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Modelling and measurement of gas flow distribution in corrugated sheet structured packings
The Chemical Engineering
Journal, 53 (1993) 55-66
55
Modelling and measurement of gas flow distribution in corrugated sheet structured packings F. Stoter, i?. Oh@*
and J. de Graauw
De@ University of Technology, Laboratory for Process Equipment,
Leeghwaterstraat 44, 2628 CA De@ (Netherlunds~
(Received January 11, 1993; in final form May 22, 1993)
Abstract
A mathematical model and calculation procedure are developed for the gas flow distribution in channels formed between tightly packed, corrugated, unperforated metal sheets. The model is a discrete cell model based on averaged mass, momentum and energy balance equations for each of numerous crossings of gas flow channels, with characteristic friction factors for gas inlet, bulk zone and wall zone as model parameters, which can be easily obtained from pressure drop measurements for each type and size of structured packing. The model enables prediction of velocity profiles leaving an element or packing layer consisting of segments of unperforated, structured packing. It is also suited for perforated packings which under operating (wetted) conditions function as a closed surface packing.
1. Introduction
It is a common belief that the gas distribution is more or less uniform in packed beds operating with a substantial pressure drop [ 11. Our large-scale experiments with a corrugated sheet structured packing gave the same impression [ 21. The lateral spreading of gas seems not to be affected by liquid within the normal operating range and common liquid loads. The extent of lateral spreading of tracer gas proved to be a function of gas load only and there was no large-scale n&distribution of gas observed during these tests. However, on the small scale, i.e. hydraulic diameter scale of gas flow channels,w&re all transport phenomena occur, the common assumption of a uniform gas distribution is a very rough approximation. In the literature [ 3-61 there are some results indicating that gas flows mainly along channels and that excessive bypassing along the walls can occur. There is no quantitative evidence available on mechanisms governing gas flow distribution and the interaction of crossing gas flows. Another important aspect is the effect of the packing surface design, the only distinction among many types of structured packings, which proved to be of major importance for liquid spread [7]. An accurate description of mass transfer in structured packings, which is the *Author to whom correspondence should be addressed.
0923-0467/93/$6.00
goal of an overall research programme, requires a detailed knowledge of gas flow behaviour in packed beds. The objective of this paper is to present a model for gas flow in structured packing elements consisting of corrugated sheets. The model parameters are deduced by fitting the computed velocity and pressure prollles to experimental ones. Gas-spreading and tracer-spreading experiments have been carried out with two types of corrugated sheet structured packings with completely different surface designs.
ultimate
2. A gas flow distribution
model
2.1. Structure of the packed bed A packed bed can be considered as a series of packing elements composed of vertically oriented, corrugated sheets (Fig. 1). Each subsequentelement is rotated by 90” with respect to the previous one, thus causing an abrupt change in fluid flow direction which ensures a large-scale radial distribution and mixing of both fluids throughout the bed. Structured packings are made of standard materials (metals and plastics) and are available in standardized surface-area-to-volume sixes. The surfaces of common packings differ considerably because they are roughened, perforated or enhanced in a/proprietary way to improve the wettability. A
0 1993 - Elsevier Sequoia. All rights reserved
F. Stoter et al. / Gas flow distribution
56
in structured packirqs
f
Surface design Ralu-pak YC
Montz-pak Bl
Fig. 2. Structure of interconnected cells (left) and corresponding channel configuration (right) of a corrugated sheet packing.
Fig. 1. Geometrical features of corrugated sheet structured packings: (a) packed bed comprising three packing elements; (b) basic structure of a packing element; (c) flow channel arrangement; (d) nature of surface of packing types considered in this study.
detailed description of surface characteristics of common corrugated sheet packings can be found in the book by Kister [ 81. Nevertheless, the basic geometry of packing elements is the same for all conventional packings. The angled corrugations of adjacent sheets are reversed with respect to each other. This forms a large number of gas flow channels. From Fig. l(c) it can be seen that the flow channel cross-section is triangular and that one (open) side of the channels consists of intersections with oppositely oriented channels of the adjacent sheet. Within the height of a packing element (usually around 200 mm) there are several intersections (corrugations) of gas flow channels. The number of these intersections per unit volume depends on the specific surface area of the packing and not on the column size, so that a model representing the basic packing structure can be used for both small and large diameter beds. The gas distribution model developed here is a discrete cell model with the structure used for the description of small-scale liquid distribution [ 9 1, with cell size and number corresponding to the specific surface size of packings considered. Figure 2 illustrates how the cells are interconnected to create the packing channels. Since the gas flow and pressure distribution are influencing each other, a complete description means writing and solving coupled mass, energy and momentum balances for each crossing of flow channels. Because of different geometries, a distinction is usually made between the bulk and wall zones of a packed bed. In this study, geometrical properties of the used experimental set-up (see next section) are taken as a basis
t
Fig. 3. Control volume for a crossing in the bulk of packing (left) and the associated channels (right).
for development and verification of the gas flow distribution model outlined in what follows. 2.2. The bulk zone The geometry of the flow channels between two corrugated sheets is such that a very complex flow pattern may exist. A typical flow channel may be considered as a series of connected intersections of channels. Therefore we have chosen to solve the integral balance over each crossing of channels. Figure 3 illustrates schematically this basic unit (control volume) of our cell model. Numbers 1 and 2 denote inlets and numbers 3 and 4 outlets of a crossing of gas flow channels (a block cell), while the dashed lines mark the interface where two flows contact each other (cross-flow contact interface). The mathematical model describing the gas flow distribution in one crossing cell can be summarized as follows. For steady state one-dimensional gas flow the mass balance is PAtu, +uz)=pA(u3
+%)
(1)
where p is the gas density, A is the flow channel cross-sectional area and u is the local gas velocity, with subscript numbers indicating the locations according to Fig. 3. The gas density is considered here to be constant, as is the cross-section of gas flow channels.
F. Stoter
The equations for the conservation of momentum with respect to a given control volume can be written as follows: y direction, Fy +A sin(ol)(P1-P3-P2+P4)
=pA sin(tr)(?&-u+ij+?g)
(2)
z direction, F'+A cos(cu>(P, -P3+P2-PJ =pA cos(cY)(t4J$-u;+u;-tg)
(3)
where F (N) is the acting force, indices z and y denote components of the force in the vertical and horizontal directions respectively, P is the pressure and a is the channel inclination angle. Since the loss of mechanical energy is caused by frictional resistance to flow, it is convenient to write an energy balance in terms of this loss:
;A(u;+u;-u+;) +A(uu,P,+uzPz-u3P3-uqP4)=Eloss
(4)
Eloss (W) is the sum of all mechanical energy losses per unit time caused by friction, which can be expressed as i=1,...4
E ,,,,=~;A&
in structured
et al. / Gas .jlow distribution
(5)
where 5 is an overall packing friction factor which stands for all friction losses involved. It can be easily obtained from pressure measurements for each type and size of structured packing. Since in the above five equations there are seven u.nlmowns, i.e. u3, u4, P,, P,, Efiiction, Fv and F,, two additional equations are needed to completely describe the problem. The y- and z-directed friction forces Fv and F, may be expressed as
F,=sin(a)(-Fl+F2--F3+F4)
(6)
F,=cos(cu)(-Fl--Fz-F3-F4)
(7)
packings
which gives the lowest energy losses per cell is chosen as a solution. 2.3. The wall zone Because of the pressure losses caused by bends and channel cross-section changes, the flow pattern in the wall zone is even more complex than that in the bulk zone. When the packing fits perfectly, there is no empty space between the wall and the periphery of the packing. This situation can be simulated by assuming total gas reflection action of the wall. However, a more realistic situation includes wiper bands around each element to avoid excessive liquid bypassing.A wall wiper band partly occupies the empty space between the packing periphery and the column wail. This situation can be simulated by partial gas flow reflection. Figure 4 illustrates schematically the situation without a wall wiper, represented in the form of two packing channels, one (1) reaching and one (4) leaving the wall zone cell with a constant crosssectional area. Subsequentwall cells form a vertical wall channel (2 and 3). Here the same balance equations can be used as in the case of the bulk zone, but the momentum balance equations differ somewhat: y direction,
Flf+ -I-&
(PI
+p,j=pA
i=l
,.--4
Fg and F, can now be written as functions of
w~x-u~
-a
(9)
z direction, F, +A-&‘:! =
PLl@~
-P3>
-
$1 + PA
cos(d(u;
-
UT>
(10)
Here F, isdefined analogously to a crossing cell in the bulk of the packing:
F,=sin(cu)(-F, +F4)-Fwau
(11)
For Fg we can write
FJY
/ ’ I ‘. \ /* \ \ --‘, ’ /
(3) Ui
(i=1,...4). By substituting eqns. (5)-(8) into eqns. (l)-(3) and some manipulations, we can express all the unknowns as a function of u4. Inserting this function of u4 into the energy balance (eqn. (4)) produces a polynomial of third order. The real value of u4
x
4 / ,- \ \
where
Fi=I~AuT,
57
/ ,<’
rgr
\
/
/
\ I3 /
; / ’ \ \ :
