Ind. E n g . C h e m . Res. 1989,28, 298-302
298
GENERAL RESEARCH Thermodynamic Analysis of Results Obtained by Examination of the Forsterite and Spinel Formation Reactions in the Process of Magnesium Oxide Sintering N. Petric* and V. Martinac Faculty of Technology, University of Split, 58000 Split, Yugoslavia
E. TkalEec and H. Ivankovid Faculty of Technology, University of Zagreb, 41000 Zagreb, Yugoslavia
B. Petric Dalmacija, Dugi Rat, Yugoslavia
The forsterite and spinel formation reactions, 2Mg0 + Si02 = MgzSi04and MgO + A l z 0 3 = MgA12O4, respectively, were examined in the process of the isothermal sintering of magnesium oxide obtained from seawater and of magnesium oxide p.a. (pro analysi purity grade). The sintering process was carried out in the temperature range from 1300 to 1600 "C, with the duration of isothermal sintering being 7 = 5 h. The reaction flow was examined by quantitative and qualitative X-ray analysis and by thermodynamic analysis of results obtained, in order to establish the conditions of formation of these minerals in various samples examined and the relationship between the quantity of minerals formed and the product properties. The specific surface, chemical composition, and dislocation density were determined for the magnesium oxide samples examined. It is of interest to find out how the presence of SiOzand A1,03, which react with magnesium oxide in the sintering process to form forsterite and spinel, respectively, affects the properties of sintered magnesium oxide, which is a high-quality refractory material (Petric et al., 1987). The magnesium oxide used was obtained from seawater by substoichiometric (80%)and overstoichiometric (120%) precipitation of magnesium hydroxide with dolomite lime. The 80% precipitation of magnesium hydroxide is a better method, as it significantly increases the thickener capacity, i.e., the precipitation rate (Petric and Petric, 1980). The process of obtaining magnesium oxide from seawater is relatively simple. Precipitation with calcium hydroxide from dolomite lime yields magnesium hydroxide which calcines into magnesium oxide (Heasman, 1979). If dolomite lime is used as a precipitation agent, the chemical reaction is as follows: BCaO.MgO(s) + 2Mg2++ SO:- + 2C1- + 4Hz0 = 4Mg(OH),(s) CaSO,(s) + (Ca2++ 2C17 (1)
+
This paper presents the results obtained by examination of reactions of MgO-SiOz and MgO-Alz03 systems utilizing magnesium hydroxide, obtained from seawater by substoichiometric and overstoichiometric precipitation methods and magnesium oxide p.a., the results having been analyzed thermodynamically,which has not been recorded in the literature so far.
Experimental Section The content of MgO and CaO in seawater used for magnesium oxide precipitation was MgO = 2.360 g dm-3 and CaO = 0.574 g dm-3. The composition of dolomite used was SiOz = 0.076%, Fez03 = 0.064%,A Z O 3= 0.04270,
Table I. Chemical Composition of Magnesium Oxide Obtained from Seawater sample MgO, % CaO, % MgO (80% pptnIn 99.49 0.33 MgO (120% pptn) 98.25 1.36 pptn is precipitation.
CaO = 57.55%, and MgO = 42.27%. The magnesium hydroxide obtained was dried at 105 "C and then calcined at 950 "C. Table I shows the chemical composition of magnesium oxide obtained from seawater, with regard to magnesium oxide and calcium oxide. The magnesium oxide p.a. used was produced by Kemika, Zagreb, Yugoslavia (MgO minimum purity 97%). For this study, mixtures were prepared containing 2 % , 5%, and 10% SiOzor Al2O3,with a stoichiometric relation of MgO and SiOz components (2:l). The SiOzp.a. and A1,0, powders (for chromatography) used in the experiments were produced by Kemika. SiOz and A1203 were added in the form of a-quartz and a-corundum, respectively. Samples were homogenized by manual mixing in absolute alcohol for 30 min. The mixture was then dried at 80 "C until all of the alcohol evaporated. After drying, the mixture was crushed into a fine powder, and the powders were mixed well again. The mixtures were compacted by a cold pressing process. Pressing was carried out in a hydraulic press at a pressure of 625 MPa. The compacts were sintered at temperatures of 1300, 1400, 1500, and 1600 "C, with an isothermal heating duration of 7 = 5 h. The sintering at 1300 and 1400 "C was carried out in an electric furnace. A gas furnace was used for sintering at 1500 and 1600 "C. The
0888-5885/ 89/ 2628-0298$01.50/0 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 299 formed and the product properties. By applying fucdamental equations (Hinz, 1971; Kriiiianovskij and Stern, 1973) and the expressions for forsterite, MgzSi04,
Table 11. Specific Surface, S , for Magnesium Oxide Samples sample S, cm2 g-' MgO (80% pptn" with dolomite lime) 14 436 13 124 MgO (120% pptn with dolomite lime) 20 108 MgO p.a.
