Article history: Received 6 February 2014 Available online 18 March 2015 Submitted by C. Gutierrez

Abstract. The focus of the present study is the modified Buckley-Leverett (MBL) equation 1 describing two-phase flow in porous media. The MBL equation differs from the classical Buckley2 Leverett (BL) equation by including a balanced diffusive-dispersive combination. The dispersive term 3 is a third order mixed derivatives term, which models the dynamic effects in the pressure difference 4 betw...

We present a stochastic analysis of immiscible two-phase flow ~Buckley–Leverett displacement! in heterogeneous reservoirs. Since the detailed spatial variabilities of reservoir properties such as permeability and porosity cannot be described deterministically, both permeability and porosity, or either, are treated as random space functions. In turn, water saturation and oil production rate are ...

We present analytical solutions for capillary-controlled displacement in one dimension by use of fractional-flow theory. We show how to construct solutions with a spreadsheet that can be used for the analysis of experiments as well as matrix-block-scale recovery in field settings. The solutions can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Lev...

To derive the fractional flow equation oil displacement will be assumed to take place under the so-called diffusive flow condition. The constraints are that fluid saturations at any point in the linear displacement path are uniformly distributed with respect to thickness; this allows the displacement to be described mathematically in one dimension. The simultaneous flow of oil and water can be ...

For the hyperbolic conservation laws with discontinuous flux function there may exist several consistent notions of entropy solutions; the difference between them lies in the choice of the coupling across the flux discontinuity interface. In the context of Buckley-Leverett equations, each notion of solution is uniquely determined by the choice of a “connection”, which is the unique stationary s...

Petroleum reservoir modelling requires effective multiscale methods for the numerical simulation of two-phase flow in porous media. This paper proposes the application of a novel meshfree particle method to the Buckley-Leverett model. The utilized meshfree advection scheme, called AMMoC, is essentially a method of characteristics, which combines an adaptive semi-Lagrangian method with local mes...

We discuss an extension of the Buckley-Leverett (BL) equation describing twophase flow in porous media. This extension includes a third order mixed derivatives term and models the dynamic effects in the pressure difference between the two phases. We derive existence conditions for traveling wave solutions of the extended model. This leads to admissible shocks for the original BL equation, which...

In this short course we will start by deriving the basic conservation laws for mass, momentum and energy. We will extend the results to mixtures in general and then to multiphase flow in porous media. We will describe the black-oil models and the Buckley-Leverett problem. Second, we will review the basic numerical methods for solving the differential equations that model a fluid in a porous med...