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INTERNATIONAL JOURNAL OF CHEMICAL

REACTOR ENGINEERING

Volume 6 2008 Article A91

CFD Simulation of Hydrodynamics, Heat

and Mass Transfer Simultaneously in

Structured Packing

M.R. Khosravi Nikou M.R. Ehsani

M. Davazdah Emami

Isfahan University of Technology, m [email protected] University of Technology, [email protected] University of Technology, [email protected]

ISSN 1542-6580

Copyright c2008 The Berkeley Electronic Press. All rights reserved.


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CFD Simulation of Hydrodynamics, Heat and Mass

Transfer Simultaneously in Structured Packing

M.R. Khosravi Nikou, M.R. Ehsani, and M. Davazdah Emami

Abstract

This paper describes the results of computational fluid dynamic modeling of

hydrodynamics, heat and mass transfer simultaneously in Flexipac 1Y operated

under a counter-current gas-liquid flow condition. The simulation was performedfor a binary mixture of methanol-isopropanol distillation. The pressure drop,

the height of equivalent to theoretical plate (HETP) and temperature distribution

across the column were calculated and compared with experimental data. The

mean absolute relative error (MARE) between CFD predictions and experimental

data for the pressure drop, HETP and temperature profile are 20.7%, 12.9% and

2.8%, respectively.

KEYWORDS: CFD, structured packing, heat and mass transfer, hydrodynamics


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1. INTRODUCTIONThe gas-liquid contactors are one of the most wide-spread chemical engineering

apparatus. Two-phase flow of liquid with countercurrent vapor is widely

encountered in many industrial applications such as structured packed columns,

reactors, evaporators, condensers, etc. In this kind of equipment, the fluxes of heatand mass transfer, in both liquid and gas phases are usually related to the flow

pattern. Therefore, many investigations are carried out to look for new structured

packing designs, to obtain hydrodynamic conditions which enhance transfer.There are numerous types of corrugated surfaces and structured packing, refer to

the work done by Taylor and Krishna (2000) for details, for few of them.

Current popular design procedures, such as those by Gualito et al. (1997)and references therein, are empirical and thus, their use beyond the range of their

validation is risky (Engel et al., 2001). It is felt that disadvantages of these

empirical models could be overcome by using more reliable modeling techniques

based on fundamental considerations.Although falling films over smooth substrates have been widely studied

both theoretically and experimentally (Oron et al., 1997; and references therein),

only few studies have examined of flow on structured packings (Shetty and Cerro,1993; Shetty, 1995; Shetty and Cerro, 1997a,b , 1998); these studies are for very

small Reynolds number and also two-dimensional.

It is well known that the most accurate methods of separation processesare based on the continuous mechanics consideration, and thus the method of

CFD represents a promising application (Mahr and Mewes, 2007). In the recent

years, there have been significant academic and industrial efforts to exploit CFD

for the design, scale-up and optimal operation of various chemical processesequipment.

The exact path and breakup of liquid films and rivulets on a section of

packing has been calculated (Hoffmann et al., 2006). Currently these approachesusing the exact packing geometry are only feasible for either gas or liquid flow

and for small segments of the packed beds only. However, the simulation of

large-scale structured columns still appears too difficult due to superposition ofdifferent scales (Petre et al. ,2003; Valluri et al. ,2005; Mahr and Mewes ,2007;

Haghshenas Fard et al. ,2007; Wen et al. ,2007; Raynal et al. ,2007).

The work discussed here concerns three-dimensional simulation ofhydrodynamic, heat and mass transfer simultaneously in structured packing

Flexipac 1Y from Koch-Glitsch Company.

Khosravi Nikou et al.: CFD Simulation of Structured Packing

Published by The Berkeley Electronic Press, 2


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2. THEORETICAL AND NUMERICAL METHODOLOGYThe Eulerian-Eulerian approach is adopted for modeling two-phase flow in the

packing. The volume of fluid (VOF) method is used to track the free surface in

this application. The VOF method allows the construction of the interface to

become part of the solution based on the same grid system, which offers a flexibleand efficient method to describe the changes in topology of a gas-liquid interface.

