Computational Fluid Dynamics (CFD) is used to investigate mass transfer from Taylor bubbles to the liquid phase in circular capillaries. The liquid phase volumetric mass transfer coefficient
k
L
a ...was determined from CFD simulations of Taylor bubbles in upflow, using periodic boundary conditions. The separate influences of the bubble rise velocity, unit cell length, film thickness, film length, and liquid diffusivity on
k
L
a were investigated for capillaries of 1.5, 2 and
3
mm
diameter. The mass transfer from the Taylor bubble is the sum of the contributions of the two bubble
caps, and the
film surrounding the bubble. The Higbie penetration model is used to describe the mass transfer from the two hemispherical caps. The unsteady-state diffusion model of Pigford is used to describe the mass transfer to the downward flowing liquid film. The developed model for
k
L
a is in good agreement with the CFD simulated values, and provides a practical method for estimating mass transfer coefficients in monolith reactors.
The Maxwell–Stefan (M–S) formulation for binary mixture diffusion in
micro-porous materials such as zeolites, metal organic frameworks (MOFs), and covalent organic frameworks (COFs), that have pore ...sizes typically smaller than 2
nm, is formulated in a manner that is consistent with corresponding description for
meso-porous systems. The M–S equations are set up in terms of species concentrations,
c
i
, defined in terms of accessible pore volume space. Molecular dynamics simulations were carried out to determine the exchange coefficients
Đ
12
for a large variety of binary mixtures in zeolites (MFI, AFI, BEA, FAU, LTA, CHA, and DDR), MOFs (CuBTC, IRMOF-1, Zn(bdc)dabco, Co(bdc)dabco, MIL-47, Co-FA, Mn-FA, and Zn(tbip)), COFs (COF-102, COF-103, and COF-108), and cylindrical silica pores of varying diameters. The exchange coefficients
Đ
12
in all structures were found to be related by a constant factor,
F, with the corresponding M–S diffusivity for binary
fluid mixture,
Đ
12
,
fl
, at the same total mixture concentration,
c
t
, as within the pores. The factor
F is primarily dictated by the degree of confinement of the guest molecules within the channels, defined as the ratio of the characteristic sizes of the guest molecules to that of the host channels. For
meso-porous cylindrical silica pores:
F=1, and
Đ
12
=
Đ
12
,
fl
. For CuBTC, MIL-47, IRMOF-1, and COFs, that have structures with a high fractional open space and channel dimensions of 0.8–1.85
nm, the factor
F is found to be in the range 0.55–0.85. For structures such as MFI, BEA, Co-FA, Mn-FA, and Zn(tbip) that have smaller fractional open space, and channels smaller than 0.6
nm, the factor
F has values <0.2. The major conclusion of this study is that fluid mixture diffusivity
Đ
12
,
fl
provides a good starting point for an engineering estimate of the exchange coefficient
Đ
12
in porous materials.
This paper presents a critical appraisal of current estimation methods for the Onsager coefficients
L
11
,
L
22
, and
L
12
for binary mixture diffusion inside nanopores using pure component ...diffusivity data inputs. The appraisal is based on extensive sets of molecular dynamics (MD) simulation data on
L
ij
for a variety of mixtures in zeolites (MFI, AFI, TON, FAU, CHA, DDR, MOR, and LTA), carbon nanotubes (CNTs: armchair and zig-zag configurations), titanosilicates (ETS-4), and metal–organic frameworks (IRMOF-1, CuBTC). The success of the
L
ij
predictions is crucially dependent on the estimates of the degree of correlations in molecular jumps for different guest–host combinations; these correlations are captured in Maxwell–Stefan approach by the exchange coefficients
Đ
ij
. Three limiting scenarios for correlation effects have been distinguished; for each of these scenarios appropriate expressions for the
L
ij
are presented. For CNTs, correlation effects are dominant and the interaction factor, defined by
α
12
=
L
12
/
L
11
L
22
, is close to unity. For cage-type zeolites such as LTA, CHA, and DDR with narrow windows separating cages, correlation effects are often, but not always, negligibly small and the assumption of uncoupled diffusion, i.e.,
α
12
=
0
, is a reasonable approximation provided the occupancies are not too high. In other cases such as zeolites with one-dimensional channel structures (AFI, TON), intersecting channels (MFI), cage-type zeolite with large windows (FAU), ETS-4, CuBTC, and in IRMOF-1, it is essential to have a reliable estimation of the
Đ
ij
; MD simulations underline the wide variety of factors that influence the
Đ
ij
.
We also highlight two situations where estimations of the
L
ij
fail completely; in both cases the failure is caused due to
segregated adsorption. In adsorption of CO
2–bearing mixtures in LTA and DDR zeolites, CO
2 is preferentially lodged at the narrow window regions and this hinders the diffusion of partner molecules between cages. The second situation arises in MOR zeolite that has one-dimensional channels connected to side pockets. Some molecules such as methane, get preferentially lodged in the side pockets and do not freely participate in the molecular thoroughfare. Current phenomenological models do not cater for segregation effects on mixture diffusion.
Diffusion of pure components (hydrogen (H
2), argon (Ar), krypton (Kr), methane (C1), ethane (C2), propane (C3),
n-butane (
nC4), and
n-hexane (
nC6)) in silica nanopores with diameters of 1, 1.5, 2, ...3, 4, 5.8, 7.6, and 10
nm were investigated using molecular dynamics (MD). The Maxwell–Stefan (M–S) diffusivity (
Đ
i
,
s
) and self-diffusivities (
D
i
,
self
,
s
) were determined for pore loadings ranging to 10
molecules nm
−3. The MD simulations show that zero-loading diffusivity
Đ
i
,
s
(0) is consistently lower, by up to a factor of 10, than the values anticipated by the classical Knudsen formula; the differences increase with increasing adsorption strength. Only when the adsorption is negligible does the
Đ
i
(0) approach the Knudsen diffusivity value.
