Chemical Engineering and Processing 38 (1999) 219224

Pressure drop of arranged packings with vertical walls

Nikolai Kolev *, Svetoslav NakovInstitute of Chemical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonche6 Str., Bl.103, 1113 Sofia, Bulgaria

Received 10 August 1998; accepted 25 January 1999

Abstract

Among the known types of packings, arranged packings with vertical walls have the lowest pressure drop for one transfer unitat comparable free volume as well as the highest efficiency at a given pressure drop. Reliable equations are derived for pressuredrop determination in industrial apparatuses filled with this kind of packing. The pressure drop is presented as a sum of twoterms-pressure drop (in the vertical channels) of the packing rows themselves and local pressure drop of the boundary sectionsbetween the rows. The experimental data for dry packing pressure drop, available in the literature and newly obtained, aredescribed by new equation with mean deviation of 9.3%. Equations for determination of wetted packings pressure drop up to theloading point and above it are obtained, too. The proposed equations can also be used to determine the loading point. 1999Elsevier Science S.A. All rights reserved.

Keywords: Packed columns; Arranged packings; Packing pressure drop; Loading point; Experiments

1. Introduction

Packings with vertical walls :PVW: belong to theoldest types of packing. As early as in 1880, prior to DrRaschig patent application, arranged ceramic ringswere applied in sulfuric acid manufacture [1]. Becauseof poor distribution of liquid phase over PVW, anadditional redistribution packing layer have to be in-stalled under the liquid phase distributor. When replacethe random packing of this layer with arranged packingspecially developed for this purpose [2,3] it becomespossible to increase liquid and gas superficial velocitiesto attain values typical for PVW. A comparison ofPVW with the most performant packings revealed thatPVW are superior in their lower pressure drop for amass transfer unit as well as in their higher masstransfer coefficient for similar pressure drop [46].

The existing equations for determination of pressuredrop were found to be inapplicable to the description ofthin wall PVW [7]. A possible reason is that they do notconsider the different effect of the free packing volumeon the pressure drop in the packing channels and onlocal pressure drop at the rows interface.

The present paper aims at deriving of more preciseequations for evaluation of pressure drop of packingswith vertical walls.

2. Pressure drop of dry packings

2.1. Present state

Dry packing pressure drop is to be known because itis used in the calculation of wetted packing pressuredrop.

Jonstone and Singh [8] suggested an equation de-scribing their own experimental data obtained with gridpackings. It is inapplicable to other packings since theequation includes only parameters typical for gridpackings-width, height, and number of packing boards.

Based on own experimental data for grid packingelements with jagged bottom edge, as well as on datafor arranged 505 mm Raschig rings, Zhavoronkov[9] has proposed the equation:

C0.784.25 de

(Fa:Fb)ReG0.375. (1)

The expression* Corresponding author.E-mail address: kolev@bas.bg (N. Kolev)

0255-2701:99:$ - see front matter 1999 Elsevier Science S.A. All rights reserved.

PII: S02 5 5 -2701 (99 )00009 -4

N. Kole6, S. Nako6 : Chemical Engineering and Processing 38 (1999) 219224220

4.25 de:h(Fa:Fb)1.37

ReG0.375

describes the local pressure drop between the packingrows. It is seen that when the term Fa:Fb is increased,the local pressure drop is reduced. According to Rammand Zakgeim [10], this effect has no theoreticalgrounds. Kolev [11] has shown that the pressure drop isreduced because the grid packing elements [9] havejagged bottom edges which has not been taken intoaccount in the determination of the term Fa:Fb. Theequation suggested by Jonstone and Singh [8] is free ofthis anomaly.

Ramm and Zakgeim [10] have suggested theequation:

Cl

1161.235o2

2.6o

deh

, (2)

where the friction coefficient l0.0075 for ceramicpackings. The calculations have revealed [11] that thesecond term in Eq. (2) becomes negative for o\0.905.Lewa [12,13] has suggested the equation:

DP0a(G2:rG), (3)

where G is the mass superficial velocity of the gasphase. The constant (depends on the nature of the gasand on the type and dimensions of the packing. Eqs. (2)and (3) do not account the effect of Reynolds numberand hence they are applicable only to very highReynolds number.

