Non-linear waves of ﬂuid pressure and contaminant density in swelling shales
The control of drilling parameters, such as salt concentration, mud percentage and temperature is of fundamental importance for maintaining borehole stability when drilling through shale sections. For this purpose, a non-linear model of mechanic and chemo-poroelastic interactions between ﬂuids, contaminants and solid matrix is presented. For the binary case we obtain a system of two non-linear coupled equations describing the isothermal evolution of ﬂuid pressure and contaminant density in shales. In addition to the usual diffusive solutions obtained in linear analyses, a novel process is found. Indeed we show the presence of intense transient phenomena, i.e. quick non-linear shock waves of both pressure and contaminant. We apply this model ﬁrst to a simple, homogeneous shale, then to more realistic cases, and ﬁnally to a non-compressive ﬁlter cake buildup. All these waves exhibit a Burgers solitary wave dynamics and can give destructive instabilities in deep drilling oil in shales.