M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q.

21 (3) 197–205 (2007) 197

CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern

M. Anil, V. K. Agarwal, M. Siraj Alam, and K. L. Wasewar*
Chemical Engineering Department, Indian Institute of Technology (IIT),
Roorkee – 247667, Uttarakhand, India Original scientific paper
Email: k_wasewar@rediffmail.com, klw73fch@iitr.ernet.in Received: August 28, 2006
Phone: +91-1332-285347; Fax: +91-1332-276535 Accepted: March 1, 2007

Bubble column (BC) or slurry bubble column (SBC) reactor has emerged as one
of the most promising devices in chemical, biochemical and environmental engineering
operations because of its simple construction, isothermal conditions, high heat and
mass transfer rates, and on-line catalyst addition and withdrawal. The present work
has been carried out to characterize the dynamics of three-phase flow in cylindrical
bubble column, run under homogeneous bubble flow and heterogeneous flow conditions
using CFD (Computational Fluid Dynamics) simulation. The investigation has been
done to study the flow pattern of three-phase bubble column along with parametric
studies. The simulations were performed for air-water-glass beads in a bubble column
of H = 0.6 m height, Di = 0.1 m and ds = 0.05 m sparger diameter to study the flow
pattern. Eulerian-Eulerian three-phase simulations with k-e turbulence for liquid phase
were carried out using the commercial flow simulation software CFX-5.6, with a
focus on characterizing the dynamics properties of gas liquid solid flows. The model
has been validated using available experimental data and is in good agreement.
Detail study of the flow pattern in three-phase bubble column has been carried out
and flow pattern has been presented in the form of contour and vector plots. The results
presented are useful for understanding the dynamics of gas liquid solid flows in bubble
column and provide a basis for further development of CFD model for three phase
systems.
Key words:
CFD, Bubble column, Euler-Euler model, three phase reactor

Introduction the aeration of activated sludge for biological oxi-

dation etc. Bubble columns are preferred over other
Bubble column (BC) or slurry bubble column multiphase reactors because it requires less mainte-
(SBC) reactor has emerged as one of the most nance due to absence of moving parts, and it also
promising devices in chemical, biochemical and en- provides higher values of effective interfacial areas,
vironmental engineering operations because of its overall mass transfer coefficients, higher heat trans-
simple construction, isothermal conditions, high fer rates per unit volume of the reactor, and easy
heat and mass transfer rates, and on-line catalyst solids handling without any erosion or plugging
addition and withdrawal. In bubble column slurry problems. At the same time these types of reactors
reactors, a gas is dispersed through a deep pool of are cheaper and require less floor space, and can
liquid containing suspended solid particles. In these easily accommodate slow reactions due to high liq-
reactors, the momentum is transferred to the liquid uid residence time.
phase and solid phase by the movement of the gas
bubbles. Bubble column reactors have a wide range Computational Fluid Dynamics (CFD) is the
of applications such as absorption, catalytic slurry science of predicting fluid flow, heat transfer, mass
reactions, bioreactions, coal liquifications etc. Bub- transfer, chemical reactions, and related phenomena
ble (slurry) reactors are used extensively to carry by solving the mathematical equations that govern
out a variety of gas liquid and gas liquid solid reac- these processes using numerical algorithms. The re-
tions. Classic examples are carbonation of lime sults of CFD analysis are relevant engineering data
slurry, chlorination of paper stock, hydrogenation used in conceptual studies of new designs, detailed
of vegetable oils, aeration of fermentation broths as product development, troubleshooting, and redesign
in the production of penicillin, production of citric and therefore CFD is gaining importance in general
acid from sugar by action of microorganisms, and process applications. CFD approaches use numeri-
cal techniques to solve the Navier-Stokes equations
for given flow geometry and boundary conditions
* Corresponding author thereby implementing models for flow aspects like
198 M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007)

