Leon Lapidus

Bio: Leon Lapidus is an academic researcher from Princeton University. The author has contributed to research in topics: Nonlinear system & Optimal control. The author has an hindex of 21, co-authored 91 publications receiving 1986 citations.

A computational model for predicting and correlating the behavior of fixed‐bed reactors: I. Derivation of model for nonreactive systems

Abstract: A mathematical model is developed for predicting the mixing characteristics of fixed beds of spheres. The model is based on a two-dimensional network of perfectly stirred tanks. By means of the conventional partial differential equation description of flow in fixed beds, the predictions of the new model are compared with experimentally observed axial and radial mixing characteristics. The introduction of a capacitance effect is shown to enable the model to predict the abnormally low axial Peclet numbers observed in liquid-phase systems in the unsteady state. The mathematical model developed in the first part of this paper is extended to cover chemical reaction in a cylindrical fixed bed of porous catalyst spheres. The mathematical effect on the model of various controlling rate steps, nonconstant property values, and multiple, non-first-order reactions is discussed. After the general discussion a simplified system is chosen to indicate the practical advantages of the model. A single, first-order, irreversible, exothermic reaction is considered to proceed according to an effectively homogeneous rate expression, which varies exponentially with the inverse of absolute temperature. Both steady state and transient cases are calculated for a reactor, the walls of which are maintained at constant temperature.

An eigensystem realization algorithm for modal parameter identification and model reduction

Abstract: A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

Pore and solid diffusion models for fixed-bed adsorbers

Abstract: Most models for fixed bed adsorbers have used either the homogeneoussolid or pore diffusion model for the pellets. When the adsorption isotherm is linear, the two models can lead to identical breakthrough curves. The conditions for this equivalence are presented here. It is shown that one of the bulk flow factors that was included in the formulation of one pore diffusion model will be significant only for feedstreams containing a relatively high concentration of adsorbate. The prosity factor of the pore model is shown to be very important, especially as the porosity decreases. The importance of the two diffusional models with respect to the predicted breakthrough curves is demonstrated. For comparable beds, it is shown that the breakthrough curve based on the homogeneous model is delayed with respect to that based on the pore model at early times, regardless of the shape of the isotherm. Finally, the various possible solutions for an irreverisble isotherm are reviewed for each of the models, and a solution is presented for the general case of a pore model with an outside film resistance.

The method of weighted residuals and variational principles

Abstract: Preface to the classics edition Preface Acknowledgments Part I. The Method of Weighted Residuals: 1. Introduction 2. Boundary-value problems in heat and mass transfer 3. Eigenvalue and initial-value problems in heat and mass transfer 4. Applications to fluid mechanics 5. Chemical reaction systems 6. Convective instability problems Part II. Variational Principles: 7. Introduction to variational principles 8. Variational principles in fluid mechanics 9. Variational principles for heat and mass transfer problems 10. On the search for variational principles 11. Convergence and error bounds Author index Subject index.