I n d . Eng. Chem. Res. 1992,31, 1216-1222
1216
Watanabe, K. A Role of Thermodynamical Properties Research on Refrigerant Mixtures. In Heat and Mass Transfer in Refrigeration and Cryogenics; Bougard, J., Afgan, N., Eds.; Hemisphere: New York, 1987; pp 343-368. Watanabe, K. Current Thermophysical Properties Research on Refrigerant Mixtures in Japan. Znt. J. Thermophys. 1990, 1 1 , 433-453. Whipple, G. H. Vapor-Liquid Equilibria of Some Fluorinated Hydrocarbon Systems. Znd. Eng. Chem. 1952,44, 1664-1667.
Yada, N.; Uematsu, M.; Watanabe, K.Study of the PVTx Properties for Binary R152a + R114 System. Trans. JAR 1988,5, 107-115. Kubota, H.; Zheng, Q.; Makita, T. High-pressure VaZheng, X.-Y.; por-Liquid Equilibrium Data of the HFC 134a + HCFC 141b System. J. Chem. Eng. Data 1990,35,441-444.
Receiued for review September 29, 1991 Revised manuscript receiued December 3, 1991 Accepted December 17,1991
Micromixing in Static Mixers: An Experimental Study John
R.Bourne,* Joachim Lenzner, and Sergio Petrozzi
Technisch- Chemisches Laboratorium, ETH, CH-8092 Zurich, Switzerland
Static mixers develop high rates of energy dissipation relative to an empty pipe and have short residence times, which are useful characteristics for those rapid reactions needing fast mixing to obtain high yield. Hardly any information on this application however exists. The competitive coupling of 1-and 2-naphthols with diazotized sulfanilic acid was applied in aqueous solution to two commercially available designs of static mixer. The rate of turbulent energy dissipation was deduced from the measured product distribution over a range of flow rates. Chemical reaction did not take place throughout a whole element, but was localized over a distance of around 0.01 m. The reaction zone shifted somewhat depending on the operating conditions, e.g., concentrations, which introduced some inaccuracy into the determination of energy dissipation due to ita inhomogeneity. Product distributions could nevertheless be adequately predicted using the engulfment model of micromixing as some operating conditions were changed. The mixer element having an open structure without excessive constriction of the flow gave faster micromixing and better energy utilization. This could be a clue to further improvements in design. 1. Introduction
Most experimental studies of micromixing refer to stirred tank reactors. Micromixing is however rapid, requiring only fractions of a second in most turbulent flows. It is only relevant in determining the final process result, e.g., the yield of a complex reaction, when the process itself is rapid, e.g., for reactions whose time constants are comparable with or shorter than that of micromixing. Static mixers seem to satisfy the two principal requirements when rapid processes are engineered, namely, (a) a short residence time on the order of fractions of a second and (b) a high rate of turbulent energy dissipation, probably of the order of 10L103 W-kg-', ensuring fast micromixing and, in the case of two-phase systems, also fine dispersion. Micromixing in static mixers, which is often relevant in controlling the product distributions of fast, complex reactions, appears to have received almost no attention (Godfrey, 1985). The first objective of this work was therefore general, namely, to explore the ability of two designs of static mixer to achieve rapid micromixing in the turbulent flow regime. A recent investigation into micromixing in three closely related types of static mixer using a superficial linear velocity (u) of 2 m d employed as a fast test reaction the diazo coupling of 1-naphthol and diazotized sulfanilic acid (Bourne and Maire, 1991a). Rates of turbulent energy dissipation (4 were found to be of the order of l@W-kg-', which was outside the normal operating range of this test reaction (Bourne and Maire, 1991b). Because of the limited reaction rate, it proved essential to slow down the mixing by adding carboxymethyl cellulose (CMC), so
raising the kinematic viscosity ( u ) of the reaction medium from 0.89 X lo4 to 7.9 X lo4 m 2 d in order to use the coupling of 1-naphthol. Direct application of aqueous solutions in static mixers demands faster test reactions, such as the competitive diazo couplings between 1naphthol and 2-naphthol (Bourne et al., 1992). The more specific objectives in this work were to illustrate the suitability of this new test system for characterizing micromixing in highly turbulent flows and to compare two designs of static mixer in achieving such fast micromixing. 2. Principles of Method
The simultaneous coupling of 1-naphthol (Al) and 2naphthol (A2) with diazotized sulfanilic acid (B) produces four dyes in proportions which depend upon the mixing intensity, here characterized by t, the energy dissipation rate. Full details of these reactions, chemical analysis, and kinetics are available (Bourne et al., 1992), so that here a summary will suffice. 1-Naphthol yields two monoazo isomers which can couple further to a single bisazo dye (S). 2-Naphthol couples to give a single monoazo dye (Q). A1 + B
(1)
p-R
(2)
S
(3)
S
(4)
0-R p-R
+ B -!%
B
kzP
ka
*Towhom correspondence should be addressed. Present address: Department of Chemical Engineering, Swiss Federal Institute of Technology Zurich, Universitiitsstrasse 6, CH-8092 Zurich, Switzerland.
