Non-isothermal reaction-diffusion systems with thermodynamically coupled heat and mass transfer

Non-isothermal reaction-diffusion (RD) systems control the behavior of many transport and rate processes in physical, chemical, and biological systems. A considerable work has been published on mathematically coupled nonlinear differential equations of RD systems by neglecting the possible thermodynamic couplings among heat and mass fluxes, and reaction velocities. Here, the thermodynamic coupling refers that a flux occurs without its primary thermodynamic driving force, which may be gradient of temperature, or chemical potential, or reaction affinity. This study presents the modeling equations of non-isothermal RD systems with coupled heat and mass fluxes excluding the coupling of chemical reactions using the linear non-equilibrium thermodynamic approach. For a slab catalyst pellet, it shows the dynamic behavior of composition and temperature profiles obtained from the numerical solutions of non-linear partial differential equations by Mathematica for two industrial reaction systems of synthesis of vinyl chloride and dissociation of N₂O.     

Multicomponent diffusion and chemical reaction of gases in porous catalysts—I: Ternary gasdiffusion and chemical reaction without volume change (ν = 0)

The overall conversion rate for catalytic reactions of gases in porous catalysts is often controlled by transport processes in the porous pellet. Since in general more than two gases take part in the reaction, one has to calculate the conversion rate by using the transport equations for multicomponent mixtures. These equations, however, are rather complicated; thus calculations of conversion rates are commonly done by using Fick's transport law.First of all it is shown that the equations for multicomponent diffusion can be reduced to simple linear laws by using the stoichiometric coupling of the fluxes. With these equations, the calculation of the conversion rate for a reaction of the general type: ν₁R₁ + ν₂R₂ ? ν₃R₃ is as simple as for the case of binary diffusion. Using the example of hydrogenolysis of ethane it is then demonstrated that in general Fick's law leads to higher conversion rates than the Maxwell-Stefan, diffusion equations. With this example some basic questions arising in the discussion of heterogeneous catalytic reactions in porous systems (e.g. the choice of the “key component”) are discussed in detail.     

Numerical study of the coupling between reaction and mass transfer for liquid‐liquid slug flow in square microchannels

While the benefits of miniaturization on processes have been widely demonstrated, its impact on microfluidics and local mechanisms such as mass transfer is still little understood. The coupling between reaction and mass transfer in microchannels is simulated for liquid‐liquid slug flow. First, the extrapolation to confined flow of the classical model used to calculate interfacial mass fluxes in reactive infinite media was studied. This model consists in estimating transferred fluxes between two phases as a function of the enhancement factor E. Its expression depends on the model used to represent interfacial mass transfer. In infinite media, Lewis and Whitman's stagnant film theory is generally preferred for its simplicity and its reliability. In the case of confined slug flow, the limitation of such a model to predict interfacial fluxes is highlighted. Second, the case of liquid‐liquid competitive consecutive reactions in microchannels is considered. The unfavorable impact of the length between droplets on selectivity is emphasized. This is a direct consequence of mass‐transport mechanisms in microchannels. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Mass flux coupling by confined equilibrium reaction

Various physical systems with either phase boundaries or semi-permeable membranes can give rise to a confined chemical reaction. An analysis was performed to show the strong and potentially important effect of this confined reaction on chemical species diffusion through the region of reaction. The reaction was treated as one near equilibrium in order to obtain an analytical solution and to illustrate the strong coupling of fluxes caused by the reaction. Some generalities, e. g., facilitated diffusion of a single species transferring, were deduced using the above conditions and assumptions. These generalities are necessarily valid only for a single near equilibrium reaction with constant diffusivity of non-diffusing species. Three examples were solved to illustrate the strong coupling of mass fluxes.     

Electro-membrane reactor: A powerful tool for green chemical engineering

Electro-membrane reactors use electro-membranes for preferentially diffusive/electrophoretic migration or electroosmotic separation of in-situ reactive products, thereby maximizing the reaction rate and transport efficiencies of the products. These reactors are widely employed in the chemical engineering sectors such as green chemical synthesis, biorefining, electrocatalytic reduction/oxidation, and water treatment. In this review article, we provide an overview of the recent advances in three categories of electro-membrane reactors in chemical engineering sectors from three categories: (1) Electro-membrane reactors based on stacked ion-exchange membranes for resources recovery; (2) Electro-membrane reactors via Faraday reactions on functional anodes/cathodes for substance transformation; and (3) Closed-loop chemical reactions and substance separation via coupling of Faraday reactions and stacked membranes. The increasing demand for low-carbon economy has accelerated the advancement of environmentally friendly chemical engineering and sustainable processes and necessitates the use of electro-membrane processes. The macro perspective provides a timely reference for researchers and engineers.     