\ I
\ /
‘/
1 Fig. 4. Control volume for a crossing at the wall (left) and the associated channels (right).
F. Stoter et cd. / Gas Jibw distribution
58
F,=cos(cu)(-Fl-FJ+(--Fz-F,)
in structured packings
(12)
where Fw4 represents an additional wall zone friction force which can be calculated from the mean pressure in the wall channel and the wall area of the control volume: F wall
(pz +
p3)A
gas inlet
(13)
= sin(cY)
The friction forces Fl to F4 as used in eqns. (11) and (12) are calculated from eqn. (8) taking 5= &,,ti for channel inlet 1 and outlet 2 and J= ltiet for channel inlet 2 and outlet 3 to include pressure loss caused in bends and the wall zone respectively. A wall wiper can be simulated by a local reduction in the wall channel cross-section as shown in Fig. 5. From the continuity equation we can calculate the velocity change caused by the wall channel cross-section reduction and from the momentum balance we can calculate the corresponding pressure change. Referring to control volume 1 or 3 (Fig. 5) we have (14)
P wall-&per=~dll
(15)
The reduced wall channel cross-section is taken into account in the calculation over the wall-crossing block cell (compare control volume 2 in Fig. 5 with the control volume in Fig. 4). 2.4. Gas inlet The crossing what different zone. Such a
zone cells in the bottom layer are somefrom the cells in the bulk or wall cell can be considered as an inlet
L Fig. 6. Packing channels in the bottom associated gas inlet compartment.
channel with two outlets (Y-junction). This means that two adjacent channels are fed by the same inlet compartment (Fig. 6) and thus have equal inlet pressure. Since the inlet flow has no horizontal component in the y direction, the horizontal momentum of the inlet flow of a channel is assumed to have a zero value. The corresponding balance equation is (y direction) Fy -A
sin(a)( -P3 +PJ =pA sin(a)(g -u;)
(16)
Fy is simply the sum of the components F4) of the acting friction force:
(F3 and
Fg = sin(a)( - F3 + F4)
(fight).
(17)
Friction forces F3 and F4 are calculated by eqn. (8) using the corresponding inlet zone friction factor (5= !Ll13* 2.5. The calculation procedure The gas flow field in the packing is obtained iteratively by successive substitutions of the outlet pressures of the crossing cells (P3 and P4), beginning from the bottom layer and going upwards, layer by layer, until the top layer of packing is reached. The input values are the given inlet flow rates entering the cells in the bottom layer and the pressure at the top of a packing element. The algorithm is shown in Fig. 7. Since the convergence proved to be rather unstable in the case of non-uniform initial velocity profiles, a convergence damping factor (c=O-1) is used to produce new values for cell pressures and velocities. 3. Experimental
Fig. 5. Control volumes for a crossing at the wall with a crosssection reduction (wall wiper) (left) and the associated channels
layer of cells and the
details
The two packings investigated here are of common corrugated metal sheet type with a surface area of
F. Stoter et cd. / Gas J%W distribuhn
in structured packings
I- Corrugated
59
packing sheet
I
cell pressure 1086 factors Inflows and Poti,
Distributor for all the cells in the Ioyer n = I u,i,i:f(inflow.P,ini_,)
-I
4
for all cells in layer n u,i,,=(l-df) “,.,,,,+df Pn,,i=(l-df)P.+,i.,.,+df
I ,
“nini-, P.wii.,
for 011cells I” Ioyer ” un,ti~f~unin,.P”nin,-ll P..i=f(u.,t,.unini.Pno,i)
I
1 2 3
5 6 7
9 10 11 12 13 1L 15 16 17
i
‘-2_ mxtswe*p i=i*l
Fig. 7. Algorithm for the calculation of the gas velocity profile leaving a packing element consisting of unperforated corrugated sheets.
250 m2rne3.However, with respect to surface design these packings represent two extremes (see the sketch in Fig. l(d)). The surface of MONTZ-PAK Bl-250 (Montz-pak) can be characterized as a shallow embossed one without any perforations (“closed surface packing”). The surface of RALU-PAK 250 YC (Rahr-pak) can be characterized as a slightly open jalousie-like one with slits lying close together. The slits change row-wise and are exposed to gas flow on one side of the channel only. The openings of the slits on the other channel wall face downwardly flowing liquid, so that this packing is highly permeable to both phases. Having in mind numerous narrowly spaced slits along a channel, we speak of an “open surface packing”. The gas distribution properties of these packings were investigated using the simple piece of equipment shown schematically in Fig. 8(a). The main part of the equipment is an open frame into which one or more packing sheets with a length of 0.5 m and a height of 0.2 m can be inserted. At the bottom there are 17 compartments each equipped with a separate gas feed line. The two outside compartments are considered as the left-hand and right-hand-sidewall compartments respectively. The top-side outlets of these compartments are the corresponding wall channels, so that 15 inlet com-
(cl no wall cnanncl
wall channel
wall channel with wl!~r
Fig. 8. Schematic representation of: (a) the experimental setup used in this study, with 15 gas inlet compartments below two or four tightly packed corrugated sheets, each with 17 flow channels; (b) the relationship between inlet compartments and outlet channels; (c) the three wall zone arrangements investigated in this study.
partments which correspond precisely to the width of a packing element (0.5 m) actually feed 17 outlet channels. The enlarged detail shown in Fig. S(b) ilhrstrates the relationship between inlet compartments and outlet channels.The front-side corrugated sheet has the channels oriented to the right-hand side and the back one to the left-hand side. We measured both the inlet flow rate and the air pressure for each compartment. Directly above the packing we measured the concentration of tracer gas (CO,) and/or the outlet velocity of each air stream leaving a channel. For the latter purpose a specially designed micro-Pit& tube was used. Thanks to its construction, this tube also enabled the de-
60
F. Stoter et al. / Gas Jaw distribution
termination of the direction and static pressure of the outlet air flows. With Montz-pak, i.e. the closed surface packing, two sheets were sufficient to create the characteristic crossing gas flow channel structure. The air was simply introduced between the two sheets. To avoid wall flow, we -first did some tests with a configuration in which the packing fitted perfectly so that there was no open space between the wall and the end of the packing channels. The influence of the initial maldistribution was investigated using point sources introduced at various locations (channel inlets). To investigate in more detail the behaviour of the wall flow, we did some tests with an open space between the outside boundary of the packing and the wall. The influence of wall wipers was simulated physically by introducing an obstacle in the wall channel at a distance of 80 mm from the top of the packing sheets. The three different wall configurations investigated are illustrated schematically in Fig. 8(c). To create a representative channel geometry for Ralu-pak, i.e. to enable a smooth communication between the two sides of the packing sheets, we used four packing sheets fitting perfectly to the side walls. The outside face of the two outer sheets was closed to prevent air escaping into the surroundings. In this case the inlet gas entered three parallel planes of flow channels. Because of the gas inlet location, some initial gas maldistribution could not be avoided during these experiments.
