Prerequisites: Introductory calculus, physics, chemistry, thermodynamics, and MATLAB programming. Fractals, their construction and dimensions, bond and site percolation, and cluster analysis. Equations of capillarity, contact angles, thermodynamics of interfaces. Creeping flow of two and three immiscible fluids in porous media. Pore-level characterization of sediments; pore networks; invasion percolation in drainage and imbibition; description of capillary pressures and relative permeabilities in two- and three-phase flow in mixed-wet rocks. Applications to geology, petroleum, environmental, geotechnical, mechanical, and chemical engineering. Most course assignments will use MATLAB.