order dissolved gas, they showed that K a so by finding K via eq 15, then a simple log-log plot of K versus Po yields the gas order. Experimental Procedures. Aliquots of 850-cm3carbonate-bicarbonate solutions were degassed and thermally equilibrated before injection into the evacuated cell. Saturated COz was then injected into the vapor phase, and stirring at 900 rpm commenced. After the requisite 30-s delay (to damp temperature rise), the pressure was continually recorded versus time. Following exposure for around 15 .min, solutions were removed and titrated to check the actual amount of COPabsorbed, relative to the amount calculated from pressure drop-off; the agreement
1
-01
4
1
=% 8.
.,1 02
_-
(25deg C)
4 a.
-
4
e
lops1
.
20 PSI 30 PSI
A
..
40 PSI
1
'
~
I
..r
-0 3
~
I -04
4
-* " AA
I . I
-0.5
CT-0
AI
, 200
400
600
800
1000
Time (sec)
Figure 7. Determination of the reaction order.
was consistently within *5%. Determination of Reaction Order. It is widely reported that low-pressure carbon dioxide absorption in carbonate buffer solutions can be taken as a pseudofirst-order reaction (Astarita et al., 1983). However, it remains to be seen if the first-order conditions prevails at higher pressures. A series of experiments was performed by varying the initial partial pressure of pure carbon dioxide from 1.68 to 3.72 atm (10 to 40 psig). Temperature was fixed at 25 "C, and the concentrations were such that [K+] = 1.0 M and the initial value off, = 0.15. Because of the short duration of an experiment, this latter value was taken to be essentially constant. Duplicate experiments were performed in all cases. All the data obtained are plotted in Figure 7 as In (Pco,(t)/Po)versus time. As can be seen, the data overlap on a single straight line. Thus, the inverse of the system time constant ( K ) is essentially invariant with respect to the various initial pressures of COz. If the reaction is nth-order COz, the slope of the straight line is (n- 1)/2 in the logarithmic plot of K versus Po as shown by Rice and Benoit (1986), so Figure 7 implies that n 1, as required. These experiments were performed a t 15, 25, 35, 45, and 55 "C. The same order was obtained for each temperature. Thus, a pseudo-first-order condition seems to exist for dissolved carbon dioxide even at elevated pressures up to 3.72 atm (40 psig). Ionic Strength Effect. Some experiments were performed to assess the effects of conversion (f,= 0.15 and 0.25) and ionic strength. The carbonate conversions so chosen are typical for operations at the top of an industrial absorption tower. The ionic strength was varied from about 0.5 to 2.5 mol/L, while a few solutions went up to about 6.4 mol/L. The temperature and the initial pressure of carbon dioxide were maintained at 25 "C and 3.04 atm (30 psig), respectively. To permit comparison with Kloosterman et al. (1987), we used their equations for estimating the physical properties
-
p
+ 0.118[KzCO,J + 0.063[KHC03] P/PH20 = 1 + 3 ( p 0.998)
= 0.998
-
(19) (20)
where the solution composition is in molarity units. The exponent on viscosity is somewhat larger than deduced by Ratcliff and Holdcroft (1963). In Figure 8, the plots of rate constant k, versus ionic strength show this is proportional to I for I I2.5 mol/L. We also show Kloosterman et a1.k (1987) results for comparison. Our results also agree with Augugliaro and Riz-
1436 Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989 1.5 I
I
1
0.5
0 0
2
1
0
I (mol/L)
Figure 8. Rate constant as a function of ionic strength: Z mol/L; physical properties were calculated from eq 19-21.
< 2.5
Table I. Comparison of t h e Ionic Strength Effect (25 "C)
M,"
f, k w , l/s L/(mol-s) source 0.46 Kloosterman et 0.20 0.03 al., 1987 0.28 Kloosterman et 0,33 0.01 al., 1987 0.23 Kloosterman et 0.50 0.03 al., 1987 0.33 0.027 , 0.365 Augugliaro and Rizzati, 1987 -0.60 present workb 0.15 0.027 0.26 0.031 0.36 present workb
method wetted wall column
0.0257 0.0257 0.016 0.03 0.03,"0.01'
4
6
I (mol/L)
Figure 9. Rate constant as a function of ionic strength: I mol/L; physical properties were calculated from eq 19-21.