Residence times,micromixing and conversion in an un-premixed feed reactor — II: Chemical reaction measurements

Conversion measurements for a number of second order chemical reactions have been made at the outlet of an un-premixed feed, confined jet reactor, for which residence time data had been previously determined. A variety of stoichiometric and non-stoichiometric mixtures were used for a range of the dimensionless reaction rate constant k_r$\text{c}$₀τ between 0·1 and 18. A stochastic micro-mixing model, involving a single mixing history parameter and the measured residence time distributions, has been shown to correlate the conversion results for a number of different hydrodynamic conditions, in a manner that suggests that prediction of the outcome of other reactions is possible. The computational and experimental techniques involved are adaptable to the design and operation of industrial reactors where interaction of the hydrodynamics and chemical reaction rates are important in determining overall performance.     

REVIEW OF REVERSE OSMOSIS MEMBRANES AND TRANSPORT MODELS

After a brief introduction to membrane processes in general, and the reverse osmosis process in particular, the structure and properties of membranes and membrane transport theory are described. The mechanism of salt rejection and transport properties of membranes are discussed in detail. Solubility, diffusivity, and permeability of membranes to solutes and solvents are reviewed critically and compared with each other. Special attention is given to two particular types of membranes, cellulose acetate (CA) and aromatic polyamide (AP) membranes, which are often used for water desalination.

The major portion of this article is devoted to the review and discussion of membrane transport theory with application to the reverse osmosis and ultrafiltralion processes. It is shown that the solvent flux can be represented reasonably well by linear models such as the solution-diffusion model (Lonsdale, et al., 1965). The contribution of pore flow to the solvent flux is small. The solute flux, however, is not linearly dependent on the driving forces and one has to solve the differential equation of transport within the membrane which results in models such as the Spiegler-Kedem (1966) or the finely-porous (Merten, 1966) models. When the wall Peclet number is small, Pe_w =uτδ/D_sw ?1, (D_sw = bD_e one can linearize the nonlinear models. This requirement is not satisfied in most practical cases. Furthermore, the pore flow has significant effect on the solute flux equation and thus it can not be neglected.

The ambiguities that exist in the literature concerning the types of fluxes are discussed. The fluxes used in models derived from irreversible thermodynamics are purely diffusive (concentration and pressure diffusion) and they do not contain any convective effects; whereas the experimentally observed fluxes are the total fluxes with respect to the membrane which consist of a diffusive flux and a convective flux. A new model, based on irreversible thermodynamics, is derived which includes a convective term.

A membrane model is especially useful when the transport coefficients which define the model are not functions of the driving forces, i.e., pressure and concentration gradients. The coefficients in the solution diffusion and sotution-diffusion-imperfection (Sherwood, et al., 1967) models are functions of both pressure and concentration, while the coefficients in the Kedem-Katchalsky (1958) model are relatively insensitive to pressure and concentration. The nonlinear model of Spiegler-Kedem (1966) further improves the Kedem-Katchalsky model.     

On diffusion, dispersion and reaction in porous media

The upscaling process of mass transport with chemical reaction in porous media is carried out using the method of volume averaging under diffusive and dispersive conditions. We study cases in which the (first-order) reaction takes place in the fluid that saturates the porous medium or when the reaction occurs at the solid–fluid interface. The upscaling process leads to average transport equations, which are expressed in terms of effective medium coefficients for (diffusive or dispersive) mass transport and reaction that are computed by solving the associated closure problems. Our analysis shows that these effective coefficients depend, in general, upon the nature and magnitude of the microscopic reaction rate as well as of the essential geometrical structure of the solid matrix and the flow rate. This study also shows that if the reaction rate at the microscale is arbitrarily large, the capabilities of the upscaled models are hindered, which is in agreement with the breakdown of the physical sense of the microscale formulation.     

Diffusion,flow, and heterogeneous reaction of ternary mixtures in porous catalytic media

Unidirectional diffusion and flow of O₂COCO₂ gas mixtures undergoing heterogeneous chemical reaction within a porous CuO-on-alumina plug flow reactor are investigated. Experimental data for spatial distributions of pressure, temperature and composition and for feed-end species fluxes exhibit reasonable agreement with theoretical results drawn from appropriate extensions of the dusty gas model. Calculations for the individual contributions of bulk, Knudsen and thermal diffusion and thermal transpiration to the total species fluxes indicate that bulk diffusion is the major component under purely diffusive conditions; however, Knudsen diffusion assumes greater significance when forced flow is introduced.The theory indicates that the contributions of thermal diffusion and thermal transpiration to the total species fluxes become more significant as the species molecular weights become more disparate. The effects are demonstrated by means of companion calculations for the O₂H₂H₂O system.     

