# Development of Solutions to Two-Resistance Mass Transport Models Based on External and Pore Diffusion. Part II Experimental Results

код для вставкиСкачатьDevelopment of Solutions to Two-Resistance Mass Transport Models Based on External and Pore Diffusion. Part II: Experimental Results G. McKay', 9. Al-Duri and Stephen McKee Department of Chemical Engineering, The Queen's University of Belfast, Belfast, BT9 5AG, Northern lrland Introduction This paper applies the theoretical mass transport models developed in Part I to experimental results for several adsorption systems. The nomenclature has been presented in Part I. All Figures, Tables and References presented are in the present paper. Discussion of Results Porosity is the main characteristic of all adsorbents since the porous structure determines the surface area and accessible adsorption sites in any sorbent. This makes the film-pore diffusion mechanism worthy of investigation as an adsorption mechanism. In general adsorption is considered a three-step process: (1) mass transport across the boundary layer surrounding the particle; (2) intraparticle diffusion through the liquid filled pores expressed by the effective pore diffusivity, (Deff); (3) adsorption at a site. Step (3) is very rapid and steps (1) and (2) are the rate controlling processes. The transport process is driven by the concentration gradient in the liquid filled pores and hence intra-particle diffusion is the main step that needs thorough investigation. First, molecules transfer from one site to another by desorption in the liquid- filled pores, then adsorption again on the new site. External mass transfer is controlling in the first few minutes of the process when sorbate molecules are diffusing through the boundary layer to the external surface. The film-pore diffusion model, according to the present solutions, assumes irreversible adsorption. Irreversibility is indicated when the adsorption and desorption data do not coincide, i.e. some of the adsorbed material is still in the solid phase even after desorption. This occurs in the cases of chemisorption when the surface functional groups on the sorbent form complexes with the sorbate molecules.' The fraction of adsorption which is reversible is due to the Van der Waal forces that are formed at some of the sorption sites. Complete irreversibility is characterized by a rectangular shaped isotherm where Y* is constant regardless of the fluid phase concentration value (Cs). The experimental isotherm shown in * To whom correspondence should be addressed. Developments in Chemical Engineering and Mineral Processing, Vol. 1, No. 2/3,Page 146 Two-Resistance Mass Transport Models 147 Adsorption isotherm Concn. in liquid, C Cz Concn. in liquid, C Figure 1 Relationship between bulk and su@ace concentration during the adsorption in batch tests. Table 1 Values of Langmuir equilibrium constants. Adsorbent Solute K (dm3 g-1 ) Chitin Chitin Activated carbon Activated carbon Silica Acid Blue 25 Acid Blue 158 Phenol p-chlorophenol Astrazone Blue 22 4.1 11.3 48 500 b (dm3 mg-') 0.12 0.019 0.050 0.11 0.016 Figure 2 is typical of the systems investigated in this work. The curve shows a degree of reversibility and a saturation monolayer which could best be described mathematically by the Langmuir equation. However, for liquid-phase equilibrium concentrations greater than 200 mg dm-3, all the points have a constant monolayer saturation value typical of the rectangular isotherm. The saturation monolayer value (Yh*)is used for the analytical solution to the adsorption problem when the operating line, and all tie lines terminate on the monolayer. For all other operating conditions, the appropriate value of Y* is used as predicted by the isotherm equation. Model I : Pseudo-analytical batch model (PAM) This is a film-pore diffusion model with the saturation isotherm constraint, i.e. it assumes complete irreversibility. This assumption enabled an analytical solution G. McKay, B. Al-Duri and S. McKee I48 Table 2 External liquid mass-transfer coeflcients (PL) and effective difisivities (Defl)for the analytical solution represented by Model 1. ~~ Adsorbent Solute PL (cm s-') Sorbsil silica A Sorbsil silica B Activated carbon Chitin Chitin Activated carbon Astrazone Blue Astrazone Blue Phenol Acid Blue 25 Acid Blue 158 p-Chlorophenol 8.of1.0 2.ofo.5 lo4 2.Mo.5 4.W1.0 5.Ok1.5 1. M . 4 1.8M.5 8.M1.0 2.5f1.0 1 3 0 . 