F. Doster1,2 and R. Hilfer3,4
1Department of Civil and Environmental Engineering, Princeton University, 08544 Princeton, NJ, USA
2Department of Mathematics, Bergen University, Bergen, Norway
3Institute for Computional Physics, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
4Institut für Physik, Universität Mainz, 55099 Mainz, Germany
Abstract.
The paper compares a theory for immiscible displacement
based on distinguishing percolating and non-percolating fluid
parts (Physica A, 371, 209 (2006))
with experimental observations from multistep outflow
experiments (Water Resources Res, 27, 2113 (1991)).
The paper focusses on hysteretic phenomena resulting from
repeated cycling between drainage and imbibition processes
in multistep pressure experiments.
Taking into account the hydraulic differences between
percolating and non-percolating fluid parts provides a
physical basis to predict quantitatively the hysterestic
phenomena observed in the experiment.
While standard hysteretic extensions of the traditional
theory are nonlocal in time the theory used in this
paper is local in time. Instead of storing the pressure
and saturation history it requires only
the current state of the system to reach
the same quantitative agreement.
