With axial dispersion

Local equihbrium 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. ScL, 26, 1571 (1971)]. It is discussed below in further detail from the standpoint of the constant pattern. 

For adsorption with axial dispersion, the material balance transforms to... 

Breakthrough Behavior for Axial Dispersion Breakthrough behavior for adsorption with axial dispersion in a deep bed is not adequately described by the constant pattern profile for this mechanism. Equation (16-128), the partial different equation of the second order Ficldan model, requires two boundaiy conditions for its solution. The constant pattern pertains to a bed of infinite depth—in obtaining the solution we apply the downstream boundaiy condition cf 0 as oo. Breakthrough behavior presumes the existence of... 

In a vessel with axial dispersion, the steady-state equation for a reaction of order q is... 

Kifietic/lransporl for isothermal Same as Case 4 Pliit -Flow Rtfaclof with Axial Dispersion... 

Axial and radial dispersion or non-ideal flow in tubular reactors is usually characterised by analogy to molecular diffusion, in which the molecular diffusivity is replaced by eddy dispersion coefficients, characterising both radial and longitudinal dispersion effects. In this text, however, the discussion will be limited to that of tubular reactors with axial dispersion only. Otherwise the model equations become too complicated and beyond the capability of a simple digital simulation language. 

In Sec. 4.4.3 the modelling of differential extraction columns with axial dispersion is discussed. The extractor is considered to be approximated by eight finite-difference elements as shown below. 

PHASE DIFFERENTIAL EXTRACTION COLUMN WITH AXIAL DISPERSION... 

Writing the model in dimensionless form, the degree of axial dispersion of the liquid phase will be found to depend on a dimensionless group vL/D or Peclet number. This is completely analogous to the case of the tubular reactor with axial dispersion (Section 4.3.6). 

DISRE - Isothermal Reactor with Axial Dispersion System... 

Differential Extraction Column with Axial Dispersion 468... 

DISRET - Non-Isothermal Tubular Reactor with Axial Dispersion 340... 

For a typical packed bed, take the value of the Peclet number (udp/eDl) as 2. Dl is the dispersion coefficient in a packed tube. Then show that for a fractional conversion of 0.99 and a ratio of dp L of 0.02, the length L of the reactor with axial dispersion exceeds the length of the simple ideal plug-flow reactor by only 4.6 per cent where dp is the diameter of the particles. 

Parallel-plate electrodes Ethane polymerization Plug flow with axial dispersion Not applicable Assumed average electron density and energy 66... 

Cylindrical tube with ring electrodes Silane decomposition and dispersion Plug flow with axial dispersion Mean electron density measured with interferometry 71... 

By At we denote the cross sectional area of the reactor tube. Then the steady-state mass balance with axial dispersion gives us the equation... 

Applying the same procedure for the heat balance with axial dispersion (axial conduction) of heat, we get... 

PDE piston flow model with axial dispersion and mass exchange... 

A far more promising approach is represented by the so-called differential models, such as the axial dispersion model (ADM) (170) as well as the piston-flow model with axial dispersion and mass exchange (PDE) (171). Experimental studies (168) show that the ADM gives an appropriate description of the nonideal flow behavior of the liquid phase in catalytic packings (see Figure 31). Considering... 

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