VOF solves a single set of momentum equations throughout the domain, where

the resulting velocity field is shared among the phases. The accumulation andconvective momentum terms in every control volume (cell) balance the pressure

forces, shear forces, gravitational body forces and additional forces. The

momentum equation is dependent on the volume fractions of all phases throughthe mean properties of the phases such as density and viscosity . In each

control volume, the volume fractions of all phases sum to unity. The tracking of

the interface(s) between the phases is accomplished by the solution of a continuity

equation for the volume fraction of one (two-phase flow) or more of the phases(Ataki and Bart, 2006).

2.1 Governing Equations

The hydrodynamic approach to multiphase-flow systems is based on the

principles of mass conservation, momentum balance and energy conservation foreach phase (Gidaspow, 1994).

- Conservation of mass for each phase

Gas phase:

. (1)Liquid phase:

. (2)

where =

N

j

j

j

ll RMm ,

= lg mm , Rj is the rate of mass transfer between gas

and liquid phases.

2 International Journal of Chemical Reactor Engineering Vol. 6 [2008], Article A

http://www.bepress.com/ijcre/vol6/A91


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- Conservation of phases

1 (3)

- Momentum equations

Gas phase:

. . ,(4)

Liquid phase:

. . , (5)- Energy equations

To treat non-isothermal multiphase flow systems the energy equations are neededto compute the heat transfer primarily due to heat exchanges.

Gas phase:

. . . , (6)

Liquid phase:

.

. ,

(7)

where




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8

(8)

2.2 Constitutive Equations

- Interphase mass transfer equations

In order to solve the conservation of mass for each phase, Rj, the rate of mass

transfer between phases must be evaluated. According to the two-film theory

(Whitman, 1923), in a binary distillation A-B, the mass transfer rate of a volatilecomponent can be determined by:

(9)

where kG and kL are the individual mass transfer coefficients of the gas and liquidphase, respectively. ae is the effective interfacial area, MA is the molecular weight

of the more volatile component A in the liquid and gas phases, and xAI and yAI arethe interfacial mole fractions of component A in the liquid and gas phases. At the

interphase, xAI and yAI are in equilibrium, and: 1 1 (10)

In addition, rearrangement of Eq.(10) results in:

(11)

1 1 (12)

where is the relative volatility. Combining Eqs.(9), (10), (11) result in:

1 1 1 1 1 1 0 (13)




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The gas and liquid phase mass transfer coefficients, kG and kL, can be

calculated, using Delft Model proposed by Olujic (2002). The model is designed

to calculate mass transfer efficiency in the preloading region, which implies a

conservative approach when extended into loading region. It utilizes zig-zagtriangular flow channels with a corresponding hydraulic diameter at crossings of

corrugations. The model is based on complete wetting of the metal surface, thusliquid holdup is determined from packing area and the average film thickness. It is

also founded on liquid film flow down inclined corrugated plates and in addition

takes into account explicitly several macro geometrical parameters which can

affect packing performance.

,

,

(14)

2 0.9 (15)

, 0.664/ , (16)

, 8 1 , /

1 12.7 8 / 1 (17)

2

22

2

.

22

(18)

, (19)




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2 2 (20)

4 (21)

3/

(22)

4 (23)

(24) 2 3.7 5.02

3.7 14.5

(25)

(26)

1 (27) (28) (29) 1 11.45. ... 45 (30) 1 1 , 0.49 1.2 (31)




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where D is the diffusion coefficient and is the corrugation inclination angle, isthe packing porosity, and represents the fraction of the packing surface areaoccupied by holes.

Equations (9)-(31) were fed to CFX, to enable the software to performlocal calculation of the mass transfer equations.

- Heat transfer equations

In order to specify temperature profile, the value of heat transfer coefficient atinterface is required. Hughmark (1967) proposed the following empirical

correlations for calculation of overall Nusselt number. His model is a single

resistance type which is applied on the continuous fluid side with zero resistanceon the dispersed phase side of the interphase (CFX

Manual, 2007). It is,

however, important to use this correlation in the recommended Prandtl number

range.

