(600aa) Computing Profiles of Porosity in a Packed Bed Using Monte Carlo Method

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.