The Effect of Column Diameter and Packing Height on the Pressure

Apr 4, 2013 - ... and 1.22 m packed with RSP 250, Mellapak 250Y, or Montz BSH 250 structured packing, and utilizing the cyclohexane/n-heptane distilla...
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The Effect of Column Diameter and Packing Height on the Pressure Drop and on the HETP of Structured Packings L. Valenz, J. Haidl, and V. Linek* Department of Chemical Engineering, Institute of Chemical Technology Prague, CZ-166 28 Prague 6 Czech Republic ABSTRACT: The standardization of the measuring method for the determination of packing separation efficiency should start with a full understanding of all the conditions that affect its measurements in order to maintain them at the identical level during the measurement of different packings with the aim of comparing or evaluating the effects of the geometric modification of newly developed/designed packings. The effect of the column diameter, the bottom concentration of the distillation mixture, and the packing height on the HETP and the pressure drop are evaluated on the basis of the data measured in columns with diameters of 0.15, 0.43, and 1.22 m packed with RSP 250, Mellapak 250Y, or Montz BSH 250 structured packing, and utilizing the cyclohexane/n-heptane distillation system. It was found that below the loading point, the pressure drop was only slightly affected by the column diameter. The difference between the pressure drops of the 0.15 and 1.22 m diameter columns was within the experimental data scatter. The effect of the concentration range of distillation mixture on the separation efficiency is more pronounced than is the effect of the column diameter. HETP increases with increasing bottom concentration and packing height, and the increase found in this paper reached 50%. The effect of the column diameter onto the packing separation efficiency is not significant. The HETP, measured in columns with widely different diameters using a distillation mixture of approximately the same concentration range, did not demonstrate any significant effect of the diameter. The presented data do not support the recommendation of Ottenbacher et al. (Chem. Eng. Res. Des., 2011, 8, 1427) to consider as relevant only the packing efficiencies measured on columns with a diameter of at least 0.4 m because the data from the smaller diameter columns are dominated by the wall effects.

1. INTRODUCTION In the article “Structured Packing EfficiencyVital Information for The Chemical Industry”, Ottenbacher et al.1 define the practices that should serve as an open standard for both the measurement and the interpretation of the separation efficiency of structured packing. The standardization of the measuring method is the basis for the comparison of the packings and for the evaluation of the effect of geometric modifications of newly designed packings. The current state of the art is such that the scatter of HETP measured by different teams on the same packing can hide the separation efficiency improvements of newly developed packings. Ottenbacher et al.1 have recommended many improvements. We consider as the most relevant the use of the CB/EB (chlorbenzene/ethylbenzene) system instead of the C6/C7 (cyclohexane/n-heptane) system, since the HETP measured using the C6/C7 system depends to a greater extent on the concentration range in comparison with that measured using the CB/EB system, due to the larger variation of the relative volatility over the concentration range. The authors published a comprehensive list of physical and thermodynamic properties of the CB/EB system. For obtaining reliable efficiency values the authors also recommend the use of columns with a diameter of at least 0.4 m because the results from columns with smaller diameters are dominated by their wall effects. There are only a few studies in the literature that deal with the effects of the column diameter on pressure drop and the HETP. Random packings in columns with a smaller diameter achieve lesser pressure drops (Billet and Mackowiak2). The packing density close to the column wall (the number of packing pieces per unit volume) is lower in comparison to the © 2013 American Chemical Society

bulk and this results in a lower local pressure drop. In small columns, there is a comparatively higher proportion of gas or vapor channels along the walls which results in a lower pressure drop in comparison to columns with a wider diameter. The effect of the column diameter on pressure drops of structured packings was studied by Olujic.3 His results, presented here in Figure 1, show an opposite behavior: in columns with a smaller diameter the Montz B1−250 structured packing has shown substantially higher pressure drops in comparison with the drops measured in columns of a larger diameter. For example, the pressure drops in a column with a

Figure 1. Effect of column diameter on pressure drops in the air− water system. Data of Montz B1 250 are redrawn from Olujic.3 Received: Revised: Accepted: Published: 5967

