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Scale‐dependent Poiseuille flow alternatively explains enhanced dispersion in geothermal environments
Author(s) -
Zheng Lizhi,
Wang Lichun
Publication year - 2018
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.13339
Subject(s) - hagen–poiseuille equation , taylor dispersion , mechanics , geothermal gradient , flow (mathematics) , dispersion (optics) , viscosity , fluid dynamics , thermodynamics , length scale , geology , physics , geophysics , diffusion , optics
Fluid flow exerts a critical impact on the convection of thermal energy in geological media, whereas heat transport in turn affects fluid properties, including fluid dynamic viscosity and density. The interplay of flow and heat transport also affects solute transport. To unravel these complex coupled flow, heat, and solute transport processes, here, we present a theory for the idealized scale‐dependent Poiseuille flow model considering a constant temperature gradient (∇ T ) along a single fracture, where fluid dynamic viscosity connects with temperature via an exponential function. The idealized scale‐dependent model is validated based on the solutions from direct numerical simulations. We find that the hydraulic conductivity ( K ) of the Poiseuille flow either increases or decreases with scales depending on ∇ T > 0°C/m or ∇ T < 0°C/m, respectively. Indeed, the degree of changes in K depends on the magnitude of ∇ T and fracture length. The scale‐dependent model provides an alternative explanation for the well‐known scale‐dependent transport problem, for example, the dispersion coefficient increases with travel distance when ∇ T > 0°C/m according to the Taylor dispersion theory, because K (or equivalently flux through fractures) scales with fracture length. The proposed theory unravels intertwined interactions between flow and transport processes, which might shed light on understanding many practical geophysical problems, for example, geothermal energy exploration.