Ind. Eng. Chem. Res. 1992, 31, 1784-1792
1784
AP
= purity enhancement C = feed concentration L = bed length P = pulse time Q = feed rate of flow R = p-xylene recovery defined by eq 2 R d = time for the peak maximum of diluent R, = time for the peak maximum of o-xylene R, = time for the peak maximum of p-xylene t , = cut time T,= cycle time T = temperature
41
I I
I
I 1
2
3 3.25
4
WATER CONTENT OF ADSORBENT
5
w.
S
WEIOCITI
Figure 8. Effect of water content of adsorbent on selectivity.
Conclusion An experimental program concerning the separation of p-xylene, o-xylene, and ethylbenzene isomers was carried out, enabling determination of evaluation criteria involving liquid adsorption in X zeolite. The preferential adsorption of p-xylene is mainly attributed to the physical interaction forces between pxylene and the surface. These forces were enhanced through the replacement of cation Na+ by Ba2+ and K+and through variation of the water content in the adsorbent. This water content is of paramount importance in the selectivity of p-xylene and o-xylene mixtures separation, showing an optimum value in the range of variables analyzed.
Greek L e t t e r
0 = Selectivity, defined by eq 1 Registry No. p-Xylene, 106-42-3; o-xylene, 9547-6; ethylbenzene, 100-41-4.
Literature Cited Carra, S.; Santacesaria, E.; Morbidelli, M.; Storti, G.; Servida, A.; Danise, P.; Mercenari, M.; Geloea, D. Separation of Xylenes on Y Zeolites. 1-3. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 440-457. Cier, H. E., Xylenes and Ethylbenzene. In Kirk-Othmer Encyclopedia of Chemical Technology, 2nd ed.; Mark, H. F., Macketta, J. J., Jr., O t h e r , D. F., Eds.; John Wiley & Sons: New York, 1970; Vol. 22, pp 467-507. Furlan, L. T. M.Eng. Dissertation, State University of Campinas, 1990. Santaceearia,E. Metodi di Separazionedegli Xileni Isomeri. Chim. Znd. (Milan) 1980,62 (4), 317-322. Receiued for review September 29, 1991 Revised manuscript receiued February 11, 1992 Accepted March 11, 1992
Nomenclature A = water content in the adsorbent
Stable Operation Conditions for Gas-Solid Contact Regimes in Conical Spouted Beds M a r t i n Olazar,* Maria J. S a n Jose, Andr6s J a v i e r Bilbao
T.Aguayo, J o s e M. Arandes, and
Departamento de Zngenieria Quimica, Universidad del Pa& Vasco, Apartado 644, 48080 Bilbao, Spain
The operation regimes of spouting and of jet spouting have been delimited in the bed expansion in conical contactors. Both contact regimes, but in particular the original regime of jet spouting, have a characteristic hydrodynamic behavior different from that of the conventional spouted bed, and they combine the characteristics of high velocity of gas and solid, typical of transport beds,with the cyclic movement typical of the spouted bed. Its interest is centered on the handling of particles of large diameter, with adherent solids and with size distribution. The ranges of the geometric factors of the contactor-particle system and of the gas velocity for stable operation in both regimes have been determined by experiments in a pilot plant using different solids. The operative ranges of both regimes in conical contactor are compared with the conventional gas-solid contact regimes. The limitations of the few correlations in the literature for design of conical spouted beds and the nonvalidity of these conventional correlations proposed for cylindricalspouted beds have been proven. Consequently, original hydrodynamic correlations for spouting and jet spouting corresponding to conical contactors have been proposed for the calculation of the minimum velocity in stable operational conditions. Introduction When using the gas-olid contact, there are situations where the regimes of fixed bed or fluidized bed are not suitable. In fast reactions, short residence times for the gas are pursued (for optimum selectivity). The innovative designs-jets (Kmiec and h c h o n s k i , 1991), cyclonic reactors (Lede et al., 1989a,b), impinging jets (Tamir, 1989), 0888-6885/92/ 2631- 1W$O3.oO/O
etc.-secure these objectives (with gas residence times between 0.03 and 1.2 a), and they even increase the demands of heat and mass transfer between phases, but they hardly combine the characteristics desired in the solid flow whose particle size or whose optimum residence time is excessively high (in cyclonic reactors for example, the residence time of the solid is between 0.07 and 1.3 e). 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1785 When the residence time of the solid is the limiting factor, complex design solutions are adopted, such as the mix system of a fluidized-cyclonic-movingbed (Hasatani et al., 1988) proposed in order to increase the residence time of the solid in the combustion of coal. In physical operations as well as in reactions, when the solid is sticky and tends to agglomerate, a regime more vigorous than bubbling fluidization, such as the turbulent fluidization or the fast fluidization (Yerushalmi and Avidan, 1985))must be used. In transport regimes, high gas velocities are attained (3-10 m/s), but the particle size is limited (50-500 pm). A solution for the problems described is the spouted bed regime in conical contactors, so that the characteristics of the solid are no longer limiting and, at the same time, the gas velocity can be as high as that of the innovative designs previously mentioned. Although the cylindrical spouted beds have been extensively studied (Mathur and Epstein, 1974a,b) and their industrial applications are countha (Grace and Lim, 1987)) there are few studies on the spouted beds in conical contactors. Especially interesting is the discovery that the expansion of a concical spouted bed leads to a contact with peculiar characteristics (Markowski and Kaminski, 1983). This regime has been named jet spouted bed, in order to take into account the characteristics of high gas velocity and the cyclic movement of the particles. In a previous paper (Bilbao et al., 19871, this regime has been sucessfdly applied for benzyl alcohol polymerization in a laboratory scale reactor. Thus it follows that the regime of spouting in conical contactors could be considered a nonconventional contact method whose application is interesting in physical operations and as a reactor. Consequently,the first aim of this research is to cover the lack of bibliographic information by exploring the following aspects: (1)definition of the different regimes in the expansion of conical contactors and the delimitation of its hydrodynamic parameters and their obtention method; (2) delimitation of the stable operation conditions; (3) comparison of ita applicability with that of the conventional contact methods. On the other hand, the definition of the hydrodynamics of the jet spouted bed is very limited, and the only correlations for its design (Markowski and Kaminski, 1983) were established from a very limited experimental base. The studies on spouted beds in exclusively conical contactors, which have a very peculiar behavior, are also very limited (Nikolaev and Golubev, 1961,Gorshtein and Mukhlenov, 1964; Romankov and Rashkovskaya, 1968;WanFyong et al., 1969; Alves-Filho, 19861, so that the valuable progress made on the comprehension and modeling of cylindrical spounted beds is not applicable.
