Page 225 - gas transport in porous media

CHAPTER 13

LATTICE BOLTZMANN METHOD FOR CALCULATING
FLUID FLOW AND DISPERSION IN POROUS AND
FRACTURED MEDIA

HARLAN W. STOCKMAN
Sandia National Laboratories, P.O.Box 5800, Albuquerque, NM, 87185, USA

13.1 INTRODUCTION

The lattice Boltzmann (LB) method is a numerical technique suited for modeling
flow of fluids, particularly those obeying the Navier-Stokes and advection-dispersion
equations (Rothman and Zaleski 1997; Martys and Chen, 1996). The strength of
the method lies in its ability to calculate transport in the presence of geometrically
complex solid boundaries and initial conditions. Added effects may include chemical
reaction, dissolution and precipitation, immiscibility, and buoyancy.
In the past ten years, the LB method has been applied increasingly to problems
involving flow through porous and fractured rocks and soils (Stockman et al., 1997;
Stockman et al., 1998; Zhang et al., 2002; Pan et al., 2004; Sukop and Or, 2004, and
references therein). While the technique can be applied to most fluids, there are some
special considerations for LB models of gases, and in particular, for assemblages
of many pores, or macroscopic fractures. These special considerations, along with
illustrative examples and benchmarks, are the subject of this chapter. The focus of
the chapter is on pore-scale models, where fluid behavior is approximated by the
Navier-Stokes equations. These pore-scale models are used to obtain permeability
and dispersion coefficients applicable to a larger scale, and the inherent and practical
limitations of the method are illustrated with examples.

13.2 METHOD

13.2.1 Basic Method
In the LB method, physical space is broken up into a set of nodes, usually on a
Cartesian grid; the set of these nodes is called the automaton. The term lu is used for
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C. Ho and S. Webb (eds.), Gas Transport in Porous Media, 221–242.
© 2006 Springer.