The Buckley-Leverett equation with spatially stochastic flux function

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 dimention 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 analized end it is proved that the sulution of this equation with Riemann initial data converges to the sulution of s(x,t)t + f(s, (x,t))x= 0 f(s) is the spatial average of f(s, x) when f(s, x) varies with position.