A dipole solution for power-law gravity currents in porous formations. (4th August 2015) - Longo, S.; Di Federico, V.; Chiapponi, L.
Abstract : A theoretical and experimental analysis of non-Newtonian gravity currents in porous media with variable properties is presented. A mound of a power-law fluid of flow behaviour index n is released into a semi-infinite saturated porous medium above a horizontal bed, and can drain freely out of the formation at the origin. The porous medium permeability varies along the vertical as z^(ω-1), porosity varies along the vertical as z^(γ-1), z being the vertical coordinate and ω and γ constant numerical coefficients. A self-similar solution describing the space–time evolution of the resulting gravity current is derived for shear-thinning fluids with n<1, generalizing earlier results for Newtonian fluids. The solution conserves a generalized dipole moment of the mound. The spreading of the current front is proportional to t^γn/(2+ω(n+1)) . Expressions for the time evolution of the outgoing flux at the origin and of the current volume are derived in closed form. The Hele-Shaw analogue is derived for flow of a power-law fluid in a porous medium with vertically variable properties. Results from laboratory experiments conducted in two Hele-Shaw cells confirm the constancy of the dipole moment, and compare well with the theoretical formulation.