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where A = 2γ2rp (eddy diffusivity term of the axial dispersion coefficient), B = 2γ1Dm (molecular diffusivity term of the axial dispersion coefficient) and C ≈ 2εb/[(1- εb)(Kki)] accounts for particle mass transfer resistance. Other variations of the model exist that include factors such as film resistance through a velocity dependency of the A term.73, 74 Differentiating between the effects of eddy turbulence and film diffusion is notoriously difficult since they both act to disperse the concentration wave in a similar manner.74 Since significant film diffusion effects were not expected, it was beyond the scope of this study to use more complex models. HETP was estimated from the height of a transfer unit (HTU) assuming HETP ≈ HTU.75 In linear chromatography, HTU = L/NTU where NTU is the number of transfer units. However, for an adsorption column, HTU is found from the expression HTU = MTZ/NTU where the calculation is performed across the defined limits of the MTZ and NTU is the integral of equation 5.1. While this approach is only strictly applicable to linear systems, it is a reasonable approximation for non-linear systems, provided it is not a strongly non-linear system. The MTZ length was found using the length of unused bed (LUB) approach.71 This approach is applicable for systems with a favorable isotherm that develop a constant profile within the column. With this method, the MTZ length is approximated from breakthrough experiments as: where uw is the wave (constant profile) velocity. The wave velocity is determined using equation 5.4: 78PDF Image | LIMITS OF SMALL SCALE PRESSURE SWING ADSORPTION
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