油藏条件下聚合物溶液老化数学模型新探

摘要

Polymer aging and degradation is an important factor influencing the effect of polymer flooding in high-temperature oil reservoirs. When the effect of polymer aging and degradation on flooding effect is evaluated by means of reservoir numerical simulation, it is critical to establish the mathematical model for polymer aging and degradation. The viscosity correction model at reservoir condi-tions was built by using the first-order ordinary differential equation of polymer aging and degradation. Then, the partial differential equation for describing the variation of polymer viscosity at reservoir conditions was presented. Combined with the mass conservation equation of polymer, it is proved that the viscosity correction model is feasible if the viscosity-concentration relation is polynomial. The viscosity correction model reveals the influential process of degradation and flowing of polymer on its viscosity at any point of oil reservoir, and describes the physical phenomenon of viscosity reduction with constant mass concentration in the process of polymer ag-ing and degradation. Compared with the viscosity models used in current commercial numerical simulators, this model can present the physical flowing of polymer in porous media more actually. The derivation and demonstration of viscosity correction model provides the theoretical support for the numerical simulation study of polymer aging and degradation.%聚合物老化降解是影响高温油藏中聚合物驱效果的重要因素。利用油藏数值模拟技术评估聚合物老化降解对驱替效果影响的技术关键在于聚合物老化降解数学模型的建立。基于聚合物老化降解的黏度一阶常微分方程建立了油藏条件下的黏度修正模型，给出了油藏条件下聚合物黏度变化的偏微分方程描述形式。结合聚合物质量守恒方程，证明了在黏浓关系是多项式关系的条件下，黏度修正模型是成立的。黏度修正模型揭示了油藏中任意一点聚合物黏度受到聚合物自身降解和流动两方面影响的过程，描述了聚合物老化降解过程中质量浓度不变，黏度降低的物理现象，比目前商业数值模拟器中的黏度模型更加贴近聚合物在多孔介质中流动的物理实际。修正黏度模型的推导与论证为聚合物老化降解的数值模拟研究提供了理论支持。