Fundamentals of Fluid Flow in Porous Media

Chapter 2

Multi-phase Saturated Rock Properties:

Phase Trapping: Snap-Off

Consider a square capillary into which a non-wetting phase has entered (Figure 2‑65). The capillary pressure at which the non-wetting fluid first enters the square capillary is approximately
Capillary Pressure Equation for Non-Wetting Fluid Entering Square Capillary

As the capillary pressure increases above this value, the wetting phase (shaded) will be pushed further into the corners as the radius of curvature of the interface decreases. (When the non-wetting phase enters at the above capillary pressure, the wetting phase will already be pushed into the corners compared to Figure 2‑65).

Suppose now the wetting phase is allowed to flow back along the corners without the end of the drop exiting the capillary. If the capillary pressure is now then decreased below P_cso, the capillary pressure of a cylindrical filament that just touches the capillary walls,

Figure 2-65: Non-Wetting Fluid Enters a Capillary Tube with Square Cross Section

Equation 2-102 Capillary Pressure of cylindrical filament that touches the capillary walls

The interface will pull away from the walls of the capillary. The non-wetting phase is now a thin filament that is unsupported by the walls. The non-wetting phase will neck down in some places and will swell in other places until it is supported by the walls of the capillary. The necking down is unstable and the non-wetting phase will ‘snap-off’ into droplets or bubbles of disconnected non-wetting phase.

Figure 2-66: Side View After Snap-Off (Cross Section From Middle of Square)

Now consider a porous media instead of the capillary tube. Suppose the porous medium is made up of pore bodies and pore necks of many different sizes as shown in Figure 2‑67. The medium is initially saturated with the wetting phase. The non-wetting phase is first allowed to enter only the largest pores as in Figure 2‑67.a and then the capillary pressure reduced to zero. Non-wetting phase will be trapped as in Figure 2‑67.b. With additional cycles with increasing initial non-wetting saturation additional trapping will occur as in Figure 2‑67.d and Figure 2‑67.f. according to the previous definition the process in Figure 2‑67.a,c,e are drainage and Figure 2‑67.b,d,f are imbibition.

Figure 2-67: Trapping in a Porous Media

[1]

Such an experiment with increasing initial saturation of the non-wetting phase saturation measuring the residual saturation at each initial saturation generates an initial – residual saturation curve as in Figure 2‑68. This curve probes the volume of non-wetting phase trapping sites as a function of entering increasingly finer pores. This curve can be used to determine the saturation of non-wetting phase that is trapped at a given saturation if information is available on the maximum non-wetting saturation attained, i.e., memory of its history is available[2].

Figure 2-68: Typical Non-Wetting Phase Trapping Characteristics of Some Reservoir Rocks[3]