ARTICLE pubs.acs.org/IECR
Designing a Packed Dividing Wall Column for an Aromatics Processing Plant arko Olujic*,§ Igor Dejanovic,† Ljubica Matijasevic,† Helmut Jansen,‡ and Z †
Faculty of Chemical Engineering and Technology, University of Zagreb, Savska cesta 16, HR-10000 Zagreb, Croatia Julius Montz GmbH, Postbox 530, 40705 Hilden, Germany § Process and Energy Laboratory, Delft University of Technology, Leegwaterstraat 44, 2628 CA Delft, The Netherlands ‡
ABSTRACT: This paper introduces a comprehensive design method assembled using facilities of a commercial software package that complemented by Excel programs, which contain own column dimensioning and well established cost estimation procedures, enables proper assessment of the industrial viability of a dividing wall column (DWC) equipped with corrugated sheet structured packings. The heart of the performance simulation tool is a detailed four-column model that in conjunction with a simple, theoretically founded short-cut method providing reliable initial values for liquid and vapor splits and a simple but effective objective function for design optimality indication allows determination of the adequate stage and reflux requirement of a DWC. The proposed dimensioning method enables a close approach in accuracy to that required at the stage of conceptual design for purposes of making a bid by an equipment manufacturer. Compared to a two-columns-in-series configuration, as employed in an aromatics processing complex within a refinery, a DWC equipped with state-of-the-art structured packing and auxiliary internals requires approximately 43% less energy to deliver three fractions at required product specifications. This, accompanied by savings of nearly 51% based on total annualized costs, indicates that implementing a DWC could lead to a significant increase in profitability of aromatics processing plants.
1. INTRODUCTION Being the most widely used and most energy intensive among large scale separation techniques, distillation became the main target of efforts oriented toward increasing the sustainability of process industries.1 However, the implementation of energysaving solutions is often capital intensive and process industries are generally reluctant to implement them if this is not associated with significant improvement in the profitability of a plant. This is particularly the case in the petroleum refining world. As elaborated in greater detail by Hartman et al.,2 catalytic reforming to process aromatics is an important economic factor for modern refineries. Reactor effluent stream is rich in benzene, toluene, ethylbenzene, xylenes, and heavier aromatics, and an aromatics complex usually contains several distillation columns arranged in trains (sequences) to recover and separate the aromatic components into individual products and/or certain component-rich fractions. A comprehensive review of the dividing wall column (DWC) state of the art, including a survey of application-related patents, indicated that aromatics complexes offer various opportunities for implementation of a DWC.3 The present paper is concerned with design of a conventional, three-product DWC suitable for a specific aromatics complex situation as encountered in a Croatian refinery. The energy-saving potential in this type as well as in many other applications is significant and can be estimated with confidence using different simulation methods. The papers by Tiantafyllou and Smith4 and Segovia-Hernandez et al.5 provide some quantification in this respect, and the obtained results agree well with the numbers reported for some real industrial applications in a paper by Kaibel et al.6 However, as indicated by Dejanovic et al.,3 and in a recent state-of-the-art paper by Asprion and Kaibel,7 the columns r 2011 American Chemical Society
dimensioning procedures still belong as proprietary knowledge to a few equipment manufacturers active in this field. In order to arrive at total annualized costs, to enable comparisons of alternatives, some dimensioning-related efforts have been undertaken in academic publications, e.g., refs 8 and 9. However, the nature of applied approximations/simplifications is such that it may lead to erroneous conclusions on both the process design side and the economics side. One should realize that hydraulic design of the partitioned part of a DWC is a delicate activity, and that pressure drop on two sides of the wall must be equal. If not properly arranged in the design phase, by adjusting the necessary amount of flow resistance exhibited by internals used in conjunction with fixed specific liquid flows, the equalization of the pressure will be imposed by nature, i.e., by spontaneous adaptation of vapor flows in two sections. This will inevitably lead to establishing operating liquid to vapor flow ratios that could differ from that required to achieve the desired degree of separation in beds on both sides of the partition wall. This most distinctive feature of hydraulic design of a DWC has not received adequate attention in the open literature so far. An objective of this paper is to fill this gap, and as will be demonstrated later on, the method proposed in this paper allows a close approach to actual design practices, as adopted by the equipment manufacturing company Julius Montz, Hilden, Germany, the pioneer in the field of design and construction of packed DWCs. Received: October 5, 2010 Accepted: February 24, 2011 Revised: January 20, 2011 Published: March 24, 2011 5680
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Table 1. Base Case Feed and Product Compositions stream name feed
C5C6
BRC
heavies
31.74
6.94
3.70
21.10
n-butane
0.019
0.088
0.000
0.000
isopentane
0.064
0.291
0.000
0.000
n-pentane
0.045
0.206
0.000
0.000
1
total flow [t h ] component mass fractions
Figure 1. Conventional, two-columns-in-series configuration (indirect sequence) for separation of a three-component or multicomponent feed into three specified products or fractions, respectively.
With proper column shell dimensions and internal configuration, it is possible to obtain reliable installed equipment cost estimates and consequently arrive at total annualized costs (TACs) with enough confidence to allow a realistic comparison with established, two-columns-in-series configurations, i.e., a proper assessment of potential benefits of implementing a DWC. As shown in what follows, the results of this study clearly indicate that adopting a DWC as the standard design for aromatics plant applications could lead to increased profitability of complex refineries.