4. Results
in structured
packings
"G
= 2.4 m/s
Outlet channels Fig. 9. Measured gas tracer distributions between two sheets of Montz-pak (tracer was introduced in channel 9 with a righthand upward orientation), with and without presence of countercurrently flowing water.
i
*
8 Measurement
O a
UG= 2.4 m/s
Calculation
UL = 0
and discussion
The influence of the nature of the packing surface will be illustrated and discussed tist. Then the velocity and pressure distribution measurement and simulation results for closed surface packing will be evaluated. 4.1. Tracer distribution pro$les The tracer distribution tests were carried out with Montz-pak and Ralu-pak under the same conditions of perfectly fitting packing, with and without the presence of countercurrently flowing water. In all tests the gas velocity profile was uniform and the tracer gas (CO,) was injected into the inlet of channel 16 (the front plate, with channels oriented to the right-hand side), which has its inlet in compartment 9 (see Fig. 8). Figure 9 shows the outlet tracer concentration profiles obtained with Montz-pak fitting perfectly to the walls. Obviously there is no effect of the counterflow of the liquid phase. In both cases the peak appears in channel 16 where the tracer was introduced. This indicates a pro-
Outlet
channels
Fig. 10. Comparison of measured distribution profiles for Montz-pak.
and calculated
gas tracer
nounced channel flow of gas. However, the presence of tracer in the central part of the left-hand-side channels indicates the existence of a certain amount of mixing of gas flows at 12 crossing interfaces along a channel. Simulation with a cell-splitting factor of 0.15 resulted in a fairly good reproduction of tracer concentration profile curves (Fig. 10). It should be noted that the profiles shown in Fig. 10 were measured with open wall channels. From a comparison with the profiles obtained with perfectly fitting packing (Fig. 9) it is obvious that possible wall flow (bypassing) does not affect the distribution of a centrally introduced tracer gas. On the other hand, the presence of a left-handside peak in profiles obtained during tests with Ralupak (Fig. 11) fitting perfectly to the walls suggests some inlet maldistribution of tracer gas as well as a smaller mixing effect of crossing flows; namely,
F. Stoter et al. / Gas jbw distributiun in structured packings
61
of structured packings with a more or less open surface. This means that the predictions of the model developed basically for closed surface packing may be valid for open surface packings at increased liquid loads.
2
4
6 Outlet
8
10
12
14
1
channels
Fig. 11. Measured gas tracer distribution profiles for Ralu-pak, with and without presence of liquid flow.
4.2. Velocity and pressure distribution proj2.e.s The outlet velocity profiles and inlet pressure profile corresponding to the situation shown in Fig. 11 (Ralu-pak, no liquid) are given in Fig. 13, where “right” and “left” refer to the channel orientations. The profiles were measured by placing the Pitot tube at the outlet of the respective channel on the front or back corrugated sheet. The difference in the level of left- and right-hand channel velocities measured at the top of the corrugated sheets is largely due to unequal initial gas distribution; however, the velocity proties can be considered as flat (within f 10%). Figure 14 shows the velocity and pressure distributions measured with Montz-pak for perfectly fitting packing obtained with a uniform initial gas profile. We can see that the outlet velocity distribution is almost flat. There is only a small disturbance near the wall. If we look at the pressure distribution at the bottom, we can see that the pressure measured
A Fig.
12. Gas flow (“slit flow”)
direction
for R.&I-pak.
a certain amount of injected tracer passes through slits into neighbouring channels, i.e. into a gas stream with a flow oriented to the left-hand side. A striking observation is the more central location of the peaks, which, as expected [6], indicates a smaller angle of gas flow with the vertical axis than in the case of closed surface packing (Montz-pak). As illustrated in Fig. 12, this means a deviation from channel flow, i.e. a smaller angle of flow with respect to the vertical axis. Another interesting observation with this packing is the changing nature of the gas flow under wet conditions. If we look at the profiles obtained with countercurrently flowing water (Fig. ll), we see that the tracer distribution profiles become similar to those obtained with closed surface packing. Since the liquid also makes use of slits as it flows down the packing [ 71, it plugs the slits and promotes a more pronounced channel flow of the gas phase. Similar behaviour can be expected from other types
Fig. 13. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two central sheets of Ralupak without wall channels, resulting from a uniform initial velocity profile (2.4 m s-l).
62
F. Stoter
et al. / Gas _f%m distribution
in structured
packings
Fig. 14. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two sheets of Montz-pak without wall channels, resulting from a uniform initial velocity profile (2.8 m s-l).
4.2. I. Interface effects Figure 15 shows the simuIated velocity distribution at the top and the simulated pressure distribution at the bottom. The simulations were carried out with a cell friction factor of 0.32 and an entrance loss factor of 1.O. The latter accounts for the pressure loss due to the large cross-section reduction at the entrance of the packing channels (Fig. 6). With these values an overall packing element friction factor of 1.l was obtained, which is equal to that obtained for a similar type of structured packing by Zogg [ 31. For the simulation of the wa.ll zone effects with perfectly fitting packing (gas is reflected by the wall, i.e. it makes a 90” bend before reentering the packing) the corresponding friction factor was assumed to be twice that for the bulk zone. In order to quantify the interaction of crossing gas flows at the interfaces within a packing element, we inserted a smooth thin plate between the two corrugated sheets. In this way a purely triangular cross-sectional area channel flow was created. The resulting flow profile shown in Fig. 16 is obviously similar to that obtained with the open channel structure (Fig. 14). Comparison of the measured inlet pressure profiles (Fig. 16 us Fig. 14) indicates a considerably lower value of the pressure drop in the case of closed channel flow, i.e. with a plate
in the compartments which feed a channel that ends at the wall is slightly higher. This is due to the additional pressure drop caused by a 90” turn in gas flow [3]. The measured (static) pressure distribution profile at the top of the packing was flat for all measurements. The measured outlet direction of the gas flow confirms that the gas flows in the channel direction (45”). This is in agreement with the observation of Stikkelman et al. [ 6 1. Comparison of the inlet pressure shown in Fig. 14 with that for Ralu-pak (Fig. 13) indicates a considerable difference in the dry pressure drop of these packings. With a correction for the difference in superficial velocities of the compared profiles, we found that the pressure drop for Ralu-pak is almost 30% lower than that of Montz-pak. Comparison with the pressure drop curves published by the manufacturers of these packings, which indicate a 25% difference, confirms this observation. The explanation for the lower pressure drop of Ralupak can be found in the more vertically oriented flow due to completely porous channel walls (Fig. 12).
Fig. 15. Simulation
-
right
results for the situation
shown in Fig. 14.
I?
