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粘弹性流体在内管带有等距环槽的同心环空中流动的数值计算

Numerical Calculation for the Flow of a Viscoelastic Fluid in Concentric Annulus with Isometric Ring Slots on the Inner Cylinder

【作者】 宋兴良

【导师】 崔海清;

【作者基本信息】 东北石油大学 , 油气井工程, 2011, 博士

【摘要】 聚合物驱是提高原油采收率的有效技术之一,其中通过带有同心环形降压槽的配注器实现的聚合物分注技术是提高注聚效果和降低成本的重要工艺措施。聚合物水溶液在带有同心环形降压槽的配注器中的流动可以视为粘弹性流体在内管带有等距环槽的同心环空中的流动。开展粘弹性流体在内管带有等距环槽的同心环空中的流动,可以为单管同心环空降压槽分注技术的参数优选提供理论依据,具有工程实际意义。利用变系数二阶流体模型描述粘弹性流体的流变性,建立了柱坐标系下变系数二阶流体在内管带有等距环槽的同心环空中流动的控制方程和压降计算公式,并给出了相应的数值计算方法。以HPAM水溶液为例,对这种流动的视粘度、流函数、速度及压降进行了数值计算,并分析了槽宽、槽深、槽间距、槽数及弹性对视粘度分布、流函数分布、速度分布及压降的影响。结果表明:对于可视为变系数二阶流体的HPAM水溶液在内管带有等距环槽的同心环空中的流动,槽宽、槽深及弹性对视粘度分布影响明显,槽间距和槽数对视粘度分布影响并不明显;槽宽、槽深及弹性对流函数分布影响明显,槽间距和槽数对流函数分布影响并不明显;槽宽、槽深及弹性对速度分布影响明显,槽间距和槽数对速度分布影响并不明显;槽宽、槽深、槽数及弹性对压降影响明显,槽间距对压降影响并不明显。推导了柱坐标系下变系数二阶流体在内管带有等距环槽的同心环空中流动的稳定性参数H的计算公式,并以HPAM水溶液为例,对这种流动的稳定性参数H进行了数值计算和分析。通过质量百分比浓度分别为0.050%、0.100%和0.125%的HPAM水溶液在内管带有等距环槽的同心环空中流动的室内实验,根据上述控制方程、压降计算公式和稳定性参数H的计算公式及相应的数值计算方法,将计算压降与实测压降进行了对比,并确定了稳定性参数H的临界最大值。结果表明:计算压降与实测压降的最大平均相对百分比误差为4.12%,可以认为本文建立的柱坐标系下变系数二阶流体在内管带有等距环槽的同心环空中流动的控制方程、压降计算公式及给出的数值计算方法是正确的;变系数二阶流体在内管带有等距环槽的同心环空中流动的稳定性参数H的临界最大值为395。

【Abstract】 Polymer injection is one of the effective technology for EOR, in which the technology of separated layer polymer injection achieved by injection allocation with concentric ring depressurization slots on it is an important technical way which can help polymer injection and cost control. Flow of polymer aqueous solution in injection allocation with concentric ring depressurization slots on it can be regarded as flow of viscoelastic fluid in concentric annulus with isometric ring slots on the inner cylinder. The research on the flow of viscoelastic fluid in concentric annulus with isometric ring slots on the inner cylinder can provide a theoretical base on optimization of working parameters for the technology of single string separated layer polymer injection with concentric ring depressurization slots on the string, which is of engineering importance.A viscoelastic fluid model of the second-order fluid with variable coefficients is used to describe rheology of the produced fluid, and the governing equation and a formula for calculation of pressure drop for the flow of the second-order fluid in concentric annulus with isometric ring slots on the inner cylinder under the cylindrical coordinate system are established, and the corresponding numerical methods are presented. Taking HPAM aqueous solutions as examples, the apparent viscosity, the stream function, the velocity and the pressure drop of the flow are numerically calculated, and the influences of slot width, slot depth, slot interval, slot number and elasticity on the apparent viscosity, the stream function distribution, the velocity distribution and pressure drop are analyzed, respectively. The results show that as to the flow of the HPAM aquoues solution, which can be regared as the second-order fluid with variable coefficients, in concentric annulus with isometric ring slots on the inner cylinder, the influences of slot width, slot depth and elasticity on the apparent viscosity distribution are obvious, while the influence of slot interval and slot number on it are not obvious;the influences of slot width, slot depth and elasticity on the stream function distribution are obvious, while the influence of slot interval and slot number on it are not obvious;the influences of slot width, slot depth and elasticity on the velocity distribution are obvious, while the influences of slot interval and slot number on it are not obvious;the influences of slot width, slot depth, slot number and elasticity on the pressure drop are obvious, while the influence of slot interval on it is not obvious. A formula of stability parameter H for the flow of the second-order fluid with variable coefficients in concentric annulus with isometric ring slots on the inner cylinder under the cylindrical system is also established, and taking HPAM aqueous solution as an example, the stability parameter H of the flow is numerically calculated and analyzed. Through the experiments of the flow of HPAM aqueous solutions, the mass percentage concentrations of which are 0.050%,0.100% and 0.125% respectively, in concentric annulus with isometric ring slots on the inner cylinder, based on the governing equation, the formula for calculation of pressure drop, the formula of stability parameter H and the corresponding numerical methods established and presented, the pressure drop numerically calculated are compared with those experimentally measured, and the critical maximum value of the stability parameter H of the flow is determined. The results show that the maximum average relative errors between the pressure drop numerically calculated and those experimentally measured is 4.12%, so that the governing equation, the formula for calculation of pressure drop and the corresponding numerical methods established and presented in this paper can be testified to be correct, and the critical maximum value of the stability parameter H of the flow of the second-order fluid with variable coefficients in concentric annulus with isometric ring slots on the inner cylinder is 395.

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