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Transient effects in oilfield cementing flows.

机译：油田固井流动中的瞬态效应。

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摘要

In this thesis we study instabilities and mud channel removal during the primary cementing of an oil well. This process involves displacement of a sequence of non-Newtonian fluids along a narrow eccentric annulus. Previously, this has been modelled as a pseudo-steady process using a Hele-Shaw approximation. In such models, the stream function is governed by a steady elliptic problem and the fluids, (modelled via a concentration equation), simply advect along the annulus. It has been shown that for certain rheological and physical parameters, the displacement front will advances much faster on the wide side of the annulus than on the narrow side. In extreme cases the displacement front does not advance at all on the narrow side of the annulus and a static mud channel results as the finger advances up the wide side. In this thesis we consider whether the interface of a progressively advancing finger will remain stable to small perturbations. There is in fact experimental evidence that interfacial instabilities can occur in this situation. We find that the interface is in fact stable whenever there is a static mud channel on the narrow side of the annulus. Consequently, we also investigate how a mud channel might be removed by pulsation of the flow rate. Study of these two phenomena cannot be undertaken with the pseudo-steady framework. Therefore, we extend this model to flows that are fully transient. The transient model consists of a nonlinear evolution equation for the stream function.; In chapter 3 we show that this transient model is in fact well-posed. In chapter 4 we study stability of multi-layer parallel flows, i.e. long fingers. If both fluids are yielded at the interface, instabilities may arise for different combinations of the 14 dimensionless parameters. These instabilities are related to a jump in tangential velocity at the interface and do not appear to have been identified before. In chapter 5 we investigate the case where a static mud channel develops on the narrow side of the annulus. Our stability theory predicts only linear stability. We therefore study the effects of a finite pulsation of the flow rates via numerical simulation. It seems that if we perturb the flow from the beginning of the displacement, the transient model fully captures the effects of the perturbation and the width of the mud channel is reduced. The pseudo-steady velocity model does not report any significant changes with respect to the results using a constant flow rate. If however, pulsation is applied after the mud channel has already formed, the removal of the mud channel will be unsuccessful.
机译：在本文中，我们研究了油井初次固井过程中的不稳定性和泥浆通道的去除。该过程涉及沿着狭窄的偏心环空位移一系列非牛顿流体。以前，已使用Hele-Shaw近似将其建模为伪稳态过程。在此类模型中，流函数受稳态椭圆问题支配，流体（通过浓度方程建模）仅沿环流平流。已经显示出，对于某些流变学和物理参数，在环的宽侧上的位移前沿比窄侧上的位移前沿快得多。在极端情况下，位移前沿根本不会在环的窄侧上前进，并且当手指沿宽侧向上前进时会形成静态泥浆通道。在本文中，我们考虑了渐进手指的界面在小扰动下是否会保持稳定。实际上，有实验证据表明这种情况下可能发生界面不稳定性。我们发现，只要环的狭窄侧上有一条静态泥浆通道，界面就实际上是稳定的。因此，我们还研究了如何通过流速脉动去除泥浆通道。使用伪稳态框架无法研究这两种现象。因此，我们将此模型扩展到完全瞬变的流。瞬态模型由一个针对流函数的非线性演化方程组成。在第3章中，我们证明了这种瞬态模型实际上是正确的。在第4章中，我们研究了多层平行流（即长手指）的稳定性。如果两种流体都在界面处产生，则对于14个无因次参数的不同组合，可能会出现不稳定性。这些不稳定性与界面处切线速度的跳跃有关，并且以前似乎没有被发现。在第5章中，我们研究了在环的狭窄侧上形成静态泥浆通道的情况。我们的稳定性理论仅预测线性稳定性。因此，我们通过数值模拟研究了流量的有限脉动的影响。看来，如果我们从位移开始就扰动了水流，那么瞬变模型将完全捕获扰动的影响，并且泥浆通道的宽度会减小。伪恒定速度模型在使用恒定流速的情况下不会报告任何明显的变化。然而，如果在已经形成泥浆通道之后施加了脉动，则泥浆通道的去除将是不成功的。

著录项

  • 作者

    Moyers Gonzalez, Miguel Angel.;

  • 作者单位

    The University of British Columbia (Canada).;

  • 授予单位 The University of British Columbia (Canada).;
  • 学科 Mathematics.; Engineering Petroleum.
  • 学位 Ph.D.
  • 年度 2006
  • 页码 192 p.
  • 总页数 192
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;石油、天然气工业;
  • 关键词

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