Mass transport with simultaneous reaction

For model building when the problem is one of mass transport with simultaneous reaction, the conservation of mass equation (Equ. 2.3a-c) is again utilized. In the one-dimensional stationary case it has the form... 

In addition to the process kinetic formulations of Atkinson, which are derived from the theory of mass transport with simultaneous biological reaction, other kinetic equations, macrokinetic in origin, are also known. 

Apecetche et al. [1] studied viscous and diffusive transport with simultaneous reaction in non-isobaric porous catalyst particles by use of the dusty gas model. A binary gaseous mixture under isothermal conditions was studied taking into account mass transfer due to the following mechanisms viscous flow, non-equimolar... 

The basic equations for an unsteady-state process of one-dimensional (in the -direction) heat and mass transport with a simultaneous chemical reaction in a porous catalyst pellet are... 

The Cu - or especially the Co-catalyzed oxidation of sulphite (Cooper, Fernstrom, and Miller, 1944 Reith, 1968) is thought to be suitable for estimating the OTR in comparing and designing gas-liquid (G L) reactors only under similar physical conditions as bioprocessing. Mass transport occurring simultaneously with a chemical reaction is a theoretical problem that results it is dealt with in Sect. 4.4. 

Substituting Equ. 6.134 for and Equ. 6.135 for into Equ. 6.132 results in an adequate reactor flow equation to be solved simultaneously with the biofilm effectiveness equation. The equation for represents the solution of the previous problem of internal transport with simultaneous enzyme reaction, described in Equ. 4.81. The effect of external mass transport, or the rate of S conversion, is included through the boundary conditions at the L S interface. Equation 4.81 and the accompanying boundary conditions expressed in dimensionless form are... 

Enhanced chemical reactivity of solid surfaces are associated with these processes. The cavitational erosion generates unpassivated, highly reactive surfaces it causes short-lived high temperatures and pressures at the surface it produces surface defects and deformations it forms fines and increases the surface area of friable solid supports and it ejects material in unknown form into solution. Finally, the local turbulent flow associated with acoustic streaming improves mass transport between the liquid phase and the surface, thus increasing observed reaction rates. In general, all of these effects are likely to be occurring simultaneously. 

Rieckmann and Volker fitted their kinetic and mass transport data with simultaneous evaluation of experiments under different reaction conditions according to the multivariate regression technique [116], The multivariate regression enforces the identity of kinetics and diffusivities for all experiments included in the evaluation. With this constraint, model selection is facilitated and the evaluation results in one set of parameters which are valid for all of the conditions investigated. Therefore, kinetic and mass transfer data determined by multivariate regression should provide a more reliable data basis for design and scale-up. 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

In this paper a transfer model will be presented, which can predict mass and energy transport through a gas/vapour-liquid interface where a chemical reaction occurs simultaneously in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the transport of mass and heat. On the basis of this model a numerical study will be made to investigate the consequences of using the Maxwell-Stefan equation for describing mass transfer in case of physical absorption and in case of absorption with chemical reaction. Despite the fact that the Maxwell-Stefan theory has received significant attention, the incorporation of chemical reactions with associated... 

What makes the fabrication of composite materials so complex is that it involves simultaneous heat, mass, and momentum transfer, along with chemical reactions in a multiphase system with time-dependent material properties and boundary conditions. Composite manufacturing requires knowledge of chemistry, polymer and material science, rheology, kinetics, transport phenomena, mechanics, and control systems. Therefore, at first, composite manufacturing was somewhat of a mystery because very diverse knowledge was required of its practitioners. We now better understand the different fundamental aspects of composite processing so that this book could be written with contributions from many composite practitioners. 

Similarly, in RA, reactions occur simultaneously with the component transport and absorptive separation, in the same column zone. These processes are used predominantly for the production of basic chemicals, e.g., sulphuric or nitric acids, and for the removal of components from gas and liquid streams. This can be either the cleanup of process gas streams or the removal of toxic or harmful substances in flue gases. Absorbers or scrubbers where RA is performed are often considered gas-liquid reactors (10). If more attention is paid to the mass transport, these apparatuses are instead treated as absorption units. 

The mathematical description of simultaneous heat and mass transfer and chemical reaction is based on the general conservation laws valid for the mass of each species involved in the reacting system and the enthalpy effects related to the chemical transformation. The basic equations may be derived by balancing the amount of mass or heat transported per unit of time into and out of a given differential volume element (the control volume) together with the generation or consumption of the respective quantity within the control volume over the same period of time. The sum of these terms is equivalent to the rate of accumulation within the control volume ... 

Transport simultaneous with reaction Mass transport (a) Effective diffusivity... 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

The overall electrode process consists of carrier transport in the semiconductor, electrochemical reactions at the interface, and mass transport of the reactants and reaction products in the electrolyte. There are a number of physical phases associated in the current path and the change of potential in each phase has a specific effect in relation to surface geometry. Also, a number of different reactions can occur simultaneously on the surface and compete in surface coverage and in reaction rate. Particularly, the anodic reactions of silicon in HF solutions have two parallel paths silicon may react with fluoride species and dissolve directly or may react with water to form oxide. 

For every electron passed upward along the conductor, a corresponding amount of reduced species must move away from, or oxidised species move toward, the conductor. This continual migration of redox-active species must be coupled with redox reactions in order to transfer charge. If redox equipotential lines are totally static, the production of reduced species at the conductor must be accompanied by the simultaneous consumption of reduced species somewhere between bedrock and the water table. This would result in the almost instantaneous transfer of electrical current despite the much longer time required for mass transport of reduced species to the ground surface (see discussion on ion mobility, below). 

If a surface reaction involving multisite adsorption exhibits a maximum with respect to concentration, slow reactant transport through the surface boundary layer can yield up to three steady states. The existence of a maximum is necessary but not sufficient for having multiplicity. The latter depends on the electrode potential, which can alter the shape and the position of the maximum, and on the magnitude of the mass transfer coefficient relative to the surface rate constant (418). Thus, as the potential becomes more negative for a reduction, the multiplicity region can be reached and oscillations may develop between two stable steady states. Oscillations could also arise from other simultaneous reactions such as oxide formation... 

Essentially all of the surface, of porous catalyst pellets is internal (see page 295). Reaction and mass and heat transfer occur simultaneously at any position within the pellet. The resulting intrapellet concentration and temperature gradients cause the rate to vary with position. At steady state the average rate for a whole pellet will be equal to the global rate at the location of the pellet in the reactor. The concentration and temperature of the bulk fluid at this location rhay not be equal to those properties at the outer surface of the pellet. The effect of such external resistances can be accounted for by the procedures outlined in Chap. 10. The objective in the present chapter is to account for internal resistances, that is, to evaluate average rates in terms of the temperature and concentration at the outer surface. Because reaction and transport occur simultaneously, differential... 

When we react a gas with a liquid or react two immiscible liquids, mass transfer occurs simultaneously with reaction. Thus, chemical kinetics is coupled with mass transport, which means we are no longer conducting a reaction, rather, we are managing a complex chemical-physical process. Such processes are usually diffusion rate limited, especially if the gas is sparingly soluble in the liquid or if one liquid is sparingly soluble in a second liquid. 

---