inequality constraints defined so that no penalty is imposed if a n inequality is satisfied-i.e.,
The aj’s are positive scaling fact,ors which weight the constraints relative to each other to facilitate the hillclimbing procedure. X method for choosing these factors automatically in the course of the optimization is described by Keefer and Got’tfried (1970). This strategy, unlike many optimization procedures, does + not require a st’artiiig point (initial value for X) that satisfies the constraiiits. This can be importaiit in certain complex applications wherein finding a “feasible point” is t’he most difficult part of the problem. I n such cases the effort required to obtain the final solution by this strategy is often not much greater than that required to find the start’ing point for some other optimization procedures. Furthermore, once a feasible point has been attained, this strategy does not limit subsequent’ moves by t’lie opt,iniizer to the feasible region. This can be a desirable feature in problems where the optimizer would have a difficult path to follow to reach the optimum if it were confined to t’hefeasible region.
-aNomenclature vector of lower bounds on independent variables =
ai = lower bound on i t h independent variable * b = vector of upper bounds on independent variables 6 , = upper bound on ith independent variable gj = j t h constraint k = number of equality coiistraint’s LOFF = number of variables moving off bounds during set of pattern iterations m = total number of constraint’s n = number of independent variables
N P T P = mapping array for pattern variables onto set of independent variables N P T S = mapping array for simplex variables onto set of independent variables KVS = number of simplex variables KVSOLD = previous number of simplex variables N V P = number of pattern variables + X = vector of independent variables x1 = i t h independent variable y = objective function z = modified objective function
GREEKLETTERS CY
6 A u
= =
= =
scaling factor forjth coiist’raint inequality constraint “off-onJJswit~ch penalty coefficient sum of constraint violations squared
literature Cited
Box, hI. J., Computer J . , 8 , 42-52ij1965). Bracken, J., McCormick, G. P., Selected Applications of Nonlinear Programming,” Wiley, New York, N. Y., 1968. Fiacco, A. V., McCormick, G. P., “Xonlinear Programming:
Sequential Unconstrained Minimization Techniques,” Wiley, New York, N. Y., 1968. Fletcher, R., Powell, M. J. D., Computer J . , 6 , 163-8 (1963). Gottfried, B. S., Bruggink, P. R., Harwood, E. R., Znd. Eng. Chem. Process Des. Develop., 9, 581-8 (1970). Hooke, R. J., Jeeves, T. A , , J . Assoc. Comp. Much., 8 , 212-29 (1961).
Keefer, D. L., Gottfried, B. S.,AIZE Trans., 11, 281-9 (1970). Koaalik, J., Osborne, AI. It., “Methods for Unconstrained Optimization Problems,’’ Elsevier, New York, N. Y., 1968. Nelder, J. -4., Mead, R., Computer J., 7, 308-13 (1964). Ypendley, W., Hext, G. IZ., Hirnsworth, F. R., Technometrics, 4.441-61 (1962).
Urnkda, T., Ichikawa, A,, Znd. Eng. Chem. Process Des. Develop., 10,229-36 (1971).
Weisrnan, J., Wood, C. F., Rivlin, L., Chem. Eng. Progr. Symp. Ser., 61, 50-63 (1965). RECEIVED for review M a y 11, 1972 ACCEPTEDAugust 10, 1972
Kinetics and Mechanism of Carbonation of Magnesium Oxide Slurries Gene 1. Smithson Saskatchewan Research Council, Saskatoon, Sask., Canada S7.2‘ 0 W O
Narendra N. Bakhshi’ Department of Chemistry and Chemical Engineering, Cniversity of Saskatchewan, Saskatoon, Sask., Canada S7.Y O W 0
T h i s paper is the second in a study of the chemical reactions encountered in the Engel-Precht process of &C03 manufacture. T h e first reaction investigated was the hydration of AlgO to l l g ( O H ) n (Smit’hson and Bakhshi, 1969). The carbonation of X g O is of interest because it’ is one method of preparing 1\IgC03.3HzO which in turn is used to produce hIgC03.I 1\Ig(HCO3)?+ 2H20 < AIg(HCOa), + 4H20
Mg(HC03)2 aqueoui
llg0
1 4 T
A
+ CO, lIgC03.5HSO + CO2 lIgC03.3HzO
14oc
(1)
(2) (3)
The time and rate a t which the precipitatioii occurs varied n ith the initial concentration of N g O , COSflow rate, stirring Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
99
Table I. Specific Surface Area and % M g O Consumed in Initial Fast Reaction During Carbonation for Six Samples of M g O Sample
Speciflc surface area, m2/g
% MgO reacted in the
80.8 59.7
95 98 90 80-90 85-90 60
1 2 3
44.0
4
38.7
5 6
34.4
12.1
-
40
initial, fast reaction
speed, and temperature. If the initial concentration of XIgO is higher than t,hat which can be completely converted t'o a stable solution of magnesium bicarbonate (= 0.25 nioljl. at' 18"C), precipitation of magnesium carbonate will occur before all of the MgO is reacted. Cnder these conditions the reaction will proceed through two distinct stages. I n the first stage, MgO reacts with COz forming a solution of magnesium bicarbonate. The second stage is initiated by the sudden precipitat'ion of magnesium carbonate and therefore consists of both the carbonation of X g O and the simultaneous precipitation of magnesium carbonate. Previous studies (Evans and St. Claire, 1949; Horiguchi, 1954; Horiguchi and Atoda, 1951; Horiguchi, 1952; Horiguchi, 1953; and Kataev et al., 1962) of this reaction have usually been limited to the first stage, as the main purpose was to determine the optimum conditions for the production of a supersaturated solution of magnesium bicarbonate. Consequently, the overall kinetics of the carbonation of X g O have not been established. The aim of this study was to establish these kinetics and to determine the reaction mechanism and rate-controlling step.