Two equations are reported In [11] derived on thebase of all experimental data for 29 PVW of differentshape and dimension, published until 1969:

C0.59 (h:de)0.5o3.13ReG0.266, (4)

C (37:ReG0.113ReG0.1) (h:de)0.51o3.42. (5)

A precise evaluation of two components of the totalpressure drop-pressure drop caused by friction andlocal pressure drop, was associated with computations,being rather heavy in 1969. On the other hand, experi-mental data were rather well described by Eqs. (4) and(5). For this reason, a further study on the separateconstituents of the total pressure drop was consideredto be inexpedient for the moment.

Our later study with thin wall packings [7] revealedthat the behavior of these new packings cannot bedescribed by Eqs. (4) and (5). In order to obtain asingle equation, able to predict the pressure drop ofarranged packings with vertical walls, it was necessaryto obtain additional experimental data including valuesof dimensionless parameters that have not been studiedtill now.

The geometric parameters of the new packings arelisted in Table 1.

The experiments were carried out in a column withrectangular cross section 224174 mm. Packing ele-

ments of the same size formed rows superimposed oneover the other. Pressure drop was measured with U-type differential manometer. Low values below 10 mmwater column were registered with a differentialmanometer equipped with optical system and micro-metric screw (precision 0.1 Pa).

2.2. New equation

Dry packing pressure drop DPo was presented as asum of two termspressure drop in the straight section(the rows) DPof and local pressure drops of the rowinterface DPol :

DPoDPofDPol. (6)

Similarly to a straight tube, Pof can be expressed by:

DPoflHde

w2r2o2

, (7)

where the friction coefficient l depends on Reynoldsnumber.

The local pressure drops in the packing Pol can bedescribed by the expression:

DPolzHh

w2r2o2

, (8)

where the local pressure drop coefficient (is a functionof the void fraction o, H:h accounts for the number oflocal pressure drops in a given height of the packing H.

Using the dimensionless pressure drop C Eq. (1)inEqs. (6)(8) and accounting for all considerationsstated above, it can be written:

Ckf h

de

1onklRem, (9)

where kf, kl, n and m are experimentally determinedconstants.

The experimental data listed in Table 1 were treatedin order to identify the corresponding values of theconstants. Eq. (9) takes the form:

C0.06 h

de

1o3.87Re0.64, (10)

The precision of these experimental constants at 95%statistical reliability is given below:

0.06090.0076; 7.0090.075; 3.890.37; 0.64

90.035.

Jonstone and Singh [8] results for grid packings in asquare column were not used in the determination ofthe constants in Eq. (10), since in ref. [8] there is noinformation about the packing void fraction. The voidfraction in [11] was calculated using the equation:

odt:(dsdt), (11)

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Table 1Pressure drop of arranged packing with vertical walls

Symbol Packing Element height h Specific surf. area aNo Inside diam. d Ref.Void fraction Equiv. diam. Material(m3 m3)(m2 m3) (dem)(m)(m)

C Rings 5050 0.052 0.0501 117 0.743 0.0254 Ceramic [11] Rings with across 0.050 0.050 190 0.6122 0.013 Ceramic [11] Honeycomb blocks 0.061 0.0203 151 0.764 0.02 Ceramic [11]

4 Honeycomb blocks 0.087 0.020 154 0.769 0.02 Ceramic [11]5 Honeycomb blocks 0.099 0.030 105 0.775 0.03 Ceramic [11]

Honeycomb blocks 0.235 0.0206 187 0.936 0.02 Plastic [7] Honeycomb blocks7 0.117 0.020 187 0.936 0.02 Plastic [7] Honeycomb blocks 0.058 0.0208 187 0.936 0.02 Plastic [7]

9 Honeycomb blocks 0.023 0.027 103 0.75 0.029 Ceramic new10 Honeycomb blocks 0.040 0.027 97.2 0.74 0.0306 Ceramic new

Honeycomb blocks 0.060 0.02711 96.4 0.75 0.0311 Ceramic new12 " Honeycomb blocks 0.021 0.020 166.6 0.733 0.0176 Ceramic New