2. DESIGN CASE Upon a recent decision to concentrate mainly on fuel production, the aromatics complex at the INA (presently MOL Group) refinery in Sisak, Croatia, has been reduced to a minimum, i.e., to a direct separation sequence containing two columns—the so-called “platformate splitter” and the “benzene recovery column”—connected in series (see Figure 1) to separate the platformer reactor effluent stream which contains some 40 components into three fractions: (1) C5C6 gasoline containing no more than 1.5 mass % benzene, (2) a benzene-rich cut (BRC) containing 68 mass % benzene, and (3) a heavy reformate stream (heavies) containing toluene, ethylbenzene, xylenes, and heavier components with no more than 0.5 mass % benzene. For purposes of this study the 40 components contained in the actual feed stream have been lumped together into a representative 15-component mixture. The mass flow rates and compositions of the feed and product streams as considered in the present simulation study are shown in Table 1. In order to provide an appropriate basis for the evaluation and comparison of related costs, two conventional columns are considered here as new designs, and to provide complete information both options, i.e., tray and packed columns, are considered. 3. STAGE AND REFLUX REQUIREMENTS The two columns of the base-case configuration (see Figure 1) have been simulated using detailed methods available in ChemCAD. Regarding the simulation approach, a DWC, shown schematically in Figure 2, has significantly more degrees of
2-methylpentane
0.080
0.351
0.026
0.000
n-hexane
0.043
0.050
0.270
0.000
benzene 3-methylhexane
0.086 0.020
0.013 0.000
0.680 0.024
0.005 0.026
toluene
0.247
0.000
0.000
0.373
ethylbenzene
0.035
0.000
0.000
0.053
p-xylene
0.042
0.000
0.000
0.064
m-xylene
0.122
0.000
0.000
0.183
o-xylene
0.055
0.000
0.000
0.083
m-ethyltoluene
0.047
0.000
0.000
0.071
1,3,5-trimethylbenzene 1,4-diethylbenzene
0.077 0.017
0.000 0.000
0.000 0.000
0.116 0.025
Figure 2. Schematic representation of a DWC with indication of design parameters.
freedom than a conventional distillation column. For instance, the number of stages for six sections needs to be provided. Additional parameters indicated as circles in Figure 2, specific to the internal configuration as encountered in a DWC, are liquid and vapor splits above and below the partition wall, respectively. A good set of initialization data is essential to ensure convergence 5681
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Figure 4. Plot indicating optimum number of stages for a DWC.
Table 2. Base Case and DWC Simulation Results base case C1
Figure 3. Four-column model used to simulate the operation of a threeproduct DWC.
of the detailed simulation method. Fortunately, these can be easily obtained using a rather simple but in this respect very effective short-cut method, introduced recently by Halvorsen10 and Halvorsen and Skogestad.11,12 Following suggestions of Halvorsen and Skogestad,9 the so-called Vmin diagram method has been implemented in ChemCAD. Since the original method requires dealing with pure components, the 15-component feed has been represented by three representative key components: 2-methylpentane, benzene, and toluene. Then, the Vmin diagram was constructed by rigorous simulation of possible binary splits, with the stage number being at least 4 times the minimum number of stages, 4Nmin, and mass recoveries of key components set to 0.999. From that diagram, appropriate estimates of required design parameters for initialization of a detailed simulation were obtained. Details related to Vmin diagram application in conjunction with a rigorous simulation model and corresponding numbers can be found elsewhere, e.g., Dejanovic et al.13 Detailed simulations have been performed using the so-called “four-column model”, shown schematically in Figure 3. This configuration was the preferred choice in this case, because the prefractionator and main column sides of the partitioned part of the column are represented by separate column sections, which makes the dimensioning effort more straightforward. Another reason is that this is the only configuration that can be used for dynamic simulation with the purpose of the control system study. A detailed elaboration of relative advantages/disadvantages of
C2
C1 þ C2
DWC
number of stages
40
38
78
86
reflux ratio
1. 70
2.39
2.80
reboiler duty (MW) condenser duty (MW)
3.55 3.16
2.63 2.51
6.18 5.67
3.50 2.76
four different configurations that can be used to simulate the performance of a three-product DWC can be found elsewhere, e.g., Dejanovic et al.3 The first step was to restore feed composition to the full 15 components. Benzene mass fractions in the distillate and the side draw liquid flow rate were set to be the same as in the base-case simulation, while the initial value for reboiler duty was set to give the required minimum vapor flow. Liquid and vapor split ratios were adjusted until the minimum possible mass fraction of benzene in the bottoms was achieved, which was the same as in the base case. The next step was to determine the actual number of stages in each section. This was done by reducing the number of stages in sections keeping the mass fractions of benzene in the distillate and bottoms, as well as liquid side draw flow rate, constant. For every converged case, an optimization was performed using the optimization tool built in ChemCAD, with the objective function being min Qr, and the independent variables the liquid and vapor split ratios. To arrive at the optimum combination of reflux ratio and the number of stages, the empirical objective function, min N(R þ 1), which approximates effectively the total annualized cost of a conventional distillation column, was used. According to Figure 4, the minimum value corresponds to 64 equilibrium stages, based on the main column stage count. The same result is obtained using all equilibrium stages contained in the DWC. In the present case the number of stages at the prefractionator side and the number of stages at the main column side are equal, i.e., 22. This means that the total number of stages contained in the DWC is 86, which means eight stages more than required in two sieve tray columns connected in series. The number of equilibrium stages of compared configurations and the corresponding reflux ratios are given in Table 2. The simulation results for conventional, two-columns-in-series sequence and a DWC 5682
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4. COLUMN DIMENSIONS Upon completion of the performance calculations, the number of equilibrium stages (theoretical plates) in each column section was fixed as well as corresponding liquid and vapor flow rates. For the tray column option, common cross-flow sieve trays have been chosen with a tray spacing of 0.6 m. Using tray efficiencies as experienced in similar applications, the platformate splitter contains 61 trays and the benzene recovery column contains 59 trays, with the feed stage in both cases in the middle of the column. For packed conventional columns and packed DWC, Montz-pak B1-350 MN, a state-of-the-art, high performance corrugated sheet structured packing was chosen. Bed heights in conventional and partitioned parts have been determined in accordance with the number of contained stages, assuming an HETP value of 0.4 m. This number including the
Figure 5. Schematic illustration of stage and reflux requirement calculation procedure.