o-R
+ -
A1 + B
k,,
A2+B-Q (5) The competitive, consecutive part of this set is characterized by the yield of S relative to the limiting reagent B, namely, XS'
0888-5885/92/2631-1216$03.00/00 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 4,1992 1217
A
while the competitive (or parallel reaction) part determines the yield of Q, namely, XQ XQ =
CQ
C0.R
+ C p R + CQ + 2cs
(7)
If only 1-naphthol is coupled, the yield of S is denoted by XS and is given by (6) with CQ = 0. The overall initial composition is defined by the stoichiometric ratios yA1and 5, where YA1 = NAlo/N& (8) t = NA20/NA10 (9) In the chemical regime, mixing would be faster than reaction and the yields of Q and S would depend only on the ratios of the rate constants and the two stoichiometric ratios after the limiting reagent (B) had been fully consumed. The reaction system is however sufficiently fast that its product distribution (and especially XQ) is strongly influenced by mixing up to e = lo5 W0kg-l (Bourne et al., 1992). Yields are then also influenced by the volume ratio (a) of the two reagent solutions, defined by (Y = v A / v B (10) and the Damkohler number E, given by
-
Da =
k20C&
E(l + a) The initial concentration of unmixed diazotized sulfanilic acid is cBoand kzo is the second-order rate constant for the coupling of p-R in the ortho position to give S, according to (4). The engulfment rate coefficient E depends upon the kinematic viscosity and the energy dissipation rate according to E = 0.058(t/~)~.~ (12) Thus XS’ (or XQ) = f(kinetics,yAl,ts,aY) (13) where numerical integration of the engulfment model of micromixing (Baldyga and Bourne, 1989,1990;Bourne and Maire, 1991b) is carried out to find the yields. If XS’ and XQ are determined spectrophotometrically (Bourne et al., 1992) for given experimental conditions (yA1, 5, a, v, cBdand all five rate constants), then E follows from (13) and t from (11)and (12). Here t is the energy dissipation consistent with application of the engulfment model to a measured product distribution. If, as often happens, spatial gradients of t occur in the reaction zone, these may either be explicitly accounted for in the model or averaged. In this work c will be the spatial average in the reaction zone. In a static mixer fitted into a tube, the voidage fraction (e)-or volume fraction of liquid-is less than unity and there are many surfaces present upon which boundary layers form. Energy dissipation to heat, manifested in a pressure drop Ap over the working or liquid volume VM, occurs by two mechanisms, (a) turbulent energy dissipation e sufficiently far from the surfaces and (b) direct dissipation E D caused by gradients of the mean velocity present in the boundary layers. The total dissipation 9 is the sum of these two terms @=€+ED (14) and is related to the pressure drop by
,q,
w,
.
,
Q
I
pP2 H A - a - a B neutralization and dllutlon
Figure 1. Reactor scheme. Table I. Characteristics of SMXL and SMV-4 Mixers (Source: Sulzer AG, Winterthur, Switzerland) characterietic outer d, mm length of one mixer, mm material (stainless steel) number of static mixers in reactor e
Ne, turbulent total length of static mixers in the tube, mm thickness of the metal sheets, mm normal distance between the sheets (Figure 2A), mm axial distance between the sheets (Figure 2A), mm width of the metal sheets, mm hydraulic diameter, mm
SMXL SMV-4 20.5 28.0 72.0 25.0 1.4571 1.4571 7 5 0.91 0.87 1.2 2.5 500 125 1.0 0.5 12.5 24.0 4.5 5.3
Pressure drop measurements were used here to calculate 9 using (15)and also to check the manufacturer’s values of Ne-the Newton number, which is a friction factor or drag coefficient defined by L Ap = (Ne)pu2; (16) where L and d are the length and diameter of the static mixer. It follows from (15) and (16) that 9 and Ne are related by I$
= u3(Ne)/ed
(17)
3. Experimental Section 3.1. Description of Apparatus. Figure 1shows the equipment used whereby the mixing elements were fixed in the transparent tube R1. Naphthol solution was circulated by the pump P1 through a 26 m long loop, while diazotized sulfanilic acid solution was fed at a constant rate by the pump P2 into the first of the mixers. Semibatch operation was thus employed. Details of the pumps, flow meters, etc., are available (Bourne and Maire, 1991a; Lenzner, 1991). The mixing elements SMXL and SMV-4, manufactured by Sulzer, Winterthur, Switzerland, had different structures, as indicated in Figure 2. Table I contains the dimensions, etc., of these elements. Type SMXL is intended for the laminar flow regime, e.g., viscous media like polymer melts. It exhibits an open structure, each element containing three X-like units (Figure 2A). Type SMV-4 resembles a screen or honeycomb, the individual passages being rhombic in cross section and running diagonally relative to the surrounding pipe. The flow was constrained in the mixer channels, whose hy-
