深井井壁不规则对注水泥顶替效率的影响

深部油气藏埋藏较深，钻遇复杂层系较多，受地质及工程因素影响，井壁坍塌或缩径现象更加突出。采用实验或理论方法研究不规则井眼注水泥问题成本高、难度大，常规数值模拟难以追踪井壁坍塌或缩径扰动引起的顶替界面突变特征。因此提出基于相场法的注水泥顶替数学模型，以表面张力为耦合变量，用Navier-Stokes方程描述流体流动，用Cahn-Hilliard方程追踪顶替界面变化，解决了井壁不规则引起的数值模拟不易收敛的难题，并通过数值方法模拟了注水泥时的流场及顶替界面演变过程，揭示了井壁坍塌或缩径对顶替效率的影响机理和规律。模拟发现井壁坍塌或缩径扰动会引起旋涡。扩径井段，旋涡强度较小时扩径区被顶替液不易被“旋出”，从而产生滞留或顶替死角；扩径率超过15%时，井壁坍塌对被顶替液滞留现象的影响越来越严重；缩径井段，旋涡会使下游产生混浆现象；缩径超过10%后，缩径对混浆影响越来越严重。研究表明，相场法解决了井壁不规则导致的注水泥顶替数值模拟时不容易收敛的问题，有助于揭示井壁坍塌或缩径影响注水泥顶替效率的作用机理。

Influence of the irregular hole on the cement displacement efficiency in deep wells

Deep oil and gas reservoirs are greater in burial depth and there are more complex series of strata. And due to the influences of geological and engineering factors, the phenomenon of hole collapse or shrinkage occurs frequently. Applying experimental or theoretical method to study the cementing operation in irregular holes is of high cost and great difficulty. And the conventional numerical simulation can hardly track the sudden change characteristics of the displacement interface induced by the disturbance of hole collapse or shrinkage. To this end, this paper proposed the mathematical model of cement displacement based on phase field method. In this model, the interfacial tension is taken as the coupling variable, the Navier-Stokes equation is used to describe fluid flow, and the Cahn-Hilliard equation is used to track the change of the displacement interface. In this way, the problem that numerical simulation is unlikely to converge due to irregular hole is settled down. In addition, the evolution processes of flow field and displacement interface in the process of cementing were simulated by means of numerical method, and the influential mechanisms and laws of hole collapse or shrinkage on displacement efficiency were revealed. It is indicated from the simulation results that the disturbance of hole collapse or shrinkage can result in swirls. Speaking of hole enlargement section, the displaced fluid in the hole enlargement zone can be hardly “swirled out” when the swirling strength is lower, so that retention or dead displacement corner is generated. And when the hole enlargement rate is over 15%, the influence of hole collapse on the retention of displaced fluid gets greater and greater. In the shrinkage section, swirls can generate the phenomenon of slurry mixing in the downstream. And when the hole shrinkage rate is over 10%, the influence of hole shrinkage on slurry mixing gets greater and greater. In conclusion, by virtue of the phase field method, the problem that the numerical simulation of cement displacement is unlikely to converge due to irregular hole is solved, which is conducive to reveal the influential mechanisms of hole collapse or shrinkage on cement displacement.