30
-
io00
100 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No. 1,
1973
3000
Figure 1. Effect of COz flow rate and M g O concentration (in slurry) on rate of reaction of M g O (sample 3, 18°C)
increase has been neglected in all calculations of yGMgO reacted. The samples were analyzed as follows: A 5-ml aliquot was pipeted directly from the stirred, reacting slurry into a sintered bottom, filtering crucible, vacuum filtered, ivashed n i t h 10-20 nd of acetone and then dried by allowing air to be drawn through for several minutes. The air-dried crucibles and contents were weighed, ignited a t 900°C for 1 hr and neighed again after cooling in a desiccator. From these two weighings and the initial weight of the crucible, the percentage of lIg0 in the form of lIgC03.3H20 or lIgCO3. 5H20can be calculated as follom: b W d
- W,) x 100%
=
WC
Experimental
The magnesium oxide samples used in this study were the same as those previously described and studied with respect to their rate of hydration (Smithson and Bakhshi, 1969). X summary of their surface areas is given in Table I. Commercial grade, liquefied carbon dioxide was used throughout. I t s delivery was controlled by means of a twostage regulator followed by a needle valve. F l o ~ vrates TTere measured by passing the gas stream through a triflat floivrator (Fisher and Porter : FP+"-20-G-5-CD glass float) calibrated for CO, rvith a soap film meter. Carbon dioxide was introduced into the l I g 0 slurry through a cylindrical gas dispersion tube (coarse fritt). The reactor was a cylindrical glass vessel having a copper coil (1/4-in. tubing) along it's inside wall (Smithson and Bakhshi, 1969). It was necessary to circulate constant temperature water through the coil (in addition to partially immersing t'he reactor in a constant temperature bath) to maintain a constant react'ion temperature. The reacting slurry was stirred with a four-blade propeller stirrer (4.5-cm diameter) at' 1600 rprn unless otherwise noted. The course of the reaction was followed by determining the amount of magnesium carbonate and magnesium oxide present as solids and then calculating the amount of Mgz' in solut'ion by difference. This was done by analyzing aliquots of the slurry removed a t various time intervals. It was assumed that each sample contained the same total amount of magnesium. This in turn assumes that the volume of the I I g O slurry does not change during carbonation. Calculations based on the specific gravity of the solids and solution present show that the maximum increase in volume on carbonation of 1 mole of 11gO in 1 liter of water is less than 1%. This slight
2000
where b
=
b=
AIgO 3H20 COz
+
70XIgO present as carbonate 40.4
=-=
98
(4)
0 412 for lIgCO3.3HzO
MgO _- _40_4_- 0 301 for XgC03.5Hz0 5Hz0 COz 134
+
lIagnesium carbonate pentahydrate is produced a t 9°C and magnesium carbonate trihydrate a t 28" and 38°C. At 18"C, magnesium carbonate trihydrate is the thermodynamically stable solid phase, but under the nonequilibrium reaction conditions a mixture of both hydrates is produced. I n this case the value of b is interpolated between 0.412 and 0.301 with respect to the ratio of tri- to pentahydrate (the ratio of the tivo hydrates 11as estimated from a microscopic crystal count). Kearly all commercial samples of MgO contain some lIg(OH)*. I n the preceding method of analysis, this Xlg(0H)z would be calculated as "70MgO present as carbonate." Consequently a correction must be made for the lnitlal AIg(OH)2 content. This AIg(OH)z is the result of postcalcination hydration of MgO by atmospheric water vapor and therefore will be confined mainly to the surface of the X g O crystallites. It should react very rapldly on contact with aqueous COP but since a large amount of the X g O surface area is contained within pores not all of this Xg(OH)2 ~ 1 1 be 1 consumed vrithin the initial stages of the reaction. An arbitrary assumption was made that not all of the lIg(OH)2 would be consumed until 50% of the MgO had been reacted. The correction is made by subtracting from the experimentally determined 70 MgO reacted, a n amount equivalent to the SIg(OH)*present, which is decreased linearly from the initial lIg(0H)z content
