Abstract Understanding the nature of fluid flow through fractured wellbore cement is fundamental for evaluating the leakage potential and risk assessments of leaky wellbores. In this study, the conditions that require considering visco-inertial flow for describing the gas flow through wellbore cement fractures were investigated. Nitrogen gas flow tests were conducted on fractured cement samples under varying pressure conditions and flow rates, covering both viscous and visco-inertial flow regimes. The data substantially deviated from Darcy's law at higher flowrates and were well-fit to Forchheimer's equation for visco-inertial flow. The inertial coefficient and critical Reynolds number were expressed as a function of the hydraulic aperture. The empirical function obtained from the experiments was used as an input to numerical simulations which showed the significant role of visco-inertial flow in wellhead pressure build-up and leakage rates, and demonstrated the importance of visco-inertial flow when modeling gas flow through wellbore cement fractures.

中文翻译：

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通过井筒水泥裂缝的粘性惯性气流

摘要 了解流体通过压裂井筒水泥流动的性质是评估泄漏井筒泄漏潜力和风险评估的基础。在这项研究中，研究了需要考虑粘性惯性流来描述通过井筒水泥裂缝的气体流动的条件。氮气流动测试是在不同压力条件和流速下对破裂的水泥样品进行的，包括粘性和粘性惯性流动状态。数据在较高流速下显着偏离达西定律，并且非常适合用于粘性惯性流的 Forchheimer 方程。惯性系数和临界雷诺数表示为液压孔径的函数。