Experimental Section Equipment and Operation Conditions. As one of the objectives is the delimitation of the application ranges of the spouting regimes in conical contactors, the experimental study should necessarily be ample, with extension to solids of different nature, with use of contactors of different geometry, and with wide ranges of gas velocity. In Figure 1,a diagrammatic representation of the unit that is designed at pilot plant scale is shown. The blower supplies a maximum air flow of 300 Nm3/h at a pressure of 1500 mm of water column. The flow is measured by means of three rotameters, which are used in the ranges of 0.3-2.5, 2.5-25, and 30-250 Nm3/h. The pressure measurements are carried out by means of four vertical pressure taps, whose radial and longitudinal
,
preirure probe0
contactor
I' 1 ;
Figure 1. Diagrammatic representation of the unit. Table I. Properties of the Solids Used material glass spheres
bean8 rice chickpeas
d,,
PI,
mm ka/m3 1 2420 2420 2 2420 3 2420 4 2420 6 2420 8 9.6 1140 3 1250 9.2 1130 6.8 1110 4.4 1190 6.1 3520 14 3.5 3.5 960 3.5 960
Ezils ceramica expanded polystyrene extruded polystyrene polystyrenepolybutadiene wood cubes 25
240
6
b
0.65 0.60 0.90 0.70 0.40 0.90 1 0.70 0.70
0.322 0.328 0.345 0.355 0.361 0.378 0.405 0.449 0.412 0.446 0.490 0.501 0.507 0.395 0.395
Geldart classification ~
1 1 1 1 1 1
0.90 0.240
B D D D D D D D D D D D
D D D D
position can be established at will inside the contactor by an externally controlled displacement device. The taps, of stainless steel, consist of a 4-mm-0.d. external pipe provided with four orifices of 1-mm of diameter at a distance of 1cm from the end, which are for the measurement of static pressure. The dynamic pressure is measured by the l/ls-in.-o.d. internal pipe of the tap. The pressures taken by the tap go to a four-way valve and from here to a differential pressure meter, whose 0-20-mA signal indicatea the value of the pressure difference, which is shown in a Sipar DR20 regulator in a 0-100 range. The absolute error range for the dynamic pressure measurement is below 0.1 Pa and for the static pressure below 1 Pa. The data reading and processing is carried out by a Tandon 386/20 computer provided with a PC-Lab-718 data acquisition card with PCLS-'IOsoftware, which permita the obtention of continuous curves of pressure drop vs velocity. The presaure drop in the bed for each velocity is calculated by considering the grid pressure drop both in the presence of a bed and in the absence of a bed, according to the correction proposed by Mathur and Epatein (1974a,b). Five conical contactors of poly(methy1 methacrylate) whose geometric characteristics are defined in the diagram of Figure 2, have been used. They have been made to the following dimensions: column diameter, D,,36 cm; contactor base diameter, Di, 6 cm; heights of the conical section, H,,36,40,45,50, and 60 cm; cone angles, 7,corre6') 33O, and sponding to the mentioned heights, 45') 39') 3 28'. With each contactor, the study has been extended to four inlet diameters, Do: 3, 4, 5, and 6 cm. The solids used correspond basically to the D group classification of Geldart (1973, 1986)) for which these
1786 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 I
',
bcm
I/
(d)
Figure 2. Geometric factors of the contactors and inlet designs studied.
