Page 245 - gas transport in porous media

Chapter 13: Lattice Boltzmann Method
241
Second part: memory to store vectors: (sites = 26×26×24×48) × (6 vectors)
× (4 bytes/vector) = 1233024 bytes= 17.8 MB.The memory to store the flow speed
is the same as in (1b).
(2) From Eq. (13.8), Pe = Re = 24 = (L = 24 lu) × (U = 0.01 lu/ts)/(ν or
2
D m = 0.01 lu /ts);Sc=1.
(3) From Section 13.4.4, a dispersive steady-state is reached after a slug travels
2
2
2
2
for a characteristic diffusion time ∼L /D m = 24 lu /0.01 (lu /ts) = 57600 ts.
The channel must be long enough to contain the entire slug during this time, else
part of the slug will “fall off” the right end of the channel, and will wrap back if
there is no concentration boundary at the channel end. While the average speed
across the channel is 0.01 lu/ts, the solute in the middle of the channel will travel
faster. In a round pipe, the middle fluid travels twice the average speed; this speed
would be reached by the solute only at very high Pe, but to be on the safe side, we
assume this factor 2. Thus the distance traveled by the leading edge of the solute,
in the characteristic diffusion time, is (57600 ts)× (2 × 0.01 lu/ts)=1152 lu. The
cloned channel is 48 × 24 = 1152 lu long, so the channel length is adequate.

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