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dependence of the pressure drop on the column diameter disappears. This limiting diameter is equal to 0.21 m for Mellapak 250Y. In accordance with this model,6 the pressure drop of dry packing in a column with a diameter 0.15 m is 15% greater than that in a column with a limiting diameter of 0.21 m. The independence of pressure drops and of the HETP of the column diameter is well documented by the data measured by Billet7 and Meier et al.8 using the CB/EB distillation system and Mellapak 250Y. The data measured7 in the small column with a diameter of 0.22 m coincided with those measured in the large column with a diameter of 1.0 m in regard to the range of the vapor capacity factor of 0.4−2.8 Pa0.5. These data are presented in Figure 8.17 of Billet’s book.7 A similar degree of consistency between the HETP measured in columns with diameters of 0.16, 0.25, and 1 m was found by Meier et al.8 The data in the literature led us to the conclusion that the recommendation to use the smallest 0.4 m diameter columns in order to obtain reliable data in regard to efficiency is not generally valid and should be analyzed in greater detail. First, the situations should be differentiated for when data are being measured for the design of large scale columns and when they are being measured for comparing the separation efficiency of the packings or for evaluating the effect of the geometric modifications on newly developed packings. The measurement of data using the large-scale columns is financially more demanding, and the data are more prone to error because of misdistribution and the nonuniformity of the flow profile through the packing. Either of these phenomena may cause a severe reduction in the separation efficiency and should be prevented during the packing test experiments. On the other hand the data from small scale columns may be dominated by the wall effects. The hydraulic wall effects are demonstrated by pressure drops. Olujic paper 3 is the only systematic experimental study dealing with the effect of the column diameter on pressure drops in structured packings. However the marked diameter effect revealed3 was not observed by other authors4,7 nor predicted by the available correlations5,6 (see also Sulcol). A similar systematic study dealing with the effect of the column diameter and concentration of the distillation mixture we did not find in literature at all. The aim of this study is to evaluate the effect of column diameter on pressure drops and on separation efficiency and the dependence of the effect on the concentration range of the distillation mixture used during the measuring.

diameter of 0.2 m are 3-times greater in comparison to those measured in a column with a diameter of 0.8 m. Olujic3 concluded that “A practical consequence of this observation is that predictions based on academic scale data can lead to grave overestimates in the pressure drop and consequently column diameter, when applied to industrial scale columns.” The recommendation to use columns with a diameter of at least 0.4 m for obtaining reliable data would make the equipment and its operation more expensive and might discriminate against academic research which is usually conducted in columns with smaller diameters. Nevertheless, the following survey of the literature shows that there is not another work which confirms such a profound effect of the column diameter onto the pressure drop or HETP. The pressure drops of the Montz B1 250 packing presented by Olujic3 are compared with those of the very similar Mellapak 250Y packing in Figure 1. These packings are of the same size and wettability of their surfaces by water and have the same corrugation angle. The diameter effect on the pressure drop of the Mellapak is described in the Sulcol software package provided by the supplier Sulzer for its own packings. It was deduced from experiments performed in columns of different diameters. Olujic’s data show three-times greater pressure drops in the column with a diameter of 0.2 m at Fv = 1 Pa0.5 than those measured in a 0.8 m diameter column, while the increase evaluated from the Sulcol is only 50% of that for the similar Mellapak 250Y packing. At low liquid flow rates (B < 10 m/h), well below the loading point, when the upwardly flowing gas does not hinder the downward flow of the liquid, the dry and wet pressure drops of the packing differ only slightly. For example, based on the data measured by Olujic,3 it makes only a maximum 15% difference in a column with d = 0.2 m and is negligible in a column with d = 0.8 m. Olujic’s data in regard to dry and wet packing are presented in Figure 1. The data for dry Mellapak 250Y measured by Stichlmair et al.4 in a column with a diameter of 0.3 m are compatible with those of the Sulcol software for d = 0.4 m. We present this data to illustrate the accuracy and reliability of this software. The models described in the literature also provide unambiguous results of the effect of the column diameter on the pressure drop of the structured packings. The models that are based2 on the difference between the packing density close the column wall and in comparison with the bulk also take into account the wall factor K, defined as follows5 2 Δp a F = λ 3 v K; H ε 2 1−ε de = 6 ap

K=1+

2 1 de ; 31−ε d

2. EXPERIMENTAL SECTION 2.1. Columns and the Data Utilized. Apart from our own measured data in Column 4, the data used are taken from the following reports: The pressure drop and the HETP measured on the Raschig Super-Pak 250 (RSP250), the Mellapak 250Y, and the Montz BSH 250 packings, employing the C6/C7 distillation system in columns of different sizes are presented. Within these reports the columns and the experimental and evaluation procedures are described in detail. We provide here the following basic information concerning the columns and the data utilized for this work. Column 1 FRI: Report “Test of RSP250” by Cai T.J., King D.W., June 15th, 2009. Report made available for the purposes of this study by Raschig. The data utilized: Fv, the pressure drop, xbottom, HETP. Conditions: p = 1.62 b; d = 1.22 m; H = 3.5 m.