AH",= -72957 A S o T = -39.73
Table 111. Dimensions of Unit Cells ( a ) ,Average Grain Size ( D ) ,and Minimal Dislocation Density ( p ) for MgO Samoles sample a,nm D,nm p , cm-2 MgO (80% pptn)" 0.4214 standard MgO (120% pptn) 0.4213 177.5 1.5 X 1O'O MgO p.a. 0.4226 22.2 6.1 X 1Ol1 ~
+ 4.35 In T + 4.69 X lO-,T + 11.64 X 105T-2
(in J/(mol K)) (5)
and spinel, MgA1204,
~~
A H o , = -21745 - 3.40T + 3.36 X 10-,T2 7.14 X 104T-' (in J/mol) (6) A S o T = 20.55 - 3.40 In T + 6.72 X lO-,T 3.57 X 104T-2 (in J/(mol K)) (7)
" pptn is precipitation. furnace was heated by burning a mixture of propane-butane in air, with oxygen added in order to achieve high temperatures. It took approximately 2 h to reach the maximum temperature in the furnace. The samples were cooled in the furnace in both cases. The specific surface (according to Blaine's method) was determined for magnesium oxide samples obtained from seawater as well as for magnesium oxide p.a. Table I1 presents the results obtained. The samples were then examined by X-ray diffraction analysis, and their minimal dislocation density was determined. The dislocation density, p , was calculated on the basis of crystallite size, Dhkl,according to the relation 3 (2)
P = -
(in J/mol) (4)
23.28 X 105T-l
" pptn is precipitation.
~~~
+ 4.35T + 23.45 X 10-4T2+
Dhkl
The crystallite size, Dhkl,was calculated from the line broadening of diffraction maxima according to the relation Dhki = ( K k )/ cos ehki) (3) Table I11 lists the results obtained. The dislocation density was determined in the Laboratory of Crystallography of the Faculty of Mining and Geology in Beograd. Tables IV and V indicate the results obtained for compacts after sintering, i.e., the results obtained by X-ray quantitative analysis for the operating conditions and additions listed. Schill's (1982) method was applied. This method is a modification of Chung's method (1974,1975).
Results Analysis The results obtained by examination of forsterite and spinel formation reactions, 2Mg0 + SiOz = MgzSi04and MgO + A1203 = MgA1204,respectively, were analyzed thermodynamically in order to determine the conditions of formation in the individual samples examined, as well as the relation between the quantity of forsterite and spinel
the data presented in Tables VI and VI1 were obtained, where AG OT is a change in standard Gibbs free energy, defined by the expression AG OT = AHoT- TAS OT, while K, is a thermodynamic equilibrium constant. The relation between AG OT and K, has been defined by the expression AG O T = -RT In K , (8) where T i s the absolute temperature and R is the general gas constant. The above data may be used to predict a theoretical yield for the reaction and the reaction equilibrium. The experimental data obtained by the quantitative analysis of forsterite/spinel formed in the process of isothermal heating (7 = 5 h, Tables IV and V) were used to calculate the degree of yield, 5, that depends on the percentage of SiOzor A 1 2 0 3 added at the temperatures given. can If the value for 5 is known, the reaction quotient, K i, be determined for the forsterite/spinel formation reaction examined that depends on the percentage of SiOz or AlZO, added at the temperatures listed. The reaction quotient, K ,.' for forsterite has been calculated according to the expression x(MgzSi04) x (SiOz)x(Mg0)2
Ki=
(9)
where x is the quantity of the reactant (x(Si02),x(Mg0)) or the reaction product (x(MgzSi04)). The reaction quotient, K i, for spinel has been calculated according to the expression
where x is the quantity of the reactant (x(Al2O3),x(Mg0)) or the reaction product (x(MgAl,O,)). Figures 1-3 show the results obtained for magnesium oxide compacts sintered at 1300 "C, namely the depen-
Table IV. Quantity of Forsterite. Mg,SiO,, Formed (Percentage) at Different Sintering TemDeratures:
T
=5h
Mg2Si0,, %
samde MgO p.a.
