1160
Ind. Eng. Chem. Res. 2006, 45, 1160-1166
Mass-Transfer-Controlled Impingement Corrosion at the Jet Inlet Zone of an Annulus under Turbulent Flow R. R. Zahran and G. H. Sedahmed* Chemical Engineering Department, Faculty of Engineering, Alexandria UniVersity, Alexandria, Egypt
O. E. Abdelwahab and W. M. El-Sarraf National Institute of Oceanography and Fisheries, Alexandria, Egypt
Diffusion-controlled impingement corrosion of the lower part of the inner cylinder of an annulus caused by a perpendicular inlet jet was studied using the diffusion-controlled dissolution of copper in acidified dichromate technique. Variables studied were solution velocity, physical properties of the solution, diameter of the perpendicular feed nozzle, and the effect of drag-reducing polymers. For blank solution, the rate of masstransfer-controlled impingement corrosion was correlated by the equation Sh ) 2.74Sc0.33 Re0.46(dn/d)-0.4. Drag-reducing polymers were found to decrease the rate of mass-transfer-controlled impingement corrosion by an amount ranging from 29.9 to 68.9% depending on electrolyte concentration, polymer concentration, and feed nozzle diameter. The importance of the present results to the design of annular equipment was noted. Introduction The annular geometry is used widely in the engineering practice to build equipment such as double tube heat exchangers, heterogeneous and electrochemical reactors, condensers, dialyzers, nuclear reactors, etc. Annular equipment usually handles corrosive fluids which limit their service life, mainly because of impingement corrosion at the inlet zone. Although the problem of inlet-zone impingement corrosion is well-described qualitatively in the literature,1,2 little has been done to quantify it. Previous studies ascribe impingement corrosion to suspended solids or turbulence which destroy the protective solid film which may exist on the metal and enhance the rate of corrodent diffusion to the bare metal surface.3-9 The aim of the present work is to correlate the rate of diffusion-controlled impingement corrosion of the inner cylinder of an annulus with the controlling variables such as solution velocity, physical properties of the solution, and inlet nozzle diameter. Advance knowledge of the rate of impingement corrosion would make it possible to assess the corrosion allowance needed in the design stage of annular equipment; it would also assist in predicting the lifetime of already-existing equipment. An accelerated technique which simulates natural diffusioncontrolled corrosion was used, namely, the diffusion-controlled dissolution of copper in acidified dichromate. Since the development of the technique by Gregory and Riddiford,10 and Madden and Nelson,11 it has been used widely to study the effect of hydrodynamic conditions and surface geometry on the rate of diffusion-controlled corrosion and solid-liquid mass transfer in view of its simplicity and accuracy. Although some work has been done on the mass-transfer behavior of the annulus in the developing12 and the fully developed flow regions,13-15 no mass-transfer study has been reported on the lower section of the inner tube facing the inlet jet. The present work aims also at testing the possibility of combating diffusion-controlled impingement corrosion with drag-reducing polymers. These polymers proved to be effective in reducing mass-transfer- and * Corresponding author.