(1)

On the basis of the large quantity of data in regard to various types of packings, Mackowiak5 recommends the value of K = 1 for structured packings, meaning that no effect of the column diameter is expected. The model created by Brunazzi and Paglianti,6 based on the losses resulting from changes in the gas flow direction that occur at the transitions between the packing elements, predicts some increase in the pressure drop in columns with smaller diameters operating at the same specific gas and liquid flow rates. This increase is proportional to the number of bends per unit of the packing height. If the column diameter is greater than the limiting diameter d = Hp/tg θ, the number of bends depends only on the element height and the 5968

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Column 2 FRI: Topical Report 108, 1990. Report made available for the purposes of this study by Montz. The data utilized: Fv, the pressure drop, xbottom, HETP, liquid concentration profile measured at positions z = 0, 0.81, 1.42, 2.03, 2.64, 3.25, 4.01 m. Conditions: p = 1.62 b; d = 1.22 m. Column 3 SRP: Report “Distillation Characteristics of the Raschig-Jaeger RSP 250 Structured Packing” by Seibert F., Perry M., Briggs S., Fair J., December 14, 2009. Report made available for the purposes of this study by Raschig. The data utilized: Fv, the pressure drop, xbottom, HETP. Conditions: p = 1.65 b; d = 0.43 m; H = 3.0 m. Column 4 our laboratory. p = 1.0 b; d = 0.15 m; H = 2.1 m. Sketch of the column and one of the internals are presented in Rejl et al.9 A description of this column follows. Column 4 was packed with 9 (RSP 250) or 10 (Mellapak 250Y) pcs of structured packing to a height of 2.1 m. Each of the packing units was equipped with two wall wipers that redirected the wall flow back into the packing. The small diameter of the column and the large number of wipers justify our assumption that the higher liquid flow close to the column wall is noticeably suppressed. An electrically heated reboiler equipped with an electric power regulator maintained constant reboiler duty for the batches of different composition. The volumetric reflux flow rate was measured to an accuracy of 0.001 L/min. A shower distributor with 25 openings (1472 holes/m2) was utilized. The column and the reboiler were thermally insulated. The heat-loss, evaluated from the temperature decrease of the hot water (90 °C) flowing through the column represented only 3% of the lowest reboiler duty utilized (8 kW). The column was provided with seven openings for placing thermistor and sampling devices at regular distances along the column for the withdrawal of liquid and vapor samples. The holes for this sampling were drilled through the structured packing using a water jet. We believe that the sampling points do not significantly affect the flow of phases in the packing since the volume of the holes affects only 3.3% of the packing volume and the pressure drop also differs undetectably between the drilled and undrilled packings (compare the empty and the full symbols, shown in Figure 2), for the undrilled and the drilled packings, respectively. 2.2. Pressure Drop Measuring Methods. Great attention has been given to the avoidance of all the possible causes of incorrect pressure drop measurements that have been thoroughly discussed by Cai and Resetarits.10 In the distillation column, the pressure tap consists of small holes with an inner diameter of 6 mm that are drilled into the column wall below and above the packing and are connected to a pressure transducer via independent tubes. To ensure that no vapor condensation occurs inside the lines, nitrogen was blown through both the lines connected to the pressure drop measurement device at extremely low flow rates eliminating any pressure drop in the lines. 2.3. HETP Measuring Methods. The HETP were measured under total reflux and evaluated on the basis of a number of theoretical stages Ntheor between the mole fractions of the light component in the liquid phase at the top and the bottom of the packed bed section H. Rigorous (stage-to-stage) calculation was used for this purpose. The equilibrium data of

Figure 2. Pressure drop and HETP of Raschig RSP 250 packing measured in C6/C7 distillation system. Filled and empty symbols are pressure drops of the packings with and without holes drilled for sampling of phases.