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common safety margin is based on total reflux test data obtained with Montz-pak B1-350MN using the chlorobenzene/ethylbenzene system at atmospheric pressure.14 The number of packed beds to be installed in rectification and stripping sections of a packed column has been determined based on a rule of thumb indicating that the single bed height should not exceed that equivalent to 20 equilibrium stages. If more than 20 stages are required in a section, then two beds should be considered, which implies providing additional column height to accommodate the necessary liquid redistribution section. The latter consist usually of a liquid collecting device, a chevron (vane) type or chimney tray type liquid collector (see Olujic et al.1 or Rix and Olujic15) installed above a narrow trough gravity liquid distributor. For conventional packed columns and similar sections in a packed DWC we have assumed a constant spacing of 1.8 m, which is appropriate for the size of columns considered in this study. With a symmetrical distribution of stages in two conventional columns, each containing around 20 stages in rectification and stripping sections, it was chosen to have two shorter beds per section. This means that both packed columns contain three liquid redistribution sections, with the middle one receiving also the feed. Since the conventional columns and the DWC considered in the present study operate at above atmospheric pressure and the feed is a slightly subcooled liquid (q = 1.064), the critical loads will be on the bottom stage of each column, which is therefore taken as the basis for determining the diameter of the two conventional columns as well as the shell of a DWC. The characteristic values are shown in Table 3 together with the tangentto-tangent length (height) of the column shells for two columns in conventional configurations, equipped with sieve trays and B1-350MN packing, respectively. 4.1. Layout of a DWC Containing Structured Packings. Arranging beds and liquid collecting and distribution become more demanding when the partitioned part of a packed DWC is considered. Figure 6 shows schematically the internal configuration of the DWC, indicating the number of stages in each column section and the corresponding vapor and liquid loads at the top and the bottom of each bed. Since the upper part of the DWC contains 26 stages, this section consists of two beds, each containing 13 stages. The bottom section contains 16 stages in one bed. Due to a pronounced difference in vapor and particularly liquid loads below the feed (F) and side product (S) drawoff points, the partition wall in the lower part is in an off-center position. That is, a much larger cross-sectional area is needed below the feed point on the prefractionator side to accommodate the feed stream that enters as slightly subcooled liquid. Adding
Table 3. Dimensions and Components of the DWC and Two Conventional Configurations configuration C1/C2 (trays)
a
C1/C2 (packings)
DWC (packings)a
column top pressure (bar)
1.7/2.7
1.7/2.7
2.7
shell diameter (m)
2/2
1.6/1.8
1.7
shell height (m)
40.5/39.5
27.1/27.5
37.3
number of trays or packed beds
61/59
4/4
7 (4)
number of distributors
4/4
7 (4)
number of liquid catchers number of support grids
4/4 4/4
7 (4) 7 (4)
Numbers in parentheses indicate devices placed in partitioned part of the column. 5683
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Figure 7. Geometry factors associated with placing the partition wall.
Regarding the dimensioning procedure, the outgoing point is the overall shell diameter determined using conventional methods for the stage with the largest vapor load. The sum of cross-sectional areas of the partitioned part of the column, which however may differ above and below the feed and side product draw-off stages, should be equal to the overall one, i.e. Ac ¼ Apc þ Amc
ð1Þ
where Ac (m2), Apc (m2), and Amc (m2) are the cross-sectional areas of the shell of the DWC, prefractionator, and main column, respectively. The cross-sectional area of the prefractionator segment of the overall cross-sectional area can be calculated from Figure 6. Internal configuration, indicating the number of stages in each bed and the corresponding liquid and vapor flows at the top and bottom of each bed.
the feed to the liquid coming from the bed above as well as a certain amount of liquid obtained due to direct condensation of the ascending vapor upon contact with subcooled feed liquid makes the liquid load of the bed below the feed nearly 5 times larger than that on the main column side. Also, on the main column side of the partition wall there is a side draw where side product is taken out of the column as a liquid. Owing to a rather small vapor load this section requires a much lower crosssectional area than the heavily liquid loaded stripping section on the prefractionator side. Although the vapor and liquid loads in sections above the feed and draw-off differ to a certain extent, the partition wall is, as indicated in Figure 6, placed in the center. This appeared to be a convenient choice in the present case, and placing a partition wall off-center, as required in the sections below the feed and draw-off stages, can easily be arranged by utilizing a nonwelded wall, which is a well-established practice in the case of DWCs equipped with structured packings.16 One should note that welding a partition wall implies separating the shell into two semicircular sections with equal crosssectional areas. Owing to different loads in the prefreactionator and the main column, this leads always to underdesign on the less critical side. This was one of the main obstacles for wider implementation of DWC in the beginning years, which, presently, can be circumvented by placing the partition wall offcenter, in the most appropriate way. Therefore, the introduction of a nonwelded, self-fixing partition wall in 1996 is considered to be a milestone in the development of DWC technology.1
Apc ¼
dc 2 ðΘ sin ΘÞ 8
ð2Þ
where dc (m) is the dividing wall column shell diameter and Θ (deg) is the angle subtended by the partition wall (see Figure 7). The latter is described as a function of the shell diameter and the distance of the partition wall from the shell on prefractionator side, lpcw (m): Θ ¼ 2 arccos
dc 2lpcw dc
ð3Þ
The cross-sectional area of the main column is obtained simply, by subtraction of prefractionator cross-sectional area from the total one, using eq 1. The obtained areas are then translated into diameters of an equivalent cylindrical column. These are used in conjunction with local vapor and liquid loads to check the upper limit with respect to flooding condition. This should not exceed 80% of that which would cause flooding. A good indication for this is the loading point, i.e., the point of onset of loading, which can be estimated with some confidence using the appropriate equation of the Delft model, shown later on. Practically, this means that, the design point corresponds approximately with the ratio of operating and loading point vapor loads, i.e., the corresponding F-factors equal 1. However, the corresponding pressure drop should not exceed 3 mbar/m. In other words, this pressure drop is taken as the upper limit value for design purposes. If the calculated pressure drop exceeds the limit in one of the partitioned sections, a possibility is to use a coarser packing or the same packing with a larger corrugation inclination angle. This is a practical option if the bed height is lower than the section height, 5684
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Table 4. Basic Dimensions and Estimated Pressure Drop per Packed Bed Section as Indicated in Figure 8
Section
Figure 8. Detailed drawing of the DWC with all major pieces of equipment indicated.