diffusion-controlled corrosion in pipelines16,17 and agitated vessels7,8 operated under turbulent flow. Drag-reducing polymers have the potential of being used in annular equipment operating under turbulent flow to reduce pumping power consumption18-20 by virtue of the ability of polymer molecules to dampen the small-scale, high-frequency energy dissipating eddies which prevail in the buffer sublayer of the hydrodynamic boundary layer.21,22 Polyox WSR-301 (polyethelene oxide), a product of Union Carbide, was used in the present work in the form of a slurry rather than a solution to minimize mechanical degradation of the polymer molecules as recommended by Little et al.23 Theory The relatively high resistance of some metals and alloys, e.g., steel, to corrosion by aqueous solutions is attributed to the existence of an adherent porous film resulting from the reaction between the cathodic and anodic products of the microscopic cells responsible for corrosion.2 For corrosion of steel to take place, dissolved oxygen (depolarizer) has to reach the cathodic sites of the corrosion cells at the metal surface across a liquidphase diffusion layer and a porous oxide film before it reacts at the cathodic sites. Using a three-step kinetic model,9 the flux of dissolved oxygen can be expressed by the equation
N)
C 1/K + 1/K1 + 1/K2
(1)
where K, K1, and K2 are the liquid mass-transfer coefficient, the mass-transfer coefficient across the porous oxide film, and the reaction rate constant, respectively. Since each gram atom of iron needs 0.5 mole of dissolved oxygen to corrode, it follows that the rate of iron corrosion is 2 N. At the inlet jet zone of an annulus (parts a and b of Figure 1), the solution is admitted to the annular space through a perpendicular nozzle; as the jet coming out of the nozzle impinges on the surface of the inner cylinder of the annulus, a stagnation zone is formed on the inner cylinder surface. The
10.1021/ie058053i CCC: $33.50 © 2006 American Chemical Society Published on Web 01/04/2006
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1161
Figure 1. (a) Approximate flow pattern in the inlet jet zone of the annulus. (b) Different flow zones in the annulus: j, inlet jet zone (L ) 2d); d.f, developing flow (L < 50d); f.d.f, fully developed flow (L > 50d).
stagnation zone is subjected to a perpendicular impact force (F) equal to the change of momentum.
F ) m(V - 0) ) FaV2
(2)
The solution leaving the stagnation zone turns around the cylinder as shown in Figure 1a to form a wall jet zone where a hydrodynamic boundary layer is built around the cylinder; in the wall jet zone, the surface of the inner cylinder is subjected to a shear stress given by
FV2 2
τ)f
(3)
Boundary layer separation takes place in the rear part of the cylinder to form an eddy wake. More turbulence is generated as the flow changes its direction from the horizontal direction to the vertical direction. The impact force (F) at the stagnation zone, the shear stress (τ) at the wall jet zone as well as the turbulence generated because of boundary layer separation and change in flow direction, and main stream turbulence may result in the destruction of the porous oxide film. The susceptibility of the protective film to failure depends not only on the prevailing hydrodynamic conditions but also on the mechanical properties of the film such as adhesion and cohesion.9 If the film breaks down, the resistance 1/K1 becomes zero, erosioncorrosion sets in, and eq 1 reduces to
N)
C 1/K + 1/K2
(4)
The above equation expresses the rate of corrosion under mixed diffusion and chemical control. If the mass-transfer step is slower than the chemical step, corrosion becomes diffusion-controlled and its rate is given by
N ) KC
(5)
To predict the rate of diffusion-controlled corrosion or partially diffusion-controlled corrosion, the mass-transfer coefficient (K) should be determined first from the equation
N ) -D
(∂C∂y ) ) KC o
(6)
To obtain the value (∂C/∂y), the concentration distribution should be determined from the convective diffusion equation.
Vx
∂C ∂ 2C )D 2 ∂x ∂y
(7)
Figure 2. Apparatus: (1) glass storage tank; (2) plastic centrifugal pump; (3) plastic valves; (4) bypass; (5) inlet jet zone; (6) outer plastic tube of the annulus; (7) inner copper tube of the annulus; (8) base of the annulus; (9) overflow weir.
To solve the above equation, the velocity distribution should be obtained first by solving simultaneously the momentum equation and the continuity equation.
