Periodic states of adsorption cycles III. Convergence acceleration for direct determination

This paper describes several enhancements to accelerate the direct determin ation of the periodic states of fixed-bed adsorption cycles. The new method s make it possible to calculate the periodic states up to 40 times faster t han our original formulation (Croft & LeVan, Chem. Eng. Sci. 49 (1994) 1821 ) and in many cases 100-1000s of times faster than by just running cycle af ter cycle. We have tested the methods on several examples and have obtained fast, stable, robust convergence. The enhancements are (i) the use of a hy brid Newton-Broyden method to reduce some of the Jacobian matrix calculatio n processes required by Newton's method. (ii) the initial application of a novel iterative-secant approach to increase stability and to avoid the calc ulation of the first Jacobian matrix for the hybrid Newton-Broyden method, (iii) the implementation of a sensitivity interpolation technique with dyna mic grid allocation, and (iv) the dynamic specification of integration erro r tolerances. (C) 2001 Elsevier Science Ltd. All rights reserved.