Page 175 - gas transport in porous media

CHAPTER 9

UNSTABLE AND FINGERING GAS FLOW
IN FRACTURES

PETER PERSOFF
Lawrence Berkeley National Laboratory, Berkeley, CA, USA

In this chapter, two causes of unstable and fingering gas flow in fractures will be
considered: capillary instability in horizontal fractures and gravitational instability in
vertical or inclined fractures.
Several physical situations may induce gas flow in unsaturated fractures. Any
chemical, biochemical, or radiolytic reaction that produces or consumes gas increases
or decreases the pressure. Gas may also be released from solution when the water
pressure is reduced. Any injection or extraction of gas through wells induces a gas
pressure gradient; changes in barometric pressures are also felt below the ground
surface. Instability results when a gas flow path does not remain continuously open,
but is intermittently blocked by water. This can occur if there is sufficient water, or
sufficient water flow, in the fracture to block the gas flow path. In this discussion,
we consider air and water as the nonwetting and wetting fluids, respectively; some
of these observations will also be applicable to oil and water or air and oil.

9.1 PARTIALLY SATURATED FRACTURES ABOVE THE WATER
TABLE

Above the water table, water is held in fractures at asperities (points of contact) and
wherever capillary forces are greater than the gravitational force tending to drain
water from the pores. That is, pores of radius smaller than r are saturated at distance
d above the water table, where r and d are related by

r = 2σ/(p g − p l ) = 2σ/ρgd (9.1)

where p is pressure, subscripts g and l are gas and liquid, g is the acceleration of gravity
and σ and ρ are the surface tension and density of water. The capillary pressure is
defined as p cap = (p g −p l ); and (p l −p g ) is also called the moisture tension. Fractures
169
C. Ho and S. Webb (eds.), Gas Transport in Porous Media, 169–178.
© 2006 Springer.