Richard G. Rice

Approximate solutions for batch, packed tube and radial flow adsorbers—comparison with experiment

Abstract Taking the intraparticle concentration profile to be parabolic leads to important simplifications in the theory of chromatography. For systems whereby solid diffusion and film resistance are important, the parabolic model leads to simple, exact and well-known mathematical solutions which are widely tabulated. Analytical solutions for three types of configuration are presented: Batch, packed tube and radial-flow adsorbers. Experiments using bifunctional resin in saline solutions are used to test the theoretical predictions for batch and packed tube systems.

On the relative importance of pore and surface diffusion in non-equilibrium adsorption rate processes

Abstract A unified treatment of adsorption processes suggests that only two key parameters control the selection amongst the six standard models. The parameter φ is the square root of the ratio of adsorption rate to the rate of pore diffusion. The second parameter, λ, is the ratio of surface to pore diffusion rates. Degenerate models occur in the limits of these parameters. Three contacting configurations are studied: batch, CSTR and dispersed PFR. A parameter-domain analysis suggests sets of experiments which can reveal rate-controlling mechanisms.

Dispersion coefficients for ideal bubbly flow in truly vertical bubble columns

Abstract A novel moving-boundary technique using acid-base neutralization was applied to truly vertical bubble columns to find axial dispersion coefficient. In addition, the effect of slight vertical misalignment (0.25 and 0.5°) was measured and showed increases in dispersion coefficient as much as two orders of magnitude. Using a punctured rubber membrane as a sparger, it was observed that ideal bubbly flow was maintained up to superficial gas velocities of around 4 cm/s for a column 14 cm in diameter. Photographic evidence along with the moving-boundary measurements suggest the proper turbulence length scale is the diameter of the bubble. The Baird-Rice isotropic turbulence model, suitably modified to account for changing length scales, produced an excellent fit of the bubbly-regime data.

BUBBLE FORMATION AT A PUNCTURE IN A SUBMERGED RUBBER MEMBRANE

Abstract Very large enhancements in volumetric mass transfer coefficients have recently been reported using a new type of sparger which is comprised of a punctured rubber membrane. The punctured sheet has been reported to produce very uniform emulsions of small bubbles, which leads to large apparent increases in gas voidage and mass transfer area. Flooding(slugging) is presumably repressed owing to the “elastic hole” phenomenom whereby the rubber sheet balloons and expands as applied pressure increases. Under conditions of expansion, a puncture in the sheet also expands thereby mitigating the occurence of jetting. In the present effort, we study a single puncture in the center of circular rubber sheets of 2, 3, and 4 inch diameters. By measuring bubble frequency and flow rate, we compute average bubble size. These results for flow rates from 0.01 to 2.0 cc/sec suggest that bubble size is practically constant over a nearly two decades of flow rate, until a flow of around 0.5 cc/sec, thence bubbles tend to ...

A SIMPLE METHOD OF DETERMINING PORE AND SURFACE DIFFUSIVITIES IN ADSORPTION STUDIES

In this paper, a new graphical method of determining pore and surface diffusivities in adsorption systems is presented. The method involves only a simple linear plot of the inverse of half time of adsorption versus a concentration factor. The pore diffusivity and the surface diffusivity are determined directly from the intercept and the slope of the straight line, respectively. Experimental data of n-butane on Ajax activated carbon are used to illustrate the potential application of this new technique in the diffusivity parameter determination.

The transient response of a CSTR containing porous catalyst pellets: Asymptotic solutions

Transient response of a CSTR containing porous catalyst pellets is analyzed theoretically using a matched asymptotic expansion technique. This singular perturbation technique leads directly to the conditions under which the minima of reservoir concentration occur. The existence of the minima may be used to estimate some inherent parameters of the catalyst pellet.

An experimental pressure-response method to measure gas-liquid kinetics

Abstract We introduce a novel physical method to ascertain gas-liquid kinetic parameters without resort to wet chemistry. The conditions whereby the controversial technique called the “chemical method” can be reliably used to measure the interfacial area in gas-liquid dispersions has been recently clarified by Schumpe and Deckwer (1980, Chem. Engng Sci. 35 , 2221-2233). Much of the disagreement arises because researchers use literature bench-scale kinetic data to estimate the interfacial area in a larger pilot-scale unit, with differing water quality and chemical purities. It is now widely recognized that in-house data, which matches the specific pilot plant condition, is the prudent course of action. Thus, a simple bench-scale unit is necessary, the description of which is the purpose of the present work. The batch method used is fast, cheap and simple, and produces reliable results, even for non-linear chemical systems. The only measured quantity is the gas-phase pressure above a reacting liquid interface. The key physical-chemical design constraint requires that the system time constant is at least an order of magnitude larger than the total experimental contact time. Under such conditions, the analysis shows that a single parameter contains all the necessary order and rate constant information. The first pressure-transient prototype is tested using the classical sulphite oxidation reaction in the presence of cobaltous catalyst. Very good agreement with literature values is obtained.

COMPARISON OF EXACT AND APPROXIMATE SOLUTIONS OF TRANSIENT RESPONSE FOR LEACHING BY SCF IN CSTR

Abstract Leaching or extraction by supercritical fluids (SCF) is a relatively new technology which offers several key advantages over traditional methods, especially enhanced solubility and rapid diffusion. Because the molecular properties are somewhere in between those of either liquid or gas, the design of SCF systems does not fit the classical mold based on intuitive or well-known rules of thumb. In the present work, transient transport for dissolution of solutes filling granulated porous media is studied for SCF leaching in spinning basket or slurry reactors. We present an approximate model based on taking the intraparticle composition profile to be always parabolic. This leads to a simple one-term expression (transportable on the back of a postage stamp) which is shown to compare very favorably with the more tedious exact solution. The approximate solution thus allows designers to quickly delineate those conditions, such as sampling times, which are realizable in the experimental sense. Moreover, it ...

Determination of the condition for the existence of composition minima in a CSTR via spectral analysis

Transient response of a CSTR containing porous catalyst pellets is analysed theoretically by a generalized integral transform, and the condition for existence of a minimum in the bulk concentration is determined via the analysis of the eigenspectrum of the governing equations. A simple unified condition for existence is found to be Vk/F (ρpSgK/e+ρpSgK)<1, irrespective of the values of any other parameters, where k is the first order rate constant, V is the reactor volume excluding pellet volume, F is the volumetric flow rate, ρp is the pellet density, Sg is the interior surface area, e is the pellet voidage and K is the slope of the linear adsorption isothern. Clearly, the continuous adsorber (k = 0) always satisfies this condition, therefore, a minimum in the transient bulk concentration is predicted to always occur. Simulations show that the minimum is sufficiently pronounced and the time scale for the minimum to occur is sufficiently practical that the occurrence of the minimum may be exploited for parameter estimation purposes.

Bubble formation from elastic holes

The elastic membrane sparger is studied by observing bubble formation at a single hole centered in a circular membrane. Two types of models are developed to forecast intrinsic properties of the elastic bubble generator: (i) flow rate as a function of pressure change (ii) bubble size as a function of flow rate. In the former, certain properties relating to the changing hole size are revealed, and in the second, the dominant bubble regime is delineated. Comparison of theory and experiment suggests the rubber sparger operates as a linear area device, that is, hole area appears to increase linearly with increasing pressure. This behavior has certain advantages over a fixed-hole sparger, for example the retardation of the onset of jetting. We next show certain modifications of the classical analysis can predict quite adequately the bubble sizes emanating from the flexible hole