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. Plain Language Summary: Underground fluid flow and chemical reactions often result in wormholes, which are channels that look like tree roots, and significantly increase the permeability of porous rocks. Wormhole formation is relevant in many natural and industrial processes, including the formation of underground caves, CO2 sequestration and enhanced oil recovery. In this study, wormholes are created in the laboratory by injecting water into porous gypsum cores, and are observed with X‐ray CT scanning. We show that the wormhole lengths, like the lengths of many other naturally created patterns (faults, river segments, and fjords), follow a power‐law distribution. By comparing the wormholes formed under different flow rates and at different moments, we show that the wormholes develop by competing for available flow. Many wormholes develop initially, but only a few win the competition to develop further. Our experimental results also show that existing models, which simulate the flow in a porous medium with two parts (one with and one without wormholes), underestimate wormhole lengths. We improve upon these models by accounting for the 3‐D radial flow near the tip of the wormhole, and accurately predict the wormhole lengths observed in the experiments. Key Points: Lengths of wormholes resulting from flow and dissolution in a 3‐D porous medium follow a power‐law distributionWormholes develop by competing for available flow, with many developing initially but a few developing furtherWe improve the wormhole length prediction by approximating the 3‐D radial flow near the wormhole tip with a Rankine ovoid model [ABSTRACT FROM AUTHOR]