Stoter et al. / Gas flow
distribution
in
structured packings
63
channel
__)
compartment
Fig. 16. Measured outlet velocity and inlet pressure profiles for the situation with a smooth plate inserted between two corrugated sheets of Montz-pak.
inserted between the corrugated sheets.With respect to the normal situation this means approximately a 50% lower value of the overall friction factor. The explanation can be found in the fact that the insertion of a smooth plate eliminated the influence of rather rough corrugation ridges and the friction between two crossing flows. A lower value of the friction factor also results in a decrease in the amount of wall flow. The corresponding simulation results are shown in F’ig. 17. This observation indicates that it is possible to increase the nominal surface area within a given packing volume without increasing the dry pressure drop. This could be of advantage in the design of packing used .as catalyst supports in some heterogeneous gas phase reaction applications [9, lo]. 4.22. Wall channel effects The velocity and pressure distribution experiment with Monk+pak (Fig. 14) has been repeated with a 10 mm spacing between the packing and the walls. This open space created wall channels with a cross-section twice that of the triangular gas flow channels. Compartments 1 and 17, situated below the wall channels,were closed to avoid direct feeding of the wall channels. The velocity profile measured at the top and the pressure profile measured at the bottom are shown in Fig. 18. From the velocity
Fig. 17. Simulation
50
left
@J-
g
30-
B k
-----C
shown in Fig.
16.
right
,
g
e g
results for the situation
‘..
20lo- n
1
01
I-
>
5”““‘“““““~;~~~~
compartment Fig. 18. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two sheets of Montz-pak with wall channels, resulting from a uniform initial velocity profile (2.4 m s-‘).
F. Stoter et al. / Gas flow distribution
64
profile it is clear that only part of the gas that reaches the wall flows back into the packing. The low velocity measured for channel 6 indicates that this is more pronounced for the bottom than other layers; namely, the gas flow leaving channel 6 is formed via wall reflection of the gas flow which enters the left-hand-oriented channel 2 (a very short channel). The low pressure at the bottom of the wall channel is a consequence of the absence of entrance effects (no inflow in the wall compartment) and causes a positive pressure gradient towards the wall, which results in gas transport in the wall direction. Comparison of the measured profiles with the simulated profiles (Fig. 19) for the velocity distribution at the top and the pressure distribution at the bottom respectively indicates good agreement obtained by using the same value of the friction factor for the wall channel and the channels in the bulk of the packing. The influence of a wall wiper on the gas flow was investigated by inserting a restriction in the wall channel at a distance of 80 mm from the top, which reduced the wall channel cross-section locally to 10%. Figure 20 shows the velocity profiles measured at the top of the packing and the pressure profile measured at the bottom of the packing. Comparison with the velocity profile obtained without the wall wiper (Fig. 20 vs Fig. 18) suggests two differences. Firstly, channels 3 and 14, which
channel Fig.
19. Simulation
results
for the situation
shown in Fig. 18.
in structured packings
----Q-
left
-----t-
right
““I
Fig. 20. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two sheets of Montz-pak with wall channels equipped with a wall wiper, resulting from a uniform initial velocity profile (2.4 m s-l).
have their inlets directly below the restrictions, exhibit local maxima. The pressure just below the restriction is so high that the gas is forced to flow back into the packing. Secondly, we see that the velocities measured in channels 3-14 are higher than is the case without the wall channel restriction. Obviously, the wall restriction causes an increased pressure in the whole section below the restriction. This means that a larger part of the gas flow that reaches the wall is forced to flow back into the packing. Because of the lowest pressure at the top, the wall channel sucks the air out of the packing, which results in very low velocities in channels l-3 and 14-l 7. The simulation results shown in Fig. 21 do not differ much from the measured ones. 4.2.3. Initial gas muldtittibutim effect To investigate the response of the packing to a severe initial maldistribution, we introduced a point source in the left-hand wall compartment (compartment 2). These tests have been performed with the packing fitting perfectly to the wall (no wall channel). If we look at the velocity profile (Fig. 22), it is clear that channels 7 and 8, where the gas goes upon reflection from the wall, exhibit peak velocities. An interesting point here is the presence
F. Stoter et cd. / Gas jbw
distriinhm
in structured packings
-
Fig.
21. Simulation results for the situation shown in Fig. 20.
Fig.
65
right
23. Simulation results for the situation shown in Fig. 22.
.
of gas in channels 9-17, which is obviously an attestation of horizontal gas transport towards the right. This is confirmed by the pressure profile (Pig. 22), which indicates the presence of a positive pressure gradient oriented towards the right-hand side. Figure 23 shows the simulated velocity and pressure prohles for this situation. If we compare the measurements with the simulations, we may say that the location of the peak is predicted fairly well by the model. channel
I-
left
it
right
1 6. Concluding
Fig. 22. Measured outlet velocities in left- and right-hand upward
directions and inlet pressures for two sheets Montz-pak fitting perfectly to the walls, resulting from a point source introduction of gas into the left-hand-side wall compartment
remarks
Packings with unperforated, tightly packed, corrugated sheets cause a pronounced channel flow of gas. A uniform initial distribution deteriorates only slightly within the height of a packing element. The packing with the open surface exhibits a more vertically oriented gas flow. However, under wet conditions the liquid plugs the slits of this packing to some extent, thus creating a more closed-surfacelike gas distribution. Because of the large-scale static mixing effect of a bed, the usual assumption of plug flow of gas in packed beds consisting of corrugated sheets with closed and open surfaces appears to be justified.
66
F. Stoter et al. / Gas Jbw
distribution
Inserting a flat plate between the corrugated sheets of the closed surface packing resulted in a lower dry pressure drop, indicating a substantial amount of inter-facial friction of gas flows at crossing interfaces of gas flow channels. On the other hand, the elimination of inter-facial friction through insertion of flat plates between corrugated sheets means a substantial enlargement of the surface area per unit volume. An investigation of the potential of this modification in the design of elements of structured packing is in progress in our laboratory. The agreement achieved between experiment and calculation emphasizes the applicability of the discrete cell approach to modelling of the gas flow distribution in packed beds consisting of corrugated sheet packings. This gas distribution model is being further developed as a tool for predicting the effects of gas maldistribution in industrial-scale columns.
Acknowledgments We are indebted to J. Montz GmbH and Raschig GmbH for providing the packing material used in this study.
in stru&ured packings
3 M. Zogg, Striimungs- und Stofaustauschuntersuchungen an der Sulzer-Gewebepackung, Dissertation No. 4886, ETH, Zurich, Hans Schellenberg, Wmterthur, 1972. 4 R.M. Stikkehnan and J.A. Wesselingh, IEChE Symp. Ser., 104 (1987) B155. 5 R.J. Kouri and J.J. Sohlo, IEChE Sgmp. SW., 104 (1987) B193. 6 R.M. Stikkelman, J. de Graauw, 8. OlujiC, H. Teeuw and J.A. Wesselingh, Chem. Eng. Technol., 12 (1989) 445. 7 F. Stoter, Z. OlujiC and J. de Graauw, AlChEAnnuulMeeting, Chicago, I990, paper no. 199c. 8 H.Kister,D&iUatianDesfgn, McGraw-Hill,NewYork, 1992, pp. 448-463. 9 J.L. De Garmo, V.N. Parulekar and V. Piqjala, Chem. Eng. Prog., 88{3) (1992) 43. 10 J.P. Stringaro and J. Luder, Chem. Plants Process., 25 (1992) 6.
