An Experimental Investigation of Gas-Bubble Breakup in Constricted Square Capillaries
Authors: Gauglitz P.A. , St. Laurent C.M. , Radkle C.J. 
Published: December 2007

Summary.
Recent advances in EOR involve generating foam within underground porous media to displace the oil. We investigate the important snap-off mechanism of gas-bubble generation in constricted square capillaries experimentally. The snap-off of smaller bubbles from a larger bubble as it moves through the constriction is recorded on 16-mm movies. The time required for bubbles to snap off once they move past the constriction and the length of the generated bubbles are obtained from viewing the movie frames. The bubble capillary number, uvT/, is varied from 10–5 to 5 × 10 -3 by adjusting the wetting-fluid viscosity, A, and the surface tension, a, by adding aqueous surfactants to mixtures of glycerol and water and by altering the bubble velocity, VT.
Results show that a dimensionless time to snap-off depends weakly on the capillary number and that the generated bubble size increases almost linearly with increasing- capillary number. Surfactants create dynamically inmobile interfaces for surfactant solutions of I wt% sodium dodecyl benzene surfactants (SDBS) and Chevron Chaser SD1000. Compared with the surfactant-free solutions, the time to breakup with surfactants increases by a factor of about 3; generated bubble length increases by a factor of at most 3.

Introduction
Use of steam foams as displacing fluids for EOR has been successful in recent field applications. Foam improves oil recovery by increasing the resistance to flow of the steam through the underground oil-bearing porous medium, thus improving mobility control and decreasing gravity override. Although foam has proved successful in field applications, modeling of foam displacement processes is still at an early stage. To understand foam flow in porous media better, we investigate the mechanisms of foam generation in porous media. Foam ‘veneration processes are important because they control the texture (i.e., the bubble size) of a foam as it flows through the medium. In turn, texture strongly affects the pressure-drop/flow-rate relationship for foam in porous media. Our objective is to quantity in a realistic single-pore model let the time required to snap off a bubble and the size of the generated bubble. The pore space between three touching spheres (an ideal porous medium) is quite angular 4 (see Fig. 1a of Ref. 4). It looks like a constricted triangular capillary. Square capillaries maintain the angularity and also are readily available. Hence, constricted square capillaries are studied in this work.
Snap-off occurs when a bubble is disconnected from a larger gas bubble by a growing liquid collar that blocks a pore neck, as shown in Fig. 1. As the gas bubble moves through a constriction, it leaves a channel of liquid in the corners of the capillary. as shown in Steps 1 and 2 of Fig.
1. Liquid then fills in at the pore neck, as depicted in Step 3. Eventually, sufficient liquid collects at the pore neck, and the liquid rearranges to form a lens that blocks the capillary, thus snapping off a bubble in Step 4.

Previous Work
Roof originally studied snap-off as a mechanism that traps oil drops in porous media. Fried, and in a more careful study, Mast Showed that snap-off is an important mechanism for bubble generation in porous media. Most investigations of snap-off are in cylindrical glass capillaries. Often, a groove is cut along the wall of the capillary to form a channel along which liquid can flow. The advantage of square capillaries is that they naturally have the channels.
Arriola et al. studied the trapping of oil drops in constricted square capillaries and determined how small oil drops snap off from a trapped drop. We also study square constricted capillaries. In our case, however, the gas bubbles are always driven through the constriction at a constant volumetric flow' and are not allowed to trap. Accordingly, we observe a mechanism of snap-off different from the one Arriola et al. reported.
Roof argued that if the hemispheric front of a nonwetting phase protrudes seven throat radii past the neck of the constriction, the front of the nonwetting phase will snap off. This is a static analysis. It cannot predict dynamic behavior. Strand et al., however, observed that the flow rate of an oil drop through a constriction is important with larger oil drops being snapped off when the oil drop is driven through a capillary at a higher velocity.
JPT
P. 1137^