The kinetics and mechanism of the carbonation of magnesium oxide slurries have been studied in a batch reactor a t 9, 18,28, and 38°C. The reaction conditions used were: COz flow rate 1 2 0 0 ml/min, stirrer speed 1600 rpm, and M g O concentration 1 g-mol/liter. The carbonation was rate controlled by a chemical reaction occurring a t the surface of the solid M g O (up to 28°C). At 38"C, the absorption of COz gas into solution limited the rate of reaction. The activation energy was 7.2 kcal/g-mol. Two reaction mechanisms have been proposed. One involves adsorption of C O z on the M g O surface and reaction between COz and OH[present as Mg(OH)Z] to form HC03-. In the other, a proton is transferred from the solvent shell surrounding COz to an OH- on the M g O surface. The net result is the formation of HzO and Mg2+ a t the solid surface and HC03- from the hydrated COz molecule.
a t the start of the reaction to zero at hiz. Even if this foregoing assumption is incorrect and all of the I\lg(OH)2 is consumed in the initial stages of the reaction, our calculations have shown t h a t the error in the rate curves will be no greater than a few per cent in the worst cases. When the initial layer of IIg(OH)* is consumed the exposed MgO surface will react with water to form a fresh layer of Mg(OH)*. According to Feitknecht and Braun (1967), the formation of Xg(OH)Z on N g O is limited to a monomolecular layer which must be removed before further reaction can take place. It has been calculated that this monomolecular layer of Mg(OH)* should never exceed 1% of the total MgO reacted and, therefore, has been neglected in the calculations. T h e following equations were used to calculate the yo AlgO reacted:
yo MgO reacted
=
W,O
-
w,x
WCO hlgO in solution
100%
+ TIME, min.
Effect of stirrer speed on the rate of carbonation of M g O (sample 3, 18°C)
MgO present as carbonate
where
C?,Ig(OH)z
=
6YCO - TV,
{l
-
b(Wd -
rC) b(Wd0 - WCO)
1)-
[y + WC Total MgO reacted
wco
MgO as Rlg(OH)z initially
C ~ I ~ ( O H is) the ~ portion of the calcination weight loss owing to the I l g ( 0 H ) present. ~ It is taken as zero when its calculated value is negative. This method of calculating "% AJgO reacted" eliminates t'he error caused by magnesium carbonat'e precipitating from solution in the sample while i t is being pipeted and filtered. Previous studies, in which only X g * + in solution was measured, will be subject to this error.
Results and Discussion
Determination of Optimum Reaction Conditions. There are four main variableg which affect t h e rate of carbonation of I l g O slurries. These a r e : stirring rate, COZ flow rate, concentration of M g O in the slurry, and t h e reaction temperature. A series of carbonations was carried out t o establish the optimum values for the first three variables. COZFlow Rate. I n the first set the COZflow rate \vas varied while the following conditions were held constant: concentration of MgO S o . 3, 1 g-mol/l.; temperature, 18OC; stirring speed, 1600 rpm. The results are plotted as the top curve in Figure 1. The rate of reaction increases with flow rate up to
about 1000 ml/min and then levels off. From this curve a flow rate of 1200 ml/min v a s selected and used in all subsequent runs unless otherwise noted. X g O Concentration. The amount of AIgO in the slurry is not too critical up to 1.5 g-mol/l. of water. I t or above this level, there is a reduction in reaction efficiency because of the thickening of the slurry. .it temperatures above 20°C with high levels of IIgO ( 3 1.5 g-mol l.), there is a further reduction in reaction efficiency following the precipitation of 11IgCOa. 3HZ0 n hich produces increased thickening of the slurry. A\t temperatures belox 18°C where IlgCOs. 5H20 precipitates, there is no additional reduction in reaction efficiency because this solid causes no additional slurry thickening. The difference in these two cases is due to the shape of the carbonate crystals. The trihydrate occurs as long, narrow, lathlike crystals which interlace to form a network entrapping water in a gel-like structure. The pentahydrate crystals are hexagonal prisms, nearly cubic, Tvhich cannot produce a n interlaced structure. Because of the slurry thickening and reduced reaction efficiency a t high MgO concentrations, all reaction rate studies were carried out with 10 g AlgO, 250 ml H20 (1 g-mol/l.). Stirrer Speed. The effect of stirrer speed on the rate of reaction is shown in Figure 2. Since the rate of reaction increases with stirrer speed, the maximum stirrer speed available (1600 rpm) was used in all subsequent runs. I n summary the optimum reaction conditions selected were: COZ flow rate, 1200 ml/min; stirrer speed, 1600 rpm; Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
101
I
TIME, min.
