摘要：In the drilling industry, Marsh funnel viscosity is only a dynamic viscosity and cannot characterize actual rheology. Thus, measuring rheology using a Marsh funnel has been drawing considerable attention. In this study, we develop simplified mathematical models for wall shear rate, wall shear stress, and their consistency plots. Moreover, we propose mathematical models for the rheological parameters of Newtonian and non‐Newtonian fluids. We compare the results of the present model with those of a ZNN‐6 viscometer, a computational fluid dynamics (CFD) model, and other analytical models. According to the quantitative analysis results, the average systematic error of the Newtonian, apparent, and plastic viscosities between the present model and the ZNN‐6 viscometer measurements is 1.35%, 8.18%, and 5.42%, respectively. The average systematic error of the yield stress is 21.43%, which is under the controllable scope. Meanwhile, results of the qualitative analysis reveal that the present model for the wall shear rate and stress agrees with the CFD model. Moreover, the flow field inside the Marsh funnel is axisymmetric and has a component velocity in the horizontal direction. In summary, the proposed model is accurate, concise, available for field applications, and beneficial for a successful and safe drilling operation. Furthermore, the CFD approach is a necessary complement to exploring the actual field flow inside the Marsh funnel.
