Departing from the classical Buckley-Leverett theory for two-phase immiscible flows in porous media, a reduced evolution equation for the water-oil displacement front is formulated and studied numerically. The reduced model successfully reproduces the basic features of the finger-forming dynamics observed in recent direct numerical simulations. PACS numbers: 47.20.Gv, 47.20.Ky, 47.20.Ma

When the reservoir parameters are stochastic, then the flow in a reservoir is described by stochastic partial differential equations. Spatial stochastic relative permeability in one spatial dimension is modeled by the stochastic Buckley–Leverett equation s(x, t)t + f(s(x, t), x)x = 0 for x > 0 and t > 0. f is the stochastic flux function and s is the saturation. This equation is analyzed, and i...

In this study, traveling wave soliton solutions of hyperbolic and trigonometric functions are successfully obtained by using the modified exponential function method Buckley-Leverett equation. addition to these, there also rational solutions. Two three-dimensional graphs real imaginary parts included with contour simulations physically analysis solution equation analyzed as a mathematical model...