Reaction-transport processes

A more active kind of chemometries aims at the integration of statistical and mathematical techniques with the analytical procedure. The conventional analytical process is modified or a completely new process is developed in studying reactions, transport processes, adsorption, absorption, etc. The ultimate aim is to obtain more and better information in an optimum way. 

A particular component of a given phase can be characterized in terms of its content and ability to partake in various processes (chemical reactions, transport processes) using the partial molar Gibbs energy. For an electrically-charged phase, this quantity is termed the electrochemical potential of the ith component... 

The production of fine particles that are either desirable (polymer colloids, ceramic precursors, etc.) or undesirable (soot, condensed matter from stack gases, etc.) involves chemical reactions, transport processes, thermodynamics, and physical processes of concern to the chemical engineer. The optimization and control of such processes and the assurance of the quality of the product requires an understanding of the fundamentals of microparticles. 

James Davis is the inventor of the levitation machine, with which a single aerosol particle can be suspended in mid-air in order to study its equilibrium and rate processes without resorting to averaging among many particles. He contributes a very strong chapter on Microchemical Engineering that involves chemical reactions, transport processes, thermodynamics and physical processes. 

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

Reaction-transport processes in heterogeneous reactors involve spatial scales in the range from 10 9 to 10 m. Here, we are going to survey simulation approaches employed on the scales of nanometers to millimeters. 

The long-term performance of the repository at Yucca Mountain will be affected by the coupling of thermal, hydrological and chemical (THC) processes in the rock around the emplacement drifts. The transport of heat, fluid, and vapor will result in changes in water and gas chemistry, as well as mineral dissolution and precipitation which may lead to permanent changes in porosity, permeability and unsaturated hydrological properties. The purpose of this contribution is to describe the approach used to model reaction-transport processes in the Drift Scale Test (DST) with comparisons of simulation results to measured geochemical data on water, gas, and minerals. 

The numerical model for reaction-transport processes in the fractured welded tuffs must account for the different rates of transport in fractures, compared to a much less permeable rock matrix. Transport rates greater than the rate of equilibration via diffusion leads to disequilibrium between waters in fractures and matrix. Because the system is unsaturated, and undergoes boiling, the transport of gaseous species, especially CO, is an important consideration. The model must also capture the differences in initial mineralogy in fractures and matrix and their evolution. 

External mass transfer. The method of moments applied to the pulse response of fixed-bed reactors [M. Suzuki and J.M. Smith, Amer. Inst. Chem. Eng. JL, 16, 882 (1970) Chem. Eng. Sci., 26, 221, (1971)] was adapted to the consideration of reac-tion/mass-transfer effects in trickle beds [N.D. Sylvester and P. Pitayagulsarn, Amer. Inst. Chem. Eng. JL, 19, 640 (1973) Can. Jl. Chem. Eng., 52, 539 (1974)]. In this latter work it was shown that the zeroth, first and second moments of the response to a pulse input can be divided rather neatly into several factors, each associated with a particular step in the overall reaction-transport process. The zeroth moment of the output is related to a series of parameters given by... 

For reaction-transport process with a linear kinetic term F(p) = rp, an alternative description has been suggested in [187], namely... 

Meyer M, Melke J, Gerteisen D (2011) Modeling and simulation of a direct ethanol fuel cell considering multistep electrochemical reactions, transport processes and mixed potentials. Electrochim Acta 56 4299 307... 

It was shown that for certain system parameters given by a critical Reynolds number, there is a possibility of propagation of the specific flow structures inside the liquid layer. The convection cells, which can appear, are similar to those observed in the Ryleigh-Benard experiment [9]. Such phenomenon can be very important for some air-water-phospholipid systems such as the pulmonary surfactant present in the natural mass exchanger - the lungs. The hydrodynamic system described in the piq er can be a very useful tool for explanation of convective diffusion-reaction transport process in case of interaction of allergens with pulmonary epithelium, causing atopy. 

Generally, the electrochemical reaction is a heterogeneous, multi-step process. These steps can be consecutive or parallel they can include homogeneous chemical reactions, transport processes, adsorption phenomena, crystals nucleation and growing, as well as formation of new phases, etc. However, one essential step, always required to occur in the electrochemical reaction is the electron transfer through the electrolyte solution-electrode phase boundary. Thus, the electronic conductivity of at least one phase is crucial for the reaction to proceed. The overall reaction can involve several electrons the electrons being transferred simultaneously or stepwise. In the latter case, other steps sometimes take place between the electron transfer steps. 

