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Mass and heat transfer at an array of vertical tubes in a square stirred tank reactor
chemical engineering research and design 9 1 ( 2 0 1 3 ) 234–243
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Mass and heat transfer at an array of vertical tubes in a square stirred tank reactor Y.O. Fouad ∗ , G.F. Malash, A.A. Zatout, G.H. Sedahmed Chemical Engineering Department, Alexandria University, Alexandria, Egypt
a b s t r a c t Rates of mass transfer at a square array of vertical cylinders contained in a square agitated vessel were measured by the diffusion controlled dissolution of copper in acidified K2 Cr2 O7 in an attempt to throw some light on the heat transfer behavior of the tube array (by analogy with mass transfer), the vertical tube array can act as a cooler or simultaneously as a cooler and a catalyst support for conducting exothermic diffusion controlled reactions. Variables studied were impeller rotation speed, cylinder diameter, cylinder spacing within the array, distance between the array and tank wall, impeller geometry (radial flow turbine and axial flow turbine) and superimposed axial solution flow. The mass transfer data for a batch reactor using a radial flow turbine were correlated by the equation: Sh = 0.85 × Sc0.33 × Re0.57 ×
0.5 s T
where s is cylinder separation within the array and T is the tank diameter. Radial flow turbine was found to produce higher rates of mass transfer than axial flow turbine. Superimposed axial flow within the range of 400 < Res < 4000 was found to decrease the rate of mass transfer especially at high impeller rotation speeds. The importance of the present results in the design and operation of catalytic stirred tank reactor with a builtin heat transfer facility suitable for diffusion controlled exothermic reactions which need rapid cooling to protect heat sensitive catalysts and heat sensitive products was noted. Also the possibility of using the mass transfer equation in predicting the rate of diffusion controlled corrosion of the metallic tube array cooler was highlighted. © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Mass transfer; Heat transfer; Stirred tank reactor; Diffusion controlled reactions
1.
Introduction
Heat and mass transfer study in agitated vessels is important for the rational design and operation of stirred tank reactors used to conduct diffusion controlled exothermic reactions. Different heat transfer facilities have been developed to remove excess heat from agitated vessels the simplest of which is cooling jackets, which have the advantage of easy maintenance. However as the volume of the reactor increases, cooling jackets become insufficient to cool the reactor. In this case internal helical cooling coils concentric with the rotating shaft are used; they have the advantage that a large amount of heat transfer surface area can be obtained for a given volume of process fluid. They are in general however more costly to fabricate and more difficult to maintain (Oldshue, 1983).
∗
A third class of coolers use vertical tubes which act also as baffles to eliminate swirl flow, the vertical tubes act also as turbulence promoters and improve the rate of heat transfer. The heat transfer behavior of such vertical tubes has been studied (Dunlap and Rushton, 1953; Havas et al., 1982; Petree and Small, 1978; Kato et al., 2007) by either measuring the rate of heat transfer or the rate of mass transfer by virtue of the analogy between heat and mass transfer (Mizushina et al., 1969; Ko et al., 2006). The majority of previous studies on heat and mass transfer in agitated vessels were conducted using cylindrical agitated vessels, rectangular agitated vessels have received little attention despite their practical importance (Kresta et al., 2006; Clark et al., 1994; El-Shazly et al., 1997; Sedahmed et al., 2004). Rectangular agitated vessels have the advantage that they do not need baffles to eliminate the undesirable swirl
Corresponding author. Tel.: +20 00239576472. E-mail address: [email protected] (Y.O. Fouad). Received 4 October 2011; Received in revised form 9 July 2012; Accepted 6 August 2012 0263-8762/$ – see front matter © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cherd.2012.08.006
chemical engineering research and design 9 1 ( 2 0 1 3 ) 234–243
235
List of symbols A a Co C di d D H K Q s t T V Z Re Res Sc Sh ε w
cylinder array area constant initial dichromate concentration dichromate concentration at any time impeller diameter cylinder diameter diffusivity solution height in the agitated vessel mass transfer coefficient solution volume cylinder separation within the array time equivalent tank diameter superimposed solution velocity during continuous operation distance between impeller and tank bottom Reynolds number of agitated vessel (w di 2 /) axial flow Reynolds number (VT/) Schmidt number (/i) Sherwood number (Kd/D) solution density specific energy consumption bulk solution viscosity impeller rotation speed (rps) kinematic viscosity
flow in favor of axial and radial flow which have a high mixing efficiency (Oldshue, 1983). The aim of the present work is to study the rate of heat and mass transfer behavior of an array of vertical tubes in a square agitated vessel using a mass transfer technique based on measuring the rate of diffusion controlled dissolution of copper in acidified dichromate the technique has been used widely to study rates of liquid–solid mass transfer under different conditions in view of its simplicity and accuracy (Gregory and Riddiford, 1960; Madden and Nelson, 1964; Abdel-Aziz et al., 2010; Gruber and Melin, 2003a,b). Beside its simple construction the outer surface of the suggested vertical tube array cooler can also act as a catalyst support to conduct liquid–solid catalytic reactions such as photocatalytic reactions, immobilized enzyme reactions, removal of organic pollutants by wet oxidation and catalytic organic synthesis. Since these reactions are often diffusion controlled, a study of the rate of mass transfer at the vertical tube array would assist in predicting the rate of the diffusion controlled reaction taking place at the outer surface of the tubes including the diffusion controlled corrosion of the tube array. The present reactor offers the advantage of rapid heat removal with a consequent protection of heat sensitive catalysts from deactivation and loss of yield and selectivity at high temperatures (Anxionnaz et al., 2008). It also protects heat sensitive products from decomposition. Development of heat exchanging reactors (multifunction reactors) has recently received a great attention in view of their compactness and low capital and operating costs (Anxionnaz et al., 2008; Zewail et al., 2010).
2.
