Analysis of the Effect of Eccentricity on Displacement of Non-Newtonian Fluids with a Hybrid Method

Abstract

Abstract The effect of eccentricity on pressure drop and mud displacement in annular flow is an important topic in drilling and cementing. Most researchers have focused on the effect of pressure drop with eccentricity and pipe rotation in drilling. In cementing, determining the fluid rheology and flow profile is important to the success of mud displacement and cement placement. Most recent researchers have adopted computational fluid dynamics (CFD) models to obtain results with Newtonian, or Power Law, or Bingham Plastic models. However, they are slow in computation and need special software to run, and thus are not readily applicable to the field. Furthermore, there are few results with the Herschel-Bulkley model, which is widely used in the industry. It is necessary to design an algorithm that can predict eccentric pressure drop, fluid rheology and flow profile in the annular cross-section accurately and efficiently. In this paper, we introduce a novel hybrid algorithm to predict the effect of eccentricity on pressure drop and fluid velocity profile in the annular cross-section. First the pressure drop with concentric wellbore geometry is calculated as an initial guess. Second, similar to CFD and finite element method (FEM), the annular cross-section is divided into small mesh elements. Equations governing the condition must be adapted to the geometry of each mesh element. Third, iterations are executed over pressure drop, fluid velocity, and flow rate in each mesh element until the total flow rate converges. Breaking the gel and critical velocity are important to determine the flow status in the mesh element. The proposed hybrid algorithm includes the Newtonian, Power Law, Bingham Plastic, and Herschel-Bulkley rheology models. Simulation and job history data are used to investigate the effect of eccentricity on the pressure drop, fluid rheology, and flow status in the annulus. Observations indicate that increasing eccentricity decreases the frictional pressure drop. This matches the results in the literature. We also observed that the fluid tends to remain stationary in regions with a narrow gap, while the wide side may maintain turbulent flow. Normally, laminar and static areas are predominant for typical fluids. In addition to predicting reasonable trends, the hybrid algorithm is efficient and accurate. A hybrid algorithm has been proposed to investigate the effect of eccentricity on frictional pressure drop and mud displacement in the annular cross-section. It is applicable to the main rheology models, and it works accurately and efficiently. The hybrid algorithm is described along with discussion of results over the typical range of geometries encountered.