Appendix A: Nomenclature gas flow channel cross-sectional
A E F P u Greek ff
5 P
mechanical energy (friction) acting force pressure superficial gas velocity
area losses
letters channel inclination angle overall friction factor density of gas phase
subscripts
References
referring to referring to referring to n referring to wall coordinates z, Y I, 3, 3, 4 referring to i
inlet
1 Z. Olujic? and J. de Graauw, Chem. Biochem. Eng. 6?., 3 (1989) 181. 2 2. Ohrjic, F. Stoter and J. de Graauw, Gas Sepor. PUT-$, 5 (1991) 59.
ith channel inlet or outlet gas inlet compartment nth cell layer wall channel channel inlet or outlet
Journal, 53 (1993) 55-66
55
Modelling and measurement of gas flow distribution in corrugated sheet structured packings F. Stoter, i?. Oh@*
and J. de Graauw
De@ University of Technology, Laboratory for Process Equipment,
Leeghwaterstraat 44, 2628 CA De@ (Netherlunds~
(Received January 11, 1993; in final form May 22, 1993)
Abstract
A mathematical model and calculation procedure are developed for the gas flow distribution in channels formed between tightly packed, corrugated, unperforated metal sheets. The model is a discrete cell model based on averaged mass, momentum and energy balance equations for each of numerous crossings of gas flow channels, with characteristic friction factors for gas inlet, bulk zone and wall zone as model parameters, which can be easily obtained from pressure drop measurements for each type and size of structured packing. The model enables prediction of velocity profiles leaving an element or packing layer consisting of segments of unperforated, structured packing. It is also suited for perforated packings which under operating (wetted) conditions function as a closed surface packing.
1. Introduction
It is a common belief that the gas distribution is more or less uniform in packed beds operating with a substantial pressure drop [ 11. Our large-scale experiments with a corrugated sheet structured packing gave the same impression [ 21. The lateral spreading of gas seems not to be affected by liquid within the normal operating range and common liquid loads. The extent of lateral spreading of tracer gas proved to be a function of gas load only and there was no large-scale n&distribution of gas observed during these tests. However, on the small scale, i.e. hydraulic diameter scale of gas flow channels,w&re all transport phenomena occur, the common assumption of a uniform gas distribution is a very rough approximation. In the literature [ 3-61 there are some results indicating that gas flows mainly along channels and that excessive bypassing along the walls can occur. There is no quantitative evidence available on mechanisms governing gas flow distribution and the interaction of crossing gas flows. Another important aspect is the effect of the packing surface design, the only distinction among many types of structured packings, which proved to be of major importance for liquid spread [7]. An accurate description of mass transfer in structured packings, which is the *Author to whom correspondence should be addressed.
0923-0467/93/$6.00
goal of an overall research programme, requires a detailed knowledge of gas flow behaviour in packed beds. The objective of this paper is to present a model for gas flow in structured packing elements consisting of corrugated sheets. The model parameters are deduced by fitting the computed velocity and pressure prollles to experimental ones. Gas-spreading and tracer-spreading experiments have been carried out with two types of corrugated sheet structured packings with completely different surface designs.
ultimate
2. A gas flow distribution
model
2.1. Structure of the packed bed A packed bed can be considered as a series of packing elements composed of vertically oriented, corrugated sheets (Fig. 1). Each subsequentelement is rotated by 90” with respect to the previous one, thus causing an abrupt change in fluid flow direction which ensures a large-scale radial distribution and mixing of both fluids throughout the bed. Structured packings are made of standard materials (metals and plastics) and are available in standardized surface-area-to-volume sixes. The surfaces of common packings differ considerably because they are roughened, perforated or enhanced in a/proprietary way to improve the wettability. A
0 1993 - Elsevier Sequoia. All rights reserved
F. Stoter et al. / Gas flow distribution
56
in structured packirqs
f
Surface design Ralu-pak YC
Montz-pak Bl
Fig. 2. Structure of interconnected cells (left) and corresponding channel configuration (right) of a corrugated sheet packing.
Fig. 1. Geometrical features of corrugated sheet structured packings: (a) packed bed comprising three packing elements; (b) basic structure of a packing element; (c) flow channel arrangement; (d) nature of surface of packing types considered in this study.
detailed description of surface characteristics of common corrugated sheet packings can be found in the book by Kister [ 81. Nevertheless, the basic geometry of packing elements is the same for all conventional packings. The angled corrugations of adjacent sheets are reversed with respect to each other. This forms a large number of gas flow channels. From Fig. l(c) it can be seen that the flow channel cross-section is triangular and that one (open) side of the channels consists of intersections with oppositely oriented channels of the adjacent sheet. Within the height of a packing element (usually around 200 mm) there are several intersections (corrugations) of gas flow channels. The number of these intersections per unit volume depends on the specific surface area of the packing and not on the column size, so that a model representing the basic packing structure can be used for both small and large diameter beds. The gas distribution model developed here is a discrete cell model with the structure used for the description of small-scale liquid distribution [ 9 1, with cell size and number corresponding to the specific surface size of packings considered. Figure 2 illustrates how the cells are interconnected to create the packing channels. Since the gas flow and pressure distribution are influencing each other, a complete description means writing and solving coupled mass, energy and momentum balances for each crossing of flow channels. Because of different geometries, a distinction is usually made between the bulk and wall zones of a packed bed. In this study, geometrical properties of the used experimental set-up (see next section) are taken as a basis
t
Fig. 3. Control volume for a crossing in the bulk of packing (left) and the associated channels (right).
for development and verification of the gas flow distribution model outlined in what follows. 2.2. The bulk zone The geometry of the flow channels between two corrugated sheets is such that a very complex flow pattern may exist. A typical flow channel may be considered as a series of connected intersections of channels. Therefore we have chosen to solve the integral balance over each crossing of channels. Figure 3 illustrates schematically this basic unit (control volume) of our cell model. Numbers 1 and 2 denote inlets and numbers 3 and 4 outlets of a crossing of gas flow channels (a block cell), while the dashed lines mark the interface where two flows contact each other (cross-flow contact interface). The mathematical model describing the gas flow distribution in one crossing cell can be summarized as follows. For steady state one-dimensional gas flow the mass balance is PAtu, +uz)=pA(u3
+%)
(1)
where p is the gas density, A is the flow channel cross-sectional area and u is the local gas velocity, with subscript numbers indicating the locations according to Fig. 3. The gas density is considered here to be constant, as is the cross-section of gas flow channels.
F. Stoter
The equations for the conservation of momentum with respect to a given control volume can be written as follows: y direction, Fy +A sin(ol)(P1-P3-P2+P4)
=pA sin(tr)(?&-u+ij+?g)
(2)
z direction, F'+A cos(cu>(P, -P3+P2-PJ =pA cos(cY)(t4J$-u;+u;-tg)
(3)
where F (N) is the acting force, indices z and y denote components of the force in the vertical and horizontal directions respectively, P is the pressure and a is the channel inclination angle. Since the loss of mechanical energy is caused by frictional resistance to flow, it is convenient to write an energy balance in terms of this loss:
;A(u;+u;-u+;) +A(uu,P,+uzPz-u3P3-uqP4)=Eloss
(4)
Eloss (W) is the sum of all mechanical energy losses per unit time caused by friction, which can be expressed as i=1,...4
E ,,,,=~;A&
in structured
et al. / Gas .jlow distribution
(5)
where 5 is an overall packing friction factor which stands for all friction losses involved. It can be easily obtained from pressure measurements for each type and size of structured packing. Since in the above five equations there are seven u.nlmowns, i.e. u3, u4, P,, P,, Efiiction, Fv and F,, two additional equations are needed to completely describe the problem. The y- and z-directed friction forces Fv and F, may be expressed as
F,=sin(a)(-Fl+F2--F3+F4)
(6)
F,=cos(cu)(-Fl--Fz-F3-F4)
(7)
packings
which gives the lowest energy losses per cell is chosen as a solution. 2.3. The wall zone Because of the pressure losses caused by bends and channel cross-section changes, the flow pattern in the wall zone is even more complex than that in the bulk zone. When the packing fits perfectly, there is no empty space between the wall and the periphery of the packing. This situation can be simulated by assuming total gas reflection action of the wall. However, a more realistic situation includes wiper bands around each element to avoid excessive liquid bypassing.A wall wiper band partly occupies the empty space between the packing periphery and the column wail. This situation can be simulated by partial gas flow reflection. Figure 4 illustrates schematically the situation without a wall wiper, represented in the form of two packing channels, one (1) reaching and one (4) leaving the wall zone cell with a constant crosssectional area. Subsequentwall cells form a vertical wall channel (2 and 3). Here the same balance equations can be used as in the case of the bulk zone, but the momentum balance equations differ somewhat: y direction,
Flf+ -I-&
(PI
+p,j=pA
i=l
,.--4
Fg and F, can now be written as functions of
w~x-u~
-a
(9)
z direction, F, +A-&‘:! =
PLl@~
-P3>
-
$1 + PA
cos(d(u;
-
UT>
(10)
Here F, isdefined analogously to a crossing cell in the bulk of the packing:
F,=sin(cu)(-F, +F4)-Fwau
(11)
For Fg we can write
FJY
/ ’ I ‘. \ /* \ \ --‘, ’ /
(3) Ui
(i=1,...4). By substituting eqns. (5)-(8) into eqns. (l)-(3) and some manipulations, we can express all the unknowns as a function of u4. Inserting this function of u4 into the energy balance (eqn. (4)) produces a polynomial of third order. The real value of u4
x
4 / ,- \ \
where
Fi=I~AuT,
57
/ ,<’
rgr
\
/
/
\ I3 /
; / ’ \ \ :