Momentum equation ∂V ∂ 2V )ν 2 ∂x ∂y
(8)
∂Vx ∂Vy + )0 ∂x ∂y
(9)
Vx Continuity equation
In view of the complex and turbulent nature of the flow in the inlet jet zone of the annulus, simultaneous analytical solution of the above equations is extremely difficult. Accordingly, the present experimental work is necessary to obtain a correlation between the mass-transfer coefficient K and the governing variables. Experimental Technique The apparatus (Figure 2) consisted of a 20 L glass storage tank, a 0.33 hp plastic centrifugal pump, and a vertical annulus of 175 cm height. The annulus was made of two concentric tubes, an inner tube of 2.5 cm diameter made of pure copper and an outer tube of 5 cm diameter made of plexiglass. The inner side of the inner copper tube was filled with wax to isolate it. The two tubes forming the annulus were fixed in position by a plexiglass base. The plexiglass base had a cylindrical cavity of 2.6 cm diameter and 5 cm depth at its center to accommodate snugly the lower epoxy-coated end of the inner cylinder. The outer tube was fixed to the plexiglass base by a bolted flange; a rubber gasket was placed between the flange and the plexiglass base to prevent solution leakage. An inlet circular nozzle made of plexiglass was fitted to the lower part of the outer tube, perpendicular to the direction of flow; the distance between the center of the inlet nozzle and the bottom of the annulus was 2.5 cm. Three different nozzle diameters were used, namely, 0.63, 1.25, and 2.5 cm. The rate of diffusion-controlled corrosion of the lower section of the inner tube located at the inlet jet zone was measured for a height of 5 cm (2d) from the bottom of the annulus. Measurements were also carried out downstream of the inlet jet zone in the entrance region where the flow is developing and in the fully developed region. Measurements in the entrance region were carried out for heights of 12.5, 25,
1162
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
50, 75, and 100 cm (i.e., 5d, 10d, 20d, 30d, and 40d). Height was controlled by insulating the undesired tube length with a Teflon tape. For fully developed flow, measurements were carried out using a dissolvable tube length of 25 cm (10d) preceded by an inert length of 125 cm (50d) and followed by an inert length of 25 cm (10d). The open top of the annulus was fitted with a plexiglass overflow weir from which the solution returns back to the storage tank. During each run, 15 L of acidified dichromate was recirculated between the storage tank and the annulus; the solution flow rate was controlled by means of a bypass and was measured by a graduated cylinder and a stop watch. Copper dissolution in acidified dichromate was followed by withdrawing 10 cm3 samples from the storage tank at 10 min time intervals for analysis. Analysis was carried out by titrating acidified dichromate against ferrous ammonium sulfate using diphenylamine as an indicator.24 Each run was conducted using a fresh solution; the inner copper tube was changed every few experiments with a new one to avoid dimensional change. Before each experiment, care was taken that the two tubes of the annulus are coaxial from the bottom to the top. Three different solution of acidified dichromate were used: K2Cr2O7 was fixed at 0.003 M while H2SO4 concentrations were 0.5, 1, and 2 M. All solutions were prepared from A.R. grade chemicals and distilled water. Solution viscosity and density needed for data correlation were determined by an Ostwald viscometer and density bottle, respectively.25 The diffusion coefficient of dichromate was taken from the literature.10 The temperature was 25 ( 1°C. To test the effect of drag-reducing polymers, Polyox WSR-301 was added to the solution in the form of a powder in concentrations of 100, 200, and 300 ppm. Experiments repeated under the same conditions gave masstransfer coefficients which differed by an amount ranging from 2 to 5%.
Figure 3. Typical ln Co/C vs t at different solution velocities in the inlet jet zone: Sc ) 960; nozzle diameter ) 2.5 cm; working section height ) 5 cm (2de). Solution velocity (cm/S): Y, 14.8; 4, 33.9; X, 42.6; O, 57.1; 0, 65.5; b, 132.8.
Results and Discussion The mass-transfer coefficient of the diffusion-controlled dissolution of the lower 5 cm (2d) section of the inner cylinder targeted at the middle by a perpendicular inlet jet was calculated from the equation27-29
-Q
dC KAC dt
(10)
which upon integration gives
ln Co/C )
KAt Q
The average deviation is (19%.
Figures 5 and 6 show the effect of Re and the dimensionless nozzle diameter, respectively, on Sh of the lower part of the inner cylinder; the data respectively fit the equations
Sh ) a1Re0.46
(11)
(13)
and
Figure 3 shows that the present dischromate concentrationtime data fit the above equation. The mass-transfer coefficient was obtained under different conditions from the slope KA/Q of ln Co/C νs t. To test the soundness of the present technique, mass-transfer coefficients were measured for the fully developed region in the mass-transfer-developed region. This was carried out by determining the rate of mass transfer at a working section of 25 cm length (10 de) preceded by an inert entrance section of 125 cm length (50 de). Figure 4 shows that the data obtained for the conditions 960 < Sc < 1364 and 6130 < Re < 27 000 agree fairly well with the Chilton-Colburn equation26
Sh ) 0.023Sc0.33 Re0.8
Figure 4. Comparison of the present mass-transfer data in the fully developed region with the Chilton-Colburn equation (eq 14): ChiltonColburn eq, s; present data, X, 960; O, 1 113; 4, 1 364.
