Many fluids used in petroleum and chemical industries are generally described as complex systems that exhibit time-independent non-Newtonian behavior. To adequately represent the rheological behavior of an oil-tolerant and salt-resistant aqueous foam system, a Carreau-Extended (Carreau-E) rheological model, which includes a yield stress, a shear-thinning parameter and a time constant, has been established based on Carreau and Herschel-Bulkley models. In the present study, generalized Reynolds number definitions are proposed for laminar and fully developed pipe flow of non-Newtonian fluids (Carreau-E, Carreau, Herschel-Bulkley and Bingham fluids). Perturbation solutions for pipe flow of a Carreau-E fluid are obtained and their ranges of validity in the problem parameter space are identified. The quantitative effects of rheological parameters (e.g., yield stress, time constant, shear-thinning parameter) and flow parameters, (e.g., pressure gradient, pipe radius) on the velocity profile and flow rate in pipe flow of a Carreau-E fluid are explored. The results obtained for the flow characteristics can be applied or extended for other types of non-Newtonian fluid flow encountered in practical applications.

通常将石油和化学工业中使用的许多流体描述为复杂的系统，这些系统表现出与时间无关的非牛顿行为。为了充分表示耐油和耐盐水性泡沫体系的流变行为，建立了Carreau-Extended（Carreau-E）流变模型，该模型包括屈服应力，剪切稀化参数和时间常数。基于Carreau和Herschel-Bulkley模型。在本研究中，为非牛顿流体（Carreau-E，Carreau，Herschel-Bulkley和Bingham流体）的层流和充分发展的管道流动提出了广义的雷诺数定义。获得了Carreau-E流体管道流动的摄动解，并确定了它们在问题参数空间中的有效范围。流变参数的定量影响（例如，研究了Carreau-E流体的速度分布和管道流速中的屈服应力，时间常数，剪切稀化参数）和流量参数（例如压力梯度，管道半径）。对于流动特性获得的结果可以应用于或扩展到实际应用中遇到的其他类型的非牛顿流体流动。