Reaction and transport in disordered composite media: Introduction of percolation concepts

Mohanty, Kishore; Ottino, Julio M.; Davis, H. T.

doi:10.1016/0009-2509(82)80179-6

Cited by 148 publications

(44 citation statements)

References 27 publications

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“…Havever, a concrete elucidation of the important role of topology and connectivity in determining transport properties in porous media was only recently obtained in fluid flow in porous media studies associated with the enhanced recovery of oil. Using lattice and network representations, Scriven, Davis and co-workers (Larson et al, 1981a, b;Heiba et al, 1982Heiba et al, , 1983Heiba et al, , 1984Mohanty et al, 1982) have successfully applied concepts from percolation theory, originating from research in physics of hetemgeneous materials (Broadbent and Hammersley, 1957;Shante and Kirkpatrick, 1971), to devise computationally simple schemes for the accurate prediction of transport properties in porous media.…”

Section: Conclusion and Significancementioning

confidence: 98%

Application of percolation theory to noncatalytic gas‐solid reactions

Yortsos

Sharma

1986

AIChE Journal

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Previous models of noncatalytic gas-solid reactions are based primarily on parallelpore representations, thus excluding important topological effects of the porous medium. This paper utilizes network representations and percolation theory to develop expressions for pore closure time and the evolution of accessible volume, effective diffmivity, and conversion rates. SCOPEMany processes pertinent to chemical engineering operations involve the physicochemical interaction of fluids with the solid surfaces of a porous medium. A particularly broad class is characterized by the continuous-in-time reduction of the available surface area as a result of surface chemical reactions (e.g., catalyst deactivation and noncatalytic gas-solid reaction processes). This reduction is manifested by progressively lower conversion rates and invariably leads to pore closure (plugging). Previous mathematical models based on parallel-pore representations (e.g., Ramachandran and Smith, 1977;C!+tman and Edgar, 1983) provide a good description of the process at the local (pore) level, but are inherently inadequate for the accurate prediction of the time rate of change of accessible surface area and volume, effective diffusivity, and ultimately conversion efficiency and pore blockage time. Subsequent investigations by Gavalas (1980), and Bhatia and Perlmutter (1980), among others, imparted considerable insight into the effects of the topology of the porous medium by utilizing random pores.In this paper we follow a somewhat different approach based on a network representation of the porous medium. By using population balances and elements from percolation theory, we develop a general theory that rigorously accounts for the effect of geometrical (e.g., pore size distribution) and topological (e.g., connectivity, accessibility) aspects of the porous structure on the evolution in time of the above quantities. The theory provides significant insight into the intricate effects of the pore structure on the performance of several such processes. CONCLUSIONS AND SIGNIFICANCEApplication of the theory to computationally manageable networks, such as Bethe lattices, allows for a direct and computationally simple calculation of the pore closure time as well as the evolution in time of accessible surface area and volume, conversion efficiency, and effective diffusivity. The input required for the implementation of the model consists of the true pore size distribution and the coordination number of the network. Closedform expressions derived for the most important quantities associated with noncatalytic gas-solid reactions, are directly applicable to processes globally in the kinetic control regime. A simpliied mathematical formulation is also developed for processes that do not satisfy the kinetic control limitations. This formulation contains a new representation of the effective diffusivity, pdously considered constant or taken to be proportional to the local prosity (Garza-Garza and Dudukovic, 1981).For illustration purposes, the results are compared to ...

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Section: Conclusion and Significancementioning

confidence: 98%

Application of percolation theory to noncatalytic gas‐solid reactions

Yortsos

Sharma

1986

AIChE Journal

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“…Among the available theories that incorporate a physically realistic description of the pore network geometry and topology and provide useful numerical values of effective transport coefficients, percolation concepts as applied to disordered porous media have exhibited great promise (Mohanty et al, 1982;Reyes and Jensen, 1985). The concept of connectedness inherent in these approaches represents a marked improvement over the simpler representations of "straight-through" pores described by Van Brake1 (1975).…”

Section: B Effective Transport Coeficientsmentioning

confidence: 99%

Simultaneous momentum, heat and mass transfer with chemical reaction in a disordered porous medium: application to binder removal from a ceramic green body

Stangle

Aksay

1990

Chemical Engineering Science

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Abstract-A theoretical model has been developed to describe simultaneous momentum, heat, and mass transfer phenomena in disordered porous materials. The model can be applied to a wide variety of engineering-related fields, e.g., the drying and/or burnout of processing aids in the colloidal processing of advanced ceramic materials. Simulations based on the model predict the local temperature and mass distribution of the porous body as a function of time and position. This information can then be coupled with known mechanical properties of the body to predict internal stresses generated during removal of liquid from the body. The theoretical model has potential application to many engineering problems, e.g., the optimization of processing conditions in the design of an improved binder removal process. The model is evaluated using experimental data on binder removal from a ceramic green compact consisting of submicron a-Al,O,

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“…Before presenting and discussing the results, we should point out that the percolation models of reaction and transport in porous medium were proposed 21,22 and have also been used by several groups. [23][24][25][26][27] The difference between our work and the previous ones is that the reaction kinetics in the present problem is strongly nonlinear which makes the numerical method more complicated and also that we used the orthogonal collocation method to solve diffusion-reaction equations.…”

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confidence: 98%

Pore network model for catalytic dehydration of methanol at particle level

Beigi¹,

Dadvar²,

Halladj³

2008

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).c-Alumina is used as a catalyst for converting methanol to dimethyl ether. The process takes place in a packed or fluidized bed reactor consisting of microporous particles with distributed pore sizes and interconnectivities. The efficiency of the process is, however, significantly affected by the pore space structure of the particles. All the previous attempts for modeling this phenomenon have used continuum formulation of the problem based on classical equations of mass transport and reaction, without any regards for the effect of pore space morphology. In this article, we study the catalyst's performance by developing a network model for the pore space, with distributed pore sizes and interconnectivities. The network model is used to study the effect of several parameters such as pore space morphology, concentration, and temperature on catalyst's effectiveness factor. The results will be used for reactor simulations.

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Reaction and transport in disordered composite media: Introduction of percolation concepts

Cited by 148 publications

References 27 publications

Application of percolation theory to noncatalytic gas‐solid reactions

Application of percolation theory to noncatalytic gas‐solid reactions

Simultaneous momentum, heat and mass transfer with chemical reaction in a disordered porous medium: application to binder removal from a ceramic green body

Pore network model for catalytic dehydration of methanol at particle level

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