Figure 3. Rate curves for sample 1
TIME, rnin
Figure 4. Rate curves for sample 2
and concentration of N g O , 10 g Alg0/250 ml HzO (1 gmol/l.). Rate Studies. When we used the selected values of COz flow rate, stirrer speed, and X g O concentration, each of the six MgO samples was carbonated a t four temperatures (9, 18, 28, and 38°C). Plots of yo MgO reacted vs. time for these samples are shown in Figures 3-8. The sets of curves are similar to one another except for the per cent conversion where they begin to level off. This leveling off in reaction rate prior to complete conversion can be attributed to several causes. One is the possibility of a n unreactive fraction being present in those samples calcined a t the higher temperatures. When N g O is heated for extended periods a t high temperatures (12OO0C),it is converted entirely to the crystalline form periclase (-hderson and Livey, 1961). This phase is extremely unreactive as compared to the lightly calcined N g O . The amount of periclase formed will be dependent on the length of time and temperature of calcination. X comparison of t'he time and temperature of calcination for each sample (Smithson and Uakhshi, 1969) with the leveling off of the rat'e curves 102 Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 1 , 1973
I
I
I
I
I
TIME, mln.
Figure 5. Rate curves for sample 3 in HzO (solid lines) and in DzO (dashed lines)
TIME, mln
Figure 6. Rate curves for sample 4
(Figures 3-8 and Table I) shows a n increase in the amount of unreactive MgO with a n increase in these calcination conditions. Another possibility for the incomplete reaction is the occlusion of X g O within growing magnesium carbonate crystals. Those samples of MgO which react more slovily should produce a greater degree of this occlusion which would account for their incomplete reaction. Many of the rate curves obtained a t 9°C exhibit a slowly decreasing rate of reaction up to about &-6OY0 1IgO reacted, a t which time there is a sudden increase in reaction rate. This increase coincides with the start of the magnesium carbonate precipit'ation as is shown in Figure 9. This refutes Horiguichi's assumption that there is a decrease in reaction rate a t this point [Horiguchi, 1953 (11 99)]. The 18 and 28OC rate curves should exhibit this same rate increase but by the time the magnesium carbonate precipitates, the amount of unreacted 1lgO is so small that t'he increase in rate is masked by experimental errors. For all samples, except sample 6, the 38OC rate curves are linear to about, 807, 1 l g O reacted. -\ny rate-cont'rolling step
TIME
, min.
yo
TiME , min.
yo
Figure 9. Relationship between M g O reacted and M g O precipitated as magnesium carbonate with respect to time (sample 3)
Figure 7. Rate curves for sample 5 7=
I
I
I
I
100
TIME, min
Figure 10. Typical plot of -In ( 1 - X > l l g 0 )vs. time. Also included are the curves (dashed lines) for % M g precipitated as magnesium carbonate with respect to time (sample TIME, min.