MgO (120% pptn)" MgO (80% pptn)
Opptn is precipitation.
t . "C
2% SiO,
5% SiO,
10% SiO,
1300 1400 1500 1600 1300 1400 1300 1400 1600
1.50 1.75 2.06 2.13
3.30 4.30 4.90 5.11 7.15 8.50 8.55 9.40 9.05
6.10 8.30 9.30 9.60 13.40 16.00 16.90 17.70 17.10
3.65 3.83 3.70
stoich. relation 26.80 24.60 28.30 31.60 36.30 35.33
300 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 Table V. Quantity of Spinel, MgAl2O4,Formed (Percentage) at t = 1300 OC and T = 5 h sample A1203, 70 MgA1204, % 2 1.67 MgO p.a. 5 3.60 10 7.00 Table VI. Changes in AH OT, A S OT, and AG OT Dependent on Temperature and K , for the Reaction 2Mg0 SiOz = MgzSi04
+
MOT,
t , "C 1300 1400 1500 1600
J/mol -58817 -57711 -56546 -55327
ASOT, J/(mol K) 0.17 0.85 1.53 2.20
AGOT, J/mol -59080 -59130 -59250 -59440
K.
I
91.27 69.96 55.50 45.33
1
I
I
I
I
2
L
6
8
10 SI02
Figure 1. Dependence of on % S O z and K'= on %SiOa for magnesium oxide p.a.: t = 1300 "C, T = 5 h.
Table VII. Changes in AH OT, A S OT, and AG O T Dependent on Temperature and K , for the Reaction MgO Al2O3= MgA1z04 U O T , ASOT, AGOT, t,"C J/mol J/(molK) Jim01 K. 8.74 6.08 -28444 1300 -18825 8.03 6.54 -29081 1400 -18072 7.48 7.02 -29766 1500 -17251 7.05 1600 -16364 7.51 -30498
+
dence of E on %SiOz and the relation of K '* and %Si02. Experiments at other temperatures yielded a similar shape for the curves obtained, the same rules applying. The data of Tables VI and VII and experimental data (K iafter 5 h of reaction) were used to calculate the change in Gibbs free energy ( A G ) for the reactions examined. A change in AG has been calculated according to the expression AG = AG " + RT In K i,which represents the basic criterion of system equilibrium. In order to determine the degree of the forsterite/spinel formation reaction yield in comparison to the theoretical yield (&) for a given temperature and quantity of Si02/ A120, added, the ratio [/& was calculated. The results obtained are listed in Tables VIII-X. Tables VI11 and IX show the results obtained at different sintering temperatures, the same %Si02 added, and the same duration of isothermal heating; Table X shows the results obtained with addition of A120, at 1300 "C. The results obtained at different temperatures indicate that, when the content of Si02added increases, the values for AG for the reaction examined become more negative in all the samples. It has been noted that the values for AG are more positive, or less negative, when MgO obtained from seawater is utilized, than with MgO p.a.: e.g., at t = 1400 "C and 5% SiOz added, AG for MgO obtained by 80% precipitation amounts to -4383 J/mol, for MgO obtained by 120% precipitation, it amounts to -16648 J/mol, and for Table VIII. [, [/&,K i,and AG for the Reaction 2Mg0 and MgO (80% Precipitation) with 2% and 5 % SiO, 2% sample t , "C 6, 70 [Itt,% 32.00 38.03 MgO p.a. 1300 1400 37.30 45.20 1500 43.98 54.36 1600 46.50 57.29 MgO (120% pptn)n 1300 1400 1300 MgO (80% pptn) 77.93 92.60 1400 82.00 99.27 1600 78.99 99.47 a
pptn is precipitation.