2 0.6.. 0 776.06 0 250 (32) 2 0.27.. 776.06 0 250 (33)

These equations are built into correlation subprograms in the CFX code,which are activated during the execution of the software.

- Height Equivalent to Theoretical Plate (HETP) relations

The mass transfer performance of a packed column in distillation or absorption isoften expressed by the HETP. Factors affecting HETP have usually been

identified as type and size of packing, physical properties of the test systems,

operating condition, and dimension of columns. According to double film theory(Whitman, 1923), the relation between HETP and height mass transfer unit for the

gas phase (HTUG) and for the liquid phase (HTUL) is given by

1 (34)

where is the stripping factor, which is defined as the slope of ratio of the slope

of the equilibrium line to that of the operating line. Equation (34) in combinationwith the definitions of HTUG and HTUL, which are based on the concentration

driving force across the gas and liquid films, yields




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where uGs and uLs are the gas and liquid phase superficial velocities, kG and kL arethe individual mass transfer coefficients of the gas and liquid phase, respectively,

and ae is the effective interfacial area provided by the packing to mass transfer.

- Turbulence model

Considering the complex nature of fluid flow in the present geometry, the

Re-Normalization Group k- (RNG k-) model is adopted for the currentsimulations to take account of the anisotropy of turbulence (CFX

Manual, 2007).

- Interphase transfer

The Particle Model is used to simulate the interaction of transported quantities at

interphase. Schiller-Naumann Drag Model is applied to calculate drag coefficientbetween liquid droplets and the gas phase. This model is used when the fluid

droplets are sufficiently small and may be considered spherical (CFX

Manual,

2007).

24 10.15. (36)

2.3 Geometrical Model and Boundary Conditions

Geometrical modeling is one of the most critical stages in CFD simulations;correct definition of the geometry provides a more realistic scenario for the

simulation, and the technique used for constructing the geometry will ensure the

feasibility of generating a mesh good enough to capture all of the phenomenainvolved in the problem.

An element of Flexipac

1Y is composed an ensemble consisting of a

large number of triangular flow channels having identical cross-sections. To forman element, the corrugated sheets are alternately positioned parallel to each other,

so that the corrugations of the contiguous sheets are inclined in opposite

directions in the column.

Because of CFD models for heat and mass transfer simulation are verycomplex, the computational domain in this study consists of two sheets at center

of the structured packing.

All the model geometry and Flexipac 1Y characteristics are given inFigure 1 and Table 1.

1

(35)




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Figure1. The model geometry

Table1. Geometrical characteristics for the simulated structured packingFlexipac 1Y

Packing type ap(m-1) (%) (deg) l(m)

Channel dimensions (m)

Base

b

Height

h

Side

s

Flexipac

1Y

(Koch-Glitsch)453 91 45 0.267 0.0127 0.0064 0.009

To obtain a solution of the CFD model, the geometry of the packing with anumerical grid must be inserted in the program. In this study, the mesh generated

for geometry was performed in CFX Mesh Generator 11 from ANSYSCompany.

The grid size used is chosen by performing a grid independence study,since the accuracy of the solution depends on the number and the size of the cells.The grid independence study was conducted by altering the cell size inside thedomain, and by refining the grid size on the corrugated walls. Simulation was

performed for 700,000, 1,100,000 and 1,500,000 cell elements and it was foundthe results for pressure drop, HETP and temperature profile slightly differs for thelast two numbers of cells(less than 0.5%). Therefore, 1,100,000 cell elementswere considered for the final simulation. Unstructured tetrahedral mesh was used,modified near the walls by applying prism layers, in order to simulate the wall

boundary layer accurately. The advantage of this grid is that it can be adapted tocomplex geometry well and optimum properties are easier to achieve than theother meshes. Since the grid lines follow the boundaries, the boundary conditionsare more easily implemented than the stepwise approximation of curved




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boundaries (Ferziger and Peric, 2002). The use of prism layers on the walls is

advised for confined geometries (CFX

Manual, 2007).

