气井多相流水击数学模型的建立和求解

针对气井关井瞬间产生的水击现象,由于井筒多相流和高压、高温以及天然气的强可压缩性特征,用于水力学的常规水击压力模型难以适用。基于水力学水击理论,分析气井水击机理,根据质量守恒定律和牛顿第二定律,建立由运动方程和连续性方程组成的描述气井多相流水击压力的数学模型;根据该方程属于拟线性双曲偏微分方程的特点,结合气井压力测试和应用需要,建立了两类边界条件:一类适用于通过井底压力计算井口及沿井深的水击压力,另一类适用于通过井口压力计算井底及沿井深的水击压力;通过特征线法对水击压力数学模型有限差分离散求解。计算结果与实测压力对比结果表明,水击压力模型能够精确地反映水击压力的大小、水击周期和水击衰减规律,从而提高压力恢复试井早期段数据质量,改善试井曲线拟合效果,提高试井解释准确度。

Establishment and solution of the mathematical model of multiphase water hammer in gas wells

Due to wellbore multiphase flow, high pressure, high temperature and the strong compressibility of natural gas, the conventional hydraulic water hammer pressure model is not applicable to study the water hammer phenomenon occurring at the moment of gas well shut-in. Then the water hammer mechanism of gas well was analyzed based on hydraulic water hammer theory. According to the mass conservation law and Newton's second law, the mathematical model consisting of motion equation and continuity equation was created for describing the multiphase water hammer pressure of gas wells. Because both were quasi-linear hyperbolic partial differential equations, two kinds of boundary conditions were further established based on gas well pressure test and application requirement. One kind was suitable for calculating the water hammer pressures at wellhead and along well depth through well bottom pressure, and the other applied to calculate the water hammer pressures at well bottom and along well depth through wellhead pressure. The characteristics method was used to solve the finite difference discrete equation of water hammer pressure mathematical model. The comparison of calculated results with the measured pressure shows that the water hammer pressure model can accurately reflect the size of water hammer pressure as well as the cycle and attenuation of water hammer and improve the data quality in the early stage of pressure buildup test, the fitting effect of well test curve and the accuracy of well test interpretation.