contact techniques can be especially interesting, and their properties are set out in Table I. Contactor Inlet Design. In previous studies (Bilbao et al., 1987; San J& et al., 1991), it has been observed that the inlet design deserves special attention, as it greatly affects the stability of spouting regimes. When the different inlet geometries are tried, the attainment of bed stability, in discontinuous as well as in continuous operation for the solid, was maintained as the main objective and every effort was made to avoid solid accumulation at the inlet. The inlet design was carried out following the previous recommendations in the literature for cylindrical spouted beds (Mathur and Gishler, 19558; Manurung, 1964; Mathur and Epstein, 1974a,b; Piccinini and Cancelli, 1983). The more representative designs tried for the inlet device are outlined in Figure 2. In every case there is a metallic grid of O.&mm mesh opening, placed at the very inlet, at the contactol-inlet device joint, in order to avoid the flow distortion observed by Malek and Lu (1965). With the inlet device of Figure 2a, the spouting regime was not stable, as the spout, instead of being well defined in the center of the bed, was continuously changing ita position (rotation). The jet spouting regime was only stable and the bed conditions were uniform for large particle diameters. For small particles (smaller than 6-mm diameter for glass spheres), the jet projected the particles vertically, starting from a position near the contactor internal wall, a position that was changed by rotation. Res u l k with similar instability have been previously obtained when no inlet device was used (with the grid as the only device or even without the grid). With the piped inlet, Figure 2b, ita protruding height was varied, and it was observed that for 2.5 cm with respect to the base level the stability was noticeably improved in both regimes. A higher protruding height hardly improved the stability; on the contrary, it provoked solid accumulation at the bottom, due to the fact the solids are projected through the spout. In this situation, lateral dead zones at the inlet pipe are generated. The composed convergent-piped inlet design, Figure 2c, does not produce a noticeable improvement with respect to the piped inlet. In the same way, when an inlet pipe with blades whose height was varied between 30 and 80
cm was used, Figure 2d, a slight improvement in stability was obtained. In view of the advantages of the piped inlet and in order to avoid the solid accumulation at the inlet, a design that consisted of a straight pipe with a diameter equal to that of the bed inlet, Figure 2e, was studied. On changing the length, it was found that stability was satisfactory for inlet pipe lengths equal to or higher than 5 times the inlet diameter. This stability is obtained for all the contactor geometries tried and for the whole range of particle diameter, as long as the inlet diameter is equal to or smaller than 5 cm (with 6-cm inlet diameter, stable regime is only attained with particles greater than 8 mm, such as was proven with vegetable seeds). When the a w e s pipe length is smaller than that pointed out, instability is produced in the jet spouting regime, giving way to jet rotation along the internal contactor wall. The length of the inlet device is recommended to be 5 times the inlet diameter or not very much greater than this, in order to avoid the pressure drop increase that this design would originate, especially for small inlet diameters.
Jet Spouted Bed Regime In order to illustrate the general characteristics of pressure drop evolution in the bed with air velocity, the results for one of the contactor geometries (y = 36O, Do = 4 cm) and for the glass spheres of 3-mm particle diameter are shown in Figure 3 as an example. The geometric places of the conditions that delimit the beginning of the spouting and jet spouting regimes are plotted in dotted lines. In the same figure, an outline of the evolution of particle population in the different regimes is shown. After the stable regime of spouting, Figure 3a, on increasing the velocity, both annular and spout zones characteristic of classical spouting become progressively confused (transition zone in Figure 3) and a particle movement outlined in Figure 3b is obtained. The transition evolves until the spout and annular zones are no longer differentiated and the bed voidage is uniform, a new situation that corresponds to incipient jet spouting. The jet spouted bed denomination corresponds originally to the work of Markowski and Kaminski (1983). Once this regime is reached, it stays stable at higher velocities, with the particle movement outlined in Figure 3c,
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1787
1200
1
800
I
400
I
J 4
0
8
12
16
20
u(
(a)
(b)
24
4 s )
(c)
Figure 3. Pressure drop evolution with the velocity for the different regimes (glass spheres, d, = 3 mm, different stagnated bed heighta) and particle states in the contactor for the different regimes.
with a constant value of pressure drop in a velocity range, and then it goes on to slowly decrease. In short, the general characteristics of the jet spouted bed are (1) high gas velocity, (2) high bed voidage, over 0.75 depending on the operating conditions, (3) cyclic movement of the particles, and (4) hydrodynamic behavior different from that of the conventional spouted bed. The hydrodynamic differences with the conventional spouted bed in conical contactors are as follows. (1)Hysteresis is nonexistent in the pressure drop vs velocity curves. (2) The experimental results of minimum jet spouting do not follow the correlations applicable to spouted beds. (3) There are lesser instability problems, although the regime hydrodynamics is very sensitive to the contactor geometric factors.
Conditions for Stable Operation The operation in the jet spouting regime (just as the operation in the spouting regime) in conical contactors, is sensitive to the value of the geometric parameters of the contactor and to the particle diameter, so it is necessary to delimit the operation conditions that strictly correspond to the regime defined as jet spouting and that allow for the gas-solid contact taking place in a stable way. With this aim, the classic diagram of stagnated bed height vs gas velocity proposed by Mathur and Gishler (1955a) has been used. In Figure 4, the diagrams for the two extreme values of particle diameter, 1and 8 mm, for the same values of cone angle, 28O, and inlet diameter, 3 cm, have been plotted as an example. The borders between the different regimes, drawn with solid lines, have been obtained experimentally (the points drawn are the experimental base for tracing these borders). In Figure 4a, a dashed line has been drawn beside the solid one to indicate the limit of the operation when the expanded bed is outside the cone. This state is reached for relatively small values of particle diameter (1and 2 mm). Nevertheless, they correspond to stable operation in the whole
-
0
0
4
8
12
16
0
20
4
8
12
16
20
u (m/s) u(4s) Figure 4. Diagram of stagnated bed height vs gas velocity: (a) y = 2 8 O , Do = 3 cm, d, = 1 mm; (b) y = 2 8 O , Do= 3 cm, d, = 8 mm.