Figure 8. Rate curves for sample 6
which is dependent 011 the surface area of Illgo, such as film diffusion or surface chemical reaction, would not give a linear rate curve because of the decrease in 1IgO surface area n i t h t'ime. This suggests that a t this temperature the rate-controlling step is involved with the absorption of CO2 into solution. If COzwere consumed as rapidly as it was absorbed, a constant' rate of react'ion would result as is observed. The absorption of COZ can remain rate limiting only as long as there is a n excess of MgO or OH- to react with the dissolved COz. Eventually the surface area of 1IgO is reduced to the point where it limits the rate of reaction (8070 1IgO reacted) and the linear region changes to a curve. Sample 6 does not exhibit this linear rate curve a t 38"C, probably because its rate of reaction is lower than the rate of C'Os absorption. At the other three temperatures studied, all samples are seen to have exponential-type rate curves. For these three temperatures, the rate-determining step is probably related t,o the surface area of 13gO and should be either film diffusion (mass transfer) or a chemical reaction taking place on or near t h e solid surface. Rate Equation and Rate-Controlling Step. D u e t o the apparent change in the rate-controlling step a t 38°C for
3) samples 1-5> these d a t a have not been used in determining t h e rate equation. F r o m t h e shape of the rate curves a t the other temperatures and sample 6 a t 38"C, it appears t h a t t h e rate of reaction is related t o t h e amount of l l g O present (the rate decreases as 1 l g O is consumed). T h e rat'e-controlling step probably involves t h e diffusion of reactants or products t o or from t h e 1 I g O surface (film diffusion control) or the formation or removal of a product' to the X g O surface (chemical reaction control). The magnitude of the act'ivat'ion energy will often distinguish between these t\vo processes [E,,, chemical react'ioii > 6 kcal,ig-mol > Eachdiffusion (Benson, 1960) 1. X rough estimate of the activat'ion energy can be obtained by plotting log (1, t ~ , ? ) vs. (1/T) for each set of rate curves. This method yields a n average activation energy of about 7 kcalig-mol. Although the value for the activation energy suggests a chemical reaction ratecontrolling step, i t is not high enough to definitely rule out film diffusion. The possibility of mass transfer (film diffusion) being the rate-controlling step can be examined by using t'he equation (Harriott, 1962) : Ssh =
2
+ 0.6 ( . Y ~ ~ ) l i * ( S s ~ ) ~ ' ~
Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 1, 1973
(6) 103
-1.5
c
observed rate curve exhibits a logarithmic relationship between (1 - X,) and time. This relationship is closely approximated by the following equation: -In (1
-40 -
I
I 33
I 35
34
I1
3.6
bT x IO' Figure 1 1. Arrhenius plot o f In kz vs. 1 / T for samples 1 to 6 in HzO and for sample 3 in DzO
Table II. Experimentally Determined Activation Energies for Carbonation of MgO Slurries
(Six samples in HzO and one sample in DzO) Sample
Activation energy, kcal/g-mol
I, HzO 2 , HzO 3, HzO 4, HzO 5, Hz0 6, Hz0 Av 3 , Dz0
7.3 7.3 7 2 6 8 7 2 7.3 7 . 2 i0.2 9.0
(7) The mass transfer coefficient can be calculated from Rate
=
k,.a.Ac
(8)
The rate of reaction and surface area are known experimentally and for Ac it should be possible to use the solubility of ?*Ig(OH)z.This assumes t h a t the concentration of OHdecreases from that of saturated ?.Ig(OH)2 a t the particle surface to near zero a t the reaction zone. K h e n k c is calculated in this manner the values of S s h for all the cases were less than 2. This is the case for diffusion from the particle into a n infinite stagnant fluid. Since all values of I Y s ~lie below this minimum, the possibility of film diffusion being rate controlling is very unlikely. The integrated rate equation for chemical reaction controlling with shrinking spherical particles is (Levenspiel, 1964) : 1-
(I -
x,)lia =
klt
(9)
Plots of 1 - (1 - X,) vs. time are not linear for the samples studied. This is not unexpect'ed as Equation 9 is derived for a single particle size whereas the JIgO powders are composed of a range of particle sizes. An investigation of the hydration of JIgO powders (Smithson and Bakhshi, 1969) has shown t h a t where individual particles obey Equation 9 kinetics, the 104 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
- X,)
=
kzt
(10)
A typical plot of this equation with experimental data is shown in Figure 10. The plots are linear over a limited degree of reaction which increases with temperature from 9-28°C. T h e deviation from linearity begins a t the start of the magnesium carbonate precipitation. Obviously, the removal or addition of certain ionic species by the precipitation process causes this change in the reaction rate and possibly the reaction mechanism. Therefore, only this initial linear portion of the -In x (1 - X,) vs. time plot is applicable to the reaction between COz and MgO, When we use the rate constant, k2, obtained from the initial linear region of Equation 10 plots, it is possible to calculate a n accurate value of the activation energy. Plots of log k 2 vs. (1/T) for all samples a t go, 18", and 28°C are shown in Figure 11. These experimentally determined activation energies are listed in Table 11. The average value is 7 . 