the C6/C7 distillation system were taken from Onken and Arlt11 and the HETP was calculated from the relation HETP =

H Ntheor

(2)

3. RESULTS 3.1. Effect of the Column Diameter on Pressure Drop and HETP in C6/C7 Distillation System. 3.1.1. Raschig Super-Pak RSP 250. The pressure drop and the HETP measured using the C6/C7 distillation system in the columns of the diameters 0.15, 0.43, and 1.22 m and at the pressures of 0.33, 1.0, and 1.65 bar are plotted in Figure 2 as a function of the gas capacity factor Fv. The pressure drops measured below the loading points in columns of different diameters and at different pressures vary only within the scatter of the experimental points. As can be expected, the highest value of the loading point, recognized as the point at which the slope of the pressure dependence on the Fv starts to increase, was found at the lowest pressure (0.33 b) and is equal to approximately 3.2 Pa0.5. The 2.5 Pa0.5 loading point found in the columns with larger diameters (0.43 and 1.22 m) at an elevated pressure of 1.65 b is consistent with the value at which the dependence curve of pressure drops starts to bend when measured in the small Column 4 of 0.15 m diameter at atmospheric pressure. The measuring of higher Fv-factors in Column 4 was restricted by the maximum output of the reflux pump. Therefore it is not possible to estimate a reliable value of the loading point in this column. The HETP measured in the different columns differ significantly, see Figure 2. The data measured in the same column with the same packing also differs. This is caused by a HETP dependence on the concentration range in which the measurement was made due to the significant variation of the relative volatility over the concentration range. In Figure 2, the concentration range is characterized in accordance with the bottom molar fraction of C6 and thereby the data measured at the same xbottom may still differ in accordance with whether they are determined in a short or a long column. The HETP 5969

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the bottom concentration from 0.20 to 0.75. The HETP dependence on xbottom ceases with concentrations higher than 0.5 as is shown by the data of the Montz packing. The HETP measured in these rich C6 mixtures fluctuates at around 0.46 m in the whole range of the Fv-factor utilized (from 0.5 to 2.1 Pa0.5). The effect of the packing height on the HETP can be assessed from the data provided by the Montz BSH 250 packing, measured at the same bottom concentration of 0.20− 0.26 using different packing heights, specifically 4 and 1.8 m. The HETP measured at the low packing height is ca. 0.34 m and is much lower than the HETP = 0.42 m measured at the higher packing height. Fitz et al.12 measured a somewhat lower HETP = 0.39 m for the Mellapak 250Y at the lower packing height of 3.5 m. 3.1.3. Concluding Remarks Concerning the Column Diameter Effect on Pressure Drops. The pressure drops presented here in regard to the RSP 250, Mellapak 250Y, and Montz BSH 250 packing and the C6/C7 distillation system measured at flow rates below the loading point in columns of different diameters (0.15−1.22 m) at total pressures (0.31− 1.65 b) show only small differences, far less than 15%, which indicate zero or an insignificant column diameter effect. 3.1.4. Concluding Remarks Concerning the Column Diameter Effect on the HETP. The effect of the column diameter on the HETP is difficult to evaluate from experiments carried out in columns with different packing heights and distillation mixtures with different concentrations, because the impact of both these conditions is more pronounced than is the potential effect of the column diameter. Nevertheless, the HETP measured in columns of widely different diameters, using distillation mixtures of approximately the same bottom concentration, did not show any significant column diameter effect that would support the recommendation1 to discount the data measured in the columns with diameters smaller than 0.4 m. For example, the HETP of the same Mellapak 250Y and Montz BSH 250 corrugated packings measured in Columns 4 and 2 of very different 1.22 and 0.15 m diameters differ only slightly (0.36 and 0.34 m, respectively) provided that the same low packing height 1.80 m and the bottom C6-concentration of 0.2 are used, as is shown in the data in Figure 3. A similar concordance exists between the data measured in Columns with xbottom higher than 0.5, in which the HETP dependence on xbottom has ceased (see Figure 4). Thanks to lower dependence of the HETP on the concentration range, as measured by the CB/EB distillation system, in comparison with the C6/C7 system (due to the