which is often the case if a part of the partition wall is placed offcenter. Additional bed height is needed to accommodate the required number of stages, because both a lower specific geometric area and an increased corrugation inclination angle are associated with less efficiency. Also the lateral position of the partition wall can be corrected accordingly, provided the other side can have it. If not, then the shell diameter of the DWC needs to be enlarged accordingly. This means that a trial-and error procedure is necessary to arrange proper lateral positioning of the partition wall. The longitudinal positioning is related to the number of stages contained on the prefractionator and the main column side, above and below the feed and side product draw-off
2.1a 2.1b
h
(m)
5.2
A
(m2)
2.27 2.27
d Δp
(m) 1.7 1.7 (mbar) 6.95 6.91
5.2
prefractionator
main column
1.1
2.2
1.2
2.3
2.4
3.6
5.2
4.8
4.0
1.135
1.599
1.135
0.671
6.4 2.27
1.20 5.75
1.43 7.95
1.20 4.25
0.92 9.76
1.7 13.51
stage, respectively. If one side contains more stages and the same packing is chosen, then the side with fewer stages will have a portion of empty space. This, however, allows installation of a coarser packing, to arrive at a lower section pressure drop, if appropriate. One should also note that additional height of the column shell may be required to accommodate inclined portions of the partition wall. This is necessary if the lateral positions of the partition wall above and bellow the feed differ (one or both on different off-center positions), as encountered in this study. A reference design for the DWC was generated using the Montz in-house method for establishing column dimensions. The diameter of the DWC shell is 1.7 m, based on the design point corresponding to 75% of the flooding vapor velocity on the bottom stage. A detailed drawing of this DWC is shown in Figure 8, indicating seven packed beds and all auxiliary devices, i.e., column internals of importance for cost estimation purposes, such as liquid collectors or catchers, an externally placed liquid splitter, the liquid distributors, the vapor distributor, and packing support grids. In all situations a narrow trough liquid distributor with drip tubes is used while the type of the liquid collector depends on the specific liquid load. For the specific liquid loads above 20 m3/ m2 h, a chimney type collector is a preferred choice. This device is also a common choice for side product draw-off location regardless of the liquid load. For lower specific liquid loads, vane (chevron) type collectors are used. In present study a chimney tray collector, placed above the vapor inlet, is used to facilitate initial vapor distribution. The proper distribution of vapor flow bellow the partition wall is the key to success with the design of a DWC. This is something that needs to be fixed in the design phase, by arranging the individual flow resistances to ensure equal pressure drop on two sides of the partition wall. This is presently done by manufacturers only, i.e., using proprietary design methods. However, as shown and demonstrated in what follows, it can be done with required accuracy using recently published methods for estimating the pressure drop of corrugated sheet structured packings and state-of-the-art packed column internals, respectively. 4.2. Pressure Drop of a Packed DWC. The heights of individual column sections are indicated in Figure 8. The bed heights and corresponding cross-sectional areas and equivalent diameters for each section are shown in Table 4. The former have been determined by multiplying the required number of theoretical plates with a constant HETP value as adopted by Montz for B1-350MN for this case (HETP = 0.4 m). One should mention here that the Delft model arrives at conservative enough values, similar to those used by Montz in the present case. However, a thorough verification effort is required before adopting this method for the determination of bed height of packed DWCs. 5685
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The heights and cross-sectional areas of individual beds allow determination of the volume of packing and in conjunction with average liquid and vapor loads serve as a basis for estimation of the pressure drop, separately, for each bed and associated liquid collecting and distributing equipment. The estimated pressure drop for each of the beds contained in two packed columns is shown in the bottom row of Table 4. These numbers have been generated using the Delft model (see Fair et al.17 or Olujic et al.18), which, as shown by Olujic et al.,19 can easily be adapted to account for any change in geometry of corrugated sheet packings. Note that during the validation of this model using the total reflux data obtained with the chlorobenzene/ethylbenzene system,14 it appeared that the trend of pressure drop curves is reproduced very well; however, the predicted values appeared to be consistently on the lower side, and the most pronounced deviation was observed at the highest test pressure. Therefore, in the present study concerned with above atmospheric operating pressures, the estimated values were multiplied by the factor 2 to generate conservative predictions, resulting in numbers somewhat larger than those estimated using the Montz in-house method. 