D.M. Scott

The linear driving force model for fast-cycle adsorption and desorption in a spherical particle

Two analytical solutions for the stepwise cyclic diffusion problem in a spherical particle have been presented. The first was based on a Fourier series expansion, and provided an exact solution to the problem. The second was based on penetration theory. Both solutions provide a direct representation of the cyclic equilibrium condition

Simulation of rapid pressure swing adsorption and reaction processes

Abstract A general model for non-isothermal adsorption and reaction in a rapid pressure swing process is described. Several numerical discretisation methods for the solution of the model are compared. These include the methods of orthogonal collocation, orthogonal collocation on finite elements, double orthogonal collocation on finite elements, and cells-in-series. Computationally, orthogonal collocation on finite elements is found to be the most efficient of these. The model is applied to air separation for oxygen production. Calculations confirm the formation of a concentration shock when an adsorbent bed is pressurised with air. The form and propagation of the shock over short times is found to be in excellent agreement with the exact similarity transformation solutions derived for an infinitely long bed. For air separation, novel experimental measurements, showing an optimum particle size for maximum product oxygen purity, are accurately described by the model. Calculations indicate that a poor separation results from ineffective pressure swing for beds containing very small particles, and from intraparticle diffusional limitations for beds containing very large particles. For adsorption coupled with reaction, finite rate and reversible reactions are considered. These include both competitive and non-competitive reaction schemes. For the test case of a dilute reaction A &.rlhar2; B + 3C, with B the only adsorbing species, bed pressurisation calculations are found to be in excellent agreement with the solutions obtained by the method of characteristics.

The Transient Response of Granular Flows in an Inclined Rotating Cylinder

This paper reports the results of an experimental and theoretical study to investigate the transient response of the granular flow through a laboratory scale inclined rotating cylinder to large step changes in one of three variables: (i) mass feed rate, (ii) rotation speed or (iii) axis inclination. Experimental measurements are reported for a range of operating conditions, sizes of step and a number of cylinder geometries. A mechanistic model for the transient response is derived based on a published steady state model. The dynamic model parameters are the cylinder radius, length, discharge dam height, axis inclination and rotation speed, the granular feed rate, and the bulk density and dynamic angle of repose of the granular material. The model has no adjustable parameters, making it useful for scale-up. The model takes the form of a non-linear partial differential equation, equivalent to a one dimensional unsteady diffusion equation with variable coefficients, and solution has been obtained numerically. Good agreement is found between the model and experiment both in the range of cases considered in the current study, and also for published experimental work, for which the cylinder size and granular material properties differ substantially from those of this work.

Adsorbent particle size effects in the separation of air by rapid pressure swing adsorption

Abstract Experimental and theoretical investigations into air separation by rapid pressure swing adsorption over zeolite 5A are presented. These concentrate on the effect of adsorbent particle size on the separation performance of the unit undergoing simple cycles consisting of pressurisation and depressurisation steps. An optimum particle size for maximum cyclic equilibrium product oxygen purity is shown to exist; this is accurately predicted by model simulation. Calculations indicate that for beds containing very small particles, a poor separation results from ineffective pressure swing, and for beds containing very large particles from intraparticle diffusional limitations. For the zeolite 5A adsorbent used in this work, theoretical calculations indicate that the rate limiting intraparticle diffusion is described by a parallel combination of molecular and Knudsen diffusion within the macropores of the adsorbent particles. Axial dispersion within the bed is also shown to have a significant effect upon the cyclic equilibrium value of the cycle-average product oxygen purity. In addition to measurements at the cyclic equilibrium, temporal profiles of the product oxygen purity during the approach to cyclic equilibrium are shown. Under certain operating conditions, an overshoot of oxygen purity is found to exist. This behaviour can be attributed to ineffective pressure swing within the product end region of the bed, and thus to the poor utilisation of adsorbent in this region.