1218 Ind. Eng. Chem. Res., Vol. 31, No. 4,1992 11. Feed Timen and Revnolds Reynolds Nnmber for Feed Pim Pipe Table 11.
A
~~
u,m d 2.5 2.0 1.5 1.0 0.5
NRS 3076 2461 1&L6 1230 615
tF? 8
463 579 772 1157 2315
Table 111. Measured Pressme Drop and Calculated Total Energy Dissipation Rate with the SMXL Mixer u,m d AP, bar Ne 4, w.kg-' 0.5 1.0 1.5
0.08 0.30 0.64
1.33 1.24 1.18
7.8
62.8 212
Table IV. Measured Pressnre Drop and Calculated Total E n e m Dissipation Rate with the SMV-4 Mixer u,ma-' AP, bar Ne W.lrg' 0.5 0.025 1.97 12.6 1.0 0.130 2.57 101 1.5 0.29 2.55 342 2.0 0.53 2.62 804 2.5 0.84 2.65 1581 3.0 1.19 2.61 2732
*,
Sectional Y i e w
Plan "lew
Fignm 2. Sulzer SMXL (A) and Sulzer SMV-4 (E!) mixing element.
draulic diameter was 0.0053 m. This element is intended for turbulent flow applications. The feed pipe for the B-solution had an internal diameter (dB) of 0.0011 m and was located coaxially in the pipe at a distance of 0.003 m from the fmt element. Results of flow visualization in this region are reported later. 3.2. Operating Conditions. All rum were made at 25 OC in dilute aqueous solutions (v = 8.9 X I@' m 2 d ) . Pressure drop measurements used water. For the diazo couplings the initial volume of naphthol solution (V,) in the loop was 0.022 m3 while the volume of the diazo solution (VB) gradually added was 0.0011 m3 (a= 20). An equimolar mixture of NaHCO, and Na,CO, was added as buffer to the A-solution, giving pH 9.9 and ionic strength 444.4 m o l m 3 during coupling. The rate constants (m3. mol-'.s-') were then k,, = 12240, k,, = 921, k, = 22.25, k, = 1.835, and k, = 124.5 (Bourne et al., 1992). Dye concentrations were determined with a diode array spectrophotometer (HF' 8452A with workstation 9153 C). The stoichiometric ratio of A1 to B was always yA1= 1.2, whereas the ratio of 2-naphthol to 1-naphthol was either E = +the 'old" reaction system in (1b(4)-or varied from E = 1-5-the *newn reaction system, including reaction (5). The superficial veloeity in the mixers (u) ranged from 0.5 to 2.5 m d . The initial concentrations of diazotized sulfanilic acid in the B-feed stream ( c d were varied hetween 1.5 and 60 m~l.m-~. Semibatch operation had been simulatd (Baldyga and Bourne, 1989) by discretizii the addition of the feed into u parts, each having a volume of VB/u and an initial concentration of c Each part, after addition, mixed by engulfment with %-rich surroundings having constant composition in a fraction of a second (details are given later). Thereafter the reaction produds were considered to blend with the remainii fluid in the reactor before the
next portion of the feed entered. This impliea that the feed rate is extremely low relative to the circulation rate in the reador. In this work B was usually added isokinetically to the circulatingA-stream, the flow rate ratio A to B b e i i a t least 346. The feed time was given by t p = 4VB/udS2u (18) The simulations showed that product distribution (XS, etc.) no longer depended upon feed discretization when u > 30. The number of A-rich fluid recirculations during the feeding of reagent B (n3 is equal to
n, = 4VB/udB2LL (19) where & = 26 m, VB = 0.0011 m3, and dB = 0.0011 m to give % = 45 in all runs. Thisexwedsthe required number 30. Feed times given by (18) and the Reynolds number in the feed pipe are detailed in Table 11. The whole semibatch reaction was modeled as a plug flow micromixing and reaction zone embedded in a well-mixed recirculation loop (Baldyga and Bourne, 1989; Bourne and Maire, 1991a). 4. Reaults 4.1. Pressure Drop ( A p ) and Total Energy Dissipation Rate (0). Table III for seven Sulzer SMXL elements-refer also to Table I-and Table IV for five Sulzer SMV-4 elements report measured pressure drops at various superiid water velocitiea. The drag coefficients (Ne) from (16) and the total energy dissipation rates (+) from (17) are also included in Tables I11 and IV. The Ne values reported by the manufacturer (Table I) for the turbulent regime are well confirmed by these measurements. 4.2. Comparisonof Old and New Reaction Systems. Table V report9 energy diasipations deduced from XS for the old system (coupling of 1-naphthol) and from XQ for the new test reactions (coupling of 1-and 2-naphthols). The old system (E = 0) was run with ch = 60 m0l.m4, this high concentration level being necessary to obtain sufficiently high XS values (0.0654.10) for accurate analysis. The new system was run with E = 1and ch = 6 m0l.m"
