Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids

Primary-cementing displacement flows occur in long narrow eccentric annuli during the construction of oil and gas wells. A common problem is that the displacing fluid fingers up the upper wide side of the annulus, leaving behind a “mud channel” of displaced fluid on the lower narrow side of the annulus. Tehrani et al. report that the interface between displacing fluid and mud channel can in certain circumstances become unstable, and a similar phenomenon has been observed in our ongoing experiments. Here an explanation for these instabilities is provided via analysis of the stability of two-layer eccentric annular Hele-Shaw flows, using a transient version of the usual Hele-Shaw approach, in which fluid acceleration terms are retained. Two Newtonian fluids are considered, as a simplification of the general case in which the fluids are shear-thinning yield-stress fluids. It is shown that negative azimuthal buoyancy gradients are in general stabilizing in inclined wells, but that buoyancy may also have a destabilizing effect via axial buoyancy forces that influence the base-flow interfacial velocity. In a variety of special cases where buoyancy is not dominant, it is found that instability is suppressed by a positive product of interfacial velocity difference and reduced Reynolds-number difference between fluids. Even a small positive azimuthal buoyancy gradient, (heavy fluid over light fluid), can be stabilized in this way. Eccentricity of the annulus seems to amplify the effect of buoyancy on stability or instability, e.g. stably stratified fluid layers become more stable as the eccentricity is increased

Turbulent impingement jet cleaning of thick viscoplastic layers

An experimental study is conducted on the use of a normally impinging turbulent water jet (with the Reynolds number of Re ≈ 11800), for cleaning thick layers of a Newtonian fluid and two viscoplastic fluids (i.e., transparent Carbopol solutions). The layer thickness is larger than the jet radius. Non-intrusive techniques are used to track the geometrical features of the cleaning process in real time. The effects of layer thickness and fluid yield stress on removal behavior, including cleaning radius, cavity radius, and angle, are investigated. A yield stress promotes the initial formation of a blister rather than a cavity, and the rate of removal decreases with increasing layer thickness and yield stress. A relation is presented for the growth of the cavity radius, which fits our experimental observations well. A comparative analysis of submerged and impinging jets reveals, for the first time, the role of air entrainment in the process, with bubble characteristics such as trajectory, size distribution (diameter), and velocity being determined by the yield stress.Financial support for the work at Universite Laval, Montreal, Canada, received from PTAC-AUPRF through Grant No. AUPRF2022-000124 and NSERC, Canada through Alliance Grant No. ALLRP577111-22 (“Towards Net-Zero Emissions: mechanics, processes and materials to support risk-based well decommissioning”). We also appreciate the support of the Canada Research Chair (CRC) in Modeling Complex Flows (Grant No. CG125810), the Canada Foundation for Innovation (Grants No. GF130120, GQ130119, and GF525075), and the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grant (Grant No. CG109154) and the Research Tools and Instruments Grant (Grant No. CG132931). Author HH also acknowledges the support of the “´EVEIL - KSA Avocats” scholarship

Transient effects in oilfield cementing flows: Qualitative behaviour

We present an unsteady Hele–Shaw model of the fluid–fluid displacements that take place during primary cementing of an oil well, focusing on the case where one Herschel–Bulkley fluid displaces another along a long uniform section of the annulus. Such unsteady models consist of an advection equation for a fluid concentration field coupled to a third-order non-linear PDE (Partial differential equation) for the stream function, with a free boundary at the boundary of regions of stagnant fluid. These models, although complex, are necessary for the study of interfacial instability and the effects of flow pulsation, and remain considerably simpler and more efficient than computationally solving three-dimensional Navier–Stokes type models. Using methods from gradient flows, we demonstrate that our unsteady evolution equation for the stream function has a unique solution. The solution is continuous with respect to variations in the model physical data and will decay exponentially to a steady-state distribution if the data do not change with time. In the event that density differences between the fluids are small and that the fluids have a yield stress, then if the flow rate is decreased suddenly to zero, the stream function (hence velocity) decays to zero in a finite time. We verify these decay properties, using a numerical solution. We then use the numerical solution to study the effects of pulsating the flow rate on a typical displacement