Experimental technique
The apparatus used in the present work (Fig. 1) consisted of 5.5 l plexiglass square vessel of 15 cm × 15 cm cross sectional
Fig. 1 – Apparatus (simple batch reactor). (1) Plexiglass container; (2) tube array; (3) impeller; (4) electrolyte level; and (5) plastic base (array holder).
area and 25 cm height. The vessel was fitted at its center with a turbine impeller (either 4 flat blade turbine or 45◦ four blade pitched turbine) mounted on a stainless steel shaft. The impeller which was made of copper and the stainless steel shaft were isolated with epoxy resin. The shaft was driven by 0.3 hp variable speed motor fitted with a variac and digital tachometer. The motor was fixed firmly against a brick wall to avoid vibrations. A square array of vertical separated cylinders made of copper was mounted around the rotating impeller, array cylinders were fixed in position by fitting the lower part of each cylinder in a hole drilled in a square plastic sheet of the dimensions 14.8 cm × 14.8 cm and a thickness 1 cm by epoxy resin, the plastic sheet holding the array was rested on the bottom of the agitated vessel. In constructing the cylinder array, 3 different cylinder diameters (0.6, 1 and 1.6 cm) were used. Cylinder spacing within the array ranged from 0.5 cm to 1.5 cm while the distance between the array and the container wall was 1.75, 2.5 and 3 cm. Table 1 shows the geometric parameters of the arrays used in the present study. In designing the present agitated vessel the following standard dimensions were used (El-Shazly et al., 1997): di /T = 0.33, H/T = 1, and Z/T = 0.33. In order to examine the effect of superimposed axial flow on the array mass transfer coefficient a batch recycle reactor was used (Fig. 2). The reactor consisted of 20 l glass storage tank, 0.5 hp plastic centrifugal pump was used to circulate the solution between the glass storage tank and the stirred tank reactor. Solution was admitted to the agitated vessel at the center of its bottom. Solution velocity was controlled by means of a bypass and was measured by a graduated cylinder
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Table 1 – Geometric characteristics of the cylinder arrays used in the present work. Cylinder diameter (cm) 1 0.6 1.6 1 1 1 1
Number of cylinders per array 20 24 15 24 12 24 16
Cylinder separation (s) (cm)
Distance from container wall (lw ) (cm)
1 1 1 1 1 0.5 1.5
and a stopwatch. In case of the batch recycle reactor the agitated vessel was fitted with an overflow weir from which the solution was returned to the storage tank. Before each run in the simple batch reactor 3 l of acidified dichromate were placed in the agitated vessel, impeller rotation speed was adjusted at the required value. Dichromate concentration–time data were recorded by withdrawing 10 cm3 solution every 3 min for analysis. Analysis was conducted by titrating the dichromate solution against 0.01 N ferrous ammonium sulphate using diphenyl amine as indicator (Vogel, 1985). Temperature was 30 ± 1 ◦ C. Three different solutions of acidified dichromate were used, namely: 0.03 M K2 Cr2 O7 + 0.5 M H2 SO4 ; 0.03 M K2 Cr2 O7 + 1 M H2 SO4 0.03 M K2 Cr2 O7 + 2 M H2 SO4 . All solutions were prepared using A.R grade chemicals and distilled water. Solution viscosity and density required to correlate the present data were determined using an Ostwald viscometer and a density bottle, respectively (Findlay and Kitchener, 1965). The diffusion coefficient of dichromate was obtained from the literature and
2.5 2.5 2.5 1.75 3 2.5 2.5
Array total area (Aa ) (cm2 ) 942 678.24 1130.4 1130.4 565.2 1130.4 753.6
Array total area/container wall area (Aa /Ac ) 1.05 0.753 1.256 1.256 0.6275 1.256 0.84
was corrected for the change in temperature using the Stokes–Einstein equation. Table 2 shows the physical properties of the solutions used at 30 ◦ C. The reproducibility of experiments ranged from 3% to 5%. In case of batch recycle reactor 15 l of acidified dichromate were placed in the storage tank, the course of the reaction was followed by withdrawing samples (10 cm3 ) of solution from the storage tank every 3 min, Copper cylinders forming the array were used to conduct only three runs after which they were replaced by new cylinders to avoid dimensional change and the development of surface roughness which may affect the hydrodynamic conditions. To correlate the present data in terms of specific energy consumption, electrical energy consumed in driving the motor was determined in air and in presence of the solution by measuring simultaneously the current and the voltage supplied to the motor (Brodberger et al., 1986). The difference between energy consumed by the motor in solution and in air gives the energy dissipated in the solution.
Fig. 2 – Batch recycle reactor. (1) Square agitated vessel; (2) array of separated cylinders; (3) agitator; (4) overflow weir; (5) storage tank; (6) centrifugal pump; and (7) by bass.
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Table 2 – Physical properties of solutions used at 30 ◦ C. Solution composition
(g/cm3 )
(poise)
0.03 M K2 Cr2 O7 + 0.5 M H2 SO4 0.03 M K2 Cr2 O7 + 1 M H2 SO4 0.03 M K2 Cr2 O7 + 2 M H2 SO4
1.023400 1.059662 1.116374
0.009273 0.010350 0.012077
3.
Results and discussion
The mass transfer coefficient at the cylinder array was calculated under different conditions from the batch reactor rate equation (Walsh, 1993). −Q ×
dC = KAC dt
(1)
which integrates to Q ln
Co = KAt C
(2)
Fig. 3 shows that the present dichromate concentration–time data fit Eq. (2) quite well, the mass transfer coefficient was obtained from the slope of the ln Co /C vs t plot. Fig. 4 shows the effect of Re on Sh at different Sc, the data fit the equation Sh = a Re0.57
(3)
Fig. 5 shows that for a given impeller rotation speed, the mass transfer coefficient decreases with increasing cylinder diameter. The above results as well as the mass transfer mechanism at the tube array may be explained in terms of the approximate flow pattern shown in Fig. 6. The flow induced by the impeller crosses the array stationary cylinders at the three different locations, namely at the impeller level B, at the tank bottom C and at the upper part of the cylinder array A. At these locations mass is transferred to the cylinder in a manner similar
D × 106 (cm2 /s)
Sc
10.6540 9.5458 8.1807
850 1023 1322
to flow past immersed bodies where a developing hydrodynamic boundary layer and a diffusion layer are formed around the cylinders; hydrodynamic boundary layer separation takes place at the rear of each cylinder with the formation of a turbulent wake. For this case Sh is related to Re by the equation (Incropera and De Witt, 1990). Sh = a1 Sc0.33 Reb
(4)
The exponent b ranges from 0.4 to 0.7 depending on Re, the higher the value of Re the higher the exponent b. The upper and lower parts of the vertical cylinders which are located between radial crossing points A, B and C of the solution are subjected to axial flow. Starting from the impeller level (location B in Fig. 6) a developing hydrodynamic boundary layer and a diffusion layer are formed along the upper part of the cylinder. Similarly a developing hydrodynamic boundary layer and a diffusion layer are formed starting from the impeller level [at location B (Fig. 6)] along the lower length of each cylinder. Mass transfer at cylinders and plates under developing flow conditions are given by (Pickett, 1977). Sh = 0.67 Sc0.33 Re0.5
(5)
Beside the above approximate flow picture it is well known that as the radial flow leaves the impeller blade, turbulence is generated at a short distance from the tip of the impeller, the intensity of this turbulence decreases as the container wall is approached (Leng, 1991; Oldshue, 1989). This turbulence contributes to enhancing the rate of mass transfer at the array cylinders especially at the rotating impeller level. In view of
3.5 o
Impeller: 4 blades 90 turbine d = 1cm Cylinder separation = 1d (1 cm); Distance from the container wall = 2.5 cm (midway) Sc = 1322
3
ln (Co/C)
2.5
50 100 150 200 250 300 350 400 450
2
1.5
1
0.5
0 0
200
400
600
800
1000
1200
1400
1600
Time (s)
Fig. 3 – ln (Co /C) vs. time for Sc = 1322 using 4 blade 90◦ turbine.