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1219 Table V. Old and New Test Reactions in the SMXL Mixer: Energy Dissipation Rates for yAI = 1.2, a = 20,[ = 0 (Old) and 1 (New) (298 K; pEI = 9.9) u,m d 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 2.0 2.0 2.0 2.0 2.5 2.5 2.5
old system 19.3 17.4 19.1 19.3 63.0 58.7 60.0
new system 20.9 19.5 21.8 18.3 70.1 81.5 74.2 83.5 200.8 195.3 172.6 195.9 367.0 360.7 334.7 369.4 484.2 517.6 524.2
@ W-kg-'
7.8
62.8
212
-6
10
s(av), W-kg-' 20 60 20 60
u,mss-' 0.5 1.0 0.5 1.0
-4
10
-3
IO
-2
10
10.l
100
-
Da
502
Figure 3. Product distribution (XQ) as a function of Damkohler number when Y~~ = 1.2 and CY = 20 (298 K; pH = 9.9): (0,+,A) measured XQ when f = 1, 3, and 5, respectively.
981
tration levels, and this is some support for the similar average t in Table V. All LR are shorter than either the normal or axial separations between the SMXL sheets. The question as to where reaction occurred remains however unanswered and will be subsequently taken up in this paper. With the new system cBpwas 25 m ~ l * mwhen - ~ u = 2 and 2.5 ms-l. Higher velocities were not studied because of increasing pressure drop and a limitation on the power of the pumps. The new system would have detected substantially higher energy dissipation rates. A regression for the new system and velocities from 0.5 to 2.5 ms-I (Table V) showed that t u204which is widely different from the exponent 3 for the total dissipation in the turbulent regime-refer to (17). This is also an indication that reaction did not take place completely within the SMXL mixing elements. 4.3. Application of New Reaction System: SMXL Mixer. Figure 3 for a = 20 and y A 1 = 1.2 shows curves which are the predicted variation of XQ with E and 5 for reactions (1)-(5). When c = 10 m ~ l - m -u~= , 2 ms-l, and 5 = 1, experiments gave 2 Q = 0.100. The micromixing model predicted this product distribution when E = 8.1 X Thus the measured XQ = 0.100 could be fitted onto the curve for 5 = 1 in Figure 3: it is the middle of the three points. With a,yA1,cB0, and u being kept constant, [ was next increased to 3 and finally to 5. From (11)E should also have remained unchanged so that the measured XQ (0.236 and 0.329) could be plotted on the vertical broken line. Figure 3 shows excellent agreement with the model curves. When a,Y ~ u,~and , XQ were kept constant, the model was used to predict % when 5 = 1,so that the required XQ (0.16) was attained. From E the necessary cBocould be calculated this gave 25.0 m ~ l - m - As ~ . the right-hand, upper result in Figure 3 shows, XQ was indeed 0.159. The required E and cB0were similarly calculated when 5 was 3 and 5 and the measured XQ under these conditions were in the range 0.165-0.172. These are the results plotted in Figure 3, which almost fall on the horizontal broken line (XQ = 0.16). Finally with a,yA1,u, and $. = 1 being kept constant, cB0and hence also E were decreased and XQ was measured. The lower, left-hand result again fell on the model curve. It was concluded that when the average rate of energy dissipation in the reaction zone is known, then the product distribution may be predicted with sufficient accuracy as
Table VI. Calculated Reaction Times and Lengths for Old and New Test Reactions cb, m~lem-~ E 60.0 0 60.0 0 6.0 1 12.0 1
105
T 3.7405 3.8086 3.5253 3.4782
LR,
0.0069 0.0081 0.0065 0.0074
when u = 0.5 m 8 - I and cBo= 12 m ~ l - mwhen - ~ u = 1ms-l. The old system could not be applied at velocities above 1ms-l because this would have called for cBoin excess of the solubility of diazotized sulfanilic acid to secure XS > 0.04 for accurate analysis. The comparison between the old and new systems in Table V is therefore limited to a narrow window, indicating however satisfactoryagreement. A crucial consideration in interpreting the results of fast reaction experiments in inhomogeneous turbulence is the location of the reaction zone. The distance traveled by fluid elements after leaving the B-feed pipe until reaction is completed depends upon first the bulk blending of fresh feed with its surroundings (macromixing) and then the local, fine-scale mixing (micromixing) leading to chemical reaction. It is reasonable to regard the distance over which blending occurs as independent