Burst dynamics, up-scaling and dissipation of slow drainage in porous media.

We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In this theory the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invasion front and the invading structure, and the exponent describing the divergence of the correlation length in percolation. This theoretical description explains how the Haines jumps' local activity and dissipation relate to dissipation on larger scales.