Accelerated computation of cyclic steady state for simulated-moving-bed processes

Industrial applications of the simulated-moving-bed (SMB) chromatographic technology have brought an emergent demand to improve the SMB process operation for higher efficiency and better robustness. Improved process modelling and more-efficient model computation will pave a path to meet this demand. However, the SMB unit operation exhibits complex dynamics, leading to challenges in SMB process modelling and model computation. One of the significant problems is how to quickly obtain the steady state of an SMB process model, as process metrics at the steady state are critical for process design and real-time control. The conventional computation method, which solves the process model cycle by cycle and takes the solution only when a cyclic steady state is reached after a certain number of switching, is computationally expensive. Adopting the concept of quasi-envelope (QE), this work treats the SMB operation as a pseudo-oscillatory process because of its large number of continuous switching. Then, an innovative QE computation scheme is developed to quickly obtain the steady state solution of an SMB model for any arbitrary initial condition. The QE computation scheme allows larger steps to be taken for predicting the slow change of the starting state within each switching. Incorporating with the wavelet-based technique, this scheme is demonstrated to be effective and efficient for an SMB sugar separation process. Moreover, investigations are also carried out on when the computation scheme should be activated and how the convergence of the scheme is affected by a variable stepsize.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.