of the chemical reaction, since such mixing is determined by inertial-convective processes. Micromixing on the other hand is determined by viscous-convective, viscous-diffusive, and reaction processes and can depend upon the chemical system in question. The engulfment micromixing model was therefore used to find the time needed for micromixing of reagents A l l A2, and B and for their reaction. An end point of 99%,conversion of B was taken here, but since the product distribution hardly changes over the last 10% or so of the conversion of the limiting reagent B, the particular end point is not critical. Table VI gives results relating to the experiments at 0.5 and 1.0 m 4 in Table V. Since the micromixing equations are integrated with respect to dimensionless time T , where T = Et (20) the values of Tin Table VI are those corresponding to 99% B-conversion. The corresponding length of the reaction zone, LR,is found from LR = u T / E (21) These results suggest that the two sets of reactions took place at similar locations, despite their different concen-
-
1220 Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 Table VII. New Test Reactions: Influence of Deviations from Isokinetic Feed Introduction (yal = 1.2, a = 20, !. = 1, ce, = 25 mol*m-' (298 K; p H = 9.9), u l = 2.5 m*s-', u = 2.0 m*s-*,u z = 1.5 m0s-l) run u, rn& XS' XQ t,W-kg-' 20 2.0 0.0090 0.1580 367.0 21 2.0 0.0090 0.1587 360.7 0.1617 334.7 0.0079 22 0.1577 369.4 0.0095 23 0.1647 310.6 0.0105 44 0.1610 340.6 0.0136 45 0.1641 315.9 0.0103 46 0.1597 351.4 0.0121 47 0.1526 420.1 0.0116 48 0.1508 440.4 0.0069 49 0.1487 465.0 0.0084 50 0.1536 409.9 0.0076 51
the concentration level and stoichiometric ratio are changed. Although a = 20 and - Y = ~ 1.2 ~ were not varied in this study, it would be expected on the basis of previous experience that the model would also adequately predict their influences on product distribution. 4.4. Influence of Nonisokinetic Feed Addition on Micromixing. Table VI1 reports first four repeat runs under isokinetic conditions. The next four repeats refer to 25% faster feed addition, whereas in the last four repeats the feed velocity was 25% lower than for isokinetic conditions. The reproducibility is also evident in Table VII. Student's t-test showed no influence on e of faster feeding, but a singificant increase in e when the feeding is slower than isokinetically. The same trends as those in Table VI1 have been observed in a turbulent tubular reactor containing no static mixers (Bourne and Tovstiga, 1988). If mixing and reaction had occurred entirely within the mixing elements, the level of turbulence as signaled by the product distribution would have been independent of the mode of feed introduction. The results in Table VI1 suggest reaction prior to the passage of the fluid through several elements and raise again the question about the location of the reaction zone. 46. Location of the Reaction Zone in SMXL Mixer. The half-life of the diazonium ion (tR) is mainly determined by reactions 1 , 2 , and 5 at high mixing intensities, as in the static mixers, so that tR
[(kl, + k 1 p + k3)C&]-'
(22)
The s u m of these rate constants is 1.33 X lo4m3.mol-'-s-' and cAo= yA1cb/a so that cAo= 1m ~ E m - ~It. follows that tR is less than 100 ps, which is sufficiently short for this reaction to be dominated by mixing, with an observed rate equal to that for an acid-base neutralization. Such a reaction decolorizes an indicator, so that the colored region corresponds to the reaction zone of the color-forming diazo couplings. Sodium hydroxide solution having a similar concentration to c during the couplings was colored an intense blue by ad%tion of thymolphthalein. It was introduced isokinetically through the B-feed pipe into hydrochloric acid solution having a concentration similiar to that of the naphthol solution. The feed stream remained intact until it met the first X of the mixing element, where it split into two streams which traveled along the metal sheets (Figure 4) and became less colored as the result of mixing and neutralization. Already at the fmt crowover point of the X and as the feed passed behind the metal sheets to join the main flow, no trace of color remained. The length of the reaction zone was defintely less than either the axial or normal distances between the sheets (Figure 2A) and was roughly 0.01 m.
