Estimating Water-Based Mud Rheology from Marsh-Funnel Drainage Using Capillary-Flow Analysis

The Marsh funnel is widely used at the rig site as a rapid drilling-fluid quality-control tool, but its conventional output—a single drainage time—does not provide full rheological characterization. This study evaluates whether Marsh-funnel drainage data can be converted into rheological information for water-based drilling muds using capillary-flow analysis, funnel-geometry variation, and statistical modeling. Nine water-based mud samples, including gel mud, KCl-polymer mud, and KCl-silicate mud, were tested with a 6-speed rotational viscometer and six funnel geometries. Drain-volume/time data were collected for immediate drainage and after 1-, 5-, and 10-minute waiting periods. Wall shear stress and corrected wall shear rate were calculated using pressure-driven-flow concepts and Weissenberg-Rabinowitsch correction, and funnel-derived rheograms were compared with 6-speed viscometer behavior. Power-law behavior described the mud samples more consistently than the Bingham plastic model, with an average R² of 0.956 compared with 0.773 for Bingham fitting. Funnel geometry affected the reliability of funnel-derived rheograms; larger orifices reduced orifice resistance and improved fluid-behavior expression, whereas the smallest orifice produced poor or invalid responses for viscous samples. Multivariable regression linked the consistency index primarily to solid content and funnel drainage-time ratios, whereas the flow-behavior index required consistency-index information for reliable prediction. A gel-strength indicator based on the area change between apparent-viscosity/shear-rate curves after static waiting detected gel response in 94 of 145 valid attempts, or 64.8%. The results support Marsh-funnel use as a supplementary field rheometry tool when calibrated against conventional viscometer data, although standalone deployment requires further validation across temperature, oil-based muds, and broader field mud systems.