1800
2000
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2.9
o
Impeller: 4 blade 90 turbine; d = 1 cm; Distance from container wall = 2.5 cm (midway) Cylinder separation = 1d (1 cm)
2.8
2.7 Sc
Log Sh
2.6
850 1023
2.5
1322
2.4
2.3
2.2
2.1 3.25
3
3.5
3.75
4
4.25
4.5
4.75
5
Log Re Fig. 4 – Log Sh vs log Re at different Sc values using 4 blade 90◦ turbine.
The increase in the tube array mass transfer coefficient with increasing tube spacing within the array may be explained in the light of flow patterns observed at banks of tubes in cross flow (Knudsen and Katz, 1958), it was found that when the tubes are widely spaced a turbulent wake occurs behind each tube, for closely spaced tubes the turbulent wake behind each tube is considerably reduced. In view of these observations it seems that the array mass transfer coefficient increases with increasing cylinder spacing because of the enhancing effect of the large turbulent wake formed behind each cylinder at locations where the solution crosses the vertical cylinders (locations A, B and C in Fig. 6). An overall mass transfer correlation was envisaged in terms of the dimensionless groups Sh, Sc and s/T, the data for the radial flow
the Re exponents of Eqs. (4) and (5) the present Re exponent 0.57 seems to be reasonable. The decrease in the mass transfer coefficient with increasing cylinder diameters as shown in Fig. 5 may be attributed to the increase in the average diffusion layer thickness around the cylinders at locations A, B and C where the solution crosses the vertical cylinders. Fig. 7 shows that for a given set of conditions array location from the container wall has little effect on Sh probably because the hydrodynamic conditions in this area is almost uniform. Fig. 8 shows that for a given set of conditions, the mass transfer coefficient increases with increasing cylinder separation s within the array according to the equation
s 0.5
(6)
T
2 o
Impeller: 4 blade 90 turbinee; Sc = 850; Cylinders separation = 1cm; om the container wall = 2.5 cm (m midway) Distance fro
1.9
1.8 Cylinder diammeter, (cm) 0.6
Log (K × 104)
Sh = a
1.7
1 1.6
1.6
1.5
1.4
1.3
1.2 0.1
2 0.2
0.3
0.4
0.5
0.6 6
0.7
0.8
0.9
Log ω
Fig. 5 – Log K vs log w for different array cylinder diameters using 4 blade 90◦ turbine.
1
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turbine under the conditions 850 < Sc < 1322, 1925 < Re < 19,200 and 0.044
Fig. 6 – Approximate flow pattern inside the reactor when a radial flow impeller is used.
4.5
s 0.5
(7)
T
With an average deviation of ±11.7% In calculating Sh array tube diameter was used, as a characteristic length while impeller diameter was used as a characteristic length in calculating Re following previous studies of transport phenomena in agitated vessels (Oldshue, 1983; Dunlap and Rushton, 1953; Havas et al., 1982; Petree and Small, 1978; Kato et al., 2007; Mizushina et al., 1969). It is noteworthy that the present Re exponent 0.57 lies within the range of Re exponents (0.5–0.67) obtained by previous studies on heat and mass transfer in agitated vessels (Oldshue, 1983; Mizushina et al., 1969; El-Shazly et al., 1997; Sedahmed et al., 2004; Askew and Beckmann, 1965; El-Shazly et al., 2004). Fig. 10 shows a comparison between the effect of flat blade turbine (radial flow impeller) and the effect of pitched blade turbine (axial flow impeller) on the rate of mass transfer at the tube array; the data show that for a given set of conditions radial flow impeller is more effective in enhancing the rate of
o
Impeller: 4 blade 90 turbine, Sc = 1023, d = 1 cm; Cylinder separation = 1d (1 cm)
4
Distance from the container wall, (cm) 1 1.75 2.5 3.5
Log Sh
3.5
3
2.5
2 3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
Log Re Fig. 7 – Log Sh vs log Re at different distances from the container wall using 4 blade 90◦ . 3 Impeller: 4 blade 90o turbine; Sc = 1322; d = 1 cm; Distance from the container wall = 2.5 cm (midway)
2.9 2.8
Re 3000
Log Sh
2.7
12000
2.6 2.5 2.4 2.3 2.2
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Log ((s/T)*103) Fig. 8 – Effect of the dimensionless cylinder separation on the rate of mass transfer at the cylinder array at different impeller Re using 4 blade 90◦ turbine.
