Local equilibrium theory

Local equilibrium theory Shows wave character—simple waves and shocks Usually indicates best possible performance Better understanding Mass and heat transfer very rapid Dispersion usually neglected If nonisothermal, then adiabatic... 

In local equilibrium theory, fluid and sorbed phases are assumed to be in local equilibrium with one another at every axial position in the bed. Thus, because of uniform concentrations, the overbar on /i is not necessary and we have Cj Cj [note Eqs. (16-52) and (I6-II9)]. 

Multiple Transition System Local equilibrium theory for multiple transitions begins with some combination of material and energy balances, written... 

Methods for analysis of fixed-bed transitions are shown in Table 16-2. Local equilibrium theory is based solely of stoichiometric concerns and system nonlinearities. A transition becomes a simple wave (a gradual transition), a shock (an abrupt transition), or a combination of the two. In other methods, mass-transfer resistances are incorporated. 

Local equilibrium theory also pertains to adsorption with axial dispersion, since this mechanism does not disallow existence of equilibrium between stationary and fluid phases across the cross section of the bed [Rhee et al., Chem. Eng. Set, 26,1571 (1971)]. It is discussed below in further detail from the standpoint of the constant pattern. 

For high feed loads, the shape of the diffuse trailing profile and the location of the leading front can be predicted from local equilibrium theory (see Fixed Bed Transitions ). This is illustrated in Fig. 16-35 for tf = 0.4. For the diffuse profile (a simple wave ), Eq. (16-131) gives ... 

FIG. 16-35 Elution curves under trace conditions with a constant separation factor isotherm for different feed loadings and N = 80. Solid lines, rate model dashed line, local equilibrium theory for ZF = 0.4. 

Displacement Development A complete prediction of displacement chromatography accounting for rate factors requires a numerical solution since the adsorption equilibrium is nonlinear and intrinsically competitive. When the column efficiency is high, however, useful predictions can be obtained with the local equilibrium theory (see Fixed Bed Transitions ). 

For example, the local equilibrium theory combined with an accurate adsorption model (fitted to experimental adsorption equilibrium data) was succesfully used to predict experimental desorption data [2,3],... 

Chemical process rate equations involve the quantity related to concentration fluctuations as a kinetic parameter called chemical relaxation. The stochastic theory of chemical kinetics investigates concentration fluctuations (Malyshev, 2005). For diffusion of polymers, flows through porous media, and the description liquid helium, Fick s and Fourier s laws are generally not applicable, since these laws are based on linear flow-force relations. A general formalism with the aim to go beyond the linear flow-force relations is the extended nonequilibrium thermodynamics. Polymer solutions are highly relevant systems for analyses beyond the local equilibrium theory. 

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