(12)
Sh ) a2
() dn d
-0.4
(14)
Figure 7 shows that the present data for the diffusion-controlled dissolution of the lower part of the inner cylinder targeted by the inlet jet under the conditions 960 < Sc < 1 364, 3 900 < Re < 36 100, 0.25 < dn/d < 1, and 3 900 < Ren < 143 250 fit the equation
Sh ) 2.74Sc0.33 Re0.46
() dn d
-0.4
(15)
with an average deviation of (17%. Annulus equivalent diameter was used as a characteristic length in calculating Sh and Re.
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1163
Figure 7. Overall mass-transfer correlation for the diffusion-controlled dissolution of the inlet jet zone: Sc ) b, 960; 2, 1 113; 0, 1364.
Figure 5. Effect of Re on Sh at different Sc in the inlet jet zone: working section height ) 5 cm; nozzle diameter ) 0.63 cm; Sc ) b, 960; 2, 1 113; 0, 1 364.
Figure 8. Effect of distance downstream of the inlet jet zone on the masstransfer coefficient at different Re: Sc ) 960; nozzle diameter ) 2.5 cm; Re ) b, 6 588; 2, 10 440; 0, 16 550.
Figure 6. Effect of nozzle diameter on Sh at different Re in the inlet jet zone: Sc ) 1364; working section height ) 5 cm; Re ) b, 6 310; 2, 7 943; 0, 10 000; O, 12 590.
To appreciate the extent to which the jetting effect enhances the rate of mass transfer and corrosion of the lower section of the inner tube compared to the downstream zone where flow is developing, rates of mass transfer were measured at different lengthes from the base of the annulus in the developing region (where the flow is developing). Figure 8 shows the distribution of the mass-transfer coefficient along the surface of the inner tube; the ratio between the lower-section mass-transfer coefficient and the mass-transfer coefficient in the developing region ranges from 3.9 to 5.5 depending on the tube length and Re, which determine the thickness of the developing hydrodynamic boundary layer and diffusion layer along the annulus. The value of 0.46 for the Re exponent shown in eq 15 seems to be reasonable in view of the fact that the average rate of mass transfer at the surface of the inner cylinder upon which
the jet is impinging involves contributions from mass transfer at the stagnation zone and the curved-wall zone. Previous studies30,31 on heat and mass transfer at the stagnation zone of a submerged jet impinging on a flat surface have shown that the mass-transfer coefficient increases with the 0.5 power of Re. Alternatively, the rate of mass transfer at the curved part (wall jet region) can be approximated by mass transfer at a cylinder in cross-flow. Previous studies on cylinders in crossflow32 have revealed that the heat or mass-transfer coefficient increases with Re raised to an exponent which depends on the range of Re. For the present Re range, the mass-transfer coefficient increases with Re raised to an exponent ranging from 0.466 to 0.618.32 Hsueh and Chin33 studied local mass transfer to a cylindrical surface from an unsubmerged impinging jet using an electrochemical technique. The authors found that the rate of mass transfer reaches a maximum at the impingement zone (x/dn ) 1 where x is the distance from the impingement zone and dn is the nozzle diameter) and then decreases with increasing x/dn till it reaches a minimum at x/dn ) 2.1; eventually it remains almost constant with further increases in x/dn. The authors correlated their local mass-transfer data by the equation
Sh ) aReBn
(16)
For Ren < 6 000, the value of B was found to be 0.6 for the stagnation zone, 0.4 at x/dn ) 2.1, and 0.6 for x/dn g 3. Despite
1164
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
Figure 9. Comparison of the present inlet jet zone mass-transfer data with the data of tube inlet jet zone: Sc ) 960; nozzle diameter ) 1.25 cm; s, present data (eq 15); - - -, eq 17.