range of conditions studied, so this aspect only affects the system geometry and its modeling, which w i l l have to take into account this conical-cylindrical geometry, but it does not affect the characteristics of the contact regime. For small cone angles and small particle diameters and basically in conditions under which the expanded bed exceeds the limits of the contactor cone, the regime that is obtained does not have a cyclic movement of the particles, but collisions among them and with the contactor wall produce a random movement of the particles, without flow lines, which is peculiar to a perfect mix. This situation could be useful in those applications that require this perfect mix as well as a very vigorous movement of the particles but not for the case of applications in which the spouted bed is chosen as a contact system because it gives rise to identical residence times and sequences of residence states for each one of the particles. The operation zone in which this circumstance occurs has been shaded in the diagram of Figure 4a. In Figure 4a, for 1-mm particle diameter, the impossibility of attaining a stable spouting is noteworthy. Upon an increase in the velocity, it goes from a fixed to an unstable state, which is defined as a fluctuation of pressure drop. The observation of the bed in this situation clearly shows the formation of a great bubble. The small bed height and the conical geometry are the cause that for a small particle diameter, as in our case, the conventional asymmetric slugging is produced among the different types of slugging (Clift and Grace, 1985). From this instability situation, a transition situation is reached and from here to jet spouting. The plot of Figure 4b corresponding to an &mm particle diameter is an example of the system in which all the different possible states appear. For small stagnated bed heights, starting from static regime, it passes to stable regime, to transition, and then to jet spouting. Nevertheless, the evolution of beds of height greater than 8 cm is different. From the static regime, it goes to an unstable regime, then to a narrow transition band, and from here to jet spouting. It is noteworthy that the instability in systems with large particles has characteristics different from the one previously explained for small particles. In this case, a slugging originated by bubbles that totally break up the bed and that produce pressure drop fluctuations greater than those corresponding to particles of smaller diameter are observed. In a comparison of these diagrams with those described in the literature for cylindrical contactors, great differences are observed. In the cylindrical contactor, the evolution between regimes is fixed bed spouting bed fluidized or slugging bed (depending on contactor geometry and particle diameter)
-
+
1788 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
On the other hand, in cylindrical contactors, there is a maximum spoutable height for any geometry, from which the top surface of the bed fluidizes if the particles are of small diameter, and slugging is produced if the particles are big (Mathur and Gishler, 1955a). In conical contactors, with a suitable geometry, the maximum spoutable height can be made to be limited by the cone height (the top cone diameter will only be limited by construction and financial restrictions). From the study of transition states between regimes for all the experimental systems, Appendix I (see the paragraph at the end of this paper regarding the availability of supplementary material), the ranges of the geometric factors of the contactor and of the contactor-particle system for the spouting and jet spouting regimes in conical contactors can be established in a general way. Inlet Diameter/Cone Bottom Diameter Ratio, D o / D i . For spouting and jet spouting, Do/Dishould be between 1/2 and 5/6. The lower limit is imposed by the pressure drop and by the formation of dead zones at the bottom (a serious problem for operation with circulation of solids). The upper limit corresponds to the jet indefinition produced at higher values of this ratio, and that gives way to an instability increase due to rotational movements. Cone Angle, y. There is no upper limit for the cone angle for spouting regime. The lower limit is 28'. As for lower angles the bed is unavoidably unstable and the Do/Di ratio should be considerably smaller than the values of the range studied, which will correspond to the optimum design dimensions of the cylindrical vessels. In the jet spouting regime, the angle must be between 28O and 45'. For smaller angles, the dparticles (1-and 2-mm diameter in our study with glass spheres) basically reach a mixing regime, without the cyclic movement characteristic of the spouting regime. Moreover, the gas velocity is limited by the particle terminal velocity. On the other hand, the operativeness for solid treatment with particle size distribution decreases when the angle decreases. For angles greater than those of this range, a considerable gas residence time distribution is produced together with rotation phenomenon in the gas circulation and the consequent bed instability (this phenomenon is clearly seen with small particle diameter). Inlet Diameter/Particle Diameter Ratio, D J d , . While in spouting in cylindrical vessels, the bed instability suggests a given Do/dpratio near 30 (Mathur and Gishler, 1955a; Passos et al., 1987), with conical vessels, stable operation is attained in a wide range of Do/dpvalues, which can be between 2 and 60. In the jet spouting regime, Do/d can be between 1and 80. These limits are not for stabihy but only for operativeness. The lower limit corresponds to voidages of the order of 0.70 for which the bed homogeneity is obtained. The upper limit corresponds to voidages of at least 0.99. As has been shown, the stability of the spouting regime in conical contactors is sensitive to the geometric factors, so the operation must be carried out within the ranges of the design variables shown previously in order to attain a stable regime. The plots of Figure 5 can be useful 'stable operation maps" for glass spheres of 1,4, and 8 mm. In this figure, the minimum gas velocity at the bottom of the contactor necessary to treat different stagnated bed heights in stable spouting regime can be seen. Each curve corresponds to one contactor geometry, that is to say, to a pair of values of angle and inlet diameter. As is observed in Figure 5 for particle diameters of 1and 4 mm, the stable operation conditions are possible for a
/
26
18
10
8
10
14
18
22
H o (em)
Figure 5. Minimum spouting velocity vs stagnated bed height, for different contactor geometries and for three values of particle diameter. umj
30
(=/a)
26 22 18 14
2
4
6
8
1
0
Ho (em)
Figure 6. Minimum jet spouting velocity VB stagnated bed height, for different contactor geometries.