2
6
L
7. S I 0 2
Figure 2. Dependence of t on % SiOz and K \ on %Si02for m a g nesium oxide (120% precipitation): t = 1300 "C, T = 5 h.
\\ \
430
\
76 -
72 I
1
2
L
1
,
I
6
0
IO
J
%Si02
Figure 3. Dependence o f t on %Si02and K =' on % S O z for magnesium oxide (80% precipitation): t = 1300 "C, T = 5 h.
MgO p.a., it amounts to -50641 J/mol. The experimental conditions being equal (the temperature and quantity of addition), noticeable differences in AG indicate that MgO obtained by 80% precipitation is the most reactive, more reactive than that obtained by 120% precipitation and much more reactive than MgO p.a.
+ SiOz = Mg2Si04,
T
= 5 h, for MgO p.a., MgO (120% Precipitation),
SiOa
K\
10
8
5% S O 2
1.42 1.92 2.81 3.07
AG, J/mol -54 880 -50 049 -44 007 -41 980
37.66 65.03 42.95
-11 585 -1 011 -838
t, % 28.20 36.50 41.85 43.67 61.00 72.60 73.01 80.30 77.29
[/Et,
33.52 44.20 51.72 55.00 72.51 88.00 86.77 97.21 97.33
K: 1.13 1.84 2.49 2.76 8.15 21.15 22.01 51.04 34.88
AG, J/mol -57 480 -50 641 -45 790 -43 617 -31 625 -16648 -18615 -4 383 -4 082
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 301
+
Table IX. ?, ?/&,K 2, and AG for the Reaction 2Mg0 SiOz = MgzSi04,T = 5 h, for MgO p.a., MgO (120% Precipitation), and MgO (80% Precipitation) with 10% SiOz and a Stoichiometric Relation of MgO and SiOz of 2 1 10% SiOz stoich. relation sample t, "C (, % (/&, % K: AG, J/mol [, % E/&, % K: AG, J/mol MgO p.a. 1300 26.05 30.96 0.99 -59 225
MgO (120% pptn)O MgO (80% pptn)
1400 1500 1600 1300 1400 1300 1400 1600
35.50 39.50 41.00 57.20 68.30 72.16 75.60 73.01
43.03 49.10 51.63 67.99 82.79 85.78 91.51 91.94
1.73 2.20 2.37 6.28 14.31 20.26 28.81 22.01
-51 499 -47 618 -45 991 -35 024 -22 086 -19699 -12 345 -11 258
26.80
32.48
1.04
-58 584
24.60 28.30 31.60 36.30 35.33
29.24 34.30 37.56 44.00 44.49
0.90 1.14 1.38 1.81 1.72
-60 -57 -54 -50 -50
196 306 864 870 988
pptn is precipitation.