the difference in the experimental conditions between the present work and the work of Hsueh and Chin, the Re exponent 0.46 obtained in the present work (eq 15) seems to agree fairly well with the results of Hsueh and Chin. Sedahmed et al.34 studied the diffusion-controlled impingement corrosion at the lower end of a vertical tube with a perpendicular inlet jet, as in the present work; the authors correlated their mass-transfer data at the lower part of the tube (height ) 2d) affected by the inlet jet for the conditions 1 688 < Sc < 1 899, 2 790< Re < 6 000, and 0.2 < dn/d < 1 by the equation
Sh ) 1.839Sc0.33 Re0.43(dn/d)-1.23
Figure 10. Effect of polyox drag-reducing polymer on Sh at different solution compositions in the inlet jet zone: working section height ) 5 cm; nozzle diameter ) 2.5 cm; polyox concentration (ppm) ) b, 0 (blank); 2, 100; 0, 200; O, 300. Table 1. Percent Decrease in the Mass-Transfer Coefficient at the Lower Section of the Inner Tube Targeted by the Inlet Jet at Different Solution Compositionsa % decrease in K at different polyox concentrations H2SO4 conc. (M)
Sc
Re
100 ppm
200 ppm
300 ppm
0.5
960
4224 6694 10608 16817 26647 33546 4224 6694 10608 16817 26647 33546 4224 6694 10608 16817 26647 22546
41.99 42.01 42.01 42.00 41.92 42.00 35.46 35.45 35.44 35.45 35.45 35.45 29.95 29.95 29.95 29.95 29.95 29.97
59.33 59.32 59.32 59.32 59.27 59.32 44.95 44.95 44.95 44.96 44.95 44.96 46.73 46.74 46.73 46.74 46.74 46.75
68.86 68.84 68.85 68.86 68.81 68.85 63.99 63.99 63.99 63.99 63.99 64.00 55.45 55.45 55.45 55.44 55.44 55.45
(17)
Figure 9 shows that, for a given set of conditions, the rate of diffusion-controlled impingement corrosion is more severe in the case of the annulus than in that of the tube. This difference in behavior may be attributed to the difference in flow conditions at the impingement zone of annulus and tube. The difference in flow conditions arises mainly from the fact that the distance between the nozzle and the surface upon which the jet is impinging is shorter in the case of the annulus. This leads to higher rates of mass transfer at the stagnation zone; the rate of mass transfer at the wall jet zone is little affected by the nozzletarget separation.30,31 Figure 10 and Tables 1 and 2 show that the presence of polyox drag-reducing polymer decreases the mass-transfer coefficient of the diffusion-controlled corrosion in the inlet jet zone of the annulus by an amount ranging from 29.95% to 68.86% depending on polymer concentration, electrolyte concentration, and inlet nozzle diameter. Unlike other cases, such as drag reduction in fully developed flow in tubes and annuli,17-21 the % reduction in K shown in Tables 1 and 2 is not sensitive to Re. Previous studies conducted in tubes under fully developed flow have shown that the % drag reduction or % decrease in K increases with Re; owing to the increase in the degree of stretching of polymer molecules under the influence of the shear stress,35 the higher the degree of stretching of the polymer molecules, the higher is their ability to dampen the small-scale, high-frequency eddies.21,35 At sufficiently high Re,
1
1113
2
1364
a K Cr O concentration ) 0.003 M; working section height ) 5 cm 2 2 7 (2d); nozzle diameter ) 2.5 cm.