large range of contactor geometries studied. As the particle diameter is increased, the operation possibilities are restricted to narrower ranges, and when the particle diameter is 8 mm, the operation must be carried out with an angle between 39O and 4 5 O and with an inlet diameter of 3 cm,
Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1789 Table 11. Literature Correlations Used To Calculate the Minimum Spouting Velocity author
equation
geometry
Nikolaev and Golubev (1964)
(d,/D,)(D,/D,)'/3[2gH0(p, - P)/PI'/~ (1) (Re), = 0.051Ar0~59(D,/Dc)0~1(Ho/Dc)0~25(2)
conical
Gorshtein and Mukhlenov (1964)
(Reo)ms= 0.174Ar0.5(Db/D0)0.85[tan (y/2)]-1.25
(3)
conical
Tsvik et al. (1967)
(Re,),, = 0.4Ar0.52(H,/ D o )1.24[ tan (y /2)] 0.42
(4)
not specified
Goltaiker (1967)
(Re,),, = 73Ar0~14(H,/Do)0~9(ps/p)0~47
(5)
not specified
Wan-Fyong et al. (1969)
(Re,),, = 1.24(Re),(H,/D,)o~s2]tan (y/2)]0.92
(6)
conical
Merry (1975)
(uJms= 0.0084((H,/D,)[(d~,)/pD,]0~35 + 5.2)2.5y0.5(D,)0.5(7)
Kmiec (1977)
U,
Mathur and Gishler (1955)
urns
=
= [/J/(dpP)] [ ~ . ~ ~ ~ ( F D / F G ) ~ A ' ] ~ ' ~ ' ~
where (FD/FG), = 0.0485t,,3'(H,/Dc)2~'5yb Markowski and Kaminski (1983)
(8)
cylindrical
any conical-cylindrical
(9)
(Re,), = 0 . 0 2 8 ~ ~ 0 ~ 5 7 ~ ~ o / ~ , ~ 0 ~ 4 8 ~ ~ c /(10) ~ 0 ~ 1 conical ~27
in order for the regime to be stable in a wide range of values for the stagnated bed height (for Do = 4 cm, the operation conditions are very restricted). Nevertheless, the jet spouting regime is more flexible from the point of view of stability. In Figure 6, the stable operation map for a particle diameter of 8 mm is shown (the plot is qualitatively similar for the other particle diameters). There are no limitations for stable operation within the geometric fador ranges shown in the figure (the same could be said in the 1-8-mmparticle diameter range). Comparison with Other Gas-Solid Contact Regimes The applicability ranges of the regimes in conical contactors are compared in Figure 7 with the application conditions of the conventional methods for gas-solid contact, in map such as the one proposed by Grace (1986) of velocity modulus, U* = u[p2/ApgpI1l3,vs the modulus related to particle size density, d,* = Ar'I3. The ranges corresponding to the Geldart classification have been expressed on the abscissa axis of Figure 7. The calculated terminal velocity curve, y,has been drawn with a stroke line. The values of minimum fluidization velocity, ud, have been drawn using a dotted line. They are within a range, as the value calculated would vary according to the correlation used. The velocity at the bottom of the vessel has been used to construct Figure 7. As can be observed, the regimes studied here combine the advantages of the "captive" beds with those of transport fluidized beds and can operate in ranges that are not attainable for the other regimes. The spouted bed in conical contactor covers a different range of application conditions (at greater height in the Figure), different to the same regime in cylindrical vessels, which allows for the treatment of large or heavy solids with gas velocities characteristic of fast fluidization. The jet spouted bed allows for the handling of these same solids with gas velocities characteristic of the transport beds or even higher, corresponding to the velocity range of new alternative designs (cyclonic reactor, two impinging streams reactor, etc.) and whose interest lies in the attainment of low gas residence times, in fast reactions in which selectivity is the design conditioning factor. Minimum Velocity The solids studied in this section are those of Table I except expanded polystyrene, polystyrenepolybutadiene, and wood cubes. The equations set out in Table I1 have been studied, which are those proposed in the literature for contactors
u+1 10'
r
10
r
DILLTBD C O h T W l N G
1 10 10' dp+ Figure 7. Operation ranges for different gas-solid contact regimes.
of conical, of conical-cylindrical, and of any geometry. Despite being proposed for cylindrical contactors, the equation of Mathur and Gishler (195513) was also applied as ita use is interesting for conical contactors, due to ita confirmed general application, either of the original expression (Mathur and Epstein, 1974a,b) or of the posterior modifications for large vessels. Spouted Bed. The values of minimum spouting velocity obtained for the different experimental systems, which are set out in Table I11 (see supplementary material), have been fitted to the equations of Table I1 by means of a complex method for nonlinear regreasion fitting. The regression coefficients (?) corresponding to the fitting are smaller than 0.70 for all the correlations, except that of Nikolaev and Golubev (1964) whose regression coefficient calculated for all the experimental values is 0.85, which is a value that can be considered acceptable by taking into accout the extent of the experimental base and the number of moduli that the equation takes into account in order to define the experimental and geometric conditions. The fitting of the classical correlation of Mathur and Gishler (1955b) for cylindrical contactors has a correlation coefficient of 0.69. The fitting to the equation of Nikolaev and Golubev (1964) is suitable for cone angles of 2 8 O , 36O,
1790 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 .Y=
460
I
0
2k
4 \
200 -
4 150 2
v
100 50
-
O L " ' " ' ' 0 4 8 12
Ho (em)
"
16
I
'
20
Ho (4
Figure 8. Values of the (Reo),/Aro" modulus calculated using eq 11 v8 the stagnated bed height, Ha.
Figure 9. Values of the (Reo),j/Ar0.35modulus calculated with eq 12 vs the stagnated bed height, Ha.