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1200 o
Impeller: 4 blade 90 turbine (radial flow Sc 1000
850 1023 1322
Sh
800
600
400
200
0 0
200
400
600
Re
800
0.57
Sc
0.33
1000
1200
1400
0.5
(s/T)
Fig. 9 – Overall mass transfer correlation at the cylinder array using 4 blade 90◦ turbine. mass transfer than axial flow impeller. This may be ascribed to the different flow pattern of the axial flow impeller where the flow is diverted downward by the impeller, then it moves radially at the container bottom before it moves vertically parallel to the container wall and finally recycled to the impeller zone. During this journey the flow crosses the cylinders twice only compared to three times in case of radial flow. As a consequence the amount of turbulence generated in the rear of the vertical cylinders due to cross flow is less in case of axial flow. Beside the average diffusion layer thickness at the vertical tubes is thicker in case of axial flow because the developing hydrodynamic boundary layer along each cylinder starts from the bottom and ends at the solution surface. Fig. 11 shows the effect of superimposed axial solution flow on the array mass transfer coefficient at different rotation speeds the data show that superimposed axial flow within the range 400 < Res < 4000 does not affect the rate of mass transfer especially at relative
low speeds of impeller rotation. However at relatively high impeller rotation speed, superimposed axial solution flow tends to decrease the rate of mass transfer probably because axial solution flow sweeps away the mass transfer enhancing turbulence generated at high impeller rotation speed from the reaction zone. It would be of interest to correlate the present data in terms of the specific energy dissipation. Based on Kolomogoroffs theory of isotropic turbulence Calderbank and Moo-Young (1961) came to the conclusion that the hydrodynamic conditions affecting the rate of heat and mass transfer under turbulent flow can be described by the specific energy dissipation. They derived the following universal relationship for the mass transfer coefficient in terms of the specific energy dissipation (ε)
K = 0.13 Sc−0.66 (ε)
0.25
(8)
2.8 Sc = 850; d = 1 cm; lw = 2.5 cm (midway)
2.6
radial impeller axial impeller
Log Sh
2.4
2.2
2
1.8
1.6 3.1
3.3
3.5
3.7
3.9
4.1
4.3
4.5
Log Re Fig. 10 – Comparison between the radial impeller performance and the radial impeller performance at Sc = 850.
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Impeller: 4 blade 90o turbine Sc = 1023; d = 1cm; Cylinder separation = 1 cm; Distance from container wall = 2.5 cm (midway)
2.4 2.3
Re
2.2
2133.0
2.1
8531.9
Log Sh
12797.9
2
19196.8
1.9 1.8 1.7 1.6 1.5 2.7
2.5
2.9
3.1
3.3
3.5
3.7
Log Res Fig. 11 – Effect of superimposed axial flow on the rate of mass transfer at the cylinder array at different impeller rotation speeds using 4 blade 90◦ turbine. The equation is supposed to be valid for turbulent flow mass and heat transfer regardless of the geometry of the transfer surface and the method of energy supply. The authors found that the above equation predicts rates of heat and mass transfer in agitated vessels, packed beds, fluidized beds and pipes. Fig. 12 shows that the present mass transfer data for the radial flow turbine fit the equation K = 5.8 Sc−0.66 (ε)
0.25
(9)
With an average deviation of ±18%. For the axial flow turbine, Fig. 13 shows that the mass transfer data fit the equation K = 3.24 Sc−0.66 (ε)
0.25
(10)
With an average deviation of ±19%.
A comparison between Eqs. (9) and (10) shows that for the same energy consumption radial flow impeller produces higher rates of mass transfer than axial flow impeller. Eqs. (9) and (10) predict higher mass transfer coefficients than predicted by the equation of Calderbank and MooYoung [Eq. (8)]. This result is consistent with the finding of other authors who studied mass transfer in agitated vessels (Kato et al., 2007; Prasher and Wills, 1973; Levins and Glastonbury, 1972; Kawase and Moo-Young, 1987; Nienow, 1975). Based on his results and the results of other authors, Nienow (1975) who studied liquid–solid mass transfer in agitated vessels questioned the universal validity of Eq. (8). He argued that local energy dissipation rates vary enormously in agitated vessels depending on impeller type, size and position.
-1.2 o
Impeller: 4 blade 90 turbine Sc -1
850 1023 1322
Log (K/Sc-0.66)
-0.8
-0.6
-0.4
-0.2
0 -4
-4.2
-4.4
-4.6
-4.8
-5
-5.2
-5.4
-5.6
Log (ε*υ) Fig. 12 – Overall mass transfer correlation at the cylinder array using 4 blade 90◦ turbine in terms of the specific energy consumption.
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-1.5 Impeller:4 blade 45o pitched turbine Sc
-1.3
850
Log (K/Sc-0.66)
-1.1
1023
1322
-0.9
-0.7
-0.5
-0.3 -4
-4.2
-4.4
-4.6
-4.8
-5
-5.2
-5.4
-5.6
-5.8
Log (ε υ) Fig. 13 – Overall mass transfer correlation at the cylinder array using 45◦ 4 blade turbine in terms of the specific energy consumption.
4.
Conclusions
(1) The high rate of mass (and heat) transfer obtained at arrays of vertical cylinders in square agitated vessels qualifies the use of such arrays as (i) coolers to remove excess heat generated in square tanks during different exothermic operations, (ii) the outer surface of the vertical tube array can serve as a catalyst support where liquid–solid diffusion controlled exothermic reactions such as photocatalytic reactions, immobilized enzyme reactions, removal of organic pollutants by wet oxidation and organic synthesis can take place. In this case the stirred vertical tube array serves the double purpose of conducting the reaction at the outer tube surface while the inner tube surface acts as a builtin cooler. This heat exchanging reactor is suitable for heat sensitive catalysts and heat sensitive products. The dimensionless mass transfer equation obtained in this study not only serves to scale up the present reactor but also serves to calculate the outerside heat transfer coefficient (by analogy) required to calculate the overall heat transfer coefficient needed to design and operate the built in cooler. (2) Since corrosion of metal tubes in aqueous solutions is often diffusion controlled (Ellison and Wen, 1981), the present mass transfer equation can be used to predict the rate of corrosion of the tube array and hence the corrosion allowance needed in the design stage of the tube array. (3) Future studies should be extended to include gas–liquid–solid reactions such as catalytic flue gas desulphurization, in this case the stirred tank will act as absorber and a reactor with a consequent saving on operating and capital costs. Also future studies should consider the use of multiple rows of vertical tubes to increase the reaction area and the cooling area. Also future studies should include flow visualization of the present reactor (Hosseini et al., 2010) in order to explain the results on a more rational basis.