Figure 4. Observed position of neutralization zone in SMXL mixer. Table VIII. Calculated Length of Zone for Micromiring and Reaction (yal = 1.2, a = 20; 99% B-Conversion (298 K , DH = 9.9)) cb, rnol~rn-~ 5 c(av), Wskg-' u, m.8-l T LR,m 3.5310 0.0061 1 360 2.0 25.0 3.6791 0.0064 1 360 2.0 16.0 3.8310 0.0066 1 360 2.0 10.0 4.0343 0.0070 1 360 2.0 5.08 3.4578 0.0060 3 360 2.0 10.0 3.2006 0.0055 5 360 2.0 10.0 3 360 2.0 3.7751 0.0065 5.08 3.9663 0.0069 5 360 2.0 2.292 3.4557 0.0063 5 20 0.5 1.5 I ,
Some indication of the radial distance which the feed B must travel in order to encounter sufficient reagent A for reaction can be obtained as follows. The following operating conditions were fairly typical: a = 20, Y~~ = 1.2, u = 2 m-s-l, cBo= 25 m ~ l - m -and ~ , cAo = 1.5 mol.mg. With u = 50, the A-concentration in the surroundings of the 50th and last drop of feed would be 0.4675 m~l.m-~. The flow rates of the recirculated A-rich stream and the B-feed stream were 6.927 X 10"' and 1.901 X lo4 m 3 d , respectively. Thus the molar fluxes of A and B into the reaction zone were 32.39 X 10" and 4.752 X m o l d , respectively. For axisymmetric dispersion of B into A, the radial distance which B must move out to encounter sufficient A for its complete consumption would be 0.004 m. The pipe radius was 0.0105 m. Even a t the end of coupling, where the smallest concentration and molar flux of A were available, there should have been no overall or macroscopic shortage of reagent A, and the reaction zone should have remained in the core of the flow. Simulations also throw some light on the likely location of the reaction zone. Results similiar to those in Table VI were calculated to see how the length of the reaction zone controlled by micromixing (LR)would change as the concentration level was varied. The energy dissipation rates appropriate to each liquid velocity, which were needed for these micromixing calculations, were taken from Table V. Table VI11 summarizes the results. Two clear trends emerge. First, as 5 increases, the competition for B from 2-naphthol increases and the length of the reaction zone decreases. Second, as the concentration level increases, reaction is accelerated and the reaction zone becomes shorter. In the chemical or slow reaction regime an inverse proportionality between LRand c would be calculated, whereas in Table VIII the much weker trend is due to the damping influence of inadequately fast mixing. The spatial distribution of c in the reaction zone is unknown. The velocity distribution and turbulence characteristics in the entry region of a static mixer do not seem to have been determined, yet it is here that reaction occurs (Figure 4). Flow visualization indicates reaction upon contact between the feed stream and the first metal sheet of the mixer (Figure 4). It is likely that e rapidly increases at the point of contact, falls off as the flow divides, increases again as it passes over the edge of a sheet and finally decreases in the wake of a sheet. Visualization implied that reaction occurred mostly in the first two of these four regions, namely, initial contact and flow division
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1221 Table IX. Measured Product Distribution and Calculated Energy Dissipation Rate Using New Test Reactions in the SMV-4 Mixer (yAl= 1.2, a = 20, u = 2 m * d (298 K pR = 9.9)) c=.. m ~ l . m - ~ € xs XQ 0.047 2 1 0.013 0.132 2 3 0.017 0.193 2 5 0.018 0.081 5 1 0.013 0.213 3 5 0.022 0.245 5 5 0.009 0.101 0.024 1 9 0.241 0.006 3 9 0.311 5 9 0.011 0.113 1 0.011 14 0.273 0.007 14 3 0.140 1 0.015 20 0.308 0.006 20 3 0.158 1 0.012 25
t,
W-kg-' 132.6 113.1 131.7 141.5 130.8 295.4 229.2 264.6 392.1 376.9 348.3 350.1 409.3 353.7
along the first sheet. This means that t was decreasing in the direction of flow. It also follows that the use of a single value of t in Table VIII, which depends only on u, is inaccurate. As cB0and/or 5 increases, L R must decrease, which shifts the reaction into a region where e must rise. The following experimental results illustrate this conclusion from the model. (a) With a = 20, yA1 = 1.2, u = 2 ms-', and cB0= 10 m ~ l - m -increasing ~, 5 from 1-3 to 5 caused the calculated average value of e to rise from 316-364 to 395 W-kg-'. (b) With a = 20, 7 A 1 = 1.2, u = 2 ms-', and 5 = 1, increasing cBofrom 5.08-10.0 to 25 m ~ l - mcaused -~ the average value of c to rise from 297-316 to 358 W-kg-'. The change in LR as a consequence of various values of c3 and 5 influences therefore e, and this fact is particularly significant in flow fields where large spatial e gradients arise. On the other hand the shift in LRhad only a small influence on the prediction of product distribution. The measured product distributions for cases a and b above have been plotted in Figure 3 (refer to the vertical broken line and the three points on the curve 5 = 1, respectively), where good agreement between measured and calculated XQ is evident. A naive interpretation of this finding is that, because G E-' an error in 5,determined from a measured XQ, will be squared when t is calculated, whereas an error in e will be reduced when G is found from its root in the course of predicting XQ. Micromixing involves complex, coupled, nonlinear processes, and any generalization needs to be suitably qualified. 