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

Abstract

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.

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

“…The fluid flow in rock fractures and/or fracture networks is commonly assumed to obey the cubic law, in which the flow rate is linearly proportional to the pressure drop [10][11][12][13][14][15][16]. However, in the karst systems and/or in the vicinity of wells during pump tests, when the flow rate/velocity is large, fluid flow enters the nonlinear flow regime and flow rate is nonlinearly correlated with pressure drop [14,[17][18][19][20].…”

Universal Relationship Between Viscous and Inertial Permeability of Geologic Porous Media

“…In many situations, the inertial versus viscous force competition and geometric variation are intertwined. On the other hand, investigations of the effects of geometric variation, for example, due to deformation and phase change, are typically constrained to noninertial, viscous flow regimes (Pyrak-Nolte & Nolte, 2016; Wang & Cardenas, 2017). On the other hand, investigations of the effects of geometric variation, for example, due to deformation and phase change, are typically constrained to noninertial, viscous flow regimes (Pyrak-Nolte & Nolte, 2016; Wang & Cardenas, 2017).…”

“…Permeability thus dictates the role of subsurface fluids in many geologic phenomena such as earthquakes (Elkhoury et al, 2006), volcanic eruptions (Okumura et al, 2009), ice sheet drainage (Das et al, 2008), planetary compositional differentiation (Ghanbarzadeh et al, 2017), and weathering of the land surface (Rempe & Dietrich, 2014). Numerous models and methods for studying permeability have therefore been developed, including some attempts for finding common attributes among geologic porous media (Bonnet et al, 2001;Liu, 2011;Pyrak-Nolte & Nolte, 2016;Wang & Cardenas, 2017;Wei et al, 2015). Numerous models and methods for studying permeability have therefore been developed, including some attempts for finding common attributes among geologic porous media (Bonnet et al, 2001;Liu, 2011;Pyrak-Nolte & Nolte, 2016;Wang & Cardenas, 2017;Wei et al, 2015).…”

“…Knowledge of permeability is crucial for the sustainable extraction of groundwater (Gleeson et al, 2014) and energy resources (Patzek et al, 2013), for assessing contaminant transport in and the vulnerability of aquifers (Burgess et al, 2010), and the security of potential reservoirs for nuclear waste (Ghanbarzadeh et al, 2015) and greenhouse gas disposal (Bickle, 2009). Numerous models and methods for studying permeability have therefore been developed, including some attempts for finding common attributes among geologic porous media (Bonnet et al, 2001;Liu, 2011;Pyrak-Nolte & Nolte, 2016;Wang & Cardenas, 2017;Wei et al, 2015). However, due to complicated and diverse pore and fracture geometries and highly varied hydrodynamic, mechanical, and environmental conditions, there is no universally predictive model applicable across all geologic porous media.…”

Scale‐dependent Poiseuille flow alternatively explains enhanced dispersion in geothermal environments

“…Indeed, the maximum aperture scales with fracture length (Olson, ; Renshaw & Park, ), suggesting that fracture heterogeneity is present across different scales. Moreover, the aperture field might be dynamically changing over geological timescale due to mechanical compaction (Pyrak‐Nolte & Nolte, ; Wang & Cardenas, ) and geochemical alteration (Elkhoury, Ameli, & Detwiler, ; Wang & Cardenas, ). Although extensive research has addressed the heterogeneity effects on fracture flow and transport (e.g., Brown, ), how temperature affects the interplay of flow and transport in a geothermal environment remains underexplored.…”