4.2.1. Pressure Drop of Corrugated Sheet Structured Packings. In order to enable direct implementation of the proposed DWC dimensioning method, the present paper contains necessary working equations of the Delft model, accounting, where appropriate, for macro geometry modifications as implemented in high performance structured packings, such as Montz-pak B1-350MN considered in this study. This packing contains a bend in the bottom part of corrugations and a corrugation angle lower than the common 45°. A specific feature of the Delft model is that it makes a distinction among three characteristic angles: the corrugation inclination angle, R (deg), that strongly influences the interaction of gas streams at the crossing planes formed between flow channels oriented in opposite directions; the effective gas flow direction change angle at the transition between packing element or layers, RDC (deg); and the effective flow angle of liquid, RL (deg), which is steeper than the corrugation inclination angle due to a more or less pronounced tendency of the liquid to flow over the corrugation ridges driven by gravity. The latter two depend on the corrugation inclination angle and can be determined using expressions given later on, where appropriate. The corrugation inclination angle is a characteristic geometric feature of corrugated sheet structured packings. The standard angle is 45°. Another commonly used (where appropriate) angle is 60°, with respect to the horizontal. Experimental evidence on the effect of the corrugation inclination angle on the mass transfer efficiency, pressure drop, and capacity of corrugated sheet structured packings can be found elsewhere, e.g., Olujic et al.19,20 4.2.1.1. Basic Geometry and Flow Related Parameters. In addition to the corrugation inclination angle, R (deg), other relevant macro geometric features of a corrugated sheet structured packing are the specific geometric area, ap (1/m), the void fraction or porosity, ε (m3/m3), and the height of a packing element, hpe (m). The requested bed height, hpb (m), is arranged by placing the required number of packing elements or layers, npe, above each other: hpb ¼ npe hpe
ð4Þ
Since the subsequent element/layers are usually rotated to each other by 90°, to maximize lateral spreading and mixing of both
phases, the number of packing elements or layers corresponds with the number of flow direction changes the vapor phase makes while ascending through the packed bed. For a packing with a smooth bend in the bottom part of the corrugations, the vapor flow direction change angle is simply 90° þ R ð5Þ 2 Assuming that only gravity and the corrugation shape affect the liquid flow, the effective liquid flow angle, RL (deg), can be described by 3 2 RDC ¼
6 6 RL ¼ a tan6 4
7 cosð90 RÞ 7 7 b 5 sinð90 RÞ cos a tan 2h
ð6Þ
where h (m) represents the height and b (m) is the width of the base of corrugations. The corresponding length of the corrugation side, s (m), follows from rffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 s¼ þ h2 ð7Þ 4 These three basic corrugation geometry dimensions depend on the specific geometric area of the packing, and, being highly influential, should be measured upon delivery of a packing, as well as the corrugation inclination angle, to avoid uncertainties later on. Assuming a standard configuration utilizing a crimp angle of 90°, which implies that b = 2h, the following expression can be used to determine the installed specific geometric area or to back calculate corrugation dimensions from the given area. 4s ð8Þ bh Another important geometry-related parameter is the V-shaped fraction of the cross section of a triangular gas flow channel occupied by liquid film: ap ¼
j¼
2s b þ 2s
ð9Þ
A geometry-related parameter of general importance is the hydraulic diameter of the triangular gas flow channels. Assuming uniform liquid distribution, i.e., constant film thickness, δ (m)
dhG
ðbh 2δsÞ2 bh ð10Þ ¼ " 2 #0:5 bh 2δs bh 2δs 2 bh 2δs þ þ 2h b 2h
Since the film thickness encountered in practice and its variations are rather small, this complex expression can be replaced without introducing a significant error by a much simpler one, valid for dry channels. dhGðdryÞ ¼
2bh b þ 2s
ð11Þ
In addition to packing geometry related parameters, R, h, b, hpe, npe, and packing porosity, ε, the Delft model requires also information on mass flow rates, densities, and viscosities of two phases, i.e., MG (kg/s), ML (kg/s), FG (kg/m3), FL (kg/m3), μG (Pa s), and μL (Pa s), respectively. These operating parameters 5686
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need to be provided for the top and bottom of each bed contained, and this information can easily be retrieved from the results of detailed performance calculations. Corresponding superficial velocities are defined as uGs ¼
4MG FG 2 ¼ pffiffiffiffiffiffi FG FG πdc
ð12Þ
and uLs ¼
4ML FL πdc 2
ð13Þ
where dc (m) denotes the diameter of the column or the equivalent diameter of a section in the partioned part of the column. FG (Pa0.5), which is generally known as the F-factor, represents the vapor load of the column section. Per definition FG ¼ uGs FG
0:5
ð14Þ
The F-factor is a highly practical design and operating parameter (square root of the vapor flow kinetic energy), because it places all distillation and similar column applications within a rather narrow range of absolute values (roughly 0.54 Pa0.5) regardless of the operating pressure. Due to the inclination of the gas flow channel within a packing element or layer, the length of the vapor flow path is larger than the bed height, and the extent of this depends on the corrugation inclination angle. This also means that effective velocities of vapor and liquid are larger than the corresponding superficial velocity, and additional enhancement depends on the reduction in flow cross-sectional area due to packing porosity and the liquid holdup, hL (m3/m3). The working expressions for respectively effective vapor and liquid velocity account for these effects: uGs uGe ¼ ð15Þ ðε hL Þ sin R
Here, Fload is an empirical correction factor that describes the amount of pressure drop enhancement within the loading region with respect to the preloading region pressure drop. !2=ðsin RÞ !0:13 FG u2Ls ð20Þ Fload ¼ 3:8 FG, lp ε2 gdhG This correction is activated when FG/FG,lp > 1, i.e., when the operating vapor load exceeds that corresponding to the point of the onset of loading, FG,lp, or, in other words, the point of departure from preloading conditions. The loading point F-factor is described reasonably well by the following empirical expression introduced by Verschoff et al.,21 which accounts explicitly for a pronounced effect of flow direction change angle. 0 @0:053ε2 gdhG
FL FG FG
!