and 39O, although the deviation between the calculated and experimental values is noteworthy for the contactor of 4 5 O . An original empirical equation that is in better agreement with the experimental results of this study has been proposed by fitting the following diqensionless moduli that will affect the value of the Reynolds modulus corresponding to the minimum spouting velocity: A,, Archimedes modulus; ratio between the stagnated bed upper diameter and the contactor inlet diameter, Db/D,; the contactor angle, y/2. As Di is constant, 6 cm, once the Db/D, ratio and the angle y/2 are given, the height of the stagnated bed, Ha, will be determined, so this variable will implicitly be considered in the correlation. These moduli are those considered in the correlation of Gorshtein and Mukhlenov (1964). By a complex method for nonlinear regression of the experimental data, the parameters of the best fit are obtained, and with those the proposed equation is
Di). The experimentation was centered on conditions under which the bed was located in the conical section. It has been determined that on the whole the fitting of this equation to our experimental data is in fact inadequate, with a coefficient ? = 0.42. The experimental values for the different systems are set out in Table IV (see supplementary material). In the same way, the equation proposed by Merry (1975), eq 7 of Table 11, has a regression coefficient of P = 0.45, so it seems that there is no similarity between the hydrodynamic regime of the jet of our experimental system and each one of the jets produced at the gas inlet in the big fluidized beds, which is the system for which the equation of Merry (1975)is one of the most frequently used with satisfactory results. The other equations of Table I1 give regression coefficients (1.2) in all the cases below 0.70. An empirical equation was proposed by using the same dimensionless moduli considered in the equation of Gorshtein and Mukhlenov (19641, eq 3 of Table 11, for spouting in conical beds. By a complex method of nonlinear regression, the parameters corresponding to the best fitting are obtained (r2= 0.95 with a standard deviation below lo%), and consequently, the equation proposed is
(Re,),, = 0.126Ar0.5(Db/D,)1.68[tan (y/2)]-0.57 (11) The regression coefficient of all the experimental data is ? = 0.964, and the maximum relative error is below 8%. The accurate fitting proves the general applicability of eq 11 in a wide range of contactor geometries, particle diameters, and material densities. In Figure 8, the values of the (Re,),/Aro.5 modulus calculated using eq 11 have been plotted w stagnated bed height, H,. When the parameters corresponding to gas flow and solid particles are grouped in the modulus studied, the effect on the hydrodynamics can be studied by this plot. Each curve corresponds to a different combination of contactor geometric factors, of cone angle, and of inlet diameter. The stretches drawn in dashed lines correspond to unstable operation conditions for the particle diameter studied in the example, 4 mm. In Figure 8, it can be appreciated for all geometries that the modulus studied increases more than proportionally with the stagnated bed height and more sharply as the angle is greater and the inlet diameter is smaller. It is clearly seen that the inlet diameter effect is more important than the cone angle for small stagnated bed heights. For high heights, the effect of the angle on the hydrodynamics is increased and is qualitatively as important as the inlet diameter. Jet Spouted Bed. The only equation of Table 11, which is of a empirical nature, proposed for jet spouting, eq 10, belongs to the authors that for the first time cited this regime, Markowski and Kaminski (19831,who carried out experiments with five conical-cylindrical beds with a constant cone angle, 37O,and with a straight inlet (Do =
(Re,),j = 6.891Ar0~35(Db/D,)1.46[tan (y/2)]-0.53
(12)
In Figure 9, the values calculated using eq 12 of the (Re,Jmj/Ar0.35modulus have been plotted vs stagnated bed height, H,,.Each curve corresponds to a different combination of cone angle and inlet diameter. The stretches drawn in dashed lines correspond to operation conditions in which the particle bed partially occupies the upper cylindrical region of the contactor. The effect of the geometric factors on the hydrodynamics is qualitatively similar to that mentioned for the spouted bed. Conclusions On the basis of on a wide experimental base (different contactor geometries and the use of solids of different characteristics), the jet spouting regime has been defined in the expansion of conical spouted beds. The design parameters have been delimited for the stable operation of the spouting regimes in conical contactore. (1)D,/Di for spouting as well as for jet spouting must be between 112 and 5/6. (2) The cone angle, y, has 28O as lower limit value for spouting, and there is no upper limit. For jet spouting, it must be between 28O and 45O.
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1791 (3) Do/d, has no stability limits (under reasonable conditions). Taking into account operativeness reasons, it can be between 2 and 60 for spouting, while in jet spouting the range is wider, between 1and 80. The wide ranges for operation variables show the versatility of these regimes for physical operations and as reactors, which in short permit the handling of solids of the D group of the Geldart classification with high gas velocities. The two regimes studied allow for a more vigorous contact between the gas and the solid than the conventional regimes, so they will be interesting-preferably the jet spouting-for the treatment of adherent solid materials. It is also noteworthy that both regimes allow for the handling of wide particle size distributions with a uniform and stable regime. Although this aspect is beyond the confines of this study, the capacity to operate with continuous circulation of the solid in both regimes studied is evident at least with no greater problems than those of the fluidized beds or those of the conventionalspouted beds. In continuous operation with solids, their residence time could be controlled in a wide range of values. For the calculation of the minimum spouting velocity in conical contactors, the equation of Nikolaev and Goulubev (1964) is applicable for angles up to 39O. Equation 11proposed in this paper takes into account the effect of cone angle up to 45O, with a better fitting of experimental data in the whole range of conditions studied. From the parametric study it is cocluded that for shallow conical beds the inlet diameter is the geometric factor for the design that has greater influence. For high stagnated bed heights, the effect of the angle on the hydrodynamics increases and is qualitatively as important as the inlet diameter. The correlation of Markowski and Kaminski (1983) has an application limited to the narrow range of the operation condition used by these authors. Equation 12 proposed here takes into account all the geometric factors for design and is of general application for very different materials.
