Approximate ODE models for population balance systems

• An extension of the method of moments covering a wide class of PBEs.
• Model design for model-based control and optimization of PBEs.
• The class of PBEs involving size-dependent growth rate and fines removal term.
• Investigation of the impact of multiple precision computation.
• Comparison to a scheme based on method of characteristics in various case-studies.

We propose an approximate polynomial method of moments for a class of first-order linear PDEs (partial differential equations) of hyperbolic type, involving a filtering term with applications to population balance systems with fines removal terms. The resulting closed system of ODEs (ordinary differential equations) represents an extension to a recently published method of moments which utilizes least-square approximations of factors of the PDE over orthogonal polynomial bases. An extensive numerical analysis has been carried out for proof-of-concept purposes. The proposed modeling scheme is generally of interest for control and optimization of processes with distributed parameters.