R. Mann

Evaluation of mercury porosimeter experiments using a network pore structure model

Abstract A square network model has been developed to interpret mercury penetration and retraction behaviour in the widely employed mercury porosimetry technique for investigating pore structure and pore size distribution. A network of arbitrary size is constructed by assembling cylindrical pore segments of equal length and pseudo-random number generation is used to assign pore diameters according to any stipulated size distribution function. Application of the simple Washburn equation then predicts movement of mercury into the network under increasing pressure (penetration) and the corresponding withdrawal under reducing pressure (retraction) The network model is superior to the classical parallel bundle model, since it implicitly produces hysteresis between penetration and retraction, predicts that mercury entrapment on retraction is a result of interconnectedness of pore segments and provides a better estimate of the intrinsic distribution of segment sizes. Comparison with porosimeter experiments on a commercial hydrodesulphurisation catalyst show that the approach can be applied to practical measurements and the model may provide an improved basis for the study of diffusion, reaction and deactivation in catalyst pellets.

Dynamic gas disengagement: A new technique for assessing the behaviour of bubble columns

Abstract A precise measure of the liquid motion and distribution of bubble sizes is essential for designing gas-liquid reactors for complex reactions in which product distribution may be a function of bubble size. A theoretical approach is presented which shows how the interaction of bubble size distribution and bubble rise velocity functions leads to predictions of the overall steady state hold-up in a bubble column within which the liquid flow is understood. Since this approach is based on a physical understanding of how bubble flow at a given superficial velocity must relate to the static hold-up, the theory can be immediately extended to describe the disengagement of gas bubbles if the gas feed is cut off. Thus the dynamic gas hold-up during gas disengagement can be used to provide new insights into the fundamentals of bubble column behaviour. In this way it becomes possible in principle to inter-relate macroscopic properties such as surface area, gas phase residence time distribution and intensity of mixing in the liquid phase. A new experimental technique is described which measures the dynamic gas hold-up during gas disengagement Experimental results at a nominal 20 mm/s gas superficial velocity are compared with various approaches based upon the theory. The effects of the accompanying induced liquid movements are represented by a simplified core-annulus circulation model. Bubble size distributions and liquid circulation can then be related to both the static and dynamic hold-up behaviour. It is shown that ambiguity due to uncertainty about the relative differences in bubble size distribution in upflow and downflow regions can be resolved from a knowledge of the surface area.

ELECTRICAL RESISTANCE TOMOGRAPHIC SENSING SYSTEMS FOR INDUSTRIAL APPLICATIONS

Abstract The effects of electrode configuration and design are investigated using a grouped node finite element method (FEM). An estimated expression for an appropriate experimental/actual electrode-angle β is given for an electrode system modelled with grouped-node FEM or single-node FEM. Analyses and methods for reducing sensor noise are discussed in practical terms. Examples of ERT sensors for different applications are given, which comprise from one to eight sensing planes sized from 6 to 1500 mm in diameter. A novel image reconstruction method based on the sensitivity theorem is presented. The capabilities of ERT and its data interpretation and image processing are discussed for pipelines, hydrocyclones and mixing vessels.

Some observations on the variation of tortuosity with thiele modulus and pore size distribution

Abstract Stochastic pore networks have been used to interpret the effects of pore structure on simultaneous diffusion and reaction in a porous catalyst. A stochastic pore network is a square network of pores, each pore segment having a radius assigned at random from any stipulated pore size distribution. The equations for diffusion and reaction within the network are solved rigorously for first order irreversible kinetics. The model is used to predict effectiveness factors and tortuosities for a hypothetical catalyst having one of four pore size distributions. The analysis predicts that tortuosity will vary with the Thiele modulus, the strength of this variation depending on the pore size distribution. It is further observed that the concentrations experienced by pores in a network are markedly different to those predicted by the parallel bundle model. This is relevant to the question of selectivity in complex reaction schemes.

Application of a stochastic network pore model to oil-bearing rock with observations relevant to oil recovery

Abstract Mercury porosimeter experiments have been traditionally used to investigate the pore structure of oil bearing rocks, although interpretation based upon the oversimplified parallel-bundle model is inadequate to explain many practical aspects of oil recovery. A technique for stochastically assigning the sizes of tubular pore segments placed in a network configuration of interconnected pores has been used to model pore structure and a trial and erro procedure has been devised which gives directly the size distribution of segments comprising the network which will exactly reproduce any observed merc porosimeter penetration curve. The theory is applied to porosimeter tests on a core sample from the Agha Jari Field (Iran). It is evident that the pore distribution function according to a network interpretation comprises a very much greater proportion of larger pores than is inferred from the parallel model. This distortion of the pore size distribution is shown to arise from the inaccessibility of larger segments when surrounded by small pores, a phenomenon that cannot be represented by the parallel-bundle approach. As a quantified interconnecting pore model, the network analysis has potential for investigating oil retention mechanisms in a reservoir, and the probable micro-scale water displacement behaviour of the pore network deduced to rep the core sample is described. Low recovery factors seem to be related to water flowing preferentially through pathways made of larger pores. Entrapment likely in large pores isolated by surrounding smaller ones.