FG, lp ¼
10:57 rffiffiffiffiffiffi!0:25 FL pffiffiffiffiffiffi uLs ðsin RDC Þ1:24 A FG FG
ð21Þ This critical load corresponds roughly with the design point, which is usually set to 0.70.8 of the flood point. However, as mentioned before, if the pressure drop corresponding to the loading point condition FG/FG,lp = 1 exceeds 3 mbar/m, the latter should be taken as the design limit. According to the Delft model, the preloading region pressure drop consists of three major contributions: the pressure drop associated with the vaporliquid interaction at the interface, ΔpGL; the pressure drop associated with the vaporvapor interaction at crossings of open sides of triangular gas flow channels, ΔpGG; and the pressure drop associated with the change in flow direction at the transitions between subsequent packing elements or layers, ΔpDC. Δppreload ¼ ΔpGL þ ΔpGG þ ΔpDC
and uLe ¼
uLs εhL sin RL
ð16Þ
Assuming uniform wetting, the liquid holdup is simply defined as a product of film thickness, δ (m), and the specific geometric area of the packing, ap (m2): hL ¼ δap
ð17Þ
This simple basic expression appeared to hold well in practice, in conjunction with well-known Nusselt laminar falling film thickness expression adapted for inclined walls: !1=3 3μL uLs ð18Þ δ¼ FL gap sin RL where g (m2/s) is gravity acceleration and RL (deg) is the effective angle of liquid film flow, defined by eq 6. 4.2.1.2. Working Pressure Drop Model Equations. The Delft model makes a distinction between the preloading region, where film flow conditions prevail, and the loading region, where a more complex fluid-dynamic situation is encountered. Δp Δp ¼ Fload ð19Þ Δz Δz preload
¼ ðζGL þ ζGG þ ζDC Þ
FG u2Ge 2
ð22Þ
Three major sources of flow resistance are expressed in terms of characteristic overall interaction coefficients. The overall gasliquid interaction coefficient is given by ζGL ¼ jξGL
hpb dhG sin R
ð23Þ
The friction factor, ξGL, described by the well-known Colebrook and White expression,22 accounts for the effect of the roughness of the interface, which is here assumed to be equal to film thickness. 2 δ=dhG 5:02 δ=dhG 14:5 þ log ξGL ¼ 2 log ReGrv ReGrv 3:7 3:7 ð24Þ Here, ReGrv represents the relative phase velocity Reynolds number: ReGrv ¼ 5687
FG ðuGe þ uLe ÞdhG μG
ð25Þ
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The gasgas interaction coefficient appeared to be a rather strong function of the corrugation inclination angle. ζGG ¼ ð1 jÞξGG
hpb dhG sin R
¼ ð1 jÞð0:722Þðcos RÞ3:14
hpb dhG sin R
ð26Þ
The direction change loss coefficient expression makes a distinction between bulk and periphery of the packing. That is, in the core of a packed bed the gas flow changes direction at transitions between packing elements or layers only. However, in the wall zone this happens also with channels ending at the wall, which means that here flow direction changes also within the height of a packing element. This appeared to be a reason for increased pressure drop observed with the same packing in columns with small diameters.23 ζDC ¼
hpb ðξ þ ψξwall Þ hpe bulk
with h2pe 2hpe 2 d ψ¼ c tan2 R πdc 2 tan R
!0:5
Table 5. Pressure Drop Caused by Narrow Trough Distributors (nt) Installed in Different Positions (1, 2, 4, 5, 8, 9, 12) along the DWC, with Indication of Free Area and Corresponding Vapor Load
ð27Þ
The pressure drop due to direction changes in the bulk appeared to be a strong function of corrugation inclination angle only:
0:445 4092u0:31 Ls þ 4715ðcos RDC Þ ReGe 0:779 þ 34:19u0:44 Ls ðcos RDC Þ
ReGe
4
8
5
9
12
type
nt
nt
nt
nt
nt
nt
nt
jnt
0.40
0.40
0.40
0.40
0.40
0.40
0.4
FG (Pa0.5)
1.16
1.23
1.41
1.14
1.00
1.65
1.40
Δp (mbar)
0.03
0.04
0.05
0.03
0.02
0.07
0.05
2 3
prefractionator
main column
6
10
7
11
13
3
2
uLe type
m /m h 16.5 15.5 cc cc
8.9 cc
39.3 ct
15.8 ct
17.9 cc
34.7 ct
jcc/ct
-
0.25 0.25
0.19
0.25
0.25
0.25
0.25
FG
Pa0.5
1.27 1.20
1.25
1.34
0.93
1.63
1.57
Δp
mbar
0.36 0.32
0.68
0.49
0.24
0.60
0.54
ζnt ¼ 1:2½1:5 jð2:5 jÞ
ð33Þ
chevron type liquid collector: ζcc ¼ 1:5ð2:5 2:5jÞ
ð30Þ
where ReGe represents the Reynolds number based on the effective gas velocity. F uGe dhG ¼ G μG
2
narrow trough liquid distributor:
In the wall zone also the liquid and vapor load play an influential role: ξwall ¼
1
Position
ð28Þ
ð29Þ
main column
Table 6. Pressure Drop Caused by Chevron (cc) and Chimney Tray (ct) Collectors Installed in Different Positions (2, 3, 6, 7, 10, 11, 13) along the DWC, with Indication of Free Area and Corresponding Vapor and Liquid Loads
hpe 2 þ arcsin π dc tan R
ξbulk ¼ 1:76ðcos RDC Þ1:63
prefractionator
chimney type liquid collector: ζct ¼ 1:2½1 þ 2:5ð1 jÞ
ð31Þ
The relative magnitudes of the three different pressure drop components depend on the corrugation inclination and flow direction change angles involved. A detailed numerical illustration of exhibited effects can be found elsewhere, e.g., Olujic et al.19 4.2.2. Pressure Drop of Liquid Distributors and Collectors. The pressure drop caused by liquid distributors and collectors can easily be determined using the recently proposed model by Rix and Olujic:15 ! ζcc, ct, nt FG2 ð32Þ Δpint ¼ j2cc, ct, nt 2 where ζ is the characteristic flow resistance coefficient and j is the free (void) area, while indices cc, ct, and nt denote respectively the chevron type liquid collector, the chimney tray liquid collector, and the narrow trough liquid distributor. The characteristic flow resistance coefficient is expressed as a function of free area using the following expressions.
