摘要
在聚驱采油工况下,抽油机井产出液在井筒中的流动可以视为粘弹性流体在内管做轴向往复运动的偏心环空中的非定常流动。开展粘弹性流体在内管做轴向往复运动的偏心环空中非定常流的研究,可为聚驱抽油机井工作参数的优选提供理论依据,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,建立了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的瞬时压力梯度方程和时均压力梯度公式,并给出了相应的数值计算方法。以HPAM水溶液为例,对这种流动的瞬时和时均压力梯度进行了数值计算,并分析了内管冲程、冲次、环空偏心度以及弹性对瞬时和时均压力梯度的影响。结果表明:对于可视为变系数二阶流体的HPAM水溶液在内管做轴向往复运动的偏心环空中非定常流,内管冲程、冲次和环空偏心度对瞬时压力梯度的影响明显;弹性对瞬时压力梯度有影响;内管冲程和冲次对时均压力梯度的影响并不明显;环空偏心度对时均压力梯度的影响较为明显;弹性对时均压力梯度有影响。还建立了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的稳定性参数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水溶液在内管做轴向往复运动的偏心环空中非定常流的室内实验,根据上述瞬时压力梯度方程、时均压力梯度公式和稳定性参数H的计算公式及相应的数值计算方法,将计算时均压力梯度与实测时均压力梯度进行了对比,并确定了稳定性参数H的临界最大值。结果表明:计算时均压力梯度与实测时均压力梯度的最大平均相对百分比误差为2.60%,可以认为本文建立的瞬时压力梯度方程和时均压力梯度公式及给出的相应数值计算方法是正确的;变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的稳定性参数H的临界最大值为380。
During the process of polymer flooding production, flow of the produced fluid in wellbore can be regarded as unsteady flow of viscoelastic fluid in eccentric annulus with the inner cylinder reciprocating axially. The research on unsteady flow of viscoelastic fluid in eccentric annulus with the inner cylinder reciprocating axially can provide a theoretical base on optimization of working parameters for rod pumped well under polymer flooding, 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 an equation of instantaneous pressure gradient and a formula of average pressure gradient for the unsteady flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially are established, and the corresponding numerical methods are presented. Taking HPAM aqueous solutions as examples, the instantaneous and the average pressure gradients of the flow are numerically calculated, and the influences of stroke and stroke-frequency of the inner cylinder, annular eccentricity and viscoelasticity on the instantaneous and the average pressure gradient are analyzed. The results show that as to the unsteady flow of the HPAM aquoues solution, which can be regared as the second-order fluid with variable coefficients, in eccentric annulus with the inner cylinder reciprocating axially, the influences of stroke and stroke-frequency of the inner cylinder and annular eccentricity on the instantaneous pressure gradient are obvious, and elasticity has influence on the instantaneous pressure gradients as well; the influences of stroke and stroke-frequency of the inner cylinder on the average pressure gradient are not obvious, while the influence of annular eccentricity on the average pressure gradient is obvious, and elasticity has influence on the average pressure gradient as well. A formula of stability parameter H for the unsteady flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially 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 unsteady flow of HPAM aqueous solutions, the mass percentage concentrations of which are 0.050%, 0.100% and 0.125% respectively, in eccentric annulus with the inner cylinder reciprocating axially, based on the equation of instantaneous pressure gradient, the formula of average pressure gradient and the corresponding numerical methods established and presented, the average pressure gradients 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 average pressure gradients numerically calculated and those experimentally measured is 2.60%, so that the equation of instantaneous pressure gradient, the formula of average pressure gradient 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 unsteady flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially is 380.
引文
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