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Mizushina, T., Ito, R., Hiraoka, S., Ibusuki, A., Sakaguchi, I., 1969. Transport phenomena at the wall of agitated vessels. J. Chem. Eng. (Japan) 2, 89–94. Nienow, A.W., 1975. Agitated vessel particle-liquid mass transfer: a comparison between theories and data. Chem. Eng. J. 9, 153–160. Oldshue, J.Y., 1983. Fluid Mixing Technology. McGraw Hill, N.Y. Oldshue, J.Y., May 1989. Fluid mixing in 1989. Chem. Eng. Process., 33–42. Petree, D.K., Small, W.M., 1978. Heat transfer and power consumption for agitated vessels with vertical plate coils. A.I.Ch.E. Symposium Series No. 174, vol. 74, pp. 53–59. Pickett, D., 1977. Electrochemical Reactor Design. Elsevier, N.Y. Prasher, B.D., Wills, G.B., 1973. Mass transfer in an agitated vessel. Ind. Eng. Chem. Proc. Des. Dev 12, 351–354. Sedahmed, G.H., Khatab, M.A., Mahgoub, F.M., Al-Azzony, M.R., 2004. Solid–liquid mass transfer at the base of a rectangular agitated vessel. Chem. Eng. Commun. 191, 168–181. Vogel, A.I., 1985. A Textbook of Quantitative Analysis. Longmans, London. Walsh, F., 1993. A First Course in Electrochemical Engineering. The Electrochemical Consultancy, Hants (U.K.). Zewail, T.M., Zatout, A.A., El-Taweel, Y.A., Sedahmed, G.H., 2010. Liquid–solid mass transfer behavior of a vertical array of closely spaced horizontal tubes in relation to catalytic and electrochemical reactor design. Chem. Eng. Technol. 33, 121–131.
Contents lists available at SciVerse ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Mass and heat transfer at an array of vertical tubes in a square stirred tank reactor Y.O. Fouad ∗ , G.F. Malash, A.A. Zatout, G.H. Sedahmed Chemical Engineering Department, Alexandria University, Alexandria, Egypt
a b s t r a c t Rates of mass transfer at a square array of vertical cylinders contained in a square agitated vessel were measured by the diffusion controlled dissolution of copper in acidified K2 Cr2 O7 in an attempt to throw some light on the heat transfer behavior of the tube array (by analogy with mass transfer), the vertical tube array can act as a cooler or simultaneously as a cooler and a catalyst support for conducting exothermic diffusion controlled reactions. Variables studied were impeller rotation speed, cylinder diameter, cylinder spacing within the array, distance between the array and tank wall, impeller geometry (radial flow turbine and axial flow turbine) and superimposed axial solution flow. The mass transfer data for a batch reactor using a radial flow turbine were correlated by the equation: Sh = 0.85 × Sc0.33 × Re0.57 ×
0.5 s T
where s is cylinder separation within the array and T is the tank diameter. Radial flow turbine was found to produce higher rates of mass transfer than axial flow turbine. Superimposed axial flow within the range of 400 < Res < 4000 was found to decrease the rate of mass transfer especially at high impeller rotation speeds. The importance of the present results in the design and operation of catalytic stirred tank reactor with a builtin heat transfer facility suitable for diffusion controlled exothermic reactions which need rapid cooling to protect heat sensitive catalysts and heat sensitive products was noted. Also the possibility of using the mass transfer equation in predicting the rate of diffusion controlled corrosion of the metallic tube array cooler was highlighted. © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Mass transfer; Heat transfer; Stirred tank reactor; Diffusion controlled reactions
1.
Introduction
Heat and mass transfer study in agitated vessels is important for the rational design and operation of stirred tank reactors used to conduct diffusion controlled exothermic reactions. Different heat transfer facilities have been developed to remove excess heat from agitated vessels the simplest of which is cooling jackets, which have the advantage of easy maintenance. However as the volume of the reactor increases, cooling jackets become insufficient to cool the reactor. In this case internal helical cooling coils concentric with the rotating shaft are used; they have the advantage that a large amount of heat transfer surface area can be obtained for a given volume of process fluid. They are in general however more costly to fabricate and more difficult to maintain (Oldshue, 1983).
∗
A third class of coolers use vertical tubes which act also as baffles to eliminate swirl flow, the vertical tubes act also as turbulence promoters and improve the rate of heat transfer. The heat transfer behavior of such vertical tubes has been studied (Dunlap and Rushton, 1953; Havas et al., 1982; Petree and Small, 1978; Kato et al., 2007) by either measuring the rate of heat transfer or the rate of mass transfer by virtue of the analogy between heat and mass transfer (Mizushina et al., 1969; Ko et al., 2006). The majority of previous studies on heat and mass transfer in agitated vessels were conducted using cylindrical agitated vessels, rectangular agitated vessels have received little attention despite their practical importance (Kresta et al., 2006; Clark et al., 1994; El-Shazly et al., 1997; Sedahmed et al., 2004). Rectangular agitated vessels have the advantage that they do not need baffles to eliminate the undesirable swirl
Corresponding author. Tel.: +20 00239576472. E-mail address: [email protected] (Y.O. Fouad). Received 4 October 2011; Received in revised form 9 July 2012; Accepted 6 August 2012 0263-8762/$ – see front matter © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cherd.2012.08.006
chemical engineering research and design 9 1 ( 2 0 1 3 ) 234–243
235
List of symbols A a Co C di d D H K Q s t T V Z Re Res Sc Sh ε w
cylinder array area constant initial dichromate concentration dichromate concentration at any time impeller diameter cylinder diameter diffusivity solution height in the agitated vessel mass transfer coefficient solution volume cylinder separation within the array time equivalent tank diameter superimposed solution velocity during continuous operation distance between impeller and tank bottom Reynolds number of agitated vessel (w di 2 /) axial flow Reynolds number (VT/) Schmidt number (/i) Sherwood number (Kd/D) solution density specific energy consumption bulk solution viscosity impeller rotation speed (rps) kinematic viscosity
flow in favor of axial and radial flow which have a high mixing efficiency (Oldshue, 1983). The aim of the present work is to study the rate of heat and mass transfer behavior of an array of vertical tubes in a square agitated vessel using a mass transfer technique based on measuring the rate of diffusion controlled dissolution of copper in acidified dichromate the technique has been used widely to study rates of liquid–solid mass transfer under different conditions in view of its simplicity and accuracy (Gregory and Riddiford, 1960; Madden and Nelson, 1964; Abdel-Aziz et al., 2010; Gruber and Melin, 2003a,b). Beside its simple construction the outer surface of the suggested vertical tube array cooler can also act as a catalyst support to conduct liquid–solid catalytic reactions such as photocatalytic reactions, immobilized enzyme reactions, removal of organic pollutants by wet oxidation and catalytic organic synthesis. Since these reactions are often diffusion controlled, a study of the rate of mass transfer at the vertical tube array would assist in predicting the rate of the diffusion controlled reaction taking place at the outer surface of the tubes including the diffusion controlled corrosion of the tube array. The present reactor offers the advantage of rapid heat removal with a consequent protection of heat sensitive catalysts from deactivation and loss of yield and selectivity at high temperatures (Anxionnaz et al., 2008). It also protects heat sensitive products from decomposition. Development of heat exchanging reactors (multifunction reactors) has recently received a great attention in view of their compactness and low capital and operating costs (Anxionnaz et al., 2008; Zewail et al., 2010).
