On the modeling of an airlift reactor

doi:10.1016/j.ijheatmasstransfer.2006.01.015

International Journal of Heat and Mass Transfer

Volume 49, Issues 13–14, July 2006, Pages 2053-2057

https://doi.org/10.1016/j.ijheatmasstransfer.2006.01.015 Get rights and content

Abstract

A model of an airlift reactor in the cases of interphase mass transfer between gas and liquid in the riser and chemical reaction in the liquid phase has been done. The model equations permit to obtain the vertical distribution of the average concentrations of an active gas component in gas and liquid phases and average concentration of the active liquid component, using average velocities and effective diffusivities in the riser and downcomer zones. The proposed model allows scale-up problem solution. An hierarchical approach for model parameter identification on the bases of experimental data has been proposed.

Introduction

The hydrodynamic behavior of the gas and liquid flows in airlift reactors is very complicated. In these conditions the convective and diffusive transfer with volume reactions are realized simultaneously. The convective transfer is result of a laminar or turbulent (large-scale pulsations) flows. The diffusive transfer is molecular or turbulent (small-scale pulsations). The volume reactions are mass sources as a result of chemical reaction and interphase mass transfer [1].

The scale-up theory [2] show, that the scale-effect in mathematical modeling is result of the radial nonuniformity of the velocity distribution in the columns. In many papers [3], [4], [5], [6] are used diffusion models, where the scale-effect is considered as an increase of the axial mixing.

The creation of the models in these conditions and solving of the scale-up problem [1] require construction of a suitable diffusion model.

Section snippets

Mathematical model

The investigation of the airlift reactors shows [7], [8], [9] that convection–diffusion equation with volume reaction may be use as a mathematical structure of the model.

Let us consider airlift reactor [10], [11], [12], [13] with a cross-section area F₀ for the riser zone and F₁ for the downcomer zone. The length of the working zones is l (Fig. 1). The gas flow rate is Q₀ and the liquid flow rate, Q₁. The gas and liquid hold-ups in the riser are ε and (1 − ε).

The concentrations of the active gas

Average concentration models

Let us consider Eq. (4). The velocity u₀(x, r) and concentration c(x, r, t) in cylindrical coordinates practical do not depend on the angular coordinate. In this case the average function values are ${\bar{u}}_{0} (x) = \frac{2}{r_{0}^{2}} \int_{0}^{r_{0}} {ru}_{0} (x, r) d r, {\bar{v}}_{0} (x) = \frac{2}{r_{0}^{2}} \int_{0}^{r_{0}} {rv}_{0} (x, r) d r, \bar{c} (x, t) = \frac{2}{r_{0}^{2}} \int_{0}^{r_{0}} rc (x, r, t) d r,$ where ${\bar{u}}_{0} (0) = {\bar{\bar{u}}}_{0}$ . The expressions (12) permit to present the velocities and concentration as $u_{0} (x, r) = {\bar{u}}_{0} (x) {\tilde{u}}_{0} (r, x), v_{0} (x, r) = {\bar{v}}_{0} (x) {\tilde{v}}_{0} (r, x), c (x, r, t) = \bar{c} (x, t) \tilde{c} (r, x),$ where ${\tilde{u}}_{0}, {\tilde{v}}_{0}$ and $\tilde{c}$ express radial nonuniformities of the

Hierarchical approach

The problems (19), (21), (23), (24), (26), (28) are mathematical model of an airlift three phase reactor. The model parameters are five types:

•
beforehand known $(c^{(0)}, c_{2}^{(0)}, R_{0}, r_{0})$ ;
•
beforehand obtained (ε, χ, α₁, α₂, k₀);
•
obtained without chemical reaction (k, D, D₀, A, B, A₀, B₀, G, G₀);
•
obtained with chemical reaction (D₁, D₂, D₃, M, M₀);
•
obtained in the modeling and specified in the scale-up (A, A₀, A₁, A₂, A₃, B, B₀, B₁, B₂, B₃, G, G₀, G₁, G₂, G₃, M, M₀).

The problems (19), (21), (23) permit to obtain (k, D, D₀, A, B, A₀, B₀, G, G₀)

Conclusions

The result obtained shows a possibility to build airlift reactor models, using average velocities and concentrations. This approach permits to solve the scale-up problem as a result to the radial nonuniformity of the velocity and concentration, using radius dependent parameters. The model parameter identification on the bases of average concentration experimental data leads to big priority in comparison with the local concentration measurements.

Acknowledgement

This work was completed with the financial support of the National Science Fund, Ministry of Education and Science, Republic of Bulgaria, under Contract 1 TH-1506/2005.

References (13)

Chr. Boyadjiev
Diffusion models and scale-up
Int. J. Heat Mass Transfer
(2006)
L. Boyadzhiev et al.
Etude de la dispersion longitudinale dansles colonness d’extraction liquid–liquid
Chem. Eng. J.
(1973)
W.A. Al Masry et al.
On the scale-up of external loop airlift reactors: Newtonian systems
Chem. Eng. Sci.
(1998)
J.J. Heijnen et al.
A simple hydrodynamic model for the liquid circulation velocity in a full-scale 2-phase and 3-phase internal airlift reactor operating in the gas recirculation regime
Chem. Eng. Sci.
(1997)
E. Camarasa et al.
A complete model for oxidation airlift reactors
Comput. Chem. Eng.
(2001)
A.P. Markusse et al.
Platinum catalyzed aqueous alcohol oxidation: experimental studies and reaction model discrimination
J. Mol. Catal. A
(2000)

There are more references available in the full text version of this article.

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On the modeling of an airlift reactor

Abstract

Introduction

Section snippets

Mathematical model

Average concentration models

Hierarchical approach

Conclusions

Acknowledgement

Int. J. Heat Mass Transfer

Chem. Eng. J.

Chem. Eng. Sci.

Chem. Eng. Sci.

Comput. Chem. Eng.

J. Mol. Catal. A