> 2.5
6 7 5.5
wetted wall column wetted wall column wetted wall column 4.5
4
\
PRC PRC
'k = kHS + MI. bPhysical properties were calculated according to eq 19-21. Table 11. k&l/s
2
Rate Constants at
Zero Ionic Strenrcth (25 OC) comments source Pins'ent et al., 1956 rapid thermal method Roberta and falling film column Danckwerta, 1962 Astarita, 1967 (20"C) Joosten, 1971 according to Kloosterman et al. (1987) Kloosterman et al., wetted wall column
4 8 3
3.2
3.4
1OOD/T (1/K)
Figure 10. Arrhenius analysis to find the activation energy. Physical properties were calculated according to eq 17 and 18. Viscosity was taken from Bocard and Mayland (1962).
of C 0 2 fixed at 3.04 atm (30 psig) and concentrations such that [K+]/2 was 2.25 mol/L and the initial f, = 0.15, so the ionic strength was about 6.41 mol/L. The Arrhenius-type rate constant can be expressed, ignoring kHzO,as
1987 Augugliaro and Rizzuti, 1987 0.027," 0.031" present workb
0:027
wetted wall column PRC method
'See Table I. bPhysical properties were calculated according to eq 1tJ-h.
zuti's work (1987)aa shown in Table I. Extending these lines to I = 0 yields the value k = kH a t 25 "C.These values were also in good agreement wit$ those reported elsewhere (see Table 11). In Figure 9, we show that sign%cant departure from linear behavior occurs for larger ionic strengths. It must be noted that when ionic strength is less than 0.5 mol/L, then conditions are such that the Hatta number 13; hence, the mass-transfer effect cannot be neglected. Under such conditions, the current chemical rate control model is invalid (e.g., Z = 0.5, Ha = 3.29; I = 0.4, Ha = 2.85). In this work, the data where I < 0.5 mol/L were excluded, since the mass-transfer coefficient was determined experimentally, so the Hatta number could be calculated with considerable certainty. We note also that, in the limit for dilute solutions, (kH,&)0.5 k L o , and the data herein reported obeyed this approximation very closely. Determination of Activation Energy. Experiments were done a t 15,25,35,45, and 55 O C , with initial pressure
-
For the calculation of the hydroxyl concentration (see eq 8), the values for the equilibrium constants K, and K2 were estimated from the equations reported by Tseng et al. (1988). The results are shown via the Arrhenius plot in Figure 10. The expression for the slope of the straight line is, using the contribution by ionic strength, suggested by Astarita et al. (1983):
+
log koH = 13.592 - 2890 0.081
T
(23)
The first two terms can be compared with those of Astarita et al. (1983): log koH = 13.635 - 2895 + 0.081
T
The activation energy using the present results is computed to be
E A = 13.22 kcal/mol
(25)
This result is in good agreement with the results published by Savage et al. (1980) at nearly the same conditions when using a wetted sphere device.
I
Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989 1437
Comments and Conclusions The pressure response cell (PRC) allows wide ranging pressure conditions to be studied, and a direct physical measurement of rate parameters evolves. Because it is a batch process, careful attention must be given to the possibility of local hot spots, which introduce errors in the computation of rate constants. The present study shows that proper cell design and good mixing can overcome most such transient heat problems. With such care, good estimates of the rate parameters are obtainable in a straightforward way. We conclude that the order for dissolved COz reacting in carbonate-bicarbonate solutions is unity even for partial pressures up to 3.72 atm (40 psig). Acknowledgment Support from the World Bank (to X. Y. Wang) and from the National Science Foundation (Grant CBT 8513174) is gratefully acknowledged.
Nomenclature A , = thermistor probe area, cm2 A = surface area of gas-liquid contact, cm2
C, = specific heat thermistor probe, cal/(g.OC) D = diffusivity of COO,cmz/s EA = activation energy for reaction, kcal/mol f, = carbonate conversion h = thermistor-water heat-transfer coefficient cal/ (cm2-s."C) Ha = Hatta number, (kD)0,5/kLo He= Henry's law constant, atm.L/mol HHz? = Henry's law constant for pure water, atm-L/mol I = ionic strength of the solution, mol/L k = rate constant, l / s kHIO = rate constant of COz with water, l / s kLo = physical mass-transfer coefficient, cm/s koH = rate constant of cos with hydroxyl ion reaction, L/ (mol-s) k , = rate constant of CO,, with pseudo-first-order reaction, l/s
K = inverse of system time constant, l / s K , = dissociation constant of HC03-, mol/L K , = solubility factor, L/mol K , = dissociation constant of water, mo12/L2 M = proportionality constant (Table 11),L/(mol-s) mp = mass of thermistor probe, g Pcoz = partial pressure of COO,atm (psi) P H ~= O partial pressure of HzO, atm (psi) R, = gas constant, 82.05 atm.cm3/(mol-K) R = rate of reaction, mol/(L.s) t , = contact time T = temperature, K V , = effective gas volume, cm3 Greek Letters density, g/cm3 p = viscosity, g.cm-'-s-' p =
Subscript
b = bulk liquid
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Received for review February 8 , 1989 Accepted June 7, 1989