2.
Experimental technique
The apparatus used in the present work (Fig. 1) consisted of 5.5 l plexiglass square vessel of 15 cm × 15 cm cross sectional
Fig. 1 – Apparatus (simple batch reactor). (1) Plexiglass container; (2) tube array; (3) impeller; (4) electrolyte level; and (5) plastic base (array holder).
area and 25 cm height. The vessel was fitted at its center with a turbine impeller (either 4 flat blade turbine or 45◦ four blade pitched turbine) mounted on a stainless steel shaft. The impeller which was made of copper and the stainless steel shaft were isolated with epoxy resin. The shaft was driven by 0.3 hp variable speed motor fitted with a variac and digital tachometer. The motor was fixed firmly against a brick wall to avoid vibrations. A square array of vertical separated cylinders made of copper was mounted around the rotating impeller, array cylinders were fixed in position by fitting the lower part of each cylinder in a hole drilled in a square plastic sheet of the dimensions 14.8 cm × 14.8 cm and a thickness 1 cm by epoxy resin, the plastic sheet holding the array was rested on the bottom of the agitated vessel. In constructing the cylinder array, 3 different cylinder diameters (0.6, 1 and 1.6 cm) were used. Cylinder spacing within the array ranged from 0.5 cm to 1.5 cm while the distance between the array and the container wall was 1.75, 2.5 and 3 cm. Table 1 shows the geometric parameters of the arrays used in the present study. In designing the present agitated vessel the following standard dimensions were used (El-Shazly et al., 1997): di /T = 0.33, H/T = 1, and Z/T = 0.33. In order to examine the effect of superimposed axial flow on the array mass transfer coefficient a batch recycle reactor was used (Fig. 2). The reactor consisted of 20 l glass storage tank, 0.5 hp plastic centrifugal pump was used to circulate the solution between the glass storage tank and the stirred tank reactor. Solution was admitted to the agitated vessel at the center of its bottom. Solution velocity was controlled by means of a bypass and was measured by a graduated cylinder
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Table 1 – Geometric characteristics of the cylinder arrays used in the present work. Cylinder diameter (cm) 1 0.6 1.6 1 1 1 1
Number of cylinders per array 20 24 15 24 12 24 16
Cylinder separation (s) (cm)
Distance from container wall (lw ) (cm)
1 1 1 1 1 0.5 1.5
and a stopwatch. In case of the batch recycle reactor the agitated vessel was fitted with an overflow weir from which the solution was returned to the storage tank. Before each run in the simple batch reactor 3 l of acidified dichromate were placed in the agitated vessel, impeller rotation speed was adjusted at the required value. Dichromate concentration–time data were recorded by withdrawing 10 cm3 solution every 3 min for analysis. Analysis was conducted by titrating the dichromate solution against 0.01 N ferrous ammonium sulphate using diphenyl amine as indicator (Vogel, 1985). Temperature was 30 ± 1 ◦ C. Three different solutions of acidified dichromate were used, namely: 0.03 M K2 Cr2 O7 + 0.5 M H2 SO4 ; 0.03 M K2 Cr2 O7 + 1 M H2 SO4 0.03 M K2 Cr2 O7 + 2 M H2 SO4 . All solutions were prepared using A.R grade chemicals and distilled water. Solution viscosity and density required to correlate the present data were determined using an Ostwald viscometer and a density bottle, respectively (Findlay and Kitchener, 1965). The diffusion coefficient of dichromate was obtained from the literature and
2.5 2.5 2.5 1.75 3 2.5 2.5
Array total area (Aa ) (cm2 ) 942 678.24 1130.4 1130.4 565.2 1130.4 753.6
Array total area/container wall area (Aa /Ac ) 1.05 0.753 1.256 1.256 0.6275 1.256 0.84
was corrected for the change in temperature using the Stokes–Einstein equation. Table 2 shows the physical properties of the solutions used at 30 ◦ C. The reproducibility of experiments ranged from 3% to 5%. In case of batch recycle reactor 15 l of acidified dichromate were placed in the storage tank, the course of the reaction was followed by withdrawing samples (10 cm3 ) of solution from the storage tank every 3 min, Copper cylinders forming the array were used to conduct only three runs after which they were replaced by new cylinders to avoid dimensional change and the development of surface roughness which may affect the hydrodynamic conditions. To correlate the present data in terms of specific energy consumption, electrical energy consumed in driving the motor was determined in air and in presence of the solution by measuring simultaneously the current and the voltage supplied to the motor (Brodberger et al., 1986). The difference between energy consumed by the motor in solution and in air gives the energy dissipated in the solution.
Fig. 2 – Batch recycle reactor. (1) Square agitated vessel; (2) array of separated cylinders; (3) agitator; (4) overflow weir; (5) storage tank; (6) centrifugal pump; and (7) by bass.
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Table 2 – Physical properties of solutions used at 30 ◦ C. Solution composition
(g/cm3 )
(poise)
0.03 M K2 Cr2 O7 + 0.5 M H2 SO4 0.03 M K2 Cr2 O7 + 1 M H2 SO4 0.03 M K2 Cr2 O7 + 2 M H2 SO4
1.023400 1.059662 1.116374
0.009273 0.010350 0.012077
3.