measured in lean cyclohexane mixtures are much lower than those measured in rich mixtures. In the short (H = 1.8 m) and the small diameter (d = 0.15 m) Column 4, the HETP increases sharply from 0.28 to 0.38 m with the bottom C6-concentration from 0.03 to 0.10. The HETP dependence on x bottom diminishes/ceases at concentrations higher than 0.32 in which the HETP values fluctuate at ca. 0.41 m in the whole range of the Fv-factor utilized (from 0.7 to 2.5 Pa0.5). The data measured in FRI Column 1 with H = 3.5 m and d = 1.22 m at low bottom concentrations of 0.10 to 0.12 lie in the 0.32−0.39 m interval and are somewhat higher (by 0.03 m approximately) than those measured in SRP Column 3 with a d = 0.43 m diameter. This small difference of the HETP may be the result of the lower packing height H = 3 m used in Column 3 in comparison with the 3.5 m used in FRI Column 1. 3.1.2. Mellapak 250Y and Montz BSH 250. Both these packings are of the same size and wettability of their surface. The pressure drop and the HETP measured in columns with diameters of 0.15 and 1.22 m at the pressures of 0.35, 1.0, and 1.65 bar are compared in Figure 3. Similarly as with RSP

Figure 3. Pressure drop and HETP of geometrically similar packings measured using the C6/C7 distillation system.

packing, the measured pressure drops below the loading points in the columns of the different diameters and at different pressures differ only in the scatter of the experimental points. Also the 2.4 Pa0.5 loading point identified in the column of greater diameter (1.22 m) is consistent with the value at which the pressure drop in the small column of 0.15 m diameter also starts to increase. The pressure drops measured below the loading points in these packings do not confirm the significant effect of the column diameter reported by Olujic.3 The HETP values measured on short packing depth (1.80 or 1.83 m) in columns of different diameters packed with Mellapak 250Y (d = 0.15 m) or Montz BSH 250 (d = 1.22 m) increase with bottom concentration in a similar manner as was revealed for the RSP in the short Column 4 (H = 1.8 m and d = 0.15 m). The HETP of the Mellapak increases from 0.3 to 0.43 m with an increase of the bottom C6-concentration from 0.03 to 0.68. Similarly, the HETP of the Montz evaluated for the short packing sections, in which ΔH = 1.83 m in Column 2, increases from 0.33 to 0.47 m with an increase of

Figure 4. HETP evaluated from short column sections heights of 1.9 ± 0.1 m plotted against C6-concentration at the bottom of the sections. 5970

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values of the xmean and the Ntheor,mean presented in the figure represent the arithmetic mean of the C6-concentrations and of the number of theoretical stages, or are measured at these points in all the experiments undertaken at the various Fv factors. The data show a steady increase in the HETP from 0.24 to 0.42 m with an increase in the packing depth from 0.76 to 4.01 m, and they have a tendency to increase further. If the HETPs were evaluated using the concentrations measured at the first sampling point located 0.76 m above the packing bottom (i.e., not from the sampling point situated below the packing), the resulting dependence of the HETP on the packing depth would have changed considerably as is shown in the upper part of Figure 6. Instead of a steady

lower variation of the relative volatility over the concentration range), the results produced by the CB/EB system are more definitive and therefore more convincing. For example, the independence of the HETP of Mellapak 250Y from the column diameter, using this system, was identified by Billet7 and Meier et al.8 The HETP measured by Billet7 in the 0.22 and 1 m diameter columns did not differ and was equal to 0.32 ± 0.01 m in the 0.4 to 2.8 Pa0.5 range of the vapor capacity factor. Meier et al.8 found a similar concordance between the HETP measured in columns with diameters of 0.16, 0.25, and 1 m at various pressures between 50 and 100 mbar and between 400 mbar and the value of the atmospheric pressure. This data did not depend on the packing heights that were used, that is, 1.4, 4.4, and 6.6 m. In contrast to the insignificant and rather incomprehensible effect of the column diameter, the effect of the concentration range in which the measurement was conducted is considerable. The HETP increases considerably with the increasing bottom concentration and the packing height, and this increase reaches up to 50% of the HETP value measured. For this reason, the effect of the concentration range is analyzed in more detail in the next section. 3.2. Analysis of the HETP Dependence on the Concentration Range Used. 3.2.1. The HETP Dependence on Bottom Concentration. The HETP evaluated for the short packing sections ΔH (Column 2, ΔH = 1.83−1.98 m; Column 4, ΔH = 1.80 m) is plotted in Figure 4 against the C6concentration at the bottom of the sections. In the small Column 4 (d = 0.15 m), the variation of xbottom was achieved utilizing different concentrations of the distillation mixture in the reboiler. In the large Column 2 (d = 1.22 m), the concentration profile was measured along the column and the HETP was evaluated between sample points remote from each other by 1.98, 1.83, and 1.83 m. The HETP increases linearly from 0.28 to 0.48 m with the increase of the xbottom from 0.02 to 0.75. The wide scatter of the data is caused by the inclusion of all the HETPs measured at various values of the Fv capacity factor. 3.2.2. The HETP Dependence on the Packing Height. The HETPs calculated from the concentration profiles measured in Column 2 are plotted in Figure 5 as a function of the packing