\ I
\ /
‘/
1 Fig. 4. Control volume for a crossing at the wall (left) and the associated channels (right).
F. Stoter et cd. / Gas Jibw distribution
58
F,=cos(cu)(-Fl-FJ+(--Fz-F,)
in structured packings
(12)
where Fw4 represents an additional wall zone friction force which can be calculated from the mean pressure in the wall channel and the wall area of the control volume: F wall
(pz +
p3)A
gas inlet
(13)
= sin(cY)
The friction forces Fl to F4 as used in eqns. (11) and (12) are calculated from eqn. (8) taking 5= &,,ti for channel inlet 1 and outlet 2 and J= ltiet for channel inlet 2 and outlet 3 to include pressure loss caused in bends and the wall zone respectively. A wall wiper can be simulated by a local reduction in the wall channel cross-section as shown in Fig. 5. From the continuity equation we can calculate the velocity change caused by the wall channel cross-section reduction and from the momentum balance we can calculate the corresponding pressure change. Referring to control volume 1 or 3 (Fig. 5) we have (14)
P wall-&per=~dll
(15)
The reduced wall channel cross-section is taken into account in the calculation over the wall-crossing block cell (compare control volume 2 in Fig. 5 with the control volume in Fig. 4). 2.4. Gas inlet The crossing what different zone. Such a
zone cells in the bottom layer are somefrom the cells in the bulk or wall cell can be considered as an inlet
L Fig. 6. Packing channels in the bottom associated gas inlet compartment.
channel with two outlets (Y-junction). This means that two adjacent channels are fed by the same inlet compartment (Fig. 6) and thus have equal inlet pressure. Since the inlet flow has no horizontal component in the y direction, the horizontal momentum of the inlet flow of a channel is assumed to have a zero value. The corresponding balance equation is (y direction) Fy -A
sin(a)( -P3 +PJ =pA sin(a)(g -u;)
(16)
Fy is simply the sum of the components F4) of the acting friction force:
(F3 and
Fg = sin(a)( - F3 + F4)
(fight).
(17)
Friction forces F3 and F4 are calculated by eqn. (8) using the corresponding inlet zone friction factor (5= !Ll13* 2.5. The calculation procedure The gas flow field in the packing is obtained iteratively by successive substitutions of the outlet pressures of the crossing cells (P3 and P4), beginning from the bottom layer and going upwards, layer by layer, until the top layer of packing is reached. The input values are the given inlet flow rates entering the cells in the bottom layer and the pressure at the top of a packing element. The algorithm is shown in Fig. 7. Since the convergence proved to be rather unstable in the case of non-uniform initial velocity profiles, a convergence damping factor (c=O-1) is used to produce new values for cell pressures and velocities. 3. Experimental
Fig. 5. Control volumes for a crossing at the wall with a crosssection reduction (wall wiper) (left) and the associated channels
layer of cells and the
details
The two packings investigated here are of common corrugated metal sheet type with a surface area of
F. Stoter et cd. / Gas J%W distribuhn
in structured packings
I- Corrugated
59
packing sheet
I
cell pressure 1086 factors Inflows and Poti,
Distributor for all the cells in the Ioyer n = I u,i,i:f(inflow.P,ini_,)
-I
4
for all cells in layer n u,i,,=(l-df) “,.,,,,+df Pn,,i=(l-df)P.+,i.,.,+df
I ,
“nini-, P.wii.,
for 011cells I” Ioyer ” un,ti~f~unin,.P”nin,-ll P..i=f(u.,t,.unini.Pno,i)
I
1 2 3
5 6 7
9 10 11 12 13 1L 15 16 17
i
‘-2_ mxtswe*p i=i*l
Fig. 7. Algorithm for the calculation of the gas velocity profile leaving a packing element consisting of unperforated corrugated sheets.
250 m2rne3.However, with respect to surface design these packings represent two extremes (see the sketch in Fig. l(d)). The surface of MONTZ-PAK Bl-250 (Montz-pak) can be characterized as a shallow embossed one without any perforations (“closed surface packing”). The surface of RALU-PAK 250 YC (Rahr-pak) can be characterized as a slightly open jalousie-like one with slits lying close together. The slits change row-wise and are exposed to gas flow on one side of the channel only. The openings of the slits on the other channel wall face downwardly flowing liquid, so that this packing is highly permeable to both phases. Having in mind numerous narrowly spaced slits along a channel, we speak of an “open surface packing”. The gas distribution properties of these packings were investigated using the simple piece of equipment shown schematically in Fig. 8(a). The main part of the equipment is an open frame into which one or more packing sheets with a length of 0.5 m and a height of 0.2 m can be inserted. At the bottom there are 17 compartments each equipped with a separate gas feed line. The two outside compartments are considered as the left-hand and right-hand-sidewall compartments respectively. The top-side outlets of these compartments are the corresponding wall channels, so that 15 inlet com-
(cl no wall cnanncl
wall channel
wall channel with wl!~r
Fig. 8. Schematic representation of: (a) the experimental setup used in this study, with 15 gas inlet compartments below two or four tightly packed corrugated sheets, each with 17 flow channels; (b) the relationship between inlet compartments and outlet channels; (c) the three wall zone arrangements investigated in this study.
partments which correspond precisely to the width of a packing element (0.5 m) actually feed 17 outlet channels. The enlarged detail shown in Fig. S(b) ilhrstrates the relationship between inlet compartments and outlet channels.The front-side corrugated sheet has the channels oriented to the right-hand side and the back one to the left-hand side. We measured both the inlet flow rate and the air pressure for each compartment. Directly above the packing we measured the concentration of tracer gas (CO,) and/or the outlet velocity of each air stream leaving a channel. For the latter purpose a specially designed micro-Pit& tube was used. Thanks to its construction, this tube also enabled the de-
60
F. Stoter et al. / Gas Jaw distribution
termination of the direction and static pressure of the outlet air flows. With Montz-pak, i.e. the closed surface packing, two sheets were sufficient to create the characteristic crossing gas flow channel structure. The air was simply introduced between the two sheets. To avoid wall flow, we -first did some tests with a configuration in which the packing fitted perfectly so that there was no open space between the wall and the end of the packing channels. The influence of the initial maldistribution was investigated using point sources introduced at various locations (channel inlets). To investigate in more detail the behaviour of the wall flow, we did some tests with an open space between the outside boundary of the packing and the wall. The influence of wall wipers was simulated physically by introducing an obstacle in the wall channel at a distance of 80 mm from the top of the packing sheets. The three different wall configurations investigated are illustrated schematically in Fig. 8(c). To create a representative channel geometry for Ralu-pak, i.e. to enable a smooth communication between the two sides of the packing sheets, we used four packing sheets fitting perfectly to the side walls. The outside face of the two outer sheets was closed to prevent air escaping into the surroundings. In this case the inlet gas entered three parallel planes of flow channels. Because of the gas inlet location, some initial gas maldistribution could not be avoided during these experiments.
