### Fluid flow in diatomites

Michiel Bertsch

Universit TorVergata

Mathematics Department

Important oil fields, for example the ones of Lost Hills and Belridge
(California), are contained in diatomites: fragile porous rocks with
high porosity but very low permeability. Engineers use hydraulic
fracturing techniques to increase the permeability and the
permeability can be considered as an increasing function of a damage
parametere. Barenblatt, Patzek, Prostokishin and Silin have made a
first attempt to model the coupled evolution of the fluid pressure and
the damage parameter. Assuming vanishing permeability in undamaged
rock, this leads to a challenging and mathematically new free boundary
problem. In this talk some we discuss some first mathematical results
which have been recently obtained in collaboration with
G.I. Barenblatt, R. Dal Passo and Carlo Nitsch.