Drilling and well construction operations involve fluid flow in the annular space between the drill string and casing or formation, or between casing and formation in the case of primary cementing operations. Knowledge of annular flow conditions is important for e.g. estimation of friction pressure losses and cuttings transport while drilling, and for predicting mud conditioning, displacement and cement placement during primary cementing. Predicting the velocity field of non-Newtonian fluids in realistic annuli containing restrictions or geometric irregularities is a formidable task that often require numerical methods.

As a step in establishing a practical laboratory geometry for conducting experiments of concentric annular flow, we investigate downscaling from field scale to a finite width rectangular duct. We focus on non-Newtonian fluids described by the Herschel-Bulkley model and on narrow annuli that are well-represented by infinitely wide slots. Downscaling from field to laboratory is performed by requiring geometric similarity and equal ratios of forces in the two systems. The effect of finite rectangular duct width on the velocity profile close to the middle of the duct is investigated numerically using an augmented Lagrangian method.

The existence of a non-zero yield stress results in a plug region in the center of the duct where the fluid flows as a rigid body. For ducts with sufficiently large width to height, the velocity in the middle of the duct is a good approximation to the velocity in a narrow concentric annulus, making the rectangular duct an attractive experiment geometry at laboratory scale.

Transparent rectangular ducts are attractive for optical velocimetry measurements since the duct has plane walls on all sides that minimizes optical distortion. Experiments in transparent laboratory scale ducts can provide insights into e.g. fluid flow past irregular geometric shapes, cuttings transport and cement placement in realistic annuli, and serve as important benchmark results for computational models.

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