Adsorption 4, 337–344 (1998) c  1998 Kluwer Academic Publishers. Manufactured in The Netherlands. Comparison of Finite Difference Techniques for Simulating Pressure Swing Adsorption YUJUN LIU, JAVIER DELGADO AND JAMES A. RITTER Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, SC 29208 Ritter@sun.che.sc.edu Abstract. Three different finite-difference routines were compared for solving the nonlinear, coupled, partial differential and algebraic equations that describe pressure swing adsorption processes. A successive substitution method (SS), a block LU decomposition procedure (BLUD), and the method of lines approach with adaptive time stepping (DASSL) were used to simulate and compare the computation times required to reach the periodic state for two different PSA systems: PSA-air drying and PSA-solvent vapor recovery. For both systems, the results showed that DASSL was nearly twice as fast as BLUD, whereas SS was nearly an order of magnitude slower than BLUD. DASSL and BLUD were also very robust and accurate, as nearly identical bed profiles were obtained from both methods under both transient and periodic state conditions. Keywords: pressure swing adsorption, mathematical models, numerical simulation, finite difference, adaptive time stepping Introduction A rigorous pressure swing adsorption (PSA) model consists of a system of coupled, partial differential and algebraic equations, which necessarily require numer- ical solution (Ruthven et al., 1994). At present, finite difference is still the most widely used method in solv- ing the PSA model equations because of its simplicity. In using finite differences, spatial and time derivatives are discretized, resulting in a set of algebraic equations. In much of the early PSA literature, the algebraic equa- tions were solved by a successive substitution method. More recently, other solution methods have been de- veloped, e.g., orthogonal collocation (Ruthven et al., 1994); however, studies comparing one technique to another have rarely been performed, with one excep- tion (Hassan et al., 1987). The simulation of some PSA systems also requires a great deal of computation time. Examples include sim- ulations of PSA-air purification (AP) (Ritter and Yang, 1991) and PSA-solvent vapor recovery (SVR) (Liu and Ritter, 1996). For very strongly adsorbed species, e.g., the DMMP-activated carbon system used in the PSA-AP study (Ritter and Yang, 1991), it may take tens of thousands of cycles to reach the periodic state, and for typical solvent vapors (e.g., benzene), it may take thousands of cycles (Liu and Ritter, 1996). The large number of cycles required by these systems are in contrast to typical PSA processes for air drying, hy- drogen purification or air separation, which generally require tens of cycles to reach the periodic state (Ruthven et al., 1994). Therefore, more efficient meth- ods are required to solve the models that are used to simulate PSA processes. One way of improving the efficiency of rigorous PSA simulations is to accelerate the convergence to the pe- riodic state (Smith and Westerberg, 1992; Croft and LeVan, 1994). These acceleration techniques are quite suitable if the periodic state is the only information de- sired. However, these techniques necessarily give rise to a fictitious transient path to the periodic state. In other words, the number of cycles and the correspond- ing dependent variable profiles are artifacts of the ac- celeration technique and have no physical significance