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

• A new numerical method is proposed to solve a chromatographic general rate model.
• The method precisely conserves mass and predicts the separation characteristic values.
• The method reaches desired accuracy with less variables and fast calculation speed.
• The method is also suitable for e.g. reactor and leaching models with particle phase.
• One real experiment is simulated to verify the method.

A new numerical method is proposed to solve a nonlinear general rate model, frequently used to describe chromatographic multicomponent separations. The method is based on minimization of errors in chromatographic column profile moments, and it belongs to the family of weighted residual methods. Compared to most traditional weighted residual methods, the present formulation has some clear advantages. Firstly, it is inherently mass conserving. Secondly, the separation characteristic values of the effluent curve (retention time, physical dispersion and skewness) are predicted with good accuracy. Thirdly, the boundary conditions are treated naturally as source terms. The method is inherently of high order, so it gives high accuracy with a relatively low number of variables. This is a remarkable benefit especially for model parameter fitting or process optimization, when the model has to be solved repeatedly.