turbulence or heat and mass transfer as relevant for modeling results were presented for bubble col-
the specific modeling task. It has also been an im- umns by Mitra-Majumdar et al.5 and for airlift loop
portant tool in air and space industry as well as ve- reactors by Padial et al.6 While the first group re-
hicle design for a long time where it deals with a ports results obtained from two-dimensional calcu-
large extent replaced time-consuming and expen- lations in cylindrical coordinates, the latter had to
sive wind tunnel experiments. Although, these ap- perform full three-dimensional calculations to
plications are of single-phase flow, but most of the achieve useful results.
applications in chemical and biochemical reactors
Further, Michele and Hempel7 reported detailed
includes multiphase flow and modeling and numeri-
cal treatment of those introduce additional chal- measurements of local dispersed phase holdups in
lenges. Therefore, multiphase CFD applications a pilot plant-sized bubble column operated at high
have gained broad attention during the last decade superficial gas velocities and solid holdups. It
with enhanced computational. Although, most of deals with the influence of superficial gas velocity,
the literatures available are limited to two-phase solid loading and sparger geometry on measured
flows, and especially gas-liquid CFD projects often and computed liquid flow velocities and holdup
deal only with very low dispersed phase holdups. In distributions. Liquid velocity measurements have
effect this means that multiphase CFD still is far been performed using the electrodiffusion method;
away from being a general tool for the practitioner modeling calculations have been carried out using
even if recent advances in computational power the computational fluid dynamics (CFD) code
available in desktop PCs do enable first steps in this CFX-4.3. The experimental setup used by them
direction. consisted of a pilot plant-sized bubble column
Bubble columns have been studied extensively (inner diameter Di = 0.63 m, height H = 6 m)
in literature, and many investigators have reported made from plexiglass which could be equipped
results on CFD simulations. Pfleger et al.1 in- with a plate sparger, a ring sparger or a central
vestigated behavior of a flat laboratory-scale rect- nozzle. Probe ports allowed for the introduction
angular two-phase bubble column using the Eu- of measurement equipment at a vertical spacing
ler-Euler approach by the help of CFX-4.2 and of h = 0.5 m, starting 0.35 m above the sparger
found that 2D modeling of a flat bubble column is level. Their measurements were taken at seven
not possible. This result is supported by the work of radial positions for each level, ranging from reactor
Sokolichin and Eigenberger2. They used in-house centre to reactor edge (spacing 0.05 m. The in-
CFD code but were unable to implement that for vestigated three-phase system consisted of de-ion-
three-dimension. Both of these studies were carried ized water supplemented with potassium sulphate at
out at extremely low superficial gas velocities (be- a concentration of c = 0.01 mol l–1, air and plexi-
low 0.01 m s–1). Krishna et al.3 reported CFD based glass granules (polymethyl-methacrylate, PMMA,
modeling of a pilot-plant size bubble column using density r = 1200 kg m–3, particle hydraulic diame-
CFX-4.2 with the Euler-Euler model as well as at ter dp = 0.003 m). The solid material was chosen as
higher superficial gas velocities (up to u = 0.28 m the model system to represent particles with a
s–1). While one of their reports is entitled biofilm growing on them as employed in biotechno-
“Three-Phase Eulerian Simulation” the reader logical applications. Solid loadings were varied
would be misled to assume that they included solid from j = 0 % (two-phase flow) to j = 10 %, super-
particles into their considerations; moreover, two ficial gas velocities ranged from u = 0.02 to 0.09
dispersed gas phases were calculated to include the m s–1.
different influences of large and small bubbles. In
addition, they calculated integral gas holdups and It is evident from the previous discussion
derived a scale-up correlation for bubble columns that the flow patterns in the bubble column and
of different sizes. Sparger influence on the flow flow parameters have lot of importance for the
structure in two-phase bubble columns with a low overall column performance. Hence, it is essential
height-to-diameter ratio of two was the aim of in- to understand the hydrodynamics of the bubble
vestigations carried out by Ranade and Tayalia4. column. It is also clear from above that most
Using the commercial code Fluent 4.5.2 with an literature reported are limited to two-phase flows,
Euler-Euler approach implementing the k-e model and especially gas-liquid CFD projects often deal
and in agreement with measurement results they only with very low dispersed phase holdups, in
found that single ring spargers induce a characteris- spite of increased computational power available
tic liquid circulation, which can not be observed in for the multiphase CFD applications. In the present
a double-ring sparger configuration. Three-dimen- paper, the flow pattern in a bubble column
sional calculations could not be avoided for a cor- using CFD based software CFX-5.6, has been stud-
rect prediction of flow fields. Three-phase CFD ied.
M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007) 199