Geometrical relationships for ternary gas diffusion balances and criteria for multicomponent phenomena

Gas mixtures of more than two components are often encountered in chemical engineering. If the species are coupled by a diffusive process in the molecular diffusion regime, special multi-component phenomena may arise. Until now, however, there is only fragmentary information in literature on this topic. It is demonstrated how to derive criteria for multicomponent phenomena—for a whole set of flux couplings—based upon a simple geometric procedure. Osmotic and reverse diffusion in ternary systems now can be predicted in a simple and comprehensive manner. It is shown that both may also occur in ternary systems with coupling of diffusion and reaction.The proposed method uses diffusion balances, which permit an insight into concentration relationships along the diffusion path as a whole, without need for solution of the differential equations of molar fluxes.Linear balances are introduced as an additional multicomponent feature. Diffusion balance diagrams are presented as a mean to represent all possible boundary values on both ends of the diffusion path in the case of a diffusion barrier.     

TAYLOR DISPERSION OF MULTICOMPONENT SOLUTES

Coupled transport of multicomponent solutes in globally continuous systems is considered in the framework of the Generalized Taylor dispersion theory. Coupling between transports of n different species at the local (or micro-) scale, is considered to result from first-order irreversible surface reactions occurring on the local space boundaries, or from the off-diagonal terms of the solute diffusivity matrices.

General expressions are obtained for the global effective (long-time) solute dispersion matrix cofficients: mean global scalar reactivity, velocity vector and dispersivity dyadic.

The effect of surface chemical reactions is to partition the matter between different solute constituents. This is manifested in a coupling of the global transport coefficients, which may be mathematically removed by a linear (canonic) transformation applied to the effective global transport equation. This type of coupling does not exist for inert solutes.

The second type of the global coupling is represented by the off-diagonal terms of the global velocity and dispersivity matrices. It exists for both reactive and inert solutes. This coupling stems from the convective dispersion process (dependence or the global velocity vector on the local space coordinate). Is shown to be irremovable from the global transport equation by any linear transformation via the solute partition matrix. In the canonic form of the global equation the irremovable coupling is manifested by the traceless parts of the global solute velocity matrix and the global solute dispersivity.

The solution scheme is illustrated by calculating the mean global diffusivity of a solute consisting of two components, transport of which is coupled at the microscale via the molecular diffusivity matrix. At the macroscale the coupling is shown to be represented by negative off-diagonal terms of the global diffusivity matrix,     

Ullmann偶联反应催化剂研究进展

Ullmann偶联反应是典型的碳碳键偶联反应,反应合成的联苯类化合物是重要有机化工原料,应用前景广阔。初期采用均相Pd催化剂,不能重复利用,工业化生产受到限制。改用多相Pd催化剂催化反应,需要添加剂导致产物分离困难。多相Au催化剂适用性受到限制,反应底物局限于碘代芳烃,双金属催化剂在催化活性与选择性方面均有较好的优势。综述Ullmann-type偶联反应中均相Pd催化体系、多相Pd催化体系、多相Au催化体系以及多相双金属催化体系催化剂的研究进展,阐述反应机理,并对Ullmann偶联反应研究进行展望。     

Computational analysis of an instantaneous chemical reaction in a T‐microreactor

We extend and apply a method for the numerical computation of convective and diffusive mixing in liquid systems with very fast irreversible chemical reaction to the case of unequal diffusivities. This approach circumvents the solution of stiff differential equations and, hence, facilitates the direct numerical simulation of reactive flows with quasi‐instantaneous reactions. The method is validated by means of a neutralization reaction which is studied in a T‐shaped micromixer and compared with existing experimental LIF‐data. Because of their large are‐to‐volume ratio, microreactors are well suited for fast chemical reactions which are seriously affected by the slow diffusive transport in aqueous media. Numerical computations for different reactor dimensions reveal the fact that, in a dimensionless setting, the obtained conversion is independent of the reactor size, if the flow conditions are the same. This corresponds to an increase of space‐time‐yield proportional to the square of the inverse scale factor. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Prediction of a high swirled natural gas diffusion flame using a PDF model

The paper deals with the numerical prediction of a high swirling non-premixed confined natural gas diffusion flame in order to predict the pollutant emissions NO_x using the PDF model coupled with the Reynolds stress model (RSM). A chemical equilibrium model in conjunction with the assumed shape of the PDF is adopted. The chemical combustion reactions are described by nine species and eight reactions [Westbrook CK, Dryer FL. Chemical kinetic modelling of hydrocarbon combustion. Progr Energy Combust Sci 1984;10:1-57]. The PDF of the mixture fraction is described with a β-function. In order to predict the NO_x emissions, a NO_x post-processor of the Fluent code has been performed. The concentration of O and OH radicals are obtained assuming the partial-equilibrium assumption and using a PDF in terms of temperature. The numerical simulation of various factors influencing the combustion process are examined and compared favourably with experimental results.