Results and discussion
The mass transfer coefficient at the cylinder array was calculated under different conditions from the batch reactor rate equation (Walsh, 1993). −Q ×
dC = KAC dt
(1)
which integrates to Q ln
Co = KAt C
(2)
Fig. 3 shows that the present dichromate concentration–time data fit Eq. (2) quite well, the mass transfer coefficient was obtained from the slope of the ln Co /C vs t plot. Fig. 4 shows the effect of Re on Sh at different Sc, the data fit the equation Sh = a Re0.57
(3)
Fig. 5 shows that for a given impeller rotation speed, the mass transfer coefficient decreases with increasing cylinder diameter. The above results as well as the mass transfer mechanism at the tube array may be explained in terms of the approximate flow pattern shown in Fig. 6. The flow induced by the impeller crosses the array stationary cylinders at the three different locations, namely at the impeller level B, at the tank bottom C and at the upper part of the cylinder array A. At these locations mass is transferred to the cylinder in a manner similar
D × 106 (cm2 /s)
Sc
10.6540 9.5458 8.1807
850 1023 1322
to flow past immersed bodies where a developing hydrodynamic boundary layer and a diffusion layer are formed around the cylinders; hydrodynamic boundary layer separation takes place at the rear of each cylinder with the formation of a turbulent wake. For this case Sh is related to Re by the equation (Incropera and De Witt, 1990). Sh = a1 Sc0.33 Reb
(4)
The exponent b ranges from 0.4 to 0.7 depending on Re, the higher the value of Re the higher the exponent b. The upper and lower parts of the vertical cylinders which are located between radial crossing points A, B and C of the solution are subjected to axial flow. Starting from the impeller level (location B in Fig. 6) a developing hydrodynamic boundary layer and a diffusion layer are formed along the upper part of the cylinder. Similarly a developing hydrodynamic boundary layer and a diffusion layer are formed starting from the impeller level [at location B (Fig. 6)] along the lower length of each cylinder. Mass transfer at cylinders and plates under developing flow conditions are given by (Pickett, 1977). Sh = 0.67 Sc0.33 Re0.5
(5)
Beside the above approximate flow picture it is well known that as the radial flow leaves the impeller blade, turbulence is generated at a short distance from the tip of the impeller, the intensity of this turbulence decreases as the container wall is approached (Leng, 1991; Oldshue, 1989). This turbulence contributes to enhancing the rate of mass transfer at the array cylinders especially at the rotating impeller level. In view of
3.5 o
Impeller: 4 blades 90 turbine d = 1cm Cylinder separation = 1d (1 cm); Distance from the container wall = 2.5 cm (midway) Sc = 1322
3
ln (Co/C)
2.5
50 100 150 200 250 300 350 400 450
2
1.5
1
0.5
0 0
200
400
600
800
1000
1200
1400
1600
Time (s)
Fig. 3 – ln (Co /C) vs. time for Sc = 1322 using 4 blade 90◦ turbine.
1800
2000
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2.9
o
Impeller: 4 blade 90 turbine; d = 1 cm; Distance from container wall = 2.5 cm (midway) Cylinder separation = 1d (1 cm)
2.8
2.7 Sc
Log Sh
2.6
850 1023
2.5
1322
2.4
2.3
2.2
2.1 3.25
3
3.5
3.75
4
4.25
4.5
4.75
5
Log Re Fig. 4 – Log Sh vs log Re at different Sc values using 4 blade 90◦ turbine.
The increase in the tube array mass transfer coefficient with increasing tube spacing within the array may be explained in the light of flow patterns observed at banks of tubes in cross flow (Knudsen and Katz, 1958), it was found that when the tubes are widely spaced a turbulent wake occurs behind each tube, for closely spaced tubes the turbulent wake behind each tube is considerably reduced. In view of these observations it seems that the array mass transfer coefficient increases with increasing cylinder spacing because of the enhancing effect of the large turbulent wake formed behind each cylinder at locations where the solution crosses the vertical cylinders (locations A, B and C in Fig. 6). An overall mass transfer correlation was envisaged in terms of the dimensionless groups Sh, Sc and s/T, the data for the radial flow
the Re exponents of Eqs. (4) and (5) the present Re exponent 0.57 seems to be reasonable. The decrease in the mass transfer coefficient with increasing cylinder diameters as shown in Fig. 5 may be attributed to the increase in the average diffusion layer thickness around the cylinders at locations A, B and C where the solution crosses the vertical cylinders. Fig. 7 shows that for a given set of conditions array location from the container wall has little effect on Sh probably because the hydrodynamic conditions in this area is almost uniform. Fig. 8 shows that for a given set of conditions, the mass transfer coefficient increases with increasing cylinder separation s within the array according to the equation
s 0.5
(6)
T
2 o
Impeller: 4 blade 90 turbinee; Sc = 850; Cylinders separation = 1cm; om the container wall = 2.5 cm (m midway) Distance fro
1.9
1.8 Cylinder diammeter, (cm) 0.6
Log (K × 104)
Sh = a
1.7
1 1.6
1.6
1.5
1.4
1.3
1.2 0.1
2 0.2
0.3
0.4
0.5
0.6 6
0.7
0.8
0.9
Log ω
Fig. 5 – Log K vs log w for different array cylinder diameters using 4 blade 90◦ turbine.
1
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turbine under the conditions 850 < Sc < 1322, 1925 < Re < 19,200 and 0.044
Fig. 6 – Approximate flow pattern inside the reactor when a radial flow impeller is used.
4.5
s 0.5
(7)
T
With an average deviation of ±11.7% In calculating Sh array tube diameter was used, as a characteristic length while impeller diameter was used as a characteristic length in calculating Re following previous studies of transport phenomena in agitated vessels (Oldshue, 1983; Dunlap and Rushton, 1953; Havas et al., 1982; Petree and Small, 1978; Kato et al., 2007; Mizushina et al., 1969). It is noteworthy that the present Re exponent 0.57 lies within the range of Re exponents (0.5–0.67) obtained by previous studies on heat and mass transfer in agitated vessels (Oldshue, 1983; Mizushina et al., 1969; El-Shazly et al., 1997; Sedahmed et al., 2004; Askew and Beckmann, 1965; El-Shazly et al., 2004). Fig. 10 shows a comparison between the effect of flat blade turbine (radial flow impeller) and the effect of pitched blade turbine (axial flow impeller) on the rate of mass transfer at the tube array; the data show that for a given set of conditions radial flow impeller is more effective in enhancing the rate of
o
Impeller: 4 blade 90 turbine, Sc = 1023, d = 1 cm; Cylinder separation = 1d (1 cm)
4
Distance from the container wall, (cm) 1 1.75 2.5 3.5
Log Sh
3.5
3
2.5
2 3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
Log Re Fig. 7 – Log Sh vs log Re at different distances from the container wall using 4 blade 90◦ . 3 Impeller: 4 blade 90o turbine; Sc = 1322; d = 1 cm; Distance from the container wall = 2.5 cm (midway)
2.9 2.8
Re 3000
Log Sh
2.7
12000
2.6 2.5 2.4 2.3 2.2
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Log ((s/T)*103) Fig. 8 – Effect of the dimensionless cylinder separation on the rate of mass transfer at the cylinder array at different impeller Re using 4 blade 90◦ turbine.