Three-dimensional coordinate system is used for computation. No slip

boundary condition is provided at the wall. All the boundary conditionsmentioned in Table 2 are considered to have a constant value at inlet, outlet and

wall.

Table2. Boundary conditions

Location Boundary condition types

InletVelocity, Volume fractions, Mass fraction of methanol,

Temperature

Outlet Velocity

Symmetry Plane Symmetry

Wall No-slip, Temperature

2.4 Simulation Scheme

The CFD software, ANSYS-CFX version 11, is used to simulate the motion ofgas-liquid two-phase flow on structured packing. A high resolution convection

scheme was chosen as the solution of the momentum and energy equations (CFX

Manual, 2007). The SIMPLEC algorithm is used to solve the pressure field.

3. RESULTS AND DISCUSSION3.1 Pressure Drop

One of the most important parameters for the packed bed design is the pressuredrop per unit length of packing (P/L). This pressure drop results from fluid

friction. Figure 2 shows result of pressure drop per unit length of packing against

parameter Fs-factor which is defined as uGG. As mentioned previously, thesimulations were carried out for two packing sheets and the CFD results are

shown for this geometry. To evaluate CFD results, experimental data (Koch-Glitsch Bulletin) are also shown in Figure 2. It can be seen from the results thatthe pressure drop for the current configuration is more than a complete packing.

This is in accordance with the findings of Wen et.al., 2007, and their explanation

about the difference is also relevant to the present case.




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Figure 2 also shows the prediction of CFD for air-water two phase flow

which is performed by authors for one complete element. The mean absolute

relative error (MARE) which is calculated by Eq.(37) between CFD predictions

and the experimental data is 20.7%.

% 100 11 . (37)It is clear from Figure 2 that CFD results can predict the trend of pressure

drop across the packing very well, but under-estimates values for pressure drop.

This can be attributed to some important phenomena which have a major effect onpressure drop but are not considered in the modeling, such as uneven gas and

liquid distribution, liquid back-mixing and flow channeling.

Figure 3(a,b,c) shows pressure profile and velocity contours of the liquidand gas phases on a plane at the center of the computational domain at

uGs=0.17m/s. A uniform pressure field at each station along the axis of the

packing is seen in the figure, which indicates that the assumption of uniform cross

sectional pressure for analyzing the packings and beds is a reasonable assumption.The velocity profiles are non-uniform in the cross sectional planes, which is a

measure of momentum exchange in these planes.

Figure2. Simulated and experimental pressure drop versus gas flow factor Fs

0

100

200

300

400

500

600

700

800

0 0.2 0.4 0.6 0.8 1 1.2

P/Z(Pa/m)

Fs m/s(kg/m3)0.5

Twosheets

Foursheets

Complete

ElementExp.




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Figure3. (a) Pressure profile, (b) liquid and (c) gas velocity contours for

Ul=0.0128 m/s, Ug=0.235 m/s, xmeth.= ymeth.= 0.7049 wt/wt

(b)

(a)

(c)




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3.2 Mass Transfer

HETP is one of the most commonly used measures to characterize the separation

efficiency of packed bed columns. HETP can be identified by using the velocity

and concentration profiles which are derived from CFD results. As mentioned

earlier, the distillation of Methanol-Isopropanol binary mixture at total reflux andatmospheric pressure conditions is simulated. Figure 4 shows a sample of

methanol mass fraction profile in the liquid phase between the sheets of the

structured packing, obtained by CFD modeling. Methanol concentration in liquidphase starts to decrease when moving from the top to the bottom of the packed

bed.