Electron transfer reactions are conceptually simple. The coupled stmctural changes may be modest, as in tire case of outer-sphere electron transport processes. Otlier electron transfer processes result in bond fonnation or... 

Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic dreoty of gases, and their interrelationship tlu ough k and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests tlrat this should be a dependence on 7 /, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to for the case of molecular inter-diffusion. The Anhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, tlren an activation enthalpy of a few kilojoules is observed. It will thus be found that when tire kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation entlralpy will be a few kilojoules only (less than 50 kJ). 

For simulation on the IBM 360/65 computer, the reaction was represented as first order to oxygen, the limiting reactant, and by the usual Arrhenius form dependency on temperature. Since the changes here were rapid, various transport processes had significant roles. The following set of differential equations was used to describe the transient system ... 

The influence of transport process in two-phase reaction systems depends on flow conditions, which change with the size of the equipment. This is the reason for the historic observation that performance changes as processes are scaled up and therefore scale-up should be done in several steps, each limited to a small increase in size. This is a slow and expensive method and still does not guarantee optimum design. 

It is not unusual for the full chemical potential of a reaction to be diminished by slower transport processes (i.e., to be transport limited). In fast liquid phase enzyme reactions, mechanical stirring rates can have a strong influence on the observed kinetics that may be limited by the rate of contacting of the reactants and enzymes. Most heterogeneous catalytic reactions take... 

Much of the difficulty in demonstrating the mechanism of breakaway in a particular case arises from the thinness of the reaction zone and its location at the metal-oxide interface. Workers must consider (a) whether the oxide is cracked or merely recrystallised (b) whether the oxide now results from direct molecular reaction, or whether a barrier layer remains (c) whether the inception of a side reaction (e.g. 2CO - COj + C)" caused failure or (d) whether a new transport process, chemical transport or volatilisation, has become possible. In developing these mechanisms both arguments and experimental technique require considerable sophistication. As a few examples one may cite the use of density and specific surface-area measurements as routine of porosimetry by a variety of methods of optical microscopy, electron microscopy and X-ray diffraction at reaction temperature of tracer, electric field and stress measurements. Excellent metallographic sectioning is taken for granted in this field of research. 

While it is inherently probable that product formation will be most readily initiated at sites of effective contact between reactants (A IB), it is improbable that this process alone is capable of permitting continued product formation at low temperature for two related reasons. Firstly (as discussed in detail in Sect. 2.1.1) the area available for chemical contact in a mixture of particles is a very small fraction of the total surface (and, indeed, this total surface constitutes only a small proportion of the reactant present). Secondly, bulk diffusion across a barrier layer is usually an activated process, so that interposition of product between the points of initial contact reduces the ease, and therefore the rate, of interaction. On completion of the first step in the reaction, the restricted zones of direct contact have undergone chemical modification and the continuation of reaction necessitates a transport process to maintain the migration of material from one solid to a reactive surface of the other. On increasing the temperature, surface migration usually becomes appreciable at temperatures significantly below those required for the onset of bulk diffusion within a product phase. It is to be expected that components of the less refractory constituent will migrate onto the surfaces of the other solid present. These ions are chemisorbed as the first step in product formation and, in a subsequent process, penetrate the outer layers of the... 

A CVD reaction is governed by thermodynamics, that is the driving force which indicates the direction the reaction is going to proceed (if at all), and hykinetics, which defines the transport process and determines the rate-control mechanism, in other words, how fast it is going. 

In the A sector (lower right), the deposition is controlled by surface-reaction kinetics as the rate-limiting step. In the B sector (upper left), the deposition is controlled by the mass-transport process and the growth rate is related linearly to the partial pressure of the silicon reactant in the carrier gas. Transition from one rate-control regime to the other is not sharp, but involves a transition zone where both are significant. The presence of a maximum in the curves in Area B would indicate the onset of gas-phase precipitation, where the substrate has become starved and the deposition rate decreased. 

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