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1200 o
Impeller: 4 blade 90 turbine (radial flow Sc 1000
850 1023 1322
Sh
800
600
400
200
0 0
200
400
600
Re
800
0.57
Sc
0.33
1000
1200
1400
0.5
(s/T)
Fig. 9 – Overall mass transfer correlation at the cylinder array using 4 blade 90◦ turbine. mass transfer than axial flow impeller. This may be ascribed to the different flow pattern of the axial flow impeller where the flow is diverted downward by the impeller, then it moves radially at the container bottom before it moves vertically parallel to the container wall and finally recycled to the impeller zone. During this journey the flow crosses the cylinders twice only compared to three times in case of radial flow. As a consequence the amount of turbulence generated in the rear of the vertical cylinders due to cross flow is less in case of axial flow. Beside the average diffusion layer thickness at the vertical tubes is thicker in case of axial flow because the developing hydrodynamic boundary layer along each cylinder starts from the bottom and ends at the solution surface. Fig. 11 shows the effect of superimposed axial solution flow on the array mass transfer coefficient at different rotation speeds the data show that superimposed axial flow within the range 400 < Res < 4000 does not affect the rate of mass transfer especially at relative
low speeds of impeller rotation. However at relatively high impeller rotation speed, superimposed axial solution flow tends to decrease the rate of mass transfer probably because axial solution flow sweeps away the mass transfer enhancing turbulence generated at high impeller rotation speed from the reaction zone. It would be of interest to correlate the present data in terms of the specific energy dissipation. Based on Kolomogoroffs theory of isotropic turbulence Calderbank and Moo-Young (1961) came to the conclusion that the hydrodynamic conditions affecting the rate of heat and mass transfer under turbulent flow can be described by the specific energy dissipation. They derived the following universal relationship for the mass transfer coefficient in terms of the specific energy dissipation (ε)
K = 0.13 Sc−0.66 (ε)
0.25
(8)
2.8 Sc = 850; d = 1 cm; lw = 2.5 cm (midway)
2.6
radial impeller axial impeller
Log Sh
2.4
2.2
2
1.8
1.6 3.1
3.3
3.5
3.7
3.9
4.1
4.3
4.5
Log Re Fig. 10 – Comparison between the radial impeller performance and the radial impeller performance at Sc = 850.
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Impeller: 4 blade 90o turbine Sc = 1023; d = 1cm; Cylinder separation = 1 cm; Distance from container wall = 2.5 cm (midway)
2.4 2.3
Re
2.2
2133.0
2.1
8531.9
Log Sh
12797.9
2
19196.8
1.9 1.8 1.7 1.6 1.5 2.7
2.5
2.9
3.1
3.3
3.5
3.7
Log Res Fig. 11 – Effect of superimposed axial flow on the rate of mass transfer at the cylinder array at different impeller rotation speeds using 4 blade 90◦ turbine. The equation is supposed to be valid for turbulent flow mass and heat transfer regardless of the geometry of the transfer surface and the method of energy supply. The authors found that the above equation predicts rates of heat and mass transfer in agitated vessels, packed beds, fluidized beds and pipes. Fig. 12 shows that the present mass transfer data for the radial flow turbine fit the equation K = 5.8 Sc−0.66 (ε)
0.25
(9)
With an average deviation of ±18%. For the axial flow turbine, Fig. 13 shows that the mass transfer data fit the equation K = 3.24 Sc−0.66 (ε)
0.25
(10)
With an average deviation of ±19%.
A comparison between Eqs. (9) and (10) shows that for the same energy consumption radial flow impeller produces higher rates of mass transfer than axial flow impeller. Eqs. (9) and (10) predict higher mass transfer coefficients than predicted by the equation of Calderbank and MooYoung [Eq. (8)]. This result is consistent with the finding of other authors who studied mass transfer in agitated vessels (Kato et al., 2007; Prasher and Wills, 1973; Levins and Glastonbury, 1972; Kawase and Moo-Young, 1987; Nienow, 1975). Based on his results and the results of other authors, Nienow (1975) who studied liquid–solid mass transfer in agitated vessels questioned the universal validity of Eq. (8). He argued that local energy dissipation rates vary enormously in agitated vessels depending on impeller type, size and position.
-1.2 o
Impeller: 4 blade 90 turbine Sc -1
850 1023 1322
Log (K/Sc-0.66)
-0.8
-0.6
-0.4
-0.2
0 -4
-4.2
-4.4
-4.6
-4.8
-5
-5.2
-5.4
-5.6
Log (ε*υ) Fig. 12 – Overall mass transfer correlation at the cylinder array using 4 blade 90◦ turbine in terms of the specific energy consumption.
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-1.5 Impeller:4 blade 45o pitched turbine Sc
-1.3
850
Log (K/Sc-0.66)
-1.1
1023
1322
-0.9
-0.7
-0.5
-0.3 -4
-4.2
-4.4
-4.6
-4.8
-5
-5.2
-5.4
-5.6
-5.8
Log (ε υ) Fig. 13 – Overall mass transfer correlation at the cylinder array using 45◦ 4 blade turbine in terms of the specific energy consumption.
4.
Conclusions
(1) The high rate of mass (and heat) transfer obtained at arrays of vertical cylinders in square agitated vessels qualifies the use of such arrays as (i) coolers to remove excess heat generated in square tanks during different exothermic operations, (ii) the outer surface of the vertical tube array can serve as a catalyst support where liquid–solid diffusion controlled exothermic reactions such as photocatalytic reactions, immobilized enzyme reactions, removal of organic pollutants by wet oxidation and organic synthesis can take place. In this case the stirred vertical tube array serves the double purpose of conducting the reaction at the outer tube surface while the inner tube surface acts as a builtin cooler. This heat exchanging reactor is suitable for heat sensitive catalysts and heat sensitive products. The dimensionless mass transfer equation obtained in this study not only serves to scale up the present reactor but also serves to calculate the outerside heat transfer coefficient (by analogy) required to calculate the overall heat transfer coefficient needed to design and operate the built in cooler. (2) Since corrosion of metal tubes in aqueous solutions is often diffusion controlled (Ellison and Wen, 1981), the present mass transfer equation can be used to predict the rate of corrosion of the tube array and hence the corrosion allowance needed in the design stage of the tube array. (3) Future studies should be extended to include gas–liquid–solid reactions such as catalytic flue gas desulphurization, in this case the stirred tank will act as absorber and a reactor with a consequent saving on operating and capital costs. Also future studies should consider the use of multiple rows of vertical tubes to increase the reaction area and the cooling area. Also future studies should include flow visualization of the present reactor (Hosseini et al., 2010) in order to explain the results on a more rational basis.
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