Figure 6. HETP calculated from concentration profiles plotted as a function of packing height taken from the first sampling points from the bottom (z = 3.25 m) and the top (z = 0.81 m) of the packing. Symbols are the same as in Figure 5.

increase, the HETPs are independent of the packing height. Similar behavior is shown by the HETP calculated at the first sampling point situated 0.81 m below the top of the packing; see the data plotted in the lower part of Figure 6. Only the HETPs calculated from the concentrations measured just below the packing are significantly lower. It seems that these concentrations are significantly undervalued. If these data are excluded from the evaluation, the HETP values fluctuate around a constant value. Similar behavior is shown by the HETP data presented in Figure 3 for Mellapak 250 Y as measured at a similarly high bottom concentration of 0.6. Apparently, the concentrations in the liquid that falls out of the packing may differ from those in the liquid at the bottom of the packing and their difference may create a significant part of an equilibrium stage. The evidence that these data are mistaken or are influenced by the end-effects is also supported by our further finding that the profiled method was not convergent, when these concentrations were taken into account for the evaluation of the concentration profiles. The end-effects may cause an erroneous appearance of an improvement in the performance of the packing. Therefore it is necessary to discount both the top and the bottom samples from the packing to obtain the correct HETP values reflecting only the improvements in the performance of the packing. 3.2.3. The Suitable Packing Height for the Measurement of the Packing Efficiency. Ottenbacher et al.1 recommend performing the measurement of the packing efficiency in a “large column comprising 15 to 20 theoretical stages (which industrial applications usually do contain); this is equivalent to a bed height of 4−6 m”. A packing height of 4 m represents approximately 10 theoretical stages of the C6/C7 distillation

Figure 5. HETP calculated for the sections ΔH of the packing taken from the bottom of the packing.

height. The heights were measured from the bottom of the packing to sampling points located at the heights of H = 0.76, 1.36, 1.98, 2.59, 3.20, and 4.01 m. The bottom concentrations were measured at a sampling point just below the packing, the head concentrations are those measured at the reflux and the remaining samples were withdrawn from the packing. The 5971

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system with the lowest concentration dependence of slope of equilibrium line m, for example, using the CB/EB distillation system rather than the C6/C7 system as recommended by Ottenbacher et al.,1 the second issue is hardly controllable. As shown in the relation 4 deduced from the basic principles of the interfacial mass transfer

system, and the further increase in the packing height dramatically augments the demands on the accuracy of the analytical method. For example, starting with a bottom C6concentration of 0.2 (the same concentration that was used in the testing of the Montz BSH 250 in Column 2), the concentration at the top of the 4 m packing, representing 10 stages, equals 0.985. In the next two stages, the C6concentrations would be 0.991 and 0.995. At such high concentrations, the experimental error of the C6-molar fraction 0.003 corresponds to one theoretical stage. In this case, the application of a packing height of more than 10 stages might lead to an unacceptable error of the HETP (>10%). A suitable packing height should be chosen in accordance with the distillation system utilized and with the accuracy of the analytical method used. 3.2.4. Comparison of the Shortcut and the Rigorous Evaluation Methods. The shortcut methods currently used for the evaluation of the HETP are based on the Fenske equation deduced for total reflux, a constant relative volatility α, and a constant molar overflow as shown in the formula

(

ln Ntheor =

xhead 1 − x bottom 1 − xhead x bottom

ln αave

);