Honeycomb blocks 0.040 0.02013 154 0.763 0.0198 Ceramic NewHoneycomb blocks 0.060 0.020 153 0.7514 0.0196 Ceramic New

Honeycomb blocks-injection [6]0.031 0.0188}0.0193 185.515 0.83 0.0179 Plasticmoduled

N. Kole6, S. Nako6 : Chemical Engineering and Processing 38 (1999) 219224222

where ds is the thickness of the grid boards and dt is thedistance between two neighboring boards. It is evidentthat the above equation is valid only when the length ofthe apparatus wall perpendicular to the grid boards isexactly divisible of the sum of ds and dt or when it ismany times higher than that sum. The power of o in Eq.(10) is rather high, which requires a precise determina-tion of o. Applying this equation to the data of Jon-stone and Singh [8], mean deviation of 32% wasregistered, all individual errors being negative exceptthat for four experimental points, i.e. in this caseEq.(10) predicts higher values than the experimentalones. For this reason the data of Jonstone and Singh [8]were not used in the determination of the constants inEq. (10).

Fig. 1 illustrates the comparison between calculatedand experimental values. The mean error of Eq. (10) is9.3%.

3. Pressure drop of wetted packings

Zhavoronkov et al. [14] have suggested a modelrepresenting the packing pressure drop as pressure dropof a tube. The wetted packing pressure drop under theloading point is described by a model similar to that fordry packing, just accounting for the reduced void frac-tion due to the liquid phase. The packing is regarded asa tube of irregular shape with a constant cross sectionalong its height. The following expression is derived:

DPDPo

(1A)3, (12)

where A represents the packing void fraction occupiedby the liquid phase or more precisely its influence on

the pressure drop. The same approach could be appliedconsidering that packing pressure drop is expressed bytwo terms-pressure drop of the straight channels andlocal pressure drops. Taking into account the effect ofthe void fraction on the local pressure drop (Eq. (10)) itcan be written:

DPDPof

(1A)3

DPol(1A)6.8

. (13)

Previous studies [7,11,15] have shown that Eq. (12) canbe applied to regimes over the loading point if the termA is presented as a sum of two constituents:

AAoDA, (14)

where Ao is the value of A below the loading point, Aoaccounts for the effect of the additional void fraction,occupied by the liquid phase retained in operationregimes above the loading point.

The gas velocity in the zones of local pressure dropsconsiderably exceeds the velocity in the straight chan-nels. Thus, the additional retention in the channelscould be neglected. Introducing DA in Eq. (13) it isobtained:

DPDPof

(1Ao)3

DPol(1AoDA)6.8

. (15)

Ao can be presented as a function of the followingparameters:

Ao f(L, mL, rL, h, a, g). (16)

Applying the dimensional analysis to the experimen-tal data for packings pressure drop below the loadingpoint and excluding the negligible terms, one can derivethe following expression for Ao :

Ao1.2ReL0.05FrL0.35. (17)

The precision of these experimental constants at 95%statistical reliability is given below:

1.290.24; 0.05090.22; 0.3590.017.

The mean error of Eq. (17) is 10.5%. Similarly, for DAit is obtained:

DA f(wo, L, rG, rL, de, h, g) (18)

DA0.8w o2

gde

0.6FrL0.5

LrLworG

0.6. (19)

The precision of these experimental constants at 95%statistical reliability is:

0.8090.15; 0.6090.17; 0.590.12; 0.690.25.

The mean error of Eq. (19) is 22.3%. This precision issatisfactory, because DA is only a correction of Ao.

Fig. 2 illustrates the comparison of experimentalpressure drop of wetted packings, both up to the load-ing point and above it, with the values calculatedthrough Eqs. (17) and (19).

Fig. 1. Comparison of experimental data for dry packings pressuredrop with results calculated by Eq. (10) (see Table 1 for symbols).

N. Kole6, S. Nako6 : Chemical Engineering and Processing 38 (1999) 219224 223

Fig. 2. Comparison of experimental data for wet packings pressuredrop below and above the loading point with results calculated Eqs.(17) and (19) (see Table 1 for symbols).