5 10" 3.0k1.0 10" 1.0M.3 lo4 Figure 2 Operating and tie lines for the adsorption of Astrazone Blue on silica. to be obtained which yields the concentration decay curve. Application of this model is restricted to system conditions where the operating line terminates on the 'plateau' of the isotherm. Equilibrium is described by the Langrnuir isotherm. Table 1 shows all isotherm constants for the systems under investigation. In the present work, results have been obtained by using a Fortran 77 program that carries out the solution method outlined in Part I. The input to the program comprises the following eight parameters: initial solute concentration, adsorbent mass, adsorbent particle diameter, adsorbent voidage and density, the external Two-Resistance Mass Transport Models 149 mass transfer coefficient, effective diffusivity, and a capacity based on the monolayer saturation capacity (Yh*). This saturation capacity is obtained by either reading the monolayer value from isotherm curve Figure 2, or evaluating it as the ratio Kib. Figure 2 shows a typical output for the adsorption of Astrazone Blue on silica type B. For a number of systems whose conditions terminate on the monolayer, it was possible to correlate theoretical and experimental concentration decay curves using a single constant external mass tIansfer coefficient and a single constant effective diffusion coefficient. The results for the adsor tion of Astrazone Blue on Sorbsil silica type A have been reported previously! the values of the mass transfer coefficients for this and other adsorption systems are compared in Table 2. This table shows the values of PL and Dew which can be used successfully as fitting paramete values. Reported literature3 values of Deff are 2.70 x lo-’, 2.80 x lo-’, 1.70 x lo4 and 1.00 x 10“ cm2 s-l for phenylacetic acid, benzoic acid, acetophenone, alizarin and crystal violet respectively, all on carbon B10. The above values have been obtained using the graphical method. Applying the present method to other systems has yielded Defi values of 18.0 x lo-’ and 2.50 x lo-’ cm2 s-l for cm2 s-l f o r a BB69Isilica and phenol/carbon and 2.50 x BB69/woodmeal system.6 Comparing these values to the present values, it is evident that the present Defi values are lower than literature values. This is due to two major factors. First, the molecular size of adsorbates. Dye molecules are considered as large organic molecules compared to phenols, erc., and hence are expected to diffuse much slower than other organics. Second, the type of adsorbent. Activated carbon is a polar adsorbent with a porous structure and controlled active sites, hence it has a high capacity or strong affinity to many organic substances. Therefore, diffusivities of these organics are expected to be strong in carbon systems, more so than other adsorbents. However, despite the model constraint that restricts the variation in system conditions, it is an easy-to-use practical model for industrial purpose^,^ and once applied it gives good agreement between experiment and theory. Model 2: Polynomial curve-fit model (POLYFIT) Typical outputs are shown in Figures 3,4 and 5 for the adsorption of Acid Blue 25 on chitin, phenol on activated carbon, and p-chlorophenol on activated carbon, respectively. The data for the adsorption of phenol on carbon are poorly correlated mainly due to the poor curve fits obtained when the concentration-time curves decay rapidly initially and then almost instantaneously level out to a plateau. Therefore, polynomial curve fits were difficult to achieve for this system. The results produced by the model were heavily dependent on the order of the polynomial chosen to describe the experimental concentration decay curve. Too small an order tended to flatten out the concentration gradient, whereas too high an order introduced fluctuations (undulations) in the theoretical concentration decay curves yielding very erroneous gradients. However, the program execution time was very short and many runs could be analysed without the need for a powerful computer. The program can be run for a small number of experimental points. The external film mass-transfer coefficients and effective diffusion coefficients are listed in Table 3. In general, the results were acceptable but it was apparent that a better curve fitting equation(s) was required. Furthermore, the mathematical forms of the equilibrium isotherms were becoming more important now that systems, whose G. McKay, B. Al-Duri and S. McKee I50 Table 3 Values of Adsorbent PL and Defifor Model 2. Solute ~ D 4 -I (cm s ) 3.0f1.0 lo4 9.of3.0 5.of1.0 1.ofo.3 2.ofl.O lo4 1.3rto.3 lo4 1.5rto0>5 PL ~~~ Silica B Chitin Chitin Activated Carbon (cm s-'1 ~ ~~ Astrazone Blue Acid Blue 25 Acid Blue 158 Phenol 1.