Mathematical modeling – Momentum transfer between the liquid and

the dispersed phases was modeled using the appro-
Multiphase CFD modeling, mainly classified into priate drag laws for the respective flow regime.
two approaches Eulerian-Eulerian and Eulerian- – Momentum transfer between the dispersed
-Lagrangian based on dispersed phase (particles, phases were neglected.
droplets or bubbles) handling considerations. The – Bubbles are assumed as rigid sphere having a
former approach assumes that the dispersed phase constant diameter.
consits of representative particles transported with
the continuous phase. A set of Navier-Stokes equa-
Conservation of mass: continuity equation
tions is solved only for the continuous phase; cou-
pling between the motion of the continuous and the The continuity equation describes the mass
dispersed phases and thus computation of the parti- flux into and out of a control volume. The continu-
cle motion is achieved by tracking the particles via ity equations for continuous as well as dispersed
drag law considerations. The Eulerian-Eulerian or phase are as follows:
multi-fluid approach assumes the dispersed and
continuous phases to be interpenetrating continua, ¶( e a r a )
+ Ñ( e a r a v a ) = 0 (1)
for both of which a complete set of Navier-Stokes ¶t
equations has to be solved. Coupling between the
motion of the dispersed and the continuous phase is where a = 1, 2, 3
achieved by implementing momentum exchange ea is the volume fraction of phase a, and
terms into the respective phase’s momentum bal-
ance equations; these terms are usually based on å e a =1 (2)
drag considerations as with the Eulerian Lagrangian a
approach.
The Eulerian-Eulerian approach has been cho- Conservation of momentum: equation of motion
sen for present study because of its obvious compu-
tational advantages at high dispersed phase con- In multiphase formulation, momentum bal-
tents: While in Eulerian–Lagrangian approach suf- ances look slightly different for continuous and dis-
fers from high demands on computational power; persed phases. The momentum balance for the con-
this renders them rather unsuitable for the computa- tinuous phase in most general formulation is:
tion of multiphase flows in real process applications ¶( e a r a v a )
where dispersed phase holdups are usually high. + Ñ 2 (e a ra v a v a )=
¶t
Therefore, in this present study the Euler-Euler or
multi-fluid approach will be implemented which al- =-e a Ñp a + Ñ( e a m a ( Ñv a + ( Ñv a ) T )) + (3)
lows for the computation of three-phase flow fields
even with high solid and gas holdups at reasonable +e a r a g + M a
computational expense.
Momentum exchange between continuous and
Hydrodynamic model dispersed phase i.e. liquid-gas and liquid-solid is:
Np
Assumptions
M a = å c a, b ( v b - v a ) (4)
The following assumptions are made for hy- b=1
drodynamic modeling of bubble column:
– 3D, transient as well as steady state. where
– Isothermal flow conditions, so no energy 3 CD
equations. c a, b = e r |v - va| (5)
4 dp b b b
– Mass transfer and chemical reactions have
been neglected. Momentum balance for the dispersed phase is:
– Buoyancy effect was included in order to
correctly model bubble rise. ¶( e b r b v b )
+ Ñ 2 (e b r bv bv b )=
– Liquid phase turbulence was modeled using ¶t
the k-e model; the dispersed phases were consid-
ered laminar. =-e b Ñp b + Ñ( e b m b ( Ñv b + ( Ñv b ) T )) + (6)
– The system of equations was solved using a
finite-volume scheme. +e b r b g + M b
200 M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007)

Momentum exchange between continuous and The source term Sle is set to zero as with Sl,k.
dispersed phase i.e. liquid-gas for gas phase and The effective liquid dynamic viscosity is com-
liquid-solid for solid phase is: bined for the turbulent case from a laminar and a
turbulent part:
M b = c a, b ( v b - v a ) (7)
where m a , turb
3 CD m a = m a , lom + (13)
c a, b = e r | u - ua | (8) sk
4 dp b b b
Where the turbulent viscosity ma;turb is com-
For liquid-gas, puted from:
CD = 0.44 Re > 1000 (9) m a , turb
m a , turb = C m r l (14)
and for liquid-solid, e