Nomenclature Ar = Archimedes number, gd 3p(p8 - p ) / p 2 C D = drag coefficient, (24/ReP(1 + 0.15Re0.6s7) Db, D,, Di, Do = top diameter of the stagnated bed, of the column, of the bed bottom, and of the inlet, respectively, cm d = particle diameter, mm ( f i D / F G ) , = ratio between drag and gravitational forces at the minimum spouting velocity referred to Db, 3 / 4 c D (Re)2/(Ar)
H,,Ho = height of the conical section and of the stagnated bed, cm = pressure drop of the bed, Pa (Re), = Reynolds number of minimum spouting referred to Dbi pu,dp/p (Re)t = terminal Reynolds number Re,,, (ReJmj,(Realms = Reynolds number, that of minimum jet spouting, and that of minimum spouting, respectively, referred to Do u,umj,u, = velocity of the gas, of minimum jet spouting, and of minimum spouting, respectively, referred to Di, m 5-l ( u ~= velocity ) ~ ~ of minimum spouting referred t o Do, m s-l umf,ut = velocity of minimum fluidization and terminal velocity, respectively, m 5-l Greek Letters eo, em = voidage of stagnated bed and of minimum spouting 4 = shape factor y, y b = cone angle and base cone angle, deg hp
p
= viscosity, kg m-l s-l
p , ps
= density of the gas and particle density, kg m-3
Supplementary Material Available: Figures (Appendix I) containing operation maps for the different experimental systems, Table 111 listing experimental values of minimum spouting velocities, and Table IV listing experimental values of minimum jet spouting velocities (27 pages). Ordering information is given on any current masthead page. Literature Cited Alves-Filho, 0. Continuous and Batch Spouted Bed Drying of Coffee Berries. In Drying ’86; Mujumdar, A. S., Ed.; Hemisphere: Washington, D. C., 1986,Vol. 2,pp 542-546. Bilbao, J.; Olazar, M.; Romero, A.; Arandes, J. M. Design and Operation of a Jet Spouted Bed Reactor with Continuous Catalyst Feed in the Benzyl Alcohol Polymerization. Znd. Eng. Chem. Res. 1987,26,1297-1304. Clift, R.; Grace, J. R. Continuous Bubbling and Slugging. In Fluidization, 2nd ed.; Davidson, J. F., Clift, R., Harrison, D., Eda.; Academic Press: Duluth, MN, 1985;pp 73-132. Geldart, D. Types of Gas Fluidization. Powder Technol. 1973, 7, 285-292. Geldart, D. Gas Fludization Technology; Wiley: New York, 1986. Goltsiker, A. D. Doctoral Dissertation, Lensovet Technology Institute, Leningrad, 1967. Gorshtein, A. E.; Mukhlenov, I. P. Hydraulic Resistence of a Fluidized Bed in a Cyclon without a Grate. Critical Gas Rate Corresponding to the Beginning of Jet Formation. Zh. Prikl. Khim. (Leningrad) 1964,37(9),1887-1893. Grace, J. R. Contacting Modes and Behaviour Classification of Gas-Solid and Other Two-Phase Suspensions. Can. J. Chem. Eng. 1986,64,353-363. Grace, J. R.; Lim, C. J. Permanent Jet Formation in Beds of Particulate Solids. Can. J. Chem. Eng. 1987,65,160-162. Hasatani, M.; Naruee, I.; Matsuda H. Combustion Limit of Coals in Two-Staged CFM-Bed with Exhaust Heat Recirculation. In Circulating Fluidized Bed Technology ZI; Basu, P., Large, J. F., Eds.; Pergamon Press: 1988;pp 547-554. Kmiec, A. Expansion of Solid-Gas Spouted Beds. Chem. Eng. J . 1977,13,143-147. Kmiec, A.; Leechonski, K. Analysis of Two-Phase in Gas-Solids Injectors. Chem. Eng. J. 1991,45,137-147. Lede, J.; Li, H. Z.;Villermaux, J. Le Ciclon Reactor. Partie I: Measure Directe de la Distribution des Temps de S6jour de la Phase Gaseuze-Lois d’Extrapolation. Chem. Eng. J. 1989a,42, 37-55. Lede, J.; Li, H. Z.;Soulignac, F.; Villermaux, J. Le Ciclon Reactor. Partie I1 Measure Directe de la Distribution des Temps de S6jour de la Phase Solide-Lois d’Extrapolation. Chem. Eng. J. 1989b,42,103-117. Malek, M. A.; Lu, B. C. Y. Pressure Drop and Spoutable Bed Height in Spouted Beds. Znd. Eng. Chem. Process Des. Deu. 1965,4, 123-128. Manurung, F. Studies in the Spouted Bed Technique with Particular Reference to Its Application to Low Temperature Carbonization. Ph. D. Thesis, University of New South Wales, Australia, 1964. Markowski, A.; Kaminski, W. Hydrodynamic Characteristics of Jet Spouted Beds. Can. J. Chem. Eng. 1983,61,377-381. Mathur, K. B.; Gishler P. E. A Study of the Application of the Spouted Bed Technique to Wheat Drying. J. Appl. Chem. (London) 19SSa,5,624-636. Mathur, K. B.; Gishler, P. E. A Technique for Contacting Gases with Coarse Solid Particles. AZChE J. 1955b,1, 157-164. Mathur, K. B.; Epstein, N. Dynamics of Spouted Beds. Adv. Chem. Eng. 1974a,9,111-192. Mathur, K.B.; Epstein, N.; Spouted Beds; Academic Press: New York, 1974b. Merry, J. M. D. Penetration of Vertical Jets into Fluidized Beds. AZChE J. 1975,21,507-510. Mukhlenov, I. P.; Gorshtein, A. E. Hydraulic Resistance of the Suspended Layer in Grateless Conical Sets. Zh. R i k l . Khim. (Leningrad) 1964,37 (3),609-615. Nikolaev, A. M.; Golubev, L. G. Basic Hydrodynamic Charaderiatics of the Spouting Bed. Zzv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1964, 7,855. Passos, M. L.; Mujumdar, A. S.; Raghavan, V. G. S. Spouted Beds for Drying: Principles and Design Considerations. In Advances
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in Drying; Mujumdar, A. S., Ed.; Hemisphere: Washington, D. C., 1987;Vol. 4,pp 359-396. Piccinini, N.; Cancelli, C. Mixture Composition Control in Continuously Operating Spouted Beds. In Fluidization; Kunii, D., Toei, R., Us.; Engineering Foundation: New York, 1983;pp 533-539. Romankov, P. G.; Rashkovskaya, N. B. Drying in a Suspended State; Chemistry Publishing House: Leningrad, 1968. San JosB, M. J.; O h ,M.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Design and Hydrodynamics of Conical Jet Spouted Beds. In RBcenta Progds en GBnie des Pm&ddC, La Fluidisation;Laguerie, C., Guigon, P., Eds.; Lavoieier-Technique et Documentation: Paris, 1991; Vol. 5, pp 146-153. Tamir, A. Process and Phenomena in Impinging-Stream Reactors. Chem. Eng. h o g . 1989,86 (9),53-61.
