Linear permeability evolution of expanding conduits due to feedback between flow and fast phase change

Conduits are ubiquitous and critical pathways for many fluids relevant for geophysical processes such as magma, water, and gases. Predicting flow through conduits is challenging when the conduit geometry coevolves with the flow. We theoretically show that the permeability (k) of a conduit whose walls are eroding due to fast phase change increases linearly with time because of a self-reinforcing mechanism. This simple result is surprising given complex feedbacks between flow, transport, and phase change. The theory is congruent with previous experimental observations of fracture dissolution in calcite. Supporting computational fracture dissolution experiments showed that k only slightly increases until the dissolution front reaches the narrowest conduit constriction, after which the linear evolution of k manifests. The theory holds across multiple scales and a broad range of Peclet and Damkohler numbers and thus advances the prediction of dynamic mass fluxes through expanding conduits in various geologic and environmental settings. Plain Language Summary Geological conduits are ubiquitous present in the subsurface. In many situations, these conduits may enlarge through time due to erosion of its walls by dissolution and melting. This leads to strongly coupled flow and reactive transport processes where the flow dictates the wall's erosion and vice versa. As the conduit expands, so does its permeability and thus flow. Thus, predicting fluid flow and relevant transport processes through expanding conduits is challenging. In this study, we presented a theory for the linear time dependence of permeability for expanding conduits. The theory is congruent with previous observations from fracture dissolution in calcite. An additional series of our own computational experiments also aligns with the theory. The theory will be of interest to geoscientists and engineers in many fields such as hydrology, glaciology, and petroleum engineering, to name a few.