ð34Þ
ð35Þ
The free areas of all (narrow trough) liquid distributors and corresponding vapor loads expressed as characteristic F-factors are shown in Table 5, while the same can be found for different types of liquid collectors in Table 6. The estimated pressure drop for each device is shown in the bottom row of Tables 5 and 6, respectively. One should mention here that the above expressions account for the observed liquid load effect and according to given constant (representative) values of coefficients the extent of this effect is most pronounced in the case of the chevron collector. The chosen value (1.5), however, may appear conservative in the case of rather low liquid loads (below 3 m3/m2 h). The experimental data that have served as the basis for development and validation of the above expressions can be found elsewhere, e.g., Rix and Olujic.15 The results are summarized in Table 7, indicating the relative magnitudes of the pressure drops of internals and the partitioned part of the column with respect to the total pressure drop. One should note that in the present case a constant free area (25%) for 5688
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all liquid collectors was chosen, except for the chimney collector on the main column side, which was reduced to 19% to ensure equal pressure drop on both sides of the partition wall. Being rather low, the pressure drop of support grids is neglected. Also, the numbers shown in Tables 5 and 6 indicate that the pressure drop of narrow trough liquid distributors is much lower than that of liquid collectors. This is mainly due to a much larger free area available for ascending vapor than in the case of liquid collectors that require relatively more crosssectional area for liquid handling. In any case, as demonstrated here, the free area of liquid collectors can serve as a means for fine-tuning the pressure drop of sections in the partitioned part of a DWC. This can be done automatically using Excel solver, which will indicate the free area bound between 5 and 30%, generating the requested pressure drop. The dimensioning procedure for a three-product DWC is shown schematically in Figure 9.
5. ECONOMIC EVALUATION AND COST ESTIMATION PROCEDURES Total annualized costs (TACs) are taken as the basis for evaluation of the economic feasibility of a DWC. Since different Table 7. Overall Pressure Drop (Δp) of Packings and Column Internals as Well as That of a DWC with Indication of the Contribution of Either of Two Sections in Partitioned Part of the Column
configurations are compared on the same basis, TACs are represented simply as a sum of the annual utility cost and 10% of the installed equipment cost. The latter is based on the assumption of a plant financial lifetime of 10 years. The yearly operation time is taken to be 8322 h, as encountered at INA. To be closer to the common European and United States situation, the following utility prices were considered in the present study: US $0.03/t for cooling water, US $13/t for steam, and US $130/t for fuel oil. The latter is used because a fired heater is necessary in conjunction with a rather high temperature of the bottoms of the platformate splitter (first column in the conventional sequence) and the DWC. The capital costs in the present cases include those associated with column shell, trays, and/or packings and, for packed columns, also liquid collectors, liquid distributors, and support grids. Important external equipment components of each distillation column are the reboiler, condenser, and reflux accumulator, respectively. The latter has not been considered in the present study. In order to bring the installed equipment costs estimated using the SI unit version of correlations from the Douglas textbook24 to the price level corresponding to the year 2009, the corresponding annual value (1468.6) of the Marshall & Swift Equipment Cost, published in the March 2010 issue of Chemical Engineering,25 has been used. The installed cost of a column shell (in US $) made of carbon steel is estimated using the correlation:
Δp (mbar)
Cshell
prefractionator
main column
mbar mbar
41.07 2.73
41.38 2.41
total
mbar
43.80
43.80
partitioned section
mbar
14.95
14.95
packings internals
1468:6 ¼ fp dc 1:066 h0:802 c, t-t 280
ð36Þ
where dc (m) is the column diameter and hc,t-t (m) is the tangentto-tangent column height, while the cost factor fp depends on the operating pressure. In the present case, for p e 3.5 bar, fp = 2981.68.
Figure 9. Schematic illustration of the DWC dimensioning procedure. 5689
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Table 8. Unit Prices of Structured Packing, Packed Column Internals, and Sieve Trays device
unit price
Table 9. Equipment Costs, Utility Costs, and Total Annualized Cost (TAC) for Conventional Sequence with Respectively Trayed and Packed Columns and a DWC (Price Reference December 2009)
600 US $/m2
sieve trays 2
3
sructured packing (250 m /m ) liquid distributor
2000 US $/m3 4000 US $/m2
liquid collector
2000 US $/m2
support grid
800 US $/m2
For the purchased cost for sieve trays (carbon steel) as well as structured packings and internals (both made of stainless steel), we have used the values approved by Montz as reasonable estimates for the purposes of this comparative study. These are summarized in Table 8. For structured packings, the price is proportional to the specific geometric area of the packing. This means that in the present case the value given in Table 8 needs to be multiplied by the factor 1.4, which is the ratio of specific geometric area of packing used in this study, i.e., B1-350 MN, and the basic type B1-250. That is, the given numbers represent the nominal specific geometric area of a packing in m2/m3. Given values are valid for conventional tray and packed columns. In order to account properly for complexities associated with building a packed DWC, the cost of both packings and related internals installed in the partitioned part is increased by 20%, i.e., the value for standard equipment multiplied by the factor 1.2. The number of beds and their volumes and the number of distributors, collectors, and support grids contained in conventional and partitioned parts of the column can be retrieved by careful inspection of the detailed drawing shown in Figure 8. Finally, to translate the purchased cost into installed cost for sieve trays and for structured packings and related internals factors 3 and 2 are used, respectively. For shell and tube condensers and reboilers, the following expression allows estimation of the installed cost in US dollars: 1468:6 ð37Þ ctype A0:65 Ccond ¼ 280 where A (m2) is the required heat transfer area and ctype is the coefficient depending on the type of heat exchanger. For condensers, ctype = 1609.13, and for kettle reboilers, ctype = 1775.26. These numbers are valid for common construction materials and the operating pressure as encountered in the present case. The installed cost (in US dollars) of a fired heater is estimated from 1468:6 ½14390:71Q 0:82 ð1:23 þ ft þ fm þ fp Þ ð38Þ Creb ¼ 280 where Q (MW) is the reboiler duty, ft is the correction factor accounting for the type of heater (for a cylindrical heater, ft = 0), fm is the correction factor that accounts for the construction material (for carbon steel, fm = 0, and for stainless steel, fm = 0.5), and fp is the correction factor for the effect of the operating pressure (for pressures below 34 bar, fp = 0). A summary of the capital, operating, and total costs for two conventional configurations and a DWC is given in Table 9. Although the conventional configuration with two columns equipped with structured packings appears more cost-effective than the conventional configuration employing tray columns, a
configuration C1C2 (tray) C1C2 (packed) DWC (packed) Installed Equipment Costs (US $) column shell
1,261,781
781,468
501,621
column internals
678,240
611,793
516,332
reboiler
443,109
401,809
259,461
condenser
399,610
386,898
203,090
total capital
2,782,740
2,181,967
1,480,504
savings (%)
21.6
46.8
Operating Costs (US $/year) cooling water fuel oil/4 bar steam
121,834 938,071
119,337 907,096
59,169 452,491
total utilities
1,059,905
1,026,433
511,660
savings (%)
3.2
51.7
TAC (US $/year) savings (%)
1,338,179
1,244,630
659,710
7.0
50.7
compact DWC is by far the most attractive option. Compared to the conventional tray column configuration, a DWC would require 46.8% less capital and 51.7% less utilities, which combined results in a 50.7% lower total annualized cost (TAC). This is really appealing, indicating that implementation of a DWC could be highly rewarding, i.e., could lead to a substantial increase in profitability of aromatics processing plants.