4. Results
in structured
packings
"G
= 2.4 m/s
Outlet channels Fig. 9. Measured gas tracer distributions between two sheets of Montz-pak (tracer was introduced in channel 9 with a righthand upward orientation), with and without presence of countercurrently flowing water.
i
*
8 Measurement
O a
UG= 2.4 m/s
Calculation
UL = 0
and discussion
The influence of the nature of the packing surface will be illustrated and discussed tist. Then the velocity and pressure distribution measurement and simulation results for closed surface packing will be evaluated. 4.1. Tracer distribution pro$les The tracer distribution tests were carried out with Montz-pak and Ralu-pak under the same conditions of perfectly fitting packing, with and without the presence of countercurrently flowing water. In all tests the gas velocity profile was uniform and the tracer gas (CO,) was injected into the inlet of channel 16 (the front plate, with channels oriented to the right-hand side), which has its inlet in compartment 9 (see Fig. 8). Figure 9 shows the outlet tracer concentration profiles obtained with Montz-pak fitting perfectly to the walls. Obviously there is no effect of the counterflow of the liquid phase. In both cases the peak appears in channel 16 where the tracer was introduced. This indicates a pro-
Outlet
channels
Fig. 10. Comparison of measured distribution profiles for Montz-pak.
and calculated
gas tracer
nounced channel flow of gas. However, the presence of tracer in the central part of the left-hand-side channels indicates the existence of a certain amount of mixing of gas flows at 12 crossing interfaces along a channel. Simulation with a cell-splitting factor of 0.15 resulted in a fairly good reproduction of tracer concentration profile curves (Fig. 10). It should be noted that the profiles shown in Fig. 10 were measured with open wall channels. From a comparison with the profiles obtained with perfectly fitting packing (Fig. 9) it is obvious that possible wall flow (bypassing) does not affect the distribution of a centrally introduced tracer gas. On the other hand, the presence of a left-handside peak in profiles obtained during tests with Ralupak (Fig. 11) fitting perfectly to the walls suggests some inlet maldistribution of tracer gas as well as a smaller mixing effect of crossing flows; namely,
F. Stoter et al. / Gas jbw distributiun in structured packings
61
of structured packings with a more or less open surface. This means that the predictions of the model developed basically for closed surface packing may be valid for open surface packings at increased liquid loads.
2
4
6 Outlet
8
10
12
14
1
channels
Fig. 11. Measured gas tracer distribution profiles for Ralu-pak, with and without presence of liquid flow.
4.2. Velocity and pressure distribution proj2.e.s The outlet velocity profiles and inlet pressure profile corresponding to the situation shown in Fig. 11 (Ralu-pak, no liquid) are given in Fig. 13, where “right” and “left” refer to the channel orientations. The profiles were measured by placing the Pitot tube at the outlet of the respective channel on the front or back corrugated sheet. The difference in the level of left- and right-hand channel velocities measured at the top of the corrugated sheets is largely due to unequal initial gas distribution; however, the velocity proties can be considered as flat (within f 10%). Figure 14 shows the velocity and pressure distributions measured with Montz-pak for perfectly fitting packing obtained with a uniform initial gas profile. We can see that the outlet velocity distribution is almost flat. There is only a small disturbance near the wall. If we look at the pressure distribution at the bottom, we can see that the pressure measured
A Fig.
12. Gas flow (“slit flow”)
direction
for R.&I-pak.
a certain amount of injected tracer passes through slits into neighbouring channels, i.e. into a gas stream with a flow oriented to the left-hand side. A striking observation is the more central location of the peaks, which, as expected [6], indicates a smaller angle of gas flow with the vertical axis than in the case of closed surface packing (Montz-pak). As illustrated in Fig. 12, this means a deviation from channel flow, i.e. a smaller angle of flow with respect to the vertical axis. Another interesting observation with this packing is the changing nature of the gas flow under wet conditions. If we look at the profiles obtained with countercurrently flowing water (Fig. ll), we see that the tracer distribution profiles become similar to those obtained with closed surface packing. Since the liquid also makes use of slits as it flows down the packing [ 71, it plugs the slits and promotes a more pronounced channel flow of the gas phase. Similar behaviour can be expected from other types
Fig. 13. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two central sheets of Ralupak without wall channels, resulting from a uniform initial velocity profile (2.4 m s-l).
62
F. Stoter
et al. / Gas _f%m distribution
in structured
packings
Fig. 14. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two sheets of Montz-pak without wall channels, resulting from a uniform initial velocity profile (2.8 m s-l).
4.2. I. Interface effects Figure 15 shows the simuIated velocity distribution at the top and the simulated pressure distribution at the bottom. The simulations were carried out with a cell friction factor of 0.32 and an entrance loss factor of 1.O. The latter accounts for the pressure loss due to the large cross-section reduction at the entrance of the packing channels (Fig. 6). With these values an overall packing element friction factor of 1.l was obtained, which is equal to that obtained for a similar type of structured packing by Zogg [ 31. For the simulation of the wa.ll zone effects with perfectly fitting packing (gas is reflected by the wall, i.e. it makes a 90” bend before reentering the packing) the corresponding friction factor was assumed to be twice that for the bulk zone. In order to quantify the interaction of crossing gas flows at the interfaces within a packing element, we inserted a smooth thin plate between the two corrugated sheets. In this way a purely triangular cross-sectional area channel flow was created. The resulting flow profile shown in Fig. 16 is obviously similar to that obtained with the open channel structure (Fig. 14). Comparison of the measured inlet pressure profiles (Fig. 16 us Fig. 14) indicates a considerably lower value of the pressure drop in the case of closed channel flow, i.e. with a plate
in the compartments which feed a channel that ends at the wall is slightly higher. This is due to the additional pressure drop caused by a 90” turn in gas flow [3]. The measured (static) pressure distribution profile at the top of the packing was flat for all measurements. The measured outlet direction of the gas flow confirms that the gas flows in the channel direction (45”). This is in agreement with the observation of Stikkelman et al. [ 6 1. Comparison of the inlet pressure shown in Fig. 14 with that for Ralu-pak (Fig. 13) indicates a considerable difference in the dry pressure drop of these packings. With a correction for the difference in superficial velocities of the compared profiles, we found that the pressure drop for Ralu-pak is almost 30% lower than that of Montz-pak. Comparison with the pressure drop curves published by the manufacturers of these packings, which indicate a 25% difference, confirms this observation. The explanation for the lower pressure drop of Ralupak can be found in the more vertically oriented flow due to completely porous channel walls (Fig. 12).
Fig. 15. Simulation
-
right
results for the situation
shown in Fig. 14.
I?
