DOI 10.1140/epje/i2003-10016-8 Eur. Phys. J. E 11, 231–241 (2003) T HE EUROPEAN P HYSICAL JOURNAL E Miscible displacement of non-Newtonian fluids in a vertical tube C. Gabard 1,2 and J.-P. Hulin 2, a 1 Laboratoire FAST (UMR 7608), Bˆ atiment 502, Campus Paris-Sud, 91405 Orsay, France 2 SRPC-D, Reservoir Development Cementing, Etudes et Productions Schlumberger, 1 rue Becquerel, BP 202, 92142 Clamart, France Received 15 February 2003 / Published online: 8 July 2003 – c  EDP Sciences / Societ`a Italiana di Fisica / Springer-Verlag 2003 Abstract. The influence of rheology on the miscible displacement of a viscous fluid by a less viscous, Newtonian one in a vertical tube is studied experimentally as a function of the flow velocity. For Newtonian displaced fluids the transient residual film thickness h ri is nearly 38% of the tube radius at large viscosity ratios between the two fluids in agreement with experimental and numerical results from the literature. For shear-thinning fluids with a zero yield stress (mostly xanthan-water solutions), h ri decreases down to 28–30% of the radius for the most concentrated solutions. For fluids with a non-zero yield stess, h ri further decreases down to 24–25% of the radius. The orders of magnitude of these values can be obtained through numerical simulations (commercial code) for the various types of fluids. Instabilities of the film at its boundary develop downstream and lead to a reduction of the final thickness of the film at longer times: this reduction is larger for lower viscosity ratios and larger velocities. PACS. 47.20.Gv Hydrodynamic stability: Viscous instability – 83.60.Wc Rheology: Flow instabilities 1Introduction The thickness and stability of residual fluid films left be- hindduringthedisplacementbyanotherfluidisanimpor- tant factor in chemical and petroleum engineering and in environmental studies. One example is the completion of oil wells [1]: it involves the successive injection of drilling muds, washer fluids and cement slurry which are often stronglynon-Newtonian.Predictingthethicknessandsta- bility of such fluid films left behind helps evaluating the riskofanunwantedmixingoffluidsinvolvedinthesepro- cesses[2,3].Thepurposeofthepresentpaperistoanalyze the influence of the rheological properties of the displaced fluid both on the transient thickness and the stability of these residual fluid films. These results will allow to se- lecttheflowpropertiesofthefluidsandtheinjectionflow rates for which the amount of residual fluid is minimal. Agreatdealoftheoreticalandexperimentalefforthas alreadybeendevotedtofluiddisplacementsinconstricted geometries.Alargefractionofthesestudiesdealswithim- miscibledisplacementsof,forinstance,low-viscosityNew- tonian fluids displacing more viscous ones in Hele-Shaw cells and tubes (viscous fingering) [4]. The opposite case of a low-viscosity fluid acting as a lubricating film on the walls of a flow channel with an immiscible viscous fluid a e-mail: hulin@fast.u-psud.fr flowing in the center has been studied in relation with applications to oil transport in pipe lines [5,6]. Such ex- perimentsrealizedinHele-Shawcellswithnon-Newtonian fluids displaced by air have demonstrated a strong influ- ence of the rheology of the fluid on the width of the dis- placement fingers [7]. The stability of these residual films in the immiscible case and for core-annular flow geometries has also been studied —mostly when the less viscous fluid covers the wall. Theoretical [5,8,9] as well as numerical [10] and experimental [11] results have been reported. A related study [12] deals with core-annular flows involving non- Newtonian Maxwell liquids. Both the dependence of the characteristic wavelength on the physical parameters of the displacement and the geometry of the instability were investigated: various types of axisymmetrical and asym- metrical patterns such as “bamboo” or “corkscrew”-like structures were in particular observed. For miscible Newtonian fluids, displacement experi- ments have already been reported in cylindrical geome- tries. For large displacement velocities [13], the fraction occupied by the displaced fluid is almost constant and nearly 61% for ratios of the viscosities of the displaced andinjectedfluidhigherthan100.Forlowerviscositycon- trasts,thisfractiondecreasessteadilydownto50%.These experimental features could be reproduced by numerical