24 In effect, this means that with the k-e model,

cD = . Re 0. 687 )
(1+ 015 Re £ 1000 (10) three additional unknowns (k, e and ma.turb) and
Re
three equations (two partial differential equations,
one algebraic equation) have been introduced into
Turbulence Modeling the calculation yielding a closed model.
Turbulence modeling is of crucial importance
for the correct description of multiphase flows in Initial and boundary conditions
CFD modeling. In this study, one of the most prom- In order to obtain a well-posed system of equa-
inent turbulence models, standard k-e model was tions, reasonable boundary conditions for the com-
considered which has been implemented in most putational domain have to be implemented.
general purpose CFD codes and is considered the
industry standard model. It has proven to be stable – With the three-dimensional calculations car-
and numerically robust and has a well-established ried out in this project, no symmetry conditions as
regime of predictive capability. For general purpose with 2D models were needed.
simulations, the k-e model offers a good compro- – At the walls, a no-slip boundary condition
mise in terms of accuracy and robustness. was implemented for liquid phase and free slip for
Since in the computations carried out here the gas and solid phase.
liquid phase is the continuous one, the conservation – For liquid and solid phase, reactor bottom
equation for the liquid turbulent kinetic energy k and top were considered as walls, while the gaseous
may be written as follows: phase was allowed to enter through a patch at the
reactor bottom the shape of which depended on the
¶ ¶ sparger geometry.
(e l rl k )+ (e l rl ul , j k )-
¶t ¶t – The sparger cannot be modeled with all its
holes but has to be modeled as a flat surface where
¶ æ æ
çe ç m l , turb ö ¶k ö
- ç lç m l , lam + ÷ ÷
÷ ÷= (11) a constant normal gas velocity and gas holdup can
¶x i è è s e ø¶x i ø be prescribed. In reality, however, the local gas ve-
locity at the small sparger holes is substantially
= e l (G - r l e ) + S l , k higher leading to a better fluidization of solid parti-
cles than in the model case.
Here, G is a turbulence production term and Slk
– At the reactor top, a special degassing bound-
is a source term; both of these may be used to e.g.
ary was set up where air and excess liquid or solid
implement turbulence effects of bubbles or particles
were allowed to leave the reactor (“overflow”).
but are not considered here and thus set to zero.
The conservation equation for the liquid turbu- – Transient calculations started from assuming
lent dissipation e is: fully fluidized state with an integral gas holdup of j
= 5 % and integral solid loading according to the de-
¶ ¶ sired value in the calculation (i. e. j = 0.5 or 10 %).
( e l r l e) + ( e l r l u l , j e) -
¶t ¶t

¶ æ æ
çe ç m l , turb ö ¶e ö Results and discussion
- ç ç m + ÷ ÷
÷ ÷= (12)
¶x i è lè l , lam s e ø¶x i ø In the present work, the flow in three phase
Bubble Column was modeled using the Eulerian-
= e l (C g 1G - C g 2 r l e ) + S l , e -Eulerian model incorporated in CFX-5.6. The de-
M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007) 201

F i g . 2 – Comparison of computed and measured gas

F i g . 1 – Unstructured tetrahedral mesh for bubble column holdup

F i g . 3 – Streamline plot of gas velocity at sparger F i g . 4 – Streamline plot of gas velocity at bottom

F i g . 5 – Streamline plot of liquid velocity at bottom F i g . 6 – Streamline plot of solid velocity at bottom
202 M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007)

F i g . 7 – Contour plot of gas vol- F i g . 8 – Vector plot of gas velocity F i g . 9 – Vector plot of liquid ve-
ume fraction locity

F i g . 1 0 – Vector plot of solid ve- F i g . 1 1 – Contour plot of solid F i g . 1 2 – Streamline plot of liquid
locity volume fraction velocity at sparger

