Moment based weighted residual method - New numerical tool for a nonlinear multicomponent chromatographic general rate model

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Zheng Liu Name of the doctoral dissertation MODELING OF MASS TRANSFER AND REACTIONS WITH THE MOMENT METHOD Publisher School of Chemical Technology Unit Department of Biotechnology and Chemical Technology Series Aalto University publication series DOCTORAL DISSERTATIONS 5/2015 Field of research Chemical Engineering Manuscript submitted 10 September 2014 Date of the defence 27 February 2015 Permission to publish granted (date) 18 November 2014 Language English Monograph Article dissertation (summary + original articles) Abstract In chemical engineering field, mass transfer and reaction process models are needed in many stages of process research and design. These models usually consist of systems of partial differential equations. The focus of this work is to study the moment method as a numerical tool to solve different mass transfer and reaction models, which can be utilized to simulate a number of chemical engineering processes e.g. chromatography, adsorption, extraction etc. The implementation procedures, the features of the moment method are introduced with different application cases in this work. The moment transformation procedure, as the key step of the moment method is discussed in great detail when the moment method is applied to solve the chromatographic model. The important features of the moment method revealed in this work include: 1) Similar with other higher order methods, the moment method reaches desired accuracy with decreased number of variables and reduced computational load; 2) The moment method predicts the chromatographic effluent curve moments with good accuracy, because the moment method is to minimize the errors in the column profile moments; 3) Based on the moment method, the spatial PDE solution inherently conserves mass if 0th order moment is included into the set of equations. Different mass transfer and reaction processes are modeled in this work. From modeling point of view, these models are highly similar to each other except some minor details e.g. boundary conditions. This characteristic naturally is beneficial for the implementation of modeling tasks.In chemical engineering field, mass transfer and reaction process models are needed in many stages of process research and design. These models usually consist of systems of partial differential equations. The focus of this work is to study the moment method as a numerical tool to solve different mass transfer and reaction models, which can be utilized to simulate a number of chemical engineering processes e.g. chromatography, adsorption, extraction etc. The implementation procedures, the features of the moment method are introduced with different application cases in this work. The moment transformation procedure, as the key step of the moment method is discussed in great detail when the moment method is applied to solve the chromatographic model. The important features of the moment method revealed in this work include: 1) Similar with other higher order methods, the moment method reaches desired accuracy with decreased number of variables and reduced computational load; 2) The moment method predicts the chromatographic effluent curve moments with good accuracy, because the moment method is to minimize the errors in the column profile moments; 3) Based on the moment method, the spatial PDE solution inherently conserves mass if 0th order moment is included into the set of equations. Different mass transfer and reaction processes are modeled in this work. From modeling point of view, these models are highly similar to each other except some minor details e.g. boundary conditions. This characteristic naturally is beneficial for the implementation of modeling tasks.