科研之友
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摘要
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((omega-1)), porosity varies along the vertical as z((gamma-1)), z being the vertical coordinate and omega and gamma 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 (gamma n/(2+omega(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.
- 出版日期2015-9