shear degradation of the polymer molecules to ineffective breakdown products takes place and the % drag reduction and % decrease in K start to decline. The degree of polymer degradation depends on polymer structure, solution composition, and Re. The insensitivity of the % decrease in K to Re as shown in Tables 1 and 2 may be explained by the high degree of turbulence and the high shear stress which prevail in the inlet jet zone even at low Re and maintain the polymer molecules in the highest possible degree of stretching allowed by other controlling factors such as the presence of electrolytes. Table 1 shows that the % reduction in the mass-transfer coefficient decreases with increasing H2SO4 concentration; this finding is consistent with the results of previous studies on the effect of electrolytes on the performance of drag-reducing
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1165 Table 2. Percent Decrease in the Mass-Transfer Coefficient at the Lower Section of the Inner Tube Targeted by the Inlet Nozzle at Different Nozzle Diametersa % decrease in K at different nozzle diameters Re
dn ) 2.5 cm
dn ) 1.25 cm
dn ) 0.63 cm
4224 6694 10608 16817 26647 33546
59.33 59.32 59.32 59.32 59.27 59.32
48.55 48.55 48.55 48.55 48.54 48.54
45.98 46.00 45.98 46.00 46.00 46.00
Sc ) 960 (0.003 M K2Cr2O7 + 0.5 M H2SO4); working section height ) 5 cm (2d); polyox concentration ) 200 ppm. a
polymers.36-38 Polymer molecules, and H+ and SO4 ions resulting from H2SO4 ionization, compete for waters of hydration. By increasing H2SO4 concentration, the amount of water available to hydrate the polymer molecules decreases with consequent production of less-stretched polymer molecules. Since the ability of water-starved, coiled polymer molecules to suppress the small-scale, high-intensity eddies is less than that of the highly hydrated stretched molecules,36-38 it follows that the % reduction in K will decrease with increasing H2SO4 concentration, as shown in Table 1. The increase in the % reduction in K with increasing polyox concentration is in agreement with previous studies on turbulent momentum transfer, heat transfer, and mass transfer at different transfer surfaces in drag-reducing fluids.21 Table 2 shows that, for a given set of conditions, the % reduction in K decreases with decreasing inlet nozzle diameter; this may be attributed to the increase of the rate of shear degradation of the stretched polymer molecules as a result of the excessive increase in nozzle Re with decreasing nozzle diameter. Comparison of the present % reduction in the rate of masstransfer-controlled corrosion with the values obtained for other geometries such as agitated vessels7 and tubes under fully developed flow17 shows that the present % reduction in the rate of diffusion-controlled corrosion is higher than those obtained in the cases of agitated vessels and tubes. It is probable that the proportion of the small-scale, high-frequency dissipating eddies which are sensitive to drag-reducing polymer molecules is higher in the turbulence spectrum of the inlet jet zone of the annulus. This speculation needs to be verified by an experimental study of the nature of turbulence prevailing in the lower section of the annulus targeted by the inlet jet.
by stabilizing the protective oxide film and, if it breaks down, the rate of diffusion-controlled corrosion would not be serious. However, before using drag-reducing polymers in practice, care should be taken that the benefits of using them outweigh their disadvantages. The benefits include corrosion inhibition, energy savings due to friction reduction, and inhibition of pump cavitation;39 the negative effects of drag-reducing polymers arise from their ability to reduce the rate of heat transfer in the case of heat transfer equipment.40,41 List of Symbols a ) cross-sectional area of the nozzle a1, a2 ) constants A ) area of the dissolving surface Co, C ) initial