## 264009 Computing Profiles of Porosity in a Packed Bed Using Monte Carlo Method

Wednesday, October 31, 2012
Hall B (Convention Center )
Genong Li, Ansys Inc., Lebanon, NH

Computing Profiles of Porosity in a Packed Bed Using Monte Carlo Method

Genong Li Ansys Inc., 10 Cavendish Court, Lebanon, NH 03766 Email: Genong.Li@ansys.com, Tel: (603)7275505

Packed beds are widely used in chemical process industries. In numerical simulations a packed bed is usually treated as a psudo-homogeneous medium. In such a treatment, the packing structure of the bed is usually described by some statistical, lumped parameters such as porosity. And the calculations of flow, heat and mass transfer are based on those lumped parameters. Due to the existence of walls, packing seems to be more structured near a wall. As a result, porosity fluctuates a lot in the near-wall region. This phenomenon has been observed by many researchers especially for low D/d ratio packed beds.

A fundamental question is how to compute porosity once a packing structure is known. Due to its importance in computational fluid dynamics (CFD) simulations, porosity profile has been studied extensively, mostly for packing of mono-sized spheres into a cylindrical column. Volume-based and area-based methods have been used to compute the radial porosity profile. To use either of the methods, one has to compute the volume of the intersection of a cylinder with a sphere in the three dimensional space. However, the calculation involves elliptic integrals and one has to rely on a numerical method to evaluate those expressions.

A Monte Carlo method is used to compute those profiles. To the authors' knowledge, the method has never been employed in this context. The procedure of using this novel method is explained in detail. Through a rigorous error analysis based on statistics, the accuracy of the simulation result can be controlled. Before any simulation, the number of sampling points needed in the Monte Carlo simulation can be determined given an accuracy requirement. The method is completely general and can be used to compute profiles of porosity in any packed bed with any shape of packing elements.

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