Fig. 3. Kh value as a function ofLrLworG

.

for all packings (see Table 1 for symbols).

If the friction losses are taken into account, thecalculated Kh value will be higher and will depend onthe ratio of friction losses and local pressure drop.

Fig. 3. represents Kh plotted versus the groupLrLworG

.

Kh values for all packings listed in Table 1 were calcu-lated using Eqs. (18)(20). Its average value is 1.10.Asit should be expected, packings with long channels andthin walls, i.e. packings with relatively lower localpressure drop as compared to friction losses, have thehighest values of Kh (see Fig. 3).

The experimental data fit fairly well to the linecalculated with Kh1.1. It proves that it is not neces-sary to account for the additional effects associatedwith the local pressure drop to friction loss ratio.

Acknowledgements

The financial support of the Bulgarian Fund forScientific Research is gratefully acknowledged.

Appendix A. Nomenclature

a specific surface of the packing (m1)effect of the part of the column freeAo

cross section occupied by the liquid onthe pressure drop, under the loadingpoint

diameter of the circle inscribed in thedpacking hole (m)

packing equivalent diameter,4oa

(m)deg gravity acceleration (m s2)h height of a packing element (m)

height of the packing layer (m)HFa maximum free section in the layer

(m2m2)Fb minimum free section in the contact field

between two neighboring rows(m2m2)

The proposed equations can be used to determine theloading point. It has been shown [11] that the loadingpoint can be defined as a point at which the term Kh

Kh1Ao

1 (AoDA), (20)

becomes noticeably different from 1. Determined on thebase of a great number of experimental loading points,the value of Kh appears to be 1.03 [11].

The value of Kh depends not only on experimentaldata but also on the relations used to estimate Ao andDA in Eq. (20). In ref. [11] Eq. (11) is used. Here thepower of (1A) is 3, while Eq. (20) is derived fromEq. (15), where the power in the expression for the localpressure drop is 6.8. In fact, the loading point is that atwhich the pressure drop calculated with account of DAdiffers considerably from the pressure drop calculatedwithout DA. In [11] DA is determined in a way to affectthe total pressure drop, while in Eq. (15) it affects onlythe local pressure drop. It is obvious that the value ofKh used in the proposed equation should exceed thevalue of Kh as determined in Eq. (11).

The lower limit of this value, supposing that thelosses caused by friction are negligible, can be obtainedhaving in mind that according to Eq. (12). Kh is a cuberoot of the ratio of the pressure drop calculated withaccount of DA and that without accounting for DA atthe point where DA begins to influence the pressuredrop. The power in the proposed Eq. (15) is 6.8 incontrast to 3 in ref. [11]. Then the lower limit of Khwill be:

1.036.8:31.0693.

N. Kole6, S. Nako6 : Chemical Engineering and Processing 38 (1999) 219224224

Kh defined in Eq. (20)L liquid phase superficial velocity (m s1)

gas phase superficial velocity (m s1)wwo gas velocity related to packing void frac-

tion (w:o, m s1)

Greek lettersincrease in Ao value over the loadingDA

pointDP wetted packing pressure drop (Pa)

dry packing pressure drop (Pa)DPoDPof pressure drop of the dry packing in the

straight section (Pa)local pressure drops in the packing (Pa)DPolcalculated data for the pressure dropDPcal

(Pa)DPexp experimental data for the pressure drop

(Pa)friction coefficientl

m dynamic viscosity (Pa s1)o void fraction (m3 m3)r density (kg m3)

local pressure drop coefficientjcalcalculated data for the friction factorCcal

equivalent to Euler numberCexp experimental data for the friction factor

equivalent to Euler number

Dimensionless numbers

ReGwederGmG

liquid phase Reynolds number

FrLL2a

gliquid phase Froude number

gas phase Reynolds numberReGwederGmG

ReL4LrLamL

liquid phase Reynolds number

dimensionless pressure dropCDPode

2HrGw o2

SubscriptsL liquid

gasG

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