Tsvik, M. Z.; Nabiev, M. N.; R i e v , N. U.; Merenkov, K. V.; Vyzgo, V. S. The Velocity for External Spouting in Then Combined Prowas for Production of Granulated Fertilizer. Uzb. Khim. Zh. 1967,21 (2),50. Wan-Fyong, F.; R~mankov,P. G.; Raehkovskaya, N. B. Research on the Hydrodynamics of the Spouting Bed. Zh. Prikl. Khim. 1969, 42 (3), 609-617. Yerushalmi, J.; Avidan, A. High-VelocityFluidization. In FluidizaAcation, 2nd ed.; Davidson, J. F., Clift, R., Harrison, D., Me.; demic Press: Duluth, MN, 1985;pp 225-291.
Receiued for reuiew October 3,1991 Revised manuscript received February 18, 1992 Accepted March 4,1992
The System Formaldehyde-Water-Methanol: Thermodynamics of Solvated and Associated Solutions Stefan0 Brandani, Vincenzo Brandad,* and Gabriele Di Giacomo Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universitd de’L’Aquila, I-67040 Monteluco di Roio, L’Aquila, Italy
The vapor-liquid equilibria in the binary mixtures water-formaldehyde and methanol-formaldehyde are satisfactorily correlated by superimposinga physical model onto the chemical theory for describing the liquid phase. In a previous work, a thermodynamic model was built up which requires three adjustable parameters to describe the behavior of the liquid phase a t isothermal conditions. The description of the isothermal vapor-liquid equilibrium requires an additional adjustable parameter: Henry’s constant of formaldehyde in the active solvent. In this work, using the parameters obtained by fitting the experimental data of two selected sets of data, the prediction of the model is compared with all the existing literature data for the binary systems water-formaldehyde and methanolformaldehyde. Moreover, we present an extension of the model for predicting vapor-liquid equilibria of the ternary system water-methanol-formaldehyde. From binary data alone the model is capable of accurately predicting vapor-liquid equilibria in a ternary mixture.
Introduction The description of the vapor-liquid equilibrium (VLE) behavior of systems which contain water-formaldehyde or methanol-formaldehyde or their ternary mixtures is of great importance for the design of separation processes in the chemical industry. In fact, formaldehyde is an important raw material in the production of plastics and adhesives. Because of its extremely high reactivity, formaldehyde is usually produced, stored, and processed in the form of aqueous solutions with methanol added as a stabilizer. In a recent publication, Maurer (1986) describes a model which accounts for physical and chemical iteractions between species in the binary mixtures of water-formaldehyde and methanol-formaldehyde. Maurer (1986)usea the UNIFAC model for the activity coefficients and two equilibrium constants for describing the liquid phase: the model requires five adjustable parameters, two UNIFAC parameters for interaction between water and formaldehyde and the three equilibrium constants. Moreover, the vapor pressure of methylene glycol is required for the description of the vaporliquid equilibrium. The principal characteristic of the model proposed by Maurer (1986) is the possibility of its extension to ternary mixtures using binary information alone. This extension was the first attempt at modeling the vapol-liquid equilibrium in waterand formaldehyde-containing multicomponent mixtures. Following another approach, Brandani et al. (1987a) describe vapol-liquid equilibrium of formaldehyde-watermethanol mixtures using the Wilson equation for the activity coefficients. More recently, Brandani et al. (1991) present a ther-
modynamic model which, for each binary system containing formaldehyde and an active solvent, requires three adjustable parameters to describe the behavior of the liquid phase at isothermal conditions. The three parameters are the thermodynamic equilibrium constant for the solvation reaction between formaldehyde and the active solvent, the thermodynamic equilibrium constant for polymer formation, and a physical parameter in the equations for the activity coefficients described by the UNIQUAC model. The description of isothermal vaporliquid equilibrium requires an additional adjustable parameter: Henry’s constant of formaldehyde in the active solvent. This approach was preferred to that proposed by Maurer (1986) since the equation for the vapor pressure of .formaldehyde is reported for a temperature range up to 251 K, while the experimental data for the vapor-liquid equilibrium of binary mixtures taken from the literature are at temperatures between 310 and 400 K. In thiswork, using the parametera obtained by Brandani et aL (1991),the prediction of the model is compared with all the existing literature data for the binary systems watepfomddehyde and methanol-formaldehyde reported in the DECHEMA collection. Moreover, we present the extension of the model for predicting the vapor-liquid equilibria of the ternary system water-methanol-formaldehyde. The extension from binary to ternary mixtures is rigorous and simple.
Comparison of Calculated and Measured VLE in the Binary Systems There are many measurements in the literature for the vapor-liquid equilibrium in the binary systems water-
0888-5885/92/2631-1792$03.00/0@ 1992 American Chemical Society
