Page 183 - gas transport in porous media

Chapter 9: Unstable Gas Flow in Fractures
into the fracture was determined not only by capillary forces but also, probably,
gravity. 177
Gas never formed as a continuous finger but always as a series of bubbles; this shape
minimizes the bubble surface area. Bubbles were always larger in dimension than the
aperture, and were therefore “squashed flat” between the fracture walls. Bubbles
were not elongated but took a distorted-circle shape determined by the aperture field
through which they flowed. Largest bubbles were formed when the fracture was
◦
◦
oriented 30 from horizontal, and smallest when it was 90 from horizontal, that
is, vertical. This suggests, in accordance with snap-off theory, that the bubble size
is controlled by the rate at which water can flow around the gas finger to snap off
the bubble (i.e., water flows more slowly when the angle is small). Bubbles rose
generally vertically, favoring larger pores, similar to the observation of Persoff and
Pruess (1995). Bubbles rose more rapidly in the vertical than inclined fracture, and
larger bubbles rose more rapidly, both explained by greater buoyancy. The flow is
unstable in the sense that it is discontinuous.
Kostakis (1998) developed a mathematical model of bubble generation and flow
in a fracture. Using an equation for the flow rate through an orifice at the point
of bubble generation, the bubble size (radius of equivalent sphere) was first solved
by a balance of all forces acting on the bubble (expressing acceleration as a vir-
tual mass force), and then the gas momentum conservation equation was solved
numerically, tracking the bubble through a 2-D grid representing the fracture.
Resulting predictions were compared favorably with data from Kostakis’ and other
experiments.

9.4 SUMMARY
Gas flow in fractures is unstable when there is sufficient water to block the gas flow
path. Below the water table, this causes gas to flow as bubbles. Above the water table
gas flow is unstable when the gas pressure is insufficient to overcome surface tension
forces that tend to draw water into the smallest pore in a gas flow path. Unstable gas
flow may cycle regularly, and if boundary conditions remain steady, may be treated
as constant in the average. Because of the greater permeability of fractures compared
to porous media, velocities may be great enough to cause non-darcy flow, in which
case pipe-flow models may be appropriate.

REFERENCES

Detwiler, R.L.; S.E. Pringle; and R.J. Glass . Measurement of fracture aperture fields using transmitted
light: An evaluation of measurement errors and their influence on simulations of flow and transport
through a single fracture , Water Resour. Res., 35(9), 2605–2617, 1999.
Faybishenko, B. Chaotic dynamics in flow through unsaturated fractured media. Advances in Water
Resources, 25, 793–816, 2002.
Finsterle, S. Inverse Modeling of Test SB4-VM2/216.7 at Wellenberg. Lawrence Berkeley Laboratory
Report LBL-35454, 1994.