Automatic differentiation-based quadrature method of moments for solving population balance equations

作者：Kariwala Vinay^*; Cao Yi; Nagy Zoltan K

来源：AICHE Journal, 2012, 58(3): 842-854.

DOI：10.1002/aic.12613

• automatic differentiation
• dynamic simulation
• particulate processes
• population balance equations
• quadrature method of moments

The quadrature method of moments (QMOM) is a promising tool for the solution of population balance equations. QMOM requires solving differential algebraic equations (DAEs) consisting of ordinary differential equations related to the evolution of moments and nonlinear algebraic equations resulting from the quadrature approximation of moments. The available techniques for QMOM are computationally expensive and are able to solve for only a few moments due to numerical robustness deficiencies. In this article, the use of automatic differentiation (AD) is proposed for solution of DAEs arising in QMOM. In the proposed method, the variables of interest are approximated using high-order Taylor series. The use of AD and Taylor series gives rise to algebraic equations, which can be solved sequentially to obtain high-fidelity solution of the DAEs. Benchmark examples involving different mechanisms are used to demonstrate the superior accuracy, computational advantage, and robustness of AD-QMOM over the existing state-of-the-art technique, that is, DAE-QMOM.

• 出版日期2012-3
• 单位南阳理工学院