Rheol Acta (2006) 46: 261–271 DOI 10.1007/s00397-006-0114-2 ORIGINAL CONTRIBUTION Alexandre Ragouilliaux Benjamin Herzhaft François Bertrand Philippe Coussot Received: 9 January 2006 Accepted: 27 April 2006 Published online: 13 June 2006 # Springer-Verlag 2006 Flow instability and shear localization in a drilling mud Abstract To have a better knowledge of problems occurring with drilling fluids in complex wells, we carried out a detailed rheological analysis of a typical drilling mud at low shear rates using both conventional rheometry and MRI velocimetry. We show the existence of a viscosity bifurcation effect: Below a critical stress value, the mud tends to completely stop flowing, whereas beyond this critical stress, it reaches an apparent shear rate larger than a finite (critical) value, and no stable flows can be obtained between this critical shear rate value and zero. These results are confirmed by MRI velocity profiles, which ex- hibit a slope break at the interface between the solid and the liquid phases inside the Couette geometry. Moreover, this viscosity bifurcation is a transient phenomenon, the progres- sive development of which can be observed by MRI. A further exami- nation of MRI data shows that, in the transient regime, the shear rate does not vary monotonously in the rheom- eter gap and is particularly large along the outer (rough) cylinder, which might be at the origin of the develop- ment of a region of constant shear rate in the apparent flow curve. Keywords Viscosity bifurcation . Yielding . Shear localization . Flow instability Introduction In the very beginnings of the oil drilling process, simple muds obtained by mixing soil material with water were used to clean the wells. Nowadays, drilling muds are very complex fluids, like suspensions, emulsions, or even foams, the formulation of which is the object of intense work. These fluids are designed to transport the rock cuttings, maintain them in suspension when the flow is stopped, ensure a (high) controlled pressure on the inner side of the well, and lubricate and clean the drill bit. To satisfy these requirements, drilling muds are typically shear thinning and thixotropic and exhibit an apparent yield stress. Their internal structure is generally complex and is liable to evolve with flow conditions. With the development of new drilling techniques, such as horizontal wells or ultradeep offshore drilling, new problems may occur, especially at low shear rates. One of the most harmful problems is barite sag, which corresponds to the settlement of the solid suspended phase under static or slow dynamic phases (Skalle et al. 1999; Dye et al. 1999; Bern et al. 1996, 2000; Aldea et al. 2001). To prevent or control these effects, a further understanding of the rheological behavior of drilling muds at low shear rates is required. In particular, it was recently shown that the flow curve of a typical drilling mud exhibits an abrupt change in the slope below a critical shear rate (Herzhaft et al. 2003), an effect which might, in practice, significantly affect the flow characteristics at low velocities. Here, we focus on a typical drilling mud formulated by mixing an emulsion in a suspension of solid particles of different sizes. We can expect that, depending on the relative fractions of these different components, this mixture may exhibit a behavior either close to that of a concentrated emulsion or close to that of a suspension with a significant colloidal fraction. The rheology of concen- trated emulsions was studied by Mason et al. (1996) [see also the review of Mason (1999)]. It was observed that, A. Ragouilliaux . F. Bertrand . P. Coussot (*) Institut Navier, Paris, France e-mail: coussot@lcpc.fr e-mail: alexandre.ragouilliaux@lcpc.fr A. Ragouilliaux . B. Herzhaft Institut Français du Pétrole, Paris, France