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.