4.6. Comparison of SMXL and SMV-4 Mixing Elements. SMV-4 elements had previously been investigated at u = 2.0 ms-l using the old test reactions at v = 7.9 X lo4 m2&, The viscosity had been raised through addition of carboxymethyl cellulose (CMC) (Bourne and Maire, 1991a). Reasons were found why CMC is not the ideal additive for such experiments. Here the faster new reactions could be employed without CMC. Table IX summarizes the new experimental results and the corresponding average values of e. The shift in the length of the reaction zone, seen in Table VI11 and discussed in the last section, also accounts for the effect of cBoon e seen in Table IX. This makes only a rough comparison between the two types of element possible. For SMXL, 17 results were available at u = 2 ms-' using the new system: The average value of e was 335 W-kg-', which was 66% of 9 (Table 111). For SMV-4, the average e was 262 Wnkg-' or 33% of (Table IV). Furthermore pressure gradients for the SMXL and SMV-4 elements were 2.3 and 4.2 bar-m-l, respectively. In the empty tube the turbulent energy
- -
+
dissipation rate was found to be 4.4 W-kg-' (Bourne and Maire, 1991a). Despite its high rate of total energy dissipation, the SMV-4 element was inferior to the SMXL element both from the relative (33 vs 66%) and absolute (262 vs 335 W-kg-l) viewpoints as a turbulence generator. It was found before (Bourne and Maire, 1991a) that narrow channels in mixing elements constrict turbulence and lower the ratio e/+. The more open structure of the SMXL was preferable for rapidly mixing miscible reagent streams. Flow visualization with SMV-4 elements was impossible because the neutralization zone could not be seen. With elements constructed from a transparent material, direct determination of the reaction zone in the SMV-4 mixer would have been possible, so enabling comparison with the SMXL mixer. For SMXL elements reaction was highly localized (Figure 4), not needing the full extent of even one X. Each element consisted of three X (Figure 2A), and in total seven elements were available; but it is clear that at most one element was needed. Another element configuration needs to be developed which generates a high level of turbulence in a small volume. If, for instance, lo4 W-kg-' were available for the new reaction system (1)-(5), micromixing could be completed (2' = 4) in about 1 ms. Devices generating lower e but for longer periods (or over more space than the process needs) are less attractive for those fast reactions where high selectivity calls for rapid mixing. Making fine droplets and bubbles (i.e. dispersion) is another field where intensive, local mixing would be of interest (Davies, 1987). 5. Conclusions The old test system (coupling between 1-naphthol and diazotized sulfanilic acid) gave comparable results to the new test system (simultaneous coupling of 1- and 2naphthols) but was limited to lower energy dissipation rates (Table V). The new system could have detected still higher t values in this investigation of static mixers, but pressure drop and pumping limitations excluded their attainment. Mixing and reaction did not occur throughout the mixing elements but were highly localized (Figure 4). Moreover the reaction zone shifted somewhat with the operating conditions. Because the turbulence was inhomogeneous, this shift meant that the average energy dissipation rates, determined from the product distribution of fast reactions, also varied with operating conditions. On the other hand good predictions of product distribution were possible from relatively uncertain energy dissipations (Figure 3). Of the two static mixer designs studied (Sulzer SMXL and SMV-I), that with the more open structure was the better generator of turbulence and made most use of the pressure drop. Better designs are however needed. More information is needed about the spatial distributions of velocity and turbulence properties (especially e) in static mixers: this would permit a more quantitative treatment of micromixing and fast reactions as well as of dispersion.
Acknowledgment We thank Sulzer AG, Switzerland, for supplying the static mixing elements free of charge.