αave =

⎛ 1 m ⎞ ln(m(uL /uV )) + HETP = uL⎜ ⎟ k Va ⎠ m(uL /uV ) − 1 ⎝ kLa

(4)

the HETP depends on the relative resistances concentrated in the individual phases. The local slope of equilibrium line m may affect considerably the role of resistances of individual phases. As a result, the HETPs measured by various distillation systems are variously sensitive/receptive to identifying an improvement of the mass transfer rate developed in one of the phases. For example, the improvement of the mass transfer coefficient achieved solely in the liquid phase is not detectable as an HETP value when measured using the distillation system with a controlling mass transfer resistance in the vapor phase. In addition, this situation is complicated by the fact that the relative resistance of the phases varies along the column height. This problem might be solved/avoided by comparison not only of the HETP values but also of the local volumetric mass transfer coefficients measured directly in the distillation columns at the same concentration and flow rates of the phases. For the determination of the coefficients, the profile method13−15 was recently developed. The method evaluates the coefficients from the concentration profiles measured along the distillation column. Presently, the physical consistency/ relevance of the evaluated coefficients is verified by comparing absorption and distillation mass transfer coefficients measured in a wetted-wall column. 3.4. Effect of the Concentration Range on the HETP Deduced from the Concentration Profiles. The concentration range in which the measurement was carried out is determined by the two following process parameters: the xbottom bottom concentration of the distillation mixture and the height H of the packing used. Their effects on the HETP measured in columns with different bottom concentrations and packing heights are quantified below for the data for Mellapak 250Y measured in Column 4 with the C6/C7 distillation system at reboiler duty of 16 kW which provides Fv = 2.05 Pa0.5 at a bottom concentration of 0.0428. The concentration profile shown in Figure 8 was obtained by the profile method applied

αheadαbottom (3)

The number of theoretical stages Ntheor evaluated using the shortcut method and the rigorous stage-to-stage method for the C6/C7 and CB/EB distillation systems are compared in Figure 7, in which their relative differences, calculated for several

Figure 7. Relative difference between number of theoretical stages calculated between xbottom and xtop by the Fenske eq 3 and by the rigorous stage-to-stage method.

values of xbottom, are plotted against xhead. The equilibrium data were taken from Onken and Arlt.11 The differences in terms of the CB/EB system are negligible (less than 0.03%) and, in terms of the C6/C7 system, are less than 2%. The linear interpolation used between zero and one equilibrium stage for an unlikely separation corresponding to less than one stage is really obscure and is probable the cause of the sinusoidal highlighted difference between the Fenske equation and the stage-to-stage calculation. The comparison shows that the shortcut method does not lead to any noticeable differences in the theoretical stages of either distillation system. 3.3. The Suitability of the HETP for the Objective Evaluation of Packing Efficiency. The two properties that preclude the HETP from providing a comprehensive comparison between different packings are (i) dependence on the concentration range within which the measurement was carried out and (ii) inability to identify and to distinguish mass transfer improvements achieved in the liquid and vapor phases. While the first issue can be minimized by using the distillation

Figure 8. Concentration profile obtained by the profile method at Fv = 2.05 Pa0.5 for various bottom concentrations of the distillation mixture. 5972

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values, that is, 15, 13, and 10 cm, with xbottom = 0.3. (iii) The conditions in which the effect of the concentration range and of an experimental concentration error on the measured value of the HETP is minimal are as follows: a packing height of 3 m and a bottom concentration of 0.2 C6-mol fraction.

onto the experimental data measured at four different bottom concentrations ranging from 0.0428 to 0.7088 at the same reboiler duty 16 kW. The method starts with the choice of the mass transfer correlation describing the dependence of the volumetric mass transfer coefficients on physical properties and phases velocities. Then, the front factors of the correlations are varied in a systematic way such that the predictions from the rate based simulation model are matched to experimental concentration profiles as closely as possible. The plug flow of both phases in the column is considered and the film model of the interfacial mass transfer is used in which the convective flow is taken into account. The profile method is described in detail by Linek et al.,13 Rejl et al.,9,14 and Valenz et al.15 For the sake of completeness, we have used two different mass transfer correlations, namely the RBF model published by Rocha et al.16,17 and the Delft model published by Olujic et al.,18 to show the effect of the choice of the mass transfer correlations on the results. The profiles obtained using the RBF and Delft model practically coincide, and their difference is not detectable in Figure 8 in which the calculated profiles are plotted together with the experimental data. The mean relative deviation between the calculated and the experimental concentrations is 3.9% for x-profiles and 2.4% for y-profiles. Using this profile, the dependence of the HETP on the bottom concentration and the packing height can be evaluated from eq 2 for H = z2 − z1 and the corresponding theoretical stages Ntheor are defined between the mole fractions xC6(z1) and xC6(z2) using rigorous stage-to-stage calculation. The dependence of the HETP on xbottom calculated for three packing heights H = 1.8, 3, and 4 m are presented in Figure 9. The

