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Comments on gas absorption and desorption with reversible instantaneous chemical reaction
Chemical Engineering Science, Vol. 47, No. Printed in Great Britain.
ooos2509/92 ss.00 + 0.00 Pcrgamm Press Ltd
12, p. 3167, 1992.
Comments on gas absorption and desorption with reversible instantaneous chemical reaction (Received
15 January 1992; accepted
Dear Sirs, me reasons for the discrepancy between the figures in the note by Katti and the figures in Astarita and Savage (1980) deserve to be discussed. There is no question aGo& thk governing equations, which are agreed upon in the two works; the discrepancy is only connected with the actual plots of the enhancement factor I vs the driving force (li - CI~. Katti calculates the plots in his figures by considering afixed value of aO. i.e., he constructs plots where (I~- a, varies because the gas-phase composition varies, but the liquidphase composition does not. Astarita and Savage (1980) constructed their plots by considering what happens along the axis of an absorption (or desorption) column, so that the composition of both phases is changing. Consider for instance absorption. The pinch will occur, in actual operation, at the lean end (it would occur at the rich end only if the liquid flow rate were less than the minimum required one, a situation which is obviously avoided in practice), where a,
Chemical Engineering Science, Vol. 47. No. Printed in Great Britain.
12, pp. 3167-3168,
15 Jcrnuury 1992)
has its lowest value, and hence the enhancement factor has its largest value [eq. (7) of Katti has a, in the denominator]. As one moves down along the column (rightwards in the plot), one moves away from the pinch, and at the same time a, increases and I decrease s-hence the plot has indeed the shape discussed by Astarita and Savage (1980). A mirror image argument applies to the desorption case, where again the pinch in actual operation is reached at the lean end (this time the bottom of the column) where a,, has its lowest value. The way that the results of Astarita and Savage (1980) were presented was perhaps somewhat misleading, and Katti’s note nicely clarifies the issue-the I vs a, - a, plot is indeed monotonous when a, is kept constant. G. ASTARITA
Department
of Chemical Engineering University of Naples 80125 Napoli, Italy
1992.
om!-2509/m ss.00 + 0.00 Pergamon Press Ltd
Buoyancy force in sedimenting and filtering systems (Received 19 August 1991: accepted
Dear Sirs, Buoyancy forces have recently come under scrutiny in the process of fluidisation [see Gibilaro et al. (1984). Clift et al. (1987) and Gibb (1991)]. The last author showed that the effective weight is I Wff
= (P. -
P)B 6
where p is the average density in (any) unit cube of the suspension. This average density can be. calculated from a knowledge of the component densities and porosity p = EP + (1 - E)P,. Thus, buoyancy force is due to the average suspension density and not the fluid density, contrary to the alternative approach adopted by Clift er al. It is well-known that sedimentation and fluidisation share similar constitutive equations; thus, the above debate is relevant to the former process. Furthermore, buoyancy is also
23 January
1992)
relevant to the process of filtration. There is, however, an additional force in sedimentation and filtration which is not present during fluidisation, that of the compressive solids stress (or pressure) gradient. Equations accounting for average suspension density in sedimentation buoyancy correction have been forwarded before (Khan and Richardson, 1990). Buoyancy correction during sedimentation of compressible materials is, however, more complex as will be shown later. Filtration also has an additional drag term due to the liquid drag over the solid particles and through the septum. Taking the average suspension density into the timedependent partial differential equation for the force balance per unit volume for these processes, and neglecting inertial terms (Holdich, 1990), gives
ap,=
ax where aP,/ax
3167
dl
- E)(P, - ii)
-k
(1)
is the solid stress gradient, k is permeability, Q
ooos2509/92 ss.00 + 0.00 Pcrgamm Press Ltd
12, p. 3167, 1992.
Comments on gas absorption and desorption with reversible instantaneous chemical reaction (Received
15 January 1992; accepted
Dear Sirs, me reasons for the discrepancy between the figures in the note by Katti and the figures in Astarita and Savage (1980) deserve to be discussed. There is no question aGo& thk governing equations, which are agreed upon in the two works; the discrepancy is only connected with the actual plots of the enhancement factor I vs the driving force (li - CI~. Katti calculates the plots in his figures by considering afixed value of aO. i.e., he constructs plots where (I~- a, varies because the gas-phase composition varies, but the liquidphase composition does not. Astarita and Savage (1980) constructed their plots by considering what happens along the axis of an absorption (or desorption) column, so that the composition of both phases is changing. Consider for instance absorption. The pinch will occur, in actual operation, at the lean end (it would occur at the rich end only if the liquid flow rate were less than the minimum required one, a situation which is obviously avoided in practice), where a,
Chemical Engineering Science, Vol. 47. No. Printed in Great Britain.
12, pp. 3167-3168,
15 Jcrnuury 1992)
has its lowest value, and hence the enhancement factor has its largest value [eq. (7) of Katti has a, in the denominator]. As one moves down along the column (rightwards in the plot), one moves away from the pinch, and at the same time a, increases and I decrease s-hence the plot has indeed the shape discussed by Astarita and Savage (1980). A mirror image argument applies to the desorption case, where again the pinch in actual operation is reached at the lean end (this time the bottom of the column) where a,, has its lowest value. The way that the results of Astarita and Savage (1980) were presented was perhaps somewhat misleading, and Katti’s note nicely clarifies the issue-the I vs a, - a, plot is indeed monotonous when a, is kept constant. G. ASTARITA
Department
of Chemical Engineering University of Naples 80125 Napoli, Italy
1992.
om!-2509/m ss.00 + 0.00 Pergamon Press Ltd
Buoyancy force in sedimenting and filtering systems (Received 19 August 1991: accepted
Dear Sirs, Buoyancy forces have recently come under scrutiny in the process of fluidisation [see Gibilaro et al. (1984). Clift et al. (1987) and Gibb (1991)]. The last author showed that the effective weight is I Wff
= (P. -
P)B 6
where p is the average density in (any) unit cube of the suspension. This average density can be. calculated from a knowledge of the component densities and porosity p = EP + (1 - E)P,. Thus, buoyancy force is due to the average suspension density and not the fluid density, contrary to the alternative approach adopted by Clift er al. It is well-known that sedimentation and fluidisation share similar constitutive equations; thus, the above debate is relevant to the former process. Furthermore, buoyancy is also
23 January
1992)
relevant to the process of filtration. There is, however, an additional force in sedimentation and filtration which is not present during fluidisation, that of the compressive solids stress (or pressure) gradient. Equations accounting for average suspension density in sedimentation buoyancy correction have been forwarded before (Khan and Richardson, 1990). Buoyancy correction during sedimentation of compressible materials is, however, more complex as will be shown later. Filtration also has an additional drag term due to the liquid drag over the solid particles and through the septum. Taking the average suspension density into the timedependent partial differential equation for the force balance per unit volume for these processes, and neglecting inertial terms (Holdich, 1990), gives
ap,=
ax where aP,/ax
3167
dl
- E)(P, - ii)
-k
(1)
is the solid stress gradient, k is permeability, Q