2 i 0.2 kcallg-mol. This agrees well with the value of 7 kca1,'g-mol estimated a t the start of this section from plots of ln(l/tl,z) vs. (1,T). Since the rate constants calculated from all the experimental data fall below the minimum theoretical value for rate control by mass transfer and because there is a reasonable fit of the rate data with the modified chemical reaction rate equation, it is concluded that the rate-controlling step is a chemical reaction occurring a t the surface of the MgO particles. Reaction Mechanism. I t has previously (Evans and St. Claire, 1949) been proposed t h a t the main reaction in the carbonation of 1 l g O is between dissolved COz and OH- in solution, the OH- being produced b y the hydration of MgO. This mechanism does not agree with the findings of the present study nor those on the hydration of 11gO (Smithson and Bakhshi, 1969). I n the first place the rate of hydration of l I g 0 is about ten times slower t h a n t h a t required to supply the OH- consumed in the carbonation of 1 I g O and secondly, in the preceding section it has been concluded t h a t the rate-controlling reaction occurs a t the LlgO surface and not in t h e fluid phase. The various reactions which may occur in this system are as follows: ;\IgO(s)
+ HzO(1)
CWg)
lIg(OH)z(s)
(11)
+ HzO(1)
COdaq)
(12)
+ OH-
HC03-
(13)
COz(aq)
+ HnO eH + + H C 0 3 l\Ig(OH)z(s) + 2COr(aq) eM g Z f + 2HC03Ng(OH)z(s) + 2 H + ?\Ig2++ 2H20 COZ(aq)
(14) (15) (16)
Reaction 11 is very rapid, i t is the subsequent removal of the l I g ( O H ) 2product which is the slow step in the hydration of I I g O (Smithson and Bakhshi, 1969). This means that, in a n aqueous slurry, MgO will always have a surface coating of RIg(OH)z. The surface layer of lIg(OH)2 can react with either H + or COz (as) (Equations 15 and 16). Since H + is produced in the hydration of Con,its availability will depend on the rate of this reaction (Equation 14). * i t pH values above 10, reaction 13 predominates over the hydration of COZ (Edsall, 1968; Mills and Urey, 1940). As the pH is decreased, reaction 14 increases as reaction 13decreases until a t a value of 7 or less, the hydration of COz becomes the predominant
reaction. In the carbonation of XgO, the initial pH of the slurry is about 10.8 and decreases throughout the reaction to a value slightly greater than 7 a t completion of t'he reaction (Figure 12). This means that the hydrat'ion of COSis a minor reaction until near t'he end of the carbonation of ilIg0. It can also be calculated, using the average of the rate const'ants tabulated by Edsall (Edsall, 1968) that even at its maximum (at pH values less than 7 ) , +he hydration of COS can only supply about one half the H T required to maintain the observed rate of MgO consumption. Therefore, throughout t'he carbonation of N g O ! the main reaction is between COs(aq) and the 31g(OH)2layer on the surface of the 1IgO particles (Equation 15). It, has been observed by Tomizawa et al. (1966) that the a h v a t i o n energy for the acid dissolution of MgO (prepared by calcining basic magnesium carbonate in a COz atmosphere) is i . l kca1,'g-mol. The close agreement b e h e e n t'he activation energy for acid dissolut'ion and carbonation of l l g 0 suggests a common rate-controlling step for these two reactions. Since the only mobile reactant (other t'lian HzO) in t'he acid dissolution is the hydrated proton, a common rat'e-cont,rollingstep should involve this ion. This hypothesis was tested by comparing the rate of reaction and activation energy for the carbonation of 1IgO in H20 and DzO. The rate of carbonation is about 457, lower in DzO as compared to H 2 0 (Figure 5 ) . I n heavy viater the activation energy increases from 7 . 2 kca1;'g-mol (in HsO) to 9.0 kcal, g-mol (Figure 11). This increase in activation energy and decrease in reaction rate confirms that protons, or in the case of heavy water, deuterons, are involved in the rate-controlling process. Since the concentration of H30+ is low throughout most of the carbonation reaction, the protons involved in the ratecontrolling process will come from free HSO or from OH- in the lIg(OH)Ssurface layer. It is possible that rupture of the 0-H bond may be the actual rate-controlling step. I n the case of heavy wat'er this would be the dissociation of the 0-D bond. T h e difference in energy required to break t'hese two bonds can be calculated from the difference in their enthalpy of formation. The mean value for the dissociation of the 0-H bond in water is 110.6 kcaljg-mol and for the 0-D bond in heavy witer is 112.4 kcall'g-mol. The energy difference between the two bonds, 1.8 kcalig-mol, is identical to the observed difference in activation energy. This supports the proposal that the dissociat'ion of the 0-H bond is t,he ratecontrolling step. As previously nieiitioned there are two possible sources of prot'ons, either from water or the OH- in the l\lg(OH)Psurface layer. If the prot'on in the rate-controlling st'ep is derived from water molecules, one possible mechanism would be as follows. When hydrated COz molecules are brought in contact with the l I g ( 0 H ) surface ~ layer, a proton could be t'ransferred from one of the water molecules in the hydration shell surrounding the COS molecule to a n OH- on t,he solid surface. This would result in the formation of H 2 0 molecules a t the solid surface followed by the release of Mg*+ into solution. The hydroxyl radical left in the hydrat,ion shell would combine with COS to form HCOa- with the net, result being formation of 1\Ig2+ and 2HC03- ill solution. The second possibility, where the rate-controlling proton comes from an OH- in the surface layer, ~ o u l dinvolve adsorptioii of COPmolecules 011 the solid surface. The first st'ep in t,lie reaction betvieen OH- and adsorbed COP would be t'he transfer of the proton from a 1 ion to one of the osygens in Con.This t,ransfer would tated by the dipole moment of COS. S e x t the previously formed 02-would join directly wit,h the C of COP to
r
r
tool
I
I
I
I
TIME , min.