6. CONCLUDING REMARKS In this paper we have demonstrated that a commercial simulator can be used in conjunction with initial guesses for governing variables obtained from a simple but theoretically founded short-cut method to generate without computation difficulties an optimized internal configuration of a DWC. Compared to the conventional two-column-in-series configuration for obtaining benzene- and toluene-rich fractions from a 15component feed, a DWC requires 43.3% less energy to get the same product specifications. The Delft model for structured packings in combination with the Rix and Olujic method for packed column internals proved to be an effective and reliable tool for preliminary dimensioning of DWCs equipped with both conventional and high performance corrugated sheet structured packings. The free area of liquid catchers appeared to be a suitable variable for tuning the pressure drop in the partitioned part of a DWC. The compact dimensions of a DWC translate into a considerably lower installed equipment cost. Expressed in total annualized costs (TACs), a DWC enables a 50.7% savings with respect to the conventional two-columns-in-series configuration employing tray columns, and 47.0% savings with respect to those employing the same type and size of structured packings. The fact that much less energy, capital, and space is needed makes a DWC a highly interesting option for implementation in aromatics processing plants. 5690
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors thank J. Montz for providing the reference designs for conventional columns and for the corresponding DWC as well as the information on purchased and installed costs of trays, packed column internals, and structured packings. We would also like to thank INA Refinery Sisak, Croatia (the MOL group), for providing actual plant data. ’ NOMENCLATURE A = cross-sectional area (m2) ap = specific geometric surface area of packing, m2/m3 ae = effective (interfacial) area, m2/m3 b = corrugation base length (m) C = installed cost of equipment (US $) ctype = heat exchanger type cost coefficient d = diameter (m) dhG = hydraulic diameter for the gas phase (m) FG = uGs(FG)0.5 = gas load factor (Pa0.5 or m/s (kg/m3)0.5) FG,lp = loading point gas load factor (m/s (kg/m3)0.5) Fload = loading effect factor f = cost-related correction factor g = gravity acceleration (m/s2) HETP = height equivalent to a theoretical plate (m) h = corrugation height (m) hc,t-t = tangent-to-tangent column height (m) hL = operating liquid holdup (m3 of liquid/m3 of bed) hpb = height of the packed bed (m) hpe = height of the packing element (m) htray = height between top and bottom tray (m) lG,pb = total length of gas flow channel in a packed bed (m) lG,pe = length of gas flow channel in a packing element (m) lpcw = distance from column shell to partition wall on prefractionator side (m) MG = mass flow rate of gas/vapor (kg/s) ML = mass flow rate of liquid (kg/s) npe = number of packing elements (layers) in a bed p = operating pressure (bar) ΔP = pressure drop (Pa or mbar) Q = reboiler duty (MW) ReGe = effective gas phase Reynolds number ReGrv = relative velocity Reynolds number ReL = Reynolds number for the liquid s = corrugation side length (m) TAC = total annualized cost (US $) uGe = effective gas velocity (m/s) uGs = superficial gas velocity (m/s) uLe = effective liquid velocity (m/s) uLs = superficial liquid velocity (m/s) Δz = unit bed height (m) Greek Symbols
R = corrugation inclination angle (deg) RL = effective liquid flow angle (deg) RDC = flow direction change angle (deg) δ = liquid film thickness (m) ε = packing porosity (m3 of voids/m3 of bed)
ARTICLE
ζ = column internals flow resistance coefficient ζDC = overall coefficient for direction change losses ζGG = overall coefficient for gasgas friction losses ζGL = overall coefficient for gasliquid friction losses Θ = angle subtended by partition wall (deg) μG = viscosity of gas (Pa s) μL = viscosity of liquid (Pa s) ξbulk = direction change factor for bulk zone ξGG = gasgas friction factor ξGL = gasliquid friction factor ξwall = direction change factor for wall zone FG = density of gas (kg/m3) FL = density of liquid (kg/m3) j = fraction of the triangular flow channel occupied by liquid j = free or void area of column internals Ψ = fraction of gas flow channels ending at column walls Subscripts
cond = condenser c = column cc = chevron collector ct = chimney tray collector DC = direction change GG = gasgas interaction GL = gasliquid interaction L = liquid lam = laminar flow m = related to construction material mc = main column nt = narrow trough distributor o = overall p = related to operating pressure pc = prefractionator column reb = reboiler shell = related to column shell t = related to fired heater type trays = related to trays turb = turbulent flow
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