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Ind. Eng. Chem. Fundam. 1981, 20, 155-161
theory predicts and experiments seem to confirm that separation rapidly diminishes as operation moves away from a condition of inifinite recycle (batch operation). The reduction in separation (expressed as inverse NTU) is predicted to be linearly related to lean-product production rate, and this forecast is apparently confirmed by the particular experiments undertaken. A design relationship has evolved which can be used for engineering estimates. Earlier experiments have confirmed that solid (resin) diffusion is the rate-limiting step for this system, and this fact is used to show that two key dimensionless groups determine the extent of separation; these are the Hodgson number (solid diffusion time constant/cycle-time) and a new group which represents the ratio of mass exchange per unit lean product removed. Acknowledgment The experimental portion of this work was undertaken a t the University of Queensland, Australia. The authors gratefully acknowledge the support of the Australian Research Grants Committee in conducting this research. Nomenclature A = fluid displacement (distance travelled per half-cycle) A, = column cross-sectional area up = packing mass transfer area per unit volume interstitial fluid b = Pigford's separation parameter (k,AT/k) C* = equilibrium fluid composition D,= effective solid diffusion coefficient D = molecular diffusion coefficient d = particle diameter If= axial dispersion coefficient H = dissipation function (stage height or HTU) k, = particle mass transfer coefficient Ij(7') = isotherm slope (defined by eq 4) K = isotherm slope at mean temperature, k ( T ) ko, k l = linear isotherm temperature parameters (defined in eq 5) L = column length LH = hot (desorption) penetration distance L c = cold (adsorption) penetration distance
NHo = Hodgson number ( d ; / t , c&,) NT = transfer number (klAT
