A Three-Dimensional Study of Wormhole Formation in a Porous Medium: Wormhole Length Scaling and a Rankine Ovoid Model

Understanding how wormholes develop and how they change the permeability of the porous medium is important for many natural and industrial processes in subsurface solid-fluid systems. We conduct core flood tests to study the wormhole formation in a porous medium under different flow rates and at different moments before breakthrough. We show that the wormholes created in core flood tests have lengths following a power-law distribution, with more short ones than long ones. This statistical nature of the wormhole lengths allow one to experimentally study the wormhole competition in 3-D: Many wormholes develop initially near the inlet, but only a few develop further. Our experimental results also show that the existing wormhole-matrix models underestimate wormhole lengths because of the neglected additional pressure drop caused by the radial flow near the wormhole tip. We improve upon the existing models by approximating the radial flow near the wormhole tip with a Rankine ovoid model.