The flow domain includes two adjacent sheets of packing that makeseveral pairs of crossing channels. Due to this channel structure, the heat and

mass transfer within the packing is highly anisotropic. Methanol concentration

profile depends not only on the liquid and gas velocity, but also on the flow

direction of gas and liquid. However, velocity constant boundary condition for theoutlet region seems to be inappropriate for the simulation. Other boundary

conditions such as pressure or distributed velocity profile may be used for further

investigation. Also, as discussed by Raynal et al. (2004), whatever the kind ofboundary conditions, imposed mass flow or imposed velocity conditions, is used,

the velocity profiles at the exit of domain are quite different from the inlet and

may have a distributed profile.A comparison between the predicted HETP values from the CFD

simulations and experimental data (Haghshenas Fard et al., 2007) can be found in

Figure 5. It is clearly seen that the CFD simulation can predict the separation

efficiency quite well over the range of gas Fs-factors. It is observed from Figure 5that the predicted HETPs from CFD results are slightly lower than the

experimental data. This may be attributed to the assumption of uniform

distributions of vapor and liquid phase in the CFD models, which causes anincreasing of mass transfer area that results in lower HETP. The mean absolute

relative error (MARE) between CFD predictions and the experimental data is

12.9%.




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Figure4. Methanol concentration in liquid phase on (a) a plane at thecenter and (b) through sections of structured packing for Ul= 0.0128 m/s,

Ug= 0.235 m/s, xmeth.= ymeth.= 0.7049 wt/wt

(b)

(a)




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Figure5. Comparison between experimental data and predicted HETP formethanol-isopropanol system

3.3 Heat Transfer

As mentioned in the previous section, in the CFD simulations, continuity,

momentum, heat and mass transfer equations have been solved simultaneously,

and, therefore, the temperature distribution through the packed bed can bepredicted directly. Figure 6 shows a contour of temperature between two

corrugated sheets and through sections of the packing. In Figure 7, comparisons

between CFD predictions and experimental data (Haghshenas Fard et al, 2007)

are shown. It is observed that there exists a good agreement between CFD andexperiments in temperature profile across the column. The mean absolute relative

error (MARE) between CFD predictions and the experimental data is 2.8%.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.1 0.2 0.3 0.4 0.5

HETP(m)

Fs(m/s)(kg/m3)0.5

RNGk

Exp.

CFD

Simulation




18/23

Figure6. Temperature profile in liquid phase on (a) a plane at the center and (b)

through sections of structured packing for Ul= 0.0128 m/s, Ug= 0.235 m/s,

xmeth.= ymeth.= 0.7049 wt/wt

(b)

(a)




19/23

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67.2

67.4

67.6

67.8

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68.2

68.4

68.6

68.8

69

69.2

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n CFD rect the presse error (M%, 12.9%

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ults andure drop,

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volume,

, m2/m

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6




20/23

D Diffusivity, m2/s

dhG Hydraulic diameter of triangular gas flow channel, m

F External body forces, kg/m.s3

Fs Gas F-factor, m/s(kg/m3)0.5H Channel height, m

HETP Height of equivalent to a theoretical plate, m

hL Liquid holdup

HTUG Height mass transfer unit for the gas phase, m

HTUL Height mass transfer unit for the liquid phase, m

kG Gas phase mass transfer coefficient, m/s

kL Liquid phase mass transfer coefficient, m/s

l Packing height, m

M Molecular weight, kg/mole

P Pressure, kg/m.s

2

R Mass transfer rate, kg/m

3.s

s Channel side, m

T Temperature, K

uGe Effective gas velocity, m/s

uGs Superficial gas velocity, m/s

uLe Effective liquid velocity, m/s

uLs Superficial liquid velocity, m/s

v Velocity, m/s

x Mole fractions

y Mole fractions

Z Packed bed height, mP Pressure drop, kg/m.s

2

Greek symbols

Relative volatility

Frictional coefficient

Inclination Angle

Liquid film thickness, m

Volume fraction, Turbulence dissipation Porosity Ratio of equilibrium line slope to operating line slope

Viscosity, kg/m.s

Density, kg/m3 Viscous stress tensor, kg/s

2

Subscripts

A ComponentB Component




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G, g Gas phase

L, l Liquid phase

Superscripts

I Interphase

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