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. \ud
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机译:在油气井的建造过程中,主要是胶结的驱替流发生在狭窄的偏心环形长环中。一个常见的问题是,将流体指状物移到环空的上宽侧上,而在环空的下窄侧上留下了置换流体的“泥浆通道”。 Tehrani等。报告指出,在某些情况下,驱替流体和泥浆通道之间的界面会变得不稳定,并且在我们正在进行的实验中也观察到了类似的现象。在此,通过使用常规Hele-Shaw方法的瞬态版本分析两层偏心环形Hele-Shaw流的稳定性,提供了这些不稳定性的解释,其中保留了流体加速度项。考虑了两种牛顿流体,以简化通常的情况,在这种情况下,流体是剪切稀化的屈服应力流体。结果表明,斜井中的方位角浮力梯度总体上是稳定的,但是浮力也可能通过影响基流界面速度的轴向浮力而失去稳定作用。在浮力不是主导的各种特殊情况下,发现不稳定性可以通过界面速度差的正积和减小的流体雷诺数差的正积来抑制。这样,即使是小的正方位浮力梯度(重流体对轻流体)也可以稳定下来。环的偏心似乎放大了浮力对稳定性或不稳定性的影响,例如对随着偏心率的增加,稳定分层的流体层变得更加稳定。 \ ud
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