Figure 12. Variation of [H+], the precipitation of magnesium carbonate, and the % MgO reacted vs. time for sample 3
( 1 8°C)
form HC03-. Since magnesium bicarbonate is a n unstable solid the resulting I\Ig2+ and HC03- ions d l immediately dissociate and go int'o solution. Additional experimental work would have to be performed to ascertain which of t,hese is the correct mechanism. Precipitation of Magnesium Carbonate. As stated i n he section on "Rate Equation," t h e selected rate equation is valid only for a n initial portion of the reaction. Deviation from this rate equation coincides with the sudden precipitation of magnesium carbonate. Magnesium carbonate precipitates from niagiiesiuni bicarbonate solutions according to t h e following equation: 11g2+
+ 2HCO3- + z H 2 0 e
+
lIgCOa.~H20 H+
+ HC03-
(17)
From this it is seen that free protons are produced which can react directly with the l I g ( 0 H ) S surface layer or AlgO itself. I n nearly all cases, XgCOa does not start to precipitate unt'il the solution is supersaturated with respect to magnesium bicarbonate, This results in t,he very rapid precipitation of l\IgCO3 and a corresponding rapid production of H'. If there is appreciable unreact,ed l I g 0 in solution this sudden release of H + will cause an observable increase in the rate of reaction. This increase in rate is most, evident at' 9°C because sufficient unreacted 1IgO is present at, the start of the l l g C 0 3 precipitation. The effect is less pronounced a t 18OC and is not observed for most samples a t 28°C because of the decreasing amounts of unreacted MgO remaining xhen precipitat'ion occurs. The release of protons during the precipitat'ion of magnesium carbonate is shown in Figure 12. There is a linear increase in H + from the start of reaction to a point past the start of the magnesium carbonate precipitation and then a sudden increase in this linear rate. The reason for the increase following 11-ell behind the magnesium carbonate precipitation is that when precipitation first starts there is some unreacted I I g O present in the slurry which consumes the excess H+. *issoon a s nearly all of the reactive X g O is consumed, the H + released in solution accumulates and produces the observed increase in the rate of H' addit'ion. The high degree of magnesium bicarbonate supersaturat'ion that occurs before precipitation of l\IgCOs begins is most likely due to the suppression of nucleation. Magnesium carbonate is quite soluble in COS saturated water, and nuclei Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
105
below a certain critical size will redissolve as long as the concentration of dissolved COz is maintained a t a high level. Supersaturation can only proceed to the point where the production and growth of nuclei exceed this redissolution barreir, after which, rapid precipitation of magnesium carbonate will occur. The effect of dissolved GOz on the delay in precipitation of magnesium carbonate can be seen in Figures 9 and 10. At g o , 18", and 28OC, the start of precipitation occurs a t 8-10 min whereas at' 38"C, precipitat'ion begins at about 5 min. This difference can be related to the level of dissolved COz in the reacting slurry. At the three lower temperatures, the rate of absorption of COz is higher than that. consumed by the chemical reaction so that the solution is kept saturated with COz. At 38"C, COz is consumed as rapidly as it is absorbed so that t'he concentration in solution is well below saturation. It is this difference in dissolved COZ content that produces the difference in the time a t which magnesium carbonate precipitates. The higher the concentration of dissolved COP, the greater is the suppression of nucleation. Further evidence of the influence of dissolved COZ on the precipitation of magnesium carbonate is shown in Figures 9 and 10. The curves of magnesium carbonate precipitated vs. time all show a low level of magnesium carbonate from near the start of the reaction to the point a t which major precipitation occurs. This initial level of magnesium carbonate is not actually present in the reaction slurry but results from the sampling procedure. When a n aliquot of slurry is removed from the reaction vessel it is saturated with COz,but this excess COz is rapidly consumed by the MgO present. Once all of the dissolved COZ in the slurry aliquot is consumed, precipitation of magnesium carbonate begins. The amount that precipitates will depend on the temperature, concentration of N g 2 + and HC03- in solution, and the time from sampling to filtration of the aliquot. Conclusions
