Invasion Percolation

Free gas moving through a sediment must first overcome the entry pressure and thereafter find the path of least resistance. Generally capillary forces outweigh the viscous forces since the flow is very slow and so the favoured path is the one which connects the largest throats through the medium however long and tortuous it may be. The mathematical concept underlying such flow through a network of pores and throats is termed percolation theory (Sahimi 1994). Its relevance to fluid flow, and particularly oil and gas migration is obvious and has been exploited (Sahimi 1995; Wagner et al. 1996 and references therein). These studies mainly refer to sandstone carrier beds, but the principle for fine sediments is identical (Fig. 6).

If there is overpressure associated with the gas source at depth then a directed advective flux of water is generated that can assist or deflect the hydrocarbon movement (but see Bjorkum et al. 1998), particularly if the head drop is concentrated across a low permeability layer (Mandl 1981). Chapman (1983) discusses such situations from a petroleum geology perspective, and details for modelling of such flows can be found in Hindle (1997). At the high saturations which may arise if gas collects in coarser layers, pressure-driven flows of gas and water can be calculated according to a relative permeability curve (Klusman 1993). Permeability of unsaturated fine grained sediment to water is typically two or more orders of magnitude lower than the water-saturated case (Corey 1994). However, in fine sediments and especially close to the hydrate zone (Claypool and Matava 1999) the probability is that gas will not collect in such high concentrations that it is the mobile phase, and the concept of relative permeability for gas is meaningless.

When gas saturation drops below a critical level, it will not form continuous stringers capable of movement by buoyancy, and will form a mist of bubbles isolated in the larger pore bodies, and detached gas patches known as residual ganglia (Lowy and Miller 1995). These are unlikely to be detached by the modest water pressure gradient generated by overpressure. Donaldson et al.

(a) (b)

Figure 6. Critically-limited non-linear flow phenomena. Invasion percolation: (a) Drainage experiments conducted by Furuberg et al. (1996) on a bead array, (b) A dynamic invasion percolation model for gas migration though mudrocks (Impey et al. 1997). Fracture flow, (c) Injection of water into fractured unlithified mud (A.J. Bolton and M.B. Clennell, unpublished results), (d) Electrical circuit with a hysteric switch. Common features are evident: Pulsatile flow, regular cycling of flow episodes, and period doubling whereby the interval between pulses reduces by half during an experiment. Higher flux would drive the system into chaos (see Acheson 1997).

Figure 6. Critically-limited non-linear flow phenomena. Invasion percolation: (a) Drainage experiments conducted by Furuberg et al. (1996) on a bead array, (b) A dynamic invasion percolation model for gas migration though mudrocks (Impey et al. 1997). Fracture flow, (c) Injection of water into fractured unlithified mud (A.J. Bolton and M.B. Clennell, unpublished results), (d) Electrical circuit with a hysteric switch. Common features are evident: Pulsatile flow, regular cycling of flow episodes, and period doubling whereby the interval between pulses reduces by half during an experiment. Higher flux would drive the system into chaos (see Acheson 1997).

(1998) showed that in aquifers with a continuous water flow the dispersive transport of dissolved oxygen can be inhibited significantly by sequestration of the gas into these trapped bubbles. In compacting sediments the pressure of capillary gas seals could help maintain overpressures (Hovland and Judd 1988, Shosa and Cathles 1996, Kuo 1997, Revil et al. 1998).

The trapping ability of sediments clearly depends on the continuity of the layers that have the highest capillary entry pressure (see Ho and Webb 1998). A thin layer of mud is just as effective a seal to two phase flow as is a thick layer (Watts 1987), but thin muds do not stop diffusive methane transport. Gas can dissolve on one side of a capillary barrier, and without the entry pressure being exceeded, pass by diffusion through the layer of fine sediment, and reappear by evanescence of the other side (Miller 1980). If the bubbles on the upper side can move away though buoyancy, then the process can continue ad infinitum.

Further, gas bubbles can exsolve in positions along the flow pathway, and eventually coalesce into a stringer that spans across the capillary barrier, without the sequential bottom-to top process of invasion percolation necessarily occurring (Li and Yortsos 1995). Bubble strings do not even need to merge completely for transport to be greatly enhanced (Fig. 7).

Fully Saturated:

diffusion in liquid phase only, low flux

Fully Saturated:

diffusion in liquid phase only, low flux

Unsaturated:

diffusion jumps in gas bubbles, high flux

Unsaturated:

diffusion jumps in gas bubbles, high flux

Figure 7. Catenary transport (Heard 1994). Methane can diffuse via a chain of gas filled bubbles separated by water filled pores in a process termed catenary transport. While the bubbles themselves are stationary, they permit a through fluxes of methane and water going from globally high to globally low chemical potentials.

The amount of methane that can be transported by advection, and the purely diffusive flux are both limited by the low level of methane saturation in the pore water. Mechanical and capillary effects on saturation discussed above are critically important when we try and predict these fluxes. Excess gas in supersaturated solution can move freely by advection though throats that would block the transport of the same gas in bubble form. If more gas is in solution in a fine layer because of capillary supersaturation, there will be a gradient in its chemical potential that has the capacity to drive a diffusive flux towards a region of normal saturation or undersaturation. On the other hand, if pore pressure drops due to mechanical disturbance, then gas can exsolve and become trapped in the new pores or fractures.

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