concentration of dichromate and concentration at time t, respectively. d ) tube diameter or equivalent diameter of the annulus (do di) do ) annulus outer tube diameter di ) annulus inner tube diameter dn ) nozzle diameter D ) diffusivity of dichromate F ) impact force f ) friction factor K ) liquid-phase mass-transfer coefficient K1 ) mass-transfer coefficient across the oxide film K2 ) rate constant of cathodic reduction of dissolved oxygen. L ) length of the annulus m ) mass flow rate N ) flux of dissolved oxygen Q ) solution volume t ) time V ) average solution velocity Vx ) point liquid velocity in x direction x ) distance in the direction of flow y ) distance perpendicular to direction of flow Sc ) Schmidth number (γ/D) Sh ) Sherwood number (Kd/D) Re ) Reynolds number (FVd/µ) Ren ) jet Reynolds number (FVndn)/µ F ) solution density γ ) kinematic viscosity µ ) solution viscosity τ ) shear stress
Conclusions (1) Mass-transfer-controlled impingement corrosion at the lower section of the inner cylinder of an annulus targeted by the inlet jet has been quantified by a dimensionless mass-transfer correlation. The rate of diffusion-controlled corrosion at the lower section was found to be higher than that of the downstream area by a factor ranging from 3.9 to 5.5 depending on the distance from the annulus base and Re. The present results would assist in calculating the corrosion allowance needed in the design of annular equipment. (2) Drag-reducing polymers were found to inhibit diffusioncontrolled impingement corrosion by an amount ranging from 29.9 to 68.9% depending on nozzle diameter, electrolyte concentration, and polymer concentration. Moreover, the presence of the drag-reducing polymer would resist the occurrence of erosion-corrosion in view of the ability of the polymer molecules to reduce the shear stress in the zone facing the inlet jet, thus protecting the oxide film which may exist on the metal from damage; i.e., drag-reducing polymers protect the inlet zone
Literature Cited (1) Pludek, V. R. Design and Corrosion Control; The Macmillan Press Ltd.: London, 1977. (2) Fontana, M. G. Corrosion Engineering; McGraw-Hill: New York, 1987. (3) Heitz, E. Mechanistically based prevention strategies of flow-induced corrosion. Electrochim. Acta 1996, 41, 503-509. (4) Webber, J. Flow induced corrosion: 25 years of industrial research. Br. Corros. J. 1992, 27, 193-199. (5) Postlethwaite, J.; Lotz, U. Mass transfer at erosion-corrosion roughened surfaces. Can. J. Chem. Eng. 1988, 66, 75-78. (6) Poulson, B. Advances in understanding hydrodynamic effects on corrosion. Corros. Sci. 1993, 655-665. (7) Sedahmed, G. H.; Farag, H. A.; Kayar, A. M.; El-Nashar, I. M. Mass transfer at the impellers of agitated vessels in relation to their flow-induced corrosion. Chem. Eng. J. 1998, 71, 57-65. (8) El-Shazly, Y. M.; Zahran, R. R.; Farag, H. A.; Sedahmed, G. H. Mass transfer in relation to flow induced corrosion of the bottom of cylindrical agitated vessels. Chem. Eng. Process. 2004, 43, 745-751. (9) Kennelly, K. J., Hausler, R. H., Silverman, D. C., Eds. Flow induced corrosion. Proceedings of NACE, Houston, TX, 1991.
1166
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
(10) Gregory, D. P.; Riddiford, A. C. Dissolution of copper in sulfuric acid solutions. J. Electrochem. Soc. 1960, 107, 950-956. (11) Madden, A. J.; Nelson, D. G. A novel technique for determining mass transfer coefficients in agitated solid-liquid systems. AIChE J. 1964, 10, 415-429. (12) Mobarak, A. A.; Farag, H. A.; Sedahmed G. H. Mass transfer in smooth and rough annular ducts under developing flow conditions. J. Appl. Electrochem. 1997, 27, 201-207. (13) Sedahmed, G. H.; Shemilt, L. W. Forced convection mass transfer at rough surfaces in annuli. Int. Commun. Heat Mass Transfer 1976, 3, 499-512. (14) Ross, T. K.; Wragg, A. A. Electrochemical mass transfer studies in annuli. Electrochim. Acta 1965, 10, 1093-1106. (15) Legrand, J.; Martemyanov, S. A. Turbulent mass transfer in small radius ratio annuli. J. Appl. Electrochem. 