4. CONCLUSIONS The pressure drops of the RSP 250, Mellapak 250Y, and Montz BSH 250 packings, measured in columns of different diameters (0.15, 0.43, and 1.22 m), using the cyclohexane/n-heptane distillation system below the loading points do not show any differences that would indicate any significant column diameter effect. In contrast to the insignificant effect of the column diameter, the effect of the concentration range in which the measurement of the HETP was carried out is considerable. The HETP increases with an increase of the bottom concentration and the packing height, and this increase can reach up to 50%. The HETP of the different packings can be compared only if the concentration range along the packings to be compared is the same. This requirement is hard to fulfill but the HETP measured in approximately the same concentration range did not show any significant column diameter effect. The results presented do not support the recommendation of Ottenbacher et al.1 to use columns with a diameter of at least 0.4 m for obtaining significant efficiency values, since the use of smaller column diameters will result in measurements that are strongly influenced by wall effects.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The supports from RASCHIG GmbH and Grant Agency of Czech Republic through the project no. 13-01251S are gratefully acknowledged.

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Figure 9. Dependences of HETP onto the bottom concentration evaluated for three packing heights.

dependences are terminated when the value of xhead reaches 0.985 that is, the value above which an experimental error of the C6-molar fraction might lead to an unacceptable error in the HETP as discussed in section 3.2.3. The line calculated for the height of H = 1.8 m corresponds well with the experimental data presented in Figure 3 for Fv = 2 ± 0.1 Pa0.5. The results presented in Figure 9 illustrate the following findings: (i) At the same bottom concentration of the distillation mixture, the HETPs measured in the lower columns are higher than those measured in the higher columns. For example, the HETP values measured at xbottom = 0.1 in the columns with packing heights of 1.8, 3, and 4 m increase to 0.32, 0.35, and 0.37 m. (ii) The sensitivity of the HETP values to changes of the bottom concentration is greater at lower concentrations and at lower packing heights. This sensitivity is defined by the local slope of the curves shown in Figure 9. The slopes equal to 33, 31, and 25 cm for the packing heights of 1.8, 3, and 4 m with xbottom = 0.1 and are approximately half of these 5973

NOMENCLATURE a = effective mass transfer area, 1/m ap = packing geometrical area, 1/m B = superficial liquid velocity, m/h c = molar concentration of more volatile component in the bulk, kmol/m3 de = equivalent diameter, m d = column diameter, m FV = uV √ρV gas capacity factor, Pa1/2 H = packing height, m Hp = height of packing element, m ΔH = height of packing section, m HETP = height equivalent to a theoretical plate calculated from eq 2, m K = wall factor given by eq 1, kLa = liquid-side volumetric mass transfer coefficient, 1/s kVa = vapor-side volumetric mass transfer coefficient, 1/s m = slope of the equilibrium line, Ntheor = number of theoretical stages p = pressure, Pa Δp/H = pressure drop, Pa u = superficial velocity, m/s x = liquid phase molar fraction of more volatile component dx.doi.org/10.1021/ie302397q | Ind. Eng. Chem. Res. 2013, 52, 5967−5974

Industrial & Engineering Chemistry Research

Article

(18) (5) Olujič, Ž .; Kamerbeek, A. B.; de Graauw, J. A. Corrugation geometry based model for efficiency of structured distillation packing. Chem. Eng. Process. 1999, 38, 683.

z = column height coordinate taken from the top of the packing (z = 0), m Greek Symbols

α = relative volatility, ε = packing porosity, λ = resistance coefficient, θ = corrugation angle, deg Indexes

bottom = bottom of packing C6 = cyclohexane head = top of packing L = liquid phase V = vapor phase

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REFERENCES

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dx.doi.org/10.1021/ie302397q | Ind. Eng. Chem. Res. 2013, 52, 5967−5974