+
Table X. ?, ?/&,K 2, and AG for the Reaction MgO A120, = MgA1204: t = 1300 "C, z = 5 h samtde A1,O1, % E, % f/f,, % K'- AG, J/mol MgO p.a. 2 60.00 88.20 5.25 -6742 5 10
52.00 50.00
76.50 73.50
3.34 2.88
-12655 -14576
This difference is more conspicuous a t higher temperatures: e.g., a t t = 1600 "C and 2% Si02 added, AG for MgO (80% precipitation) is only -838 J/mol, while for MgO p.a. it amounts to -41 980 J/mol. When the sintering temperature increases and the SiOl content and duration of the isothermal heating remain the same, values for AG become more positive, which means that the system approaches equilibrium. The results presented indicate that in all samples examined the increase in the temperature leads to the increase in forsterite formation reaction yield as compared to theoretical yield. With magnesium oxide obtained by substoichiometric precipitation from seawater, the values for AG indicate that the reaction yield closely approaches the theoretical one, especially if 2% Si02 is added. This can also be seen from the value for E / & . For example, at t = 1600 "C and 2% Si02added, the value for [ / E t amounts to 99.47%. The comparison of the results obtained closely indicates that the values for [ / E t for magnesium oxide obtained from seawater are higher than those obtained for MgO p.a.; e.g., a t a temperature of 1400 "C and 5% Si02added, the E / E t value amounts to 99.27% for MgO obtained by 80% precipitation, to 88.00% for MgO obtained by 120% precipitation, and to 45.20% for MgO p.a. which also indicates a higher reactivity of MgO obtained from seawater by substoichiometric (80% ) precipitation. The experimental results shown (Table X) for spinel also indicate that, when the addition of A1,0, increases, the reaction yield falls below the theoretical one, which is confirmed by the ratio .$/Et. The results obtained for the spinel formation, as well as for the forsterite formation, indicate that the highest reactivity may be expected when MgO obtained from seawater is used, especially if obtained by substoichiometric precipitation (80%). The differences noted in the reactivity of samples examined are caused by differences in specific surfaces, chemical composition, structural irregularities (dislocation density) between MgO p.a. and MgO obtained from seawater. Thus, it follows that the differences in K are directly caused by these factors. When the equilibrium for a fine dispersed system is calculated (Karapetyants, 1978), the following expression applies:
:
Ka AG, = RT In 7 Ktl
Table XI. AGs for the Relation of MgO p.a. and MgO (80% Precipitation) AG-, J/mol. at S O 2 ,% 1300 "C 1400 O C -42 896 -38 832
2 5
-48 995 -46 218
Table XII. AGBfor the Relation of MgO p.a. and MgO (120% Precipitation) AGB, J/mol, a t SiO,, 9'0 1300 "C 1400 " C 5 10
-25 839 -24 111
-33 965 -29 388
where AG, is a change in Gibbs free energy due to different surface energy of reactants and K is the value of the equilibrium constant, taking into account the influence of the surface energy. When the above expression was applied to our system, AG, was determined in order to compare magnesium oxide p.a. and magnesium oxide obtained from seawater. The constants K , and K 'a were substituted by appropriate experimental values for K 2; i.e., Ka K for MgO p.a. and K K for MgO from seawater. The results calculated for the relation of MgO p.a. and MgO obtained from seawater by 80% precipitation are listed in Table XI. The results calculated for the relation of MgO p.a. and MgO obtained from seawater by 120% precipitation are shown in Table XII.
-
:
-
:
Discussion The results of examination of the forsterite formation process show that the highest degree of yield, 5, is obtained when 2% SiOz is added, then 5% and 10%)the lowest degree of yield being achieved at stoichiometric relation of MgO and Si02 in all samples examined. Thus, if the quantity of SiOz added increases, the yield degree for the reaction decreases, as well as the value for the reaction quotient at all temperatures applied. The graphic presentation of the data (dependence on %SiOz) can be used to extrapolate 4 for the smaller percentage of SiOzadded, which is more difficult to determine accurately by experimentation. The same dependence has been established in the spinel formation process. The degree of yield for the forsterite formation reaction has been found to be higher when magnesium oxide obtained from seawater is used, especially if it is obtained by 80% precipitation, than when magnesium oxide p.a. is used, at all sintering temperatures. Calculations of AG have proved that, when the sintering temperature increases and the quantity of SiOzadded and the duration of isothermal heating remain the same, the system gets closer to an equilibrium state.
Ind. Eng. Chem. R e s . 1989, 28, 302-315
302
Values determined for AG at a given temperature, under the same experimental conditions, i.e., addition of SiOzand duration of isothermal heating, indicate that magnesium oxide obtained by 80% precipitation with dolomite lime is the most reactive; Le., the forsterite formation process is nearest to the equilibrium state. Magnesium obtained from seawater by 120% precipitation follows next, and then comes magnesium oxide p.a. Differences in the value of AG are more conspicuous at higher temperatures. The results of examination of AG, indicate that differences in values of AG, increase as differences in K ’x of various samples examined increase for the given temperature. Differences in reactivity noted in the isothermal sintering process in the samples examined are due to differences in specific surfaces, chemical composition, and structural irregularities (dislocation density) between magnesium oxide obtained from seawater and magnesium oxide p.a. The thermodynamic analysis of experimental results yields a better insight into the forsterite/spinel formation reaction and also into the sintering process with regard to the properties of products obtained, by comparing the results obtained with the theoretical values. The thermodynamic analysis, namely calculation of AG and AG,, thus provides a definite insight into the mechanism and
rate of the forsterite/spinel formation process in the samples examined and makes it possible to predict the product properties in advance.