The no-flow problem for granular material in rotating kilns and dish granulators

Abstract Granular material, contained in a long, inclined cylinder, slowly rotating about its axis, forms a flat surface whose intersection with the cylinder is an ellipse. We postulate that the granular material falls in a thin layer along the line of steepest descent in the surface, which line is inclined at the angle of repose to the horizontal; the granular material then rotates with the cylinder in `solid body’ motion. With no axial flow, each particle remains in the same plane normal to the axis of the cylinder. The predicted length of the ellipse, measured in the direction of the axis of the cylinder, is in excellent agreement with experiments using sand or TiO 2 . The same theory is applied to granular material in a dish granulator operated at low speed, so the bed surface is flat. The theory for no-flow gives results for the position of the bed surface which are in fair agreement with published data at small feed rate. For the case when centrifugal accelerations are small, but not negligible, theory is given which predicts their effect.

The scale-up of large bubbles attached to spargers in downward two-phase flow

Abstract A large stationary air bubble hanging beneath an air sparger in a downward liquid flow can exist at flow rates substantially greater than flow rates which would wash away large free bubbles (sometimes known as slugs). This is detrimental because the driving force for circulation is reduced, potentially leading to the fermenter stalling. This kind of bubble was studied experimentally using a vertical flow circuit of internal diameter 0.105 m, which is twice the size of the apparatus used by Bacon et al. (1995) for similar experiments. Liquid flow rates used ranged between 0.003 and 0.015 m 3 /s. Air supply was achieved using four different sparger designs—two spargers consisted of horizontal brass pipes, with downward-facing air holes, and two more, within a section of full-bore pipe, injecting air from either six or eight inlets evenly distributed in a horizontal plane along the pipe periphery. Experiments have been carried out to measure the stable bubble length at various liquid flow rates. The two horizontal pipe spargers gave very similar results; so did the two peripheral sparger designs. The peripheral spargers showed superior characteristics compared to the horizontal ones, but suffered from sudden bubble length fluctuations. The kind of unbounded bubble growth reported by Bacon et al. (1995) was observed for all the sparger designs investigated. These bubble runaway results have been successfully analysed along with those of Bacon et al. (1995) using dimensional analysis, and the following scale-up correlations developed:Horizontal sparger:Fr G,max Eo −5 = 0.00271 (Fr L ) 0.1525 − 0.0213. Peripheral sparger: Fr G,max Eo −5 N 0.07 μ = 0.0039 Fr L +0.0002.

The linear driving force model for cyclic adsorption and desorption: the effect of shape

The purpose of the note is to extend the Fourier series approach to non-spherical particles, in particular to slabs and cylinders

Axial dispersion in rich, binary gas mixtures: model form and boundary conditions

This communication recommends the boundary conditions (BCs) and the form of Fickian flux model to use in an axially dispersed plug flow (ADPF) model for rich, binary gas mixtures in any devices subject to an axial pressure gradient; for instance, a packed bed. We illustrate the arguments with reference to pressure swing adsorption (PSA) and, in particular, rapid pressure swing adsorption (RPSA). The standard flux model and Danckwerts BCs are shown to be inappropriate since they imply (1) an unphysical zero pressure gradient at the exit, (2) a separation paradox, i.e. an unphysical separation of components, and (3) violation of conservation of mass. A numerical example shows that under particular practical conditions, the special case of a non-adsorbing packed bed at steady state will be predicted to destroy 7.4% of the total incoming mass of an air flow, while enriching its oxygen content by 8%. The proposed formulation has been used before, but without critical comparison with alternatives. Indeed, we can find no evidence that it has been realised that there is any fundamental difference between the various formulations reported in the literature. The purpose is to identify and explain the superiority of the formulation that we advocate.

Effects of bed pressure drop on adsorption and desorption with langmuir isotherms

Abstract Breakthrough calculations using the method of characteristics are reported for a dilute adsorbate with a Langmuir isotherm, where the steady pressure and velocity distributions of the inert carrier gas in the adsorbing bed are found from Erguns equation. Equilibrium, isothermal adsorption is considered, and axial dispersion is ignored. Studies are made of the responses to step increases, step decreases and Dirac δ-function impulses in inlet concentration. The results will be useful in analysing experimental measurements from adsorbing beds where pressure drop is important. The case of linear isotherms is also discussed.