Residual drilling mud during conditioning of uneven boreholes in primary cementing. Part 1: Rheology and geometry effects in non-inertial flows

We perform a detailed computational study of the flow of a Bingham fluid along a narrow channel, with one locally uneven wall. This uneven section of the channel represents a washed out section of an oil well about to be cemented. By studying a wide range of different washout geometries, of differing shape characterized by dimensionless height h and length L, we discover that the flows exhibit a type of self-similarity in the limit of large h and B. More specifically, in this limit we find that regardless of the washout geometry, the area of the channel that contains moving fluid is the same for each L. Essentially, uneven and distant parts of the washout become full of static fluid, below the yield stress, while the flow self-selects its own unique geometry. The washout geometry with the largest flowing region within the washout, appears to be the square wave. We show how a simple correction can be calculated that allows one to predict the flowing area for other washout geometries. Lastly, we examine the effect on the pressure drop of different washout geometries.