MD simulations of diffusion in binary mixtures C1–H
2, C1–Ar, C1–C2, C1–C3, C1–
nC4, C1–
nC6, C2–
nC4, C2–
nC6, and
nC4–
nC6 in the different pores were also performed to determine the three parameters
Đ
1,
s
,
Đ
2,
s
, and
Đ
12, arising in the M–S formulation for binary mixture diffusion. The
Đ
i
,
s
in the mixture were found to be practically the same as the values obtained for unary diffusion, when compared at the same total pore loading. Also, the
Đ
i
,
s
of any component was practically the same, irrespective of the partner molecules in the mixture. Furthermore the intermolecular species interaction parameter
Đ
12, could be identified with the binary M–S diffusivity in a
fluid mixture at the same concentration as within the silica nanopore. The obtained results underline the overwhelming advantages of the M–S theory for mixture diffusion in nanopores.
Our study underlines the limitations of the commonly used dusty-gas approach to pore diffusion in which Knudsen and surface diffusion mechanisms are considered to be additive.
The adsorption and intra-crystalline diffusion of
n-butane (nC4), iso-butane (iC4), 2-methylbutane (2MB), and 2,2-dimethylpropane (neoP) in CuBTC (Cu
3(BTC)
2 where BTC
=
...benzene-1,3,5-tricarboxylate) has been investigated using infrared microscopy (IRM), combined with molecular simulations. Both experiments and simulations show strong inflection characteristics in the adsorption isotherms. The primary cause of the inflection is due to the strong preference for adsorption within, and in the regions close to the mouths of tetrahedral pockets. The isotherm inflection has a significant influence on the dependence of the Maxwell–Stefan diffusivity,
Ð
i
, on the fractional occupancy,
Ð
i
. Both IRM experiments and simulations show that the
Ð
i
–
θ
i
behavior appears to be influenced by the loading dependence of the inverse thermodynamic factor
1
/
Γ
i
=
d
ln
θ
i
/
d
ln
p
i
. For nC4 and iC4, the
Ð
i
increase sharply by about one order of magnitude as the occupancy
θ
i
increases from 0 to about 0.2. This increase is caused by the fact that the diffusion characteristics undergo a transition from being dominated by hops across narrow 4.6
Å windows at low loadings to hops across large 9
Å windows for loadings higher than 8 molecules per unit cell. For loadings higher than 8 molecules per unit cell the
Ð
i
–
θ
i
dependence of nC4 and iC4 is dictated by 1/
Γ
i
, characteristic of more open channel structures such as FAU zeolite. For 2MB and neoP, the IRM experiments show evidence of phase transition and except for the region in which this occurs the
Ð
i
follows the occupancy dependence of 1/
Γ
i
for the entire range of loadings.
Branched and cyclic hydrocarbons such as
iso-butane, 2-methylpentane, 3-methylpentane, 2,2-dimethyl-butane and benzene are preferentially adsorbed at the intersections of the channels of MFI zeolite; ...they serve as bottlenecks for molecular traffic in mixtures with linear C1–C6 alkanes. Molecular dynamics simulations show that as the loadings of tardier
iC4, 2MP, 3MP, 22DMB, and Bz is progressively increased to four molecules per unit cell the diffusivity of the more mobile linear alkane reduces nearly to zero. The reduction in the
n-alkane diffusivity is quantitatively similar irrespective of the branched/cyclic hydrocarbon.
Computational fluid dynamics is used to investigate the mass transfer from the liquid phase to the channel wall for Taylor flow of bubbles rising in circular capillaries. The separate influences of ...the Taylor bubble rise velocity, unit cell length, gas holdup, and liquid diffusivity on mass transfer were investigated for capillaries of 1.5, 2 and 3
mm diameter. A correlation is proposed for estimation of the wall mass transfer coefficient and this correlation has been tested against published experimental data.
Mass transfer in bubble columns Krishna, R.; van Baten, J.M.
Catalysis today,
04/2003, Letnik:
79
Journal Article, Conference Proceeding
Recenzirano
Bubble columns are operated either in the homogeneous or heterogeneous flow regime. In the homogeneous flow regime, the bubbles are nearly uniform in size and shape. In the heterogeneous flow regime, ...a distribution of bubble sizes exists. In this paper, a computational fluid dynamics (CFD) model is developed to describe the hydrodynamics, and mass transfer, of bubble columns operating in either of the two flow regimes. The heterogeneous flow regime is assumed to consist of two bubble classes: “small” and “large” bubbles. For the air–water system, appropriate drag relations are suggested for these two bubble classes.
Interactions between both bubble populations and the liquid are taken into account in terms of momentum exchange, or drag, coefficients, which differ for the “small” and “large” bubbles. The turbulence in the liquid phase is described using the
k–
ε model.
For bubble columns operating with the air–water system, CFD simulations have been carried out for superficial gas velocities,
U, in the range 0–0.08
m/s, spanning both regimes. These simulations reveal some of the characteristic features of homogeneous and heterogeneous flow regimes, and of regime transition on the gas holdup and mass transfer. By comparing the simulations with measured experimental data, it is concluded that mass transfer from the large bubble population is significantly enhanced due to frequent coalescence and break-up into smaller bubbles. The CFD simulations also underline the strong influence of column diameter on hydrodynamics and mass transfer.