~o.2 Table 4 Values of PL and Degfor Model 3. Adsorbent Solute PL (cm s-') Carbon Silica Chitin Chitin Phenol Astrazone Blue Acid Blue 158 Acid Blue 25 2.Mo.5 4.W.O lo4 1.Mo.5 1.Mo.3 D qf -I (cm s 1 1.4rto.4 1.0rto.2 3.0k1.5 lo4 1.5H.5 lod operating and tie lines did not terminate on the monolayer, were being analysed. Table 3 shows the values of the Langmuir isotherm equilibrium constants. Model 3: Exponential curve-fit Model (EXPOFIT) As explained in Part I, this is a film pore-diffusion model with a more advanced solution method, such that the saturated isotherm constraint is no longer required, . ~ technique and it provides more accurate results than the graphical s ~ l u t i o nThis has widened the range of experimental conditions over which the model can be applied, leading to further investigation of intraparticle diffusion. In the present model, ranges of PL and D,ff values are input to the Fortran 77 program, which responds with the best five combinations of PL and Deff based on the minimum residual R'. Figures 6, 7 and 8 show the quality of the curve-fit for the adsorption of phenol on carbon, Astrazone Blue on silica, and Acid Blue 158 on chitin, respectively. The values of and Deff for the experimental systems are given in Table 4. The variations in PL and D,ff are shown in Table 5 for the adsorption of phenol. The data listed are those based on the minimum residual for each particular analysis. This program requires a longer execution time than Model 2, largely due to the detailed procedures in the program. The program also requires more data points (AO) than Model 2 to fit the exponential series equations. A closer inspection of Tables 1, 2 and 4 allows comparison of the D,ff values from the present systems, obtained by the three different solution methods. Table 6 shows that generally, D,ff values obtained by PAM and EXPOFIT are nearly equal, whereas those of POLYFIT are much lower values for AB158/chitin PL Two-Resistance Mass Transport Models I51 systems compared to PAM and EXPOFIT. This can be explained in terms of the relatively poor fit of the curves obtained by the POLYFIT program, and makes EXPOFIT the preferred method rather than POLYFIT. However, further investigations on a wider range of systems is needed before drawing final conclusions. The time of application is also worth considering. Table 7 shows that EXPOFIT has been used to fit data up to 100 minutes, i.e. 1-2 hours. For this period it has been possible to describe the whole range of conditions by a single .-C E Sherwood number 3 0 m a 0 c 0 0 Sherwood rumber Figure 3 Plots of Sherwood number versus time curves for the adsorption of Acid Blue 25 dye on chitin. 152 G. McKay, B. Al-Duri and S. McKee D e value ~ nearly equal to the Deff used in PAM. However, previous studies’ with other systems have shown that when the kinetic data supplied is for 24 hours, Deff varies with C,. Since the present data does not exceed 120 minutes, this point is beyond the scope of this work. Model 4: ‘Tes@t’ program Program ‘Testfit’ was developed to be run prior to using the pseudo-analytical Models 2 and 3. The program reads in the time-concentration coordinates and uses three methods for fitting curves and hence determining the concentration gradients. The previous two methods for polynomial and exponential series ;re Sherwood number Sherwood number Figure 4 Plots of Shewood number versus time curves f o r the adsorption of phenol on activated carbon. I53 Two-ResistanceMass Transport Models used, and also a finite difference program. The finite difference technique assumes that the concentration gradient at a point is the average of the straight line gradients before and after that point, as defined by: (60) (dC/dt) = [(Cj - Ci-I)/(tj - tj-1) + (Ci+1 - Ci)/($+l - $)]I2 The results produced by this program will enable the user to compare the exponential and polynomial curve-fit data with the gradients predicted by the finite difference method. In this way the number of possibilities can be reduced before trying the selected curve-fit equations in the main programs. Typical outputs from the testfit program are shown in Table 7 for the adsorption of Acid Blue 25 on chitin. Only three sets of results are presented and 0 Sherwood number In Sherwood number Figure 5 Plots of Shenvood number versus time for the adsorption of p-chlorophenol on activated carbon. I G.McKay, B. Al-Duri and S.McKee I54 Table 5 Values of PL and D,,, for phenol adsorption onto carbon. Initial concentration (mg dm-3) Adsorbent mass (g) PL (cm s-') 400 400 400 300 300 300 300 300 200 200 1.70 2.66 3.20 0.85 1.70 2.81 6.31 7.77 0.85 1.70 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.2 0.2 D 105) (cm$ff-l s 0.8 1.1 1.4 1.2 1.8 1.3 1.3 2.0 3.5 3.4 11 l0C - Theoretical 0 C,= 200mg dm-3 3 Time (minsl Figure 6 Plots