Acknowledgment The authors thank the Republic Council for Scientific Research of Croatia for financial support (Contract 1.01.02.02.04,1987). Registry No. MgO, 1309-48-4; A1203,1344-28-1; Si02,763186-9; forsterite, 15118-03-3; spinel, 1302-67-6.
Literature Cited Chung, F. H. J . Appl. Crystallogr. 1974, 7, 519-526. Chung, F. H. J. Appl. Crystallogr. 1975, 8, 17. Heasman, N. Gas Wurme Znt. 1979,28, 392. Hinz, W. Silikaty (Moscow) 1971, 75-97. Karapetyants, M. Kh. Chemical Thermodynamics; Leib, G., Transl.; Mir Publishers: Moscow, 1978. Kriiiianovskij, P. E.; Stern, 2. Yu. TeplofiziEeskie suoistua nemetaliEeskih materialou; Energija: Leningrad, 1973. Petric, B.; Petric, N. Znd. Eng. Chem. Process Des. Deu. 1980, 19, 329. Schill, P. Silikaty (Moscow) 1982,26, 355.
Received f o r review February 16, 1988 Revised manuscript received July 15, 1988 Accepted August 5, 1988
Analysis of Impingement Mixing-Reaction Data: Use of a Lamellar Model To Generate Fluid Mixing Information Henry A. Kusch and Julio M. Ottino* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
Dave M. Shannon Central Research Engineering Research Laboratory, Dow Chemical Company, Midland, Michigan 48640
Central to reaction injection molding (RIM) is the mixing by impingement of reacting monomer streams. Mixing occurs a t relatively low Reynolds numbers, O(lo2);however, little theoretical or experimental guidance exists for this case. Most previous studies focused on fast reactions in turbulent flows with little attention given to laminar or transitional flows. In this work, mixing is studied using simple chemical reactions with known kinetics. The data collected are mixing-dependent selectivity versus Reynolds number from competitive-consecutive azo-coupling reactions at complete conversion. Selectivity bounds on the experimental data points are developed to account for incomplete conversion of the limiting reactant to measurable products. Average fluid mixing information is backed out by matching solutions of a lamellar model to one set of experimental data. A sensitivity analysis is presented. Reaction injection molding (RIM) is an industrially important process critically dependent upon mixing; poor mixing results in poor polymeric parts (Kolodziej et al., 1982). Virtually all current mixing designs are based on “head-on”impingement of two reactive monomer jets in a small cylindrical chamber. Usually, the Reynolds number, based on the more viscous jet diameter, is of the range 200-400 (Lee et al., 1980). However, in spite of commerical success, very little quantitative information about impingement mixing exists in the open literature, and retrofitting to changes in the chemistry of the reacting system is often empirical. Experimental and modeling studies
* Author to whom
correspondence should be addressed.
088S-5885/89/2628-0302$01.50/0
have been carried out to clarify the mixing process, but a clear picture has not yet emerged. Flow visualization reveals that mixing in the zone of impingement is intense, but intermittent and far from homogeneous, and that the mixing quickly decays to zero as a Poiseuille flow develops in the runner (Sandell et al., 1985). In fact, when contrasted with classical turbulence studies, mixing occurs at a relatively low Reynolds number. This does not simplify matters and indeed makes the analysis harder rather than simpler, since the theoretical guidance and intuition developed for highly turbulent flows, e.g., isotropy and homogeneity, are far from being reasonable assumptions in this case. The possibility of analysis based on direct computational simulations seems at best remote. The 1989 American Chemical
Society