F i g . 1 3 – Streamline plot of solid veloc- F i g . 1 4 – Streamline plot of gas F i g . 1 5 – Streamline plot of gas
ity at sparger velocity at center velocity at top
M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007) 203

F i g . 1 6 – Streamline plot of liquid velocity at top F i g . 1 7 – Streamline plot of solid velocity at top

T a b l e 1 – The standard reactor geometry used to study the tails of the standard geometry and three phase sys-
flow pattern in bubble column tem used to study the flow pattern are given in Ta-
Bubble column height, H 0.6 m ble 1 and Table 2 respectively. Unstructured tetra-
hedral mesh was generated for bubble column and
Bubble column diameter, D 0.1 m surface mesh is shown in Fig. 1. The range of pro-
cess variables and design variables used for the
Plate sparger diameter, ds 0.05 m
parametric sensitivity studies are given in Table 3
Gas velocity, u 0.6 m s–1 and Table 4 respectively.
Solid loading, j 10 %
Model validation
Average mesh width / grid cell edge length 1 cm
For a better quantitative assessment, which
Reference Pressure, pref 1 bar more clearly shows possibilities and limitations of
the model, integral gas holdup has been computed
for all the calculations presented as well and can
T a b l e 2 – The three phases in the system in bubble column easily be compared to experimental results of
Michele and Hempel.7 Fig. 2 shows a comparison of
Diameter, Density, computed and measured integral gas holdups for
Material Morphology
d/mm r/kg m–3 bubble column height of 5 m, diameter H = 0.63 m,
Air Dispersed fluid 5 1.185 sparger diameter D = 0.57 m, and solid loading j =
10 %. Agreement between measurement and mod-
Water Continuous fluid – 997.0 eling results with respect to integral gas holdup is
Glass beads Dispersed solid 1 1200
quite good. While the model is capable of capturing
the right order of magnitude of gas holdup and gen-
eral dependency of gas holdup on superficial gas
velocity, it cannot account for the different flow re-
T a b l e 3 – Range of process variables used gimes observed in the measurements. While mea-
Inlet gas velocity, m s–1 0.06, 0.08, 0.1, 0.2, 0.4, 0.6, 0.8, 1 surement data clearly show the division line be-
tween homogeneous and heterogeneous flow re-
Solid loading, % 0, 5, 10, 15, 20 gime at a superficial gas velocity of approximately
u = 0.03 m s–1 (marked by a distinct decrease of the
Particle diameter, dp/mm 0.2, 0.4, 0.6, 0.8
graph’s slope), the modeling calculations yield a
slightly linear relation between superficial gas ve-
locity and integral gas holdup for the whole range
T a b l e 4 – Range of design variable used under consideration, where agreement with the ex-
H/D ratio 2, 4, 6, 8, 10, 12, 14 perimental data is best at very low and very high
superficial gas velocities. This could be due to
Sparger diameter, ds/cm 2, 4, 5, 6, 8 non-inclusion of magus force and effect of surface
tension. Thus, further model improvements are
Taperness, dout/dinl 1, 1.2, 1.4, 1.6, 1.8, 2
needed to deal primarily with correctly covering the
204 M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007)

