Hydrodynamic dispersion in steady buoyancy‐driven geological flows

Abstract

An analytical model is developed to evaluate mixing induced by natural convection in a fluid‐saturated porous medium. First, the velocity and concentration fields are decoupled to generate a steady state velocity field and initiate a naturally convective system. In order to decouple the velocity and concentration fields, a steady thermal natural convection is established by imposing a destabilizing vertical temperature gradient across a porous layer and then introducing a passive tracer into the system. Based on the steady velocity field, effective longitudinal and transverse dispersion coefficients are evaluated using the shear flow dispersion theory, and convective mixing of the passive tracer is obtained using the developed analytical mixing model. The estimated dispersion coefficients and convective mixing are then characterized by the system Rayleigh and Sherwood numbers. The mixing obtained by the analytical model is then compared with high‐resolution numerical simulations. The results reveal that the simple analytical solution represents the nonlinear mixing involved in such a system and agrees with the numerical results. The developed model has potential applications in geophysical and geothermal buoyancy‐driven flows.