A networks-of-zones analysis of mixing and mass transfer in three industrial bioreactors

Abstract The original version of the networks-of-zones (N-o-Z) model developed for the description of gas–liquid flow in stirred-vessel reactors (R. Mann, Gas–liquid stirred vessel mixers: towards a unified theory based on network of zones, Transactions of the Institution of Chemical Engineers 64 (1986) 23–34) has been extended and enhanced to cover distributed bubble sizes, gas–liquid mass transfer, bioreaction kinetics and multiple-impeller operation. In addition, a modified version of the N-o-Z model for bubble columns has been simply derived from the impeller version, assuming the existence of a two-loop axisymmetrical circulation pattern induced by the non-uniform distribution of gas holdup in bubble columns. The liquid circulation velocity has been expressed as a function of gas flow rate and the density difference between the gas and liquid phases, based on Zehners circulation model (P. Zehner, G. Schuh, A concept for the description of gas phase mixing in bubble columns, German Chemical Engineering 5 (1985) 282–289). These two variants of the N-o-Z model have been used for modelling three different industrial fermenters: 3 and 31 m 3 triple-impeller stirred reactors, and a 236 m 3 bubble column reactor. The performance of these three reactors, typical of the fine chemicals, bioprocessing and pharmaceutical process industries was evaluated and compared in terms of geometry/size, gas flows, power inputs, pressure, liquid mixing, oxygen mass transfer, reaction speed and spatial variability of behaviour. This provides potentially valuable insights into the relative factors influencing the selection of an appropriate reactor type.

Deactivation of a supported zeolitic catalyst: Diffusion, reaction and coke deposition in stochastic pore networks

Abstract The decline in activity of a commercial, supported catalyst has been interpreted using a model of zeolitic micropores uniformly distributed within a network of macropores representing the silica/alumina support. Using this model, simultaneous deactivation by site coverage and pore plugging can be simulated. Changes in network structure due to fouling are monitored by generation of theoretical adsorption isotherms for both fresh and fouled networks. The observed deactivation for catalytic cumene cracking in a plug flow reactor at 500°C was modelled by a series coking mechanism with the coke reducing the macropore radii by approximately 30 Angstrom.

Support-pore architecture optimization in FCC catalyst particles using designed pore networks

Abstract SEM images of FCC catalyst particles reveal the internal pore space to consist of massive networks of randomly interconnected pores of varying sizes and orientation. Until recently, design of catalyst particles has been restricted mainly to composition, particle size and pore size distribution with little attention paid to pore architecture. With recent advances in computing technology and catalyst characterization techniques it is now possible to move from these ‘jumbled’ configurations towards more structured controlled pore architectures that could greatly enhance effective utilization of catalyst pore space. In this paper, an application of 2D stochastic networks to investigate the direct influence of pore assembly on diffusion and reaction in FCC catalyst particles is described. Coke burn-off in heavily coked particles was used. Various pore architectural structures were tested including random, positively spiralled, negatively spiralled, structured and interspersed 2D networks. The interspersed network exhibited fastest burn-off kinetics relative to other structures while the random configuration, which probably characterizes most current catalyst particles, showed results better only than the negatively spiralled network. This can be attributed to enhanced reactant accessibility resulting from absence of transport inefficient micro- and macro-pore clusters and an increase in direct micro–macro pore links characteristic of the designed interspersed network.

Deactivation of a supported zeolite catalyst: Simulation of diffusion, reaction and coke deposition in a parallel bundle

Abstract A theoretical framework has been assembled for elucidation of the deactivation of a supported zeolite cracking catalyst used in a fixed bed, plug flow reactor. Intraparticle processes are based upon a parallel bundle model for the macropores and mesopores associated with the silica alumina support. Zeolite micropores contained within crystallites are assumed to be uniformly distributed along the walls of the support pores. Coke accumulation upon the support is represented by a wedge layering mechanism, which accounts for interactions of the support pore volume and coke deposits, giving rise to possible plugging of support pores. Discrimination of deactivation mechanisms can be achieved by reconciling timewise activity loss with changes in pore structure indicated by adsorption isotherms. The support pore plugging process shows up clearly in the isotherms. Illustrations are provided for a deactivation where the zeolite and support activities are equal. Experimental results for the cracking of cumene at 500°C indicate a rapid loss of zeolite activity followed by a slower support pore deactivation which includes the plugging of pores smaller than 150 A in diameter.

Tomographic imaging of fluid mixing in three dimensions for single-feed semi-batch operation of a stirred vessel

With fast data acquisition and good spatial discrimination, electrical resistance tomography (ERT) provides a non-invasive and non-intrusive technique to interrogate, in three dimensions, the concentration fields inside a typical stirred vessel. A newly refurbished vertically assembled 16-sensor eight-ring electrode array has been used to image the full volume of a 23001 pilot-scale vessel for single-feed semi-batch operation. Images reconstructed from the raw ERT data are represented first as pixel conductivity distributions and secondly as time incremented three-dimensional solid-body colour-scaled isosurfaces thereby providing a five-dimensional representation of the mixing process. When operating in this single-feed semi-batch mode, the ERT system can clearly distinguish the higher conductivity feed plume. The ERT also images the subsequent mixing in the vessel after the semi-batch feed addition has stopped, thus additionally characterizing the role of macro-mixing in achieving final homogeneity after a period of semi-batch operation. The results to be presented are extremely useful for the validation of CFD predictions of mixing behaviour.