different flow regimes, e.g. by implementing mod- The applicability of CFD package for deter-
els for bubble size distribution depending on the su- mining the flow patterns in a bubble column was
perficial gas velocity. The similar type of limita- tested. The results were compared with the experi-
tions was observed in computation of local liquid mental results available in literature and there exists
flow velocities. The similar results were obtained a good agreement between the two.
by Michele and Hempel.7 During the study of flow pattern it was ob-
served that higher gas velocities, higher values of
Flow pattern in three-phase bubble column solid loading and lower particle diameter makes the
system dynamics faster. The results presented are
The simulation starts with gas injection useful for understanding the dynamics of gas liquid
through the sparger. The liquid and solid phase was solid flows in bubble column and provide a basis
at rest at that moment. After few seconds liquid ve- for further development of CFD model for three
locity in most parts of reactor was greater than zero. phase systems
It can be seen from Fig. 3 and Fig. 4 that how the Further, the effect of design variables and pro-
gas bubbles enters the slurry at sparger position. cess variables on flow pattern in three phase bubble
The gas bubbles start rising to the surface as a reac- column has been going on. A separate communica-
tion to upward directed forces. Buoyancy and drag tion will be done on these aspects.
forces are the two main components of the vertical
force balance. The movement of the slurry phase is
a result of the acting drag forces to the fluid ele- Nomenclature
ments. After the surface break-through as seen in
a – specific gas-liquid interfacial area, m2 m–3
Fig. 5 and Fig. 6, the bubble swarm stays quite in
the centre of the column for a while. The bubble A – projected area, m2
swarm begins its swinging after a certain start pe- Ap – area of a single particle projected in the flow di-
riod as seen in Fig. 7. This specific movement can- rection, m2
not be covered by two-dimensional simulation. The CD – Drag coefficient, s–1
simulation results showed in Fig. 8, 9, and 10 are a dp – diameter of sinlge particle, m
dynamic behavior of the flow with several circula- ds – sparger diameter, m
tion zones and wavy motion of bubble swarm. It
Di – column inner diameter, m
was observed from Fig. 11 that solid particle con-
centration decrease with height of bubble column D – Drag force, N
because of the action of sedimentation process on g – gravitational acceleration, m s–1
solid particle, the higher particle concentration pre- H – column height, m
vails at the bottom. At lower region of bubble col- k – turbulence kinetic energy, m2 s–2
umn there is a circulation zone of liquid and solid M – momentum exchange term, kg m–2 s–2
phase as seen in Fig. 12 and 13. At the centres in
Fig. 14, there is a wavy motion of bubble swarm nP,V – number of particles per unit volume
and at the upper region as shown in Fig. 15, 16, and p – pressure, Pa
17, liquid and solid phase is circulated back into the R – universal gas constant, Pa m3 kg–1 mol–1 K–1
bubble column and air is allowed to pass through t – time, s
the top due to degassing boundary condition. The u – superficial fluid phase velocity, m s–1
results presented are useful for understanding the
(ua – ub) – relative velocity between two phases, m s–1
dynamics of gas liquid solid flows in bubble
column and provide a basis for further development n – velocity, m s–1
of CFD model for three phase systems Vp – volume of a single particle

Greek letters
Conclusion
r – phase density, kg m–3
The need to establish a rational basis for the in- s – interfacial tension, N m–1
terpretation of the interaction of fluid dynamic vari- n – kinematic viscosity, m2 s–1
ables was the primary motivation for active re- e – turbulence eddy dissipation, m2 s–3
search in the area of bubble column modeling based
ea – holdup of phase a
on computational fluid dynamics (CFD) tools in the
last decade. An appropriate mesh and a robust nu- m – phase viscosity, kg m–1 s–1
merical solver are crucial for getting accurate t – shear stress, N m–2
solutions. j – volume fraction, %
M. ANIL et al., CFD Modeling of Three-phase Bubble Column: 1. Study of Flow Pattern, Chem. Biochem. Eng. Q. 21 (3) 197–205 (2007) 205

Subscripts References

a – phase 1. Pfleger, D., Gomes, S., Gilbert, N., Wagner, H. G., Chem.
Eng. Sci. 54 (1999) 5099.
g – gas phase 2. Sokolichin, A., Eigenberger, G., Chem. Eng. Sci. 49
l – liquid phase (1994) 5735.
3. Krishna, R., van Baten, J. M., Urseanu, M. I., Chem. Eng.
lam – laminar
Sci. 55 (2000) 3275.
s – solid phase 4. Ranade, V. V., Tayalia, Y., Chem. Eng. Sci. 56 ( 2001)
T – transpose 1667.
5. Mitra-Majumdar, D., Farouk, B., Shah, Y. T., Chem. Eng.
turb – turbulent Sci. 52(1997) 4485.
1 – gas phase 6. Padial, N. T., VanderHeyden, W. B., Rauenzahn, R. M.,
Yarbro, S. L., Chem. Eng. Sci. 55 (2000) 3261
2 – liquid phase
7. Michele, V., Hempel, D. C., Chem. Eng. Sci. 57 (2002)
3 – solid phase 1899.