1994, 24, 737-744. (16) Shehata, A. S.; Nosier, S. A.; Sedahmed, G. H. The role of mass transfer in the flow-induced corrosion of equipments employing decaying swirl flow. Chem. Eng. Process. 2002, 41, 659-666. (17) Sedahmed, G. H.; Fawzy, M. A. Corrosion inhibition in pipelines by drag reducing polymers. Br. Corros. J. 1986, 21, 225-227 (18) Rubin, H.; Elata, C. Turbulent flow of dilute polymer solutions through an annulus. AIChE J. 1971, 17, 990-996. (19) Shenoy, A. V.; Shintre. Developing and fully developed turbulent flow of drag reducing fluids in an annular duct. Can. J. Chem. Eng. 1986, 64, 190-195. (20) Tiu, C.; Chee, N. Turbulent flow behaviour of dilute poymer solutions in an annulus. Can. J. Chem. Eng. 1979, 57, 572-577. (21) Hoyt, J. W. The effect of additives on fluid friction. Trans. ASME, J. Basic Eng. 1972, 94, 253-285. (22) Sellin, R. H.; Hoyt, J. W.; Serivener, O. The effect of drag-reducing additives on fluid flows and their industrial applications. Part I: Basic aspects. J. Hydraulic Res. 1982, 20, 29-67. (23) Little, R.; Smidt, S.; Huang, P.; Romans, J; Dedrick, J.; Matuszko, J. S. Improved drag reduction by control of polymer particle size. Ind. Eng. Chem. Res. 1991, 30, 403-407. (24) Vogel, A. I. A text book of quantatiVe inorganic analysis; Longmans: London, 1961. (25) Findly, A.; Ketchener, J. K. Practical Physical chemistry; Longmans: London, 1965. (26) Pickett, D. Electrochemical Reactor Design; Elsevier: New York, 1977. (27) Walsh, F. A first course in electrochemical engineering, The electrochemical consultancy; Hants, U. K., 1993.
(28) Pickett, D. J. The analysis of a batch electrochemical reactor with continuously recirculating electrolyte. Electrochim. Acta 1973, 18, 835837. (29) Matic, Dj. Packed-bed reactor with continuous recirculation of electrolyte. J. Appl. Electrochem. 1979, 9, 15-20. (30) Webb, B. W.; Ma, C. F. Single-phase liquid jet impingement heat transfer. AdV. Heat Transfer 1995, 26, 105-217. (31) Chia, C. J.; Girall, F.; Trass, O. Mass transfer in axisymmetric turbulent impinging jets. Ind. Eng. Fundam. 1977, 16, 28-35. (32) Incropera, F. P.; DeWitt, D. Fundamentals of heat and mass transfer; John Wiley & Sons: New York, 1990. (33) Hsueh, K. L.; Chin, D. T. Mass transfer to a cylindrical surface from an unsumerged impinging jet. J. Electrochem. Soc. 1986, 133, 7581. (34) Sedahmed, G. H.; Abdo, M. S.; Amer, M.; Abdel-Latif, G. Mass transfer at a pipe inlet zone in relation to impingement corrosion. Int. Commun. Heat Mass Transfer 1998, 25, 443-451. (35) White, D.; Gordon, R. J. The influence of polymer conformation on turbulent drag reduction. AIChE J. 1975, 21, 1027-1029. (36) Little, R. C.; Patterson, R. L. Turbulent friction by aqueous poly(ethylene oxide) polymer solution as a function of salt concentration. J. Appl. Polym. Sci. 1974, 18, 1529-1539. (37) Bailey, F. E.; Callard, R. W. Some properties of poly(ethylene oxide) in aqueous solution. J. Appl. Polym. Sci. 1959, 1, 56-62. (38) Little, R. C.; Hansen, R. J.; Hunston, D. L.; Kim, O. K.; Patterson, R. L.; Ting, R. Y. The drag reduction phenomenon: Characteristics, improved agents and proposed mechanisms. Ind. Eng. Chem. Fundam. 1975, 14, 283-295. (39) Sellin, R. H.; Hoyt, J. W.; Serivener, G. The effect of drag-reducing additives on fluid flows and their industrial applications. Part II: Present applications and future proposals. J. Hydraulic Res. 1982, 20, 235-291. (40) Smith, K. A.; Keuroghlian, G. H.; Virk, P. S.; Merrill, E. W. Heat transfer to drag reducing polymer solutions. AIChE J. 1969, 15, 294-297. (41) Dudukovic, A. Momentum, heat and mass transfer analogy for dragreducing solutions. Ind. Eng. Chem. Res. 1995, 34, 3538-3541.
ReceiVed for reView June 3, 2005 ReVised manuscript receiVed October 18, 2005 Accepted October 18, 2005 IE058053I