Wit'h respect to the reactor and the selected esperimental conditions used in this study, the carbonation of X g O in a n aqueous slurry is rate controlled by a chemical reaction occurring a t the surface of the solid MgO (up to 28°C). Under these same conditions the absorpt,ion of COZ gas into solution becomes rate limiting a t higher temperatures (Le., 38°C). The activation energy determined for this reaction is 7.2 i 0.2 kcal/g-mol. Two mechanisms have been proposed. One involves adsorption of CO2 on the MgO surface and reaction between COz and OH- [present as lIg(OH)e]to form HC03-. I n the alternative mechanism. a proton is transferred from the solvent shell surrounding COz t'o a n OH- on the MgO surface. The net result, is the formation of HzOand l 1 g 2 +a t the solid surface and HC03- from the hydrated CO, molecule. I n eit,her of the proposed mechanisms the rate-controlling step is proton transfer. This is confirmed by the difference in activation energy when the carbonation reaction is carried out in D20 as compared to H20 (1.8 kcalig-mol experimental as compared to 1.8 kcal/g-mol t'heoretical). The precipitation of h\lgCOs midway through the reaction produces an observable increase in reaction rate. This action is
106 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
due to the release of reactive H + when the magnesium bicarbonate solution decomposes to form magnesium carbonate solid. Acknowledgment
This project was carried out in the laboratories of the Saskatchewan Research Council, Saskatoon, Sask. The authors thank G . B. Gunn and J. H. Hudson for their interest and time spent in discussing the interpretation of data in this study. Nomenclature
concentration difference, g-mol//l. part'icle diameter, cm D, diffusivity, cm*/sec k, mass transfer coefficient, cm/sec kl = rate constant Equation 10, sec-' k p = rate constant Equation 11,sec-I ;\TR~ = Reynolds number for a particle, ( d p v s p ) / p LVsc = Schmidt number, p / ( p D v ) A'8h = Sherwood number, (k,d,)/D, tliz = time required for 50% completion of reaction, sec T = absolute temperature, OK TI-, = calcined weight of solids contained in 5 ml of slurry, grams TT',o = calcined weight of solids contained in 5 ml of slurry sampled just prior to the introduction of CO,, grams T d = dry ITeight of solids contained in 5 ml of slurry, grams IV,o = dry tveight of soIids contained in 5 nil of slurry sampled just prior to the introduction of COS, grams Xs ' = fract'ion of component B reacted XJIgo = fraction of MgO reacted AC
d,
= = = =
GREEKLETTERS p
=
p
= =
Y,
viscosity, CP fluid density, g/cm3 slip velocity, cm/sec
literature Cited
Anderson, P. J., Livey, D T., Powder Met., 7,189 (1961). Benson, S. W., The Foundations of Chemical Kinetics, p 499, McGraw-Hill, Toronto, Canada, 1960. Edsall, J. T., U. S. National Aeronautics and Space Administration, Special Publication #188, pp 15-27, 1968. Evans, R. L., St. Claire, H. W., Ind. Eng. Chem., 41, 2814 (1949). Feitknecht, W., Braun, H., Helv. Chim. Acta, 50, 2040 (1967). Harriott, P., A.I.Ch.E.J.,8,93(1962). Horiguchi, Yoshikazu, J . S c i . Res. Inst , Tokyo, 48,27 (1954). Horiguchi, Y., Atoda, T., ibid.,45, 144 (1961). Horiguchi, Y., Atoda, T., ibid.,p 193. Horiguchi, Y., ibid., 46, 258 (1952). Horiguchi, Y., ibid., 47,30 (1953). Horiguchi, Y., ibid., p 46. Horiguchi, Y., ibid.,p 99. Kataev. G. A.. Kulikov, B. A., Tr. Tomsk. Gos. Cniv., Ser. Khim., 154,78-86 (1962).
Levenspiel, O., "Chemical Reaction Engineering," p 350, Wiley, New Pork, X.Y., 1964. Mills, A. G., Urey, H. C., J . Amer. Chem. SOC.,62, 1019 (1940). Smithson, G. L., Bakhshi, N. N., Can. J . Chem. Eng., 47, 508 (1969).
Tomizawa, T., Hashimoto, H., Aloteki, K., Kogyo Kagaku Zasshi, 69,2263 (1966).
RECEIVED for review May 15, 1972 Accepted September 6, 1972