Nomenclature A1 = 1-naphthol A2 = 2-naphthol B = diazotized sulfanilic acid = feed concentration of B (m~l.m-~) Da = Damkohler number d = diameter of static mixer (m) dB = internal diameter of feed pipe (m)
Znd. Eng. Chem. Res. 1992, 31, 1222-1227
1222
e = fractional liquid holdup in mixer E = engulfment rate coefficient (8-l) ED = direct energy dissipation rate (W-kg-') k = rate constant (rn3.mol-'.s-') L = length of mixer (m) LL = length of loop reactor (m) LR = length of reaction zone (m) N e = Newton number nZ = number of recirculations of A-solution during feeding of B-solution o-R, o = ortho monoazo dyestuff (2-[ (4-~ulfophenyl)azo]-lnaphthol) p - R , p = para monoazo dyestuff (4-[(4-sulfophenyl)azo]-lnaphthol) Ap = pressure drop over static mixer (bar) Q = 2-naphthol monoazo dyestuff (1-[(4-sulfophenyl)azo]-2naphthol) Q* = volumetric flow rate ( m 3 d ) S = bisazo dyestuff (2,4-bis[(4-sulfophenyl)azo]-l-naphthol) T = dimensionless time for mixing tF= feed time (8) u = velocity (ms-') VA = volume of naphthol solution (m3) V , = volume of diazotized sulfanilic acid solution (m3) VM = volume of liquid in static mixer (m3) XS' = product yield (new test reaction) XS = product yield (old test reaction) XQ = product yield (new test reaction)
Greek Letters a = volume ratio v A / V B yA1= stoichiometric ratio N A , , / N b
= turbulent energy dissipation rate (W-kg-') 0 = total energy dissipation rate (W-kg-')
t
Y
= kinematic viscosity ( m 2 d )
Subscripts 0 = initial
s,s=s
Literature Cited Baldyga, J.; Bourne, J. R. Simplification of micromixing calculations, Part 1. Chem. Eng. J. 1989, 42, 83. Baldyga, J.; Bourne, J. R. The effect of micromixing on parallel reactions. Chem. Eng. Sci. 1990, 45, 907. Bourne, J. R.; Tovstiga, G. Micromixing and fast chemical reactions in a turbulent tubular reactor. Chem. Eng. Res. Des. 1988,66,26. Bourne, J . R.; Maire, H. Micromixing and fast chemical reactions in static mixers. Chem. Eng. Process. 1991a, 30, 23. Bourne, J. R.; Maire, H. Influence of the Kinetic Model on Simulating the Micromixing of l-Naphthol and Diazotized Sulfanilic Acid. Ind. Eng. Chem. Res. 1991b, 30, 1285. Bourne, J. R.; Kut, Oe. M.; Lenzner, J. An Improved Reaction System To Investigate Micromixing in High-Intensity Mixers. Znd. Eng. Chem. Res. 1992, 31, 949. Davies, J. T. A physical interpretation of drop sizes in homogenizers and agitated tanks,including the dispersion of viscous oil. Chem. Eng. Sci. 1987, 42, 1671. Godfrey, J. C. Static mixer. In Miring in the process industries; Harnby, N., Edwards, M. F., Nienow, A. W., Eds.; Butterworth: London, 1985. Lenzner, J. Der Einsatz rascher, kompetitiver Reaktionen zur Untersuchung von Mischeinrichtungen. Ph.D. Thesis No. 9469, ETH Ziirich, 1991.
( = stoichimetric ratio NA2,,/NAl0 p
--
lo = reaction A 1 o-R l p = reaction A 1 p-R 20 = reaction p - R S 2p = reaction o-R S 3 = reaction A2 Q A1 = l-naphthol A2 = 2-naphthol B = diazotized sulfanilic acid o = O-R p = p-R R = sum of o-R and p - R
Received for review October 1, 1991 Accepted January 13, 1992
= fluid density (kgm-3)
Calculation of the Thermodynamic Data for Zinc Extraction from Chloride Solutions with Di-n -pentyl Pentanephosphonate Ruey-Shin Juang* and Jiann-Der Jiang Department of Chemical Engineering, Yuan-Ze Institute of Technology, Nei-Li, Taoyuan, 32026,
Taiwan, ROC
The thermodynamic data for the extraction of zinc from chloride solutions with di-n-pentyl pentanephosphonate (DPPP) dissolved in kerosene have been calculated on the basis of the temperature dependence of extraction equilibrium constanta over the temperature range of 20-55 "C.The method, employing either Bromley or the simplified Pitzer equations to estimate the stoichiometric activity coefficient of various species in the aqueous phase, is found to be effective for the evaluation of the thermodynamic data. The extraction reaction is favored by the enthalpy change and unfavored by the entropy change. Introduction In recent years numerous papers concerning the various factors affecting the extraction of a metal chelate have been found. However, only a few thermodynamic studies have been done. It was reported that the thermodynamic data could support the mechanism for synergism of metal extraction with 2-thenoyltrifluoroacetone and neutral phosphorus-based compounds (Nash and Choppin, 1977; *To whom all correspondence should be addressed.
0888-5885/92/2631-1222$03.00/0
Kandil and Ramadan. 1980) or with diDhenvlcarbazone and pyridine (Yamada'et al.,'1982). It isthoight that the thermodynamic data can provide valuable information regarding the extraction mechanism. For the thermodynamic approach of extraction reactions, the enthalpy change (AH) was generally obtained on the basis of the van't Hoff relation from the temperature dependence either of the distribution ratio (Patil et al., 1973; Otu and Westland, 1990) or of the extraction constant (Nash and Choppin, 1977; Kandil and Ramadan, 1980; Kalina et al., 1981; Yamada et al., 1982). However, 0 1992 American Chemical Society