Stoter et al. / Gas flow
distribution
in
structured packings
63
channel
__)
compartment
Fig. 16. Measured outlet velocity and inlet pressure profiles for the situation with a smooth plate inserted between two corrugated sheets of Montz-pak.
inserted between the corrugated sheets.With respect to the normal situation this means approximately a 50% lower value of the overall friction factor. The explanation can be found in the fact that the insertion of a smooth plate eliminated the influence of rather rough corrugation ridges and the friction between two crossing flows. A lower value of the friction factor also results in a decrease in the amount of wall flow. The corresponding simulation results are shown in F’ig. 17. This observation indicates that it is possible to increase the nominal surface area within a given packing volume without increasing the dry pressure drop. This could be of advantage in the design of packing used .as catalyst supports in some heterogeneous gas phase reaction applications [9, lo]. 4.22. Wall channel effects The velocity and pressure distribution experiment with Monk+pak (Fig. 14) has been repeated with a 10 mm spacing between the packing and the walls. This open space created wall channels with a cross-section twice that of the triangular gas flow channels. Compartments 1 and 17, situated below the wall channels,were closed to avoid direct feeding of the wall channels. The velocity profile measured at the top and the pressure profile measured at the bottom are shown in Fig. 18. From the velocity
Fig. 17. Simulation
50
left
@J-
g
30-
B k
-----C
shown in Fig.
16.
right
,
g
e g
results for the situation
‘..
20lo- n
1
01
I-
>
5”““‘“““““~;~~~~
compartment Fig. 18. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two sheets of Montz-pak with wall channels, resulting from a uniform initial velocity profile (2.4 m s-‘).
F. Stoter et al. / Gas flow distribution
64
profile it is clear that only part of the gas that reaches the wall flows back into the packing. The low velocity measured for channel 6 indicates that this is more pronounced for the bottom than other layers; namely, the gas flow leaving channel 6 is formed via wall reflection of the gas flow which enters the left-hand-oriented channel 2 (a very short channel). The low pressure at the bottom of the wall channel is a consequence of the absence of entrance effects (no inflow in the wall compartment) and causes a positive pressure gradient towards the wall, which results in gas transport in the wall direction. Comparison of the measured profiles with the simulated profiles (Fig. 19) for the velocity distribution at the top and the pressure distribution at the bottom respectively indicates good agreement obtained by using the same value of the friction factor for the wall channel and the channels in the bulk of the packing. The influence of a wall wiper on the gas flow was investigated by inserting a restriction in the wall channel at a distance of 80 mm from the top, which reduced the wall channel cross-section locally to 10%. Figure 20 shows the velocity profiles measured at the top of the packing and the pressure profile measured at the bottom of the packing. Comparison with the velocity profile obtained without the wall wiper (Fig. 20 vs Fig. 18) suggests two differences. Firstly, channels 3 and 14, which
channel Fig.
19. Simulation
results
for the situation
shown in Fig. 18.
in structured packings
----Q-
left
-----t-
right
““I
Fig. 20. Measured outlet velocities in left- and right-hand upward directions and inlet pressures for two sheets of Montz-pak with wall channels equipped with a wall wiper, resulting from a uniform initial velocity profile (2.4 m s-l).
have their inlets directly below the restrictions, exhibit local maxima. The pressure just below the restriction is so high that the gas is forced to flow back into the packing. Secondly, we see that the velocities measured in channels 3-14 are higher than is the case without the wall channel restriction. Obviously, the wall restriction causes an increased pressure in the whole section below the restriction. This means that a larger part of the gas flow that reaches the wall is forced to flow back into the packing. Because of the lowest pressure at the top, the wall channel sucks the air out of the packing, which results in very low velocities in channels l-3 and 14-l 7. The simulation results shown in Fig. 21 do not differ much from the measured ones. 4.2.3. Initial gas muldtittibutim effect To investigate the response of the packing to a severe initial maldistribution, we introduced a point source in the left-hand wall compartment (compartment 2). These tests have been performed with the packing fitting perfectly to the wall (no wall channel). If we look at the velocity profile (Fig. 22), it is clear that channels 7 and 8, where the gas goes upon reflection from the wall, exhibit peak velocities. An interesting point here is the presence
F. Stoter et cd. / Gas jbw
distriinhm
in structured packings
-
Fig.
21. Simulation results for the situation shown in Fig. 20.
Fig.
65
right
23. Simulation results for the situation shown in Fig. 22.
.
of gas in channels 9-17, which is obviously an attestation of horizontal gas transport towards the right. This is confirmed by the pressure profile (Pig. 22), which indicates the presence of a positive pressure gradient oriented towards the right-hand side. Figure 23 shows the simulated velocity and pressure prohles for this situation. If we compare the measurements with the simulations, we may say that the location of the peak is predicted fairly well by the model. channel
I-
left
it
right
1 6. Concluding
Fig. 22. Measured outlet velocities in left- and right-hand upward
directions and inlet pressures for two sheets Montz-pak fitting perfectly to the walls, resulting from a point source introduction of gas into the left-hand-side wall compartment
remarks
Packings with unperforated, tightly packed, corrugated sheets cause a pronounced channel flow of gas. A uniform initial distribution deteriorates only slightly within the height of a packing element. The packing with the open surface exhibits a more vertically oriented gas flow. However, under wet conditions the liquid plugs the slits of this packing to some extent, thus creating a more closed-surfacelike gas distribution. Because of the large-scale static mixing effect of a bed, the usual assumption of plug flow of gas in packed beds consisting of corrugated sheets with closed and open surfaces appears to be justified.
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distribution
Inserting a flat plate between the corrugated sheets of the closed surface packing resulted in a lower dry pressure drop, indicating a substantial amount of inter-facial friction of gas flows at crossing interfaces of gas flow channels. On the other hand, the elimination of inter-facial friction through insertion of flat plates between corrugated sheets means a substantial enlargement of the surface area per unit volume. An investigation of the potential of this modification in the design of elements of structured packing is in progress in our laboratory. The agreement achieved between experiment and calculation emphasizes the applicability of the discrete cell approach to modelling of the gas flow distribution in packed beds consisting of corrugated sheet packings. This gas distribution model is being further developed as a tool for predicting the effects of gas maldistribution in industrial-scale columns.
Acknowledgments We are indebted to J. Montz GmbH and Raschig GmbH for providing the packing material used in this study.
in stru&ured packings
3 M. Zogg, Striimungs- und Stofaustauschuntersuchungen an der Sulzer-Gewebepackung, Dissertation No. 4886, ETH, Zurich, Hans Schellenberg, Wmterthur, 1972. 4 R.M. Stikkehnan and J.A. Wesselingh, IEChE Symp. Ser., 104 (1987) B155. 5 R.J. Kouri and J.J. Sohlo, IEChE Sgmp. SW., 104 (1987) B193. 6 R.M. Stikkelman, J. de Graauw, 8. OlujiC, H. Teeuw and J.A. Wesselingh, Chem. Eng. Technol., 12 (1989) 445. 7 F. Stoter, Z. OlujiC and J. de Graauw, AlChEAnnuulMeeting, Chicago, I990, paper no. 199c. 8 H.Kister,D&iUatianDesfgn, McGraw-Hill,NewYork, 1992, pp. 448-463. 9 J.L. De Garmo, V.N. Parulekar and V. Piqjala, Chem. Eng. Prog., 88{3) (1992) 43. 10 J.P. Stringaro and J. Luder, Chem. Plants Process., 25 (1992) 6.
Appendix A: Nomenclature gas flow channel cross-sectional
A E F P u Greek ff
5 P
mechanical energy (friction) acting force pressure superficial gas velocity
area losses
letters channel inclination angle overall friction factor density of gas phase
subscripts
References
referring to referring to referring to n referring to wall coordinates z, Y I, 3, 3, 4 referring to i
inlet
1 Z. Olujic? and J. de Graauw, Chem. Biochem. Eng. 6?., 3 (1989) 181. 2 2. Ohrjic, F. Stoter and J. de Graauw, Gas Sepor. PUT-$, 5 (1991) 59.
ith channel inlet or outlet gas inlet compartment nth cell layer wall channel channel inlet or outlet