of Shenvood number versus time for the adsorption of phenol on activated carbon. it can be seen that the curve-fit equations for the exponential and polynomial series are in agreement with experimental results. However, when the gradients are compared, the exponential function gives much closer agreement to the finite difference method. Furthermore, after the first seven points in Table 7,the slope of the gradient changes in the wrong direction obviously due to a fluctuation. This was characteristic of polynomials with more than four terms, and often with only four terms. These equations, therefore, were applicable only for a short period of time, but by reducing the order of the polynomial the gradients exhibited greater deviation. Two-Resistance Mass Transport Models 155 36. 32 - Vol ( u n 3 1 = 1700 PL (cmls) 3300 x 10-3 28 . A5 2 c -c - Theoretical - 1i: - I n 0 C,= 300 mg dm-3 C,= lOOmg dm-3 - 12 84 L. z 0 3 Time (mins) Figure 7 Plots of Sherwood number versus time f o r the adrorption of Astrazone Blue Dye on silica. R (cm) = 0 0302 V o l . ( c d I = 1700 PL (cm/s 1 = o 900 x 10-2 - Theoretical C0=50mgdm-3 In 10 0 10 20 30 LO 50 60 70 80 90 Time Imins) Figure 8 Plot of Shenvood number versus time for the adsorption of Acid Blue 158 dye on chitin. 1 0 G. McKay, B. Al-Duriand S. McKee 156 Table 6 Mean diffusion coeficients (cm2 s-l lo7)for the systems under investigation. BB69/Silica B AB 1WChitin AB25IChitin PAM POLYFIT EXPOFIT 0.8 30 15 1.o 13 20 1.o 30 15 Table 7 Comparison between theoretical concentration predicted by Model 4 and experimental results. Time (min) 0.0 1.o 2.0 4.0 9.0 16 25 36 49 64 100 Experimental concentration (mg dms) 100 96 94 92 87 83 79 75 71 68 63 Theoretical concentration (mg d ~ n - ~ ) 100 96 94 92 87 83 79 75 71 68 63 Gradient (mg dm-3 min-') -4.00 -3.00 -1.50 -1.00 -0.785 -0.507 -4.404 -0.335 -0.253 -0.169 -0.138 Conclusions and Significance Model 1 is useful for predicting mass transfer coefficients and effective diffusivities for adsorption systems in which the operating lines and tie lines terminate on the monolayer of a pseudo-irreversible isotherm. The analysis is based on external liquid mass transfer and internal pore-diffusion mass transport, and the model has been applied successfully to several systems. Models 2, 3 and 4 were developed to extend the use of the above basic model for adsorption systems in which operating and tie lines terminated anywhere on the equilibrium isotherm. The value of the concentration gradient with respect to time, (dC/dt),, is needed and had been determined graphically in previous work.3 Consequently, these models tested curve fitting equations and gradient determination by polynomial series equations (model 2), exponential series equations, and finite difference techniques. It was decided that exponential series equations are most useful for this procedure after comparing the outputs from a number of tests on the computer. Both curve-fit equations were applied successfully to a number of systems. . Two-ResistanceMass Transport Models 157 Future work will involve the application of the exponential solution for: (i) longer time periods; (ii) other single component systems; (iii) multicomponent adsorption systems. References 1 Mattson, J.S.,Mark, H.B., Malbin. M.D., Weber, W.J. and Crittenden, J.C. 1969. Surface chemistry of active carbon: specific adsorption of phenols. J. Colloid Interface Sci., 31, 116-121. 2 McKay, G. 1984. Analytical solution using a pore diffusion model for a pseudo-irreversible isotherm for the adsorption of basic dye on silica. AIChEJ, 30(4), 692-697. 3 Spahn, H. and Schlunder, E.U. 1975. The scale-up of activated carbon columns for water purification, based on results from batch tests (PartI). Chem. Eng. Sci., 30,529-537. 4 Bino, M.J. 1983. Mass Transfer Processes in the Adsorption of Industrial Pollutants onto Activated Carbon. Ph.D Thesis, The Queen's University of Belfast. 5 McKay, G.and Bino, M. 1985. Application of two resistance mass transfer model to adsorption systems. Chem. Eng. Res. Des., 63, 168-178. 6 McConvey, I.F. and McKay, G. 1985. Mass transfer model for the adsorption of basic dyes on woodmeal in agitated batch adsorbers. Chem.Eng. Proc., 19,267-277. 7 Neretnieks, I. 1974. Adsorption of components having a saturation isotherm. Swedish Paper J., 77,4074 13. 8 Al-Dun, B. and McKay, G. 1990. Comparison in theory and application of several mathematical models to predict kinetics of single component batch adsorption systems. Proc. Safety Environ. Protn. (Trans. I. Chem E.), 68B,254-268. Received: 27 February 1991; Accepted: 10 April 1992.

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