A CFD Study of the Flow of a Power-Law Fluid in Annuli With Variable Eccentricity

Abstract

Some industrials processes are associated with flow of non-Newtonian fluids in annular spaces. Examples are found in oil industry and food industrial processing. In some cases, gravitational forces cause internal pipe deflection and, consequently, the eccentricity changes along of axis of the annular space. So, flow patterns are modified respect to those found in constant eccentricity annular spaces. Current industrial practice consists on extrapolate predictions based on flow patterns from the constant eccentricity critical scenario, corresponding to the critical region where both boundaries are closer, to the variable eccentricity actual scenario. In practice, using this approach, flow pattern predictions could significantly deviate from the actual profile, and variables such as shear stress at walls or pressure gradient could not be estimated with adequate accuracy. This work consists of a Computational Fluid Dynamics study, aimed to state the implications of evaluating flow patterns, assuming constant eccentricity, in opposition to a more realistic scenario, considering deflection path along the annular space, using a commercial code. A particular application is made to mud removal during well cementing operations in oil industry. For the casing in the hole, the deflection equation is solved and eccentricity along of the system axis is found. Flow of a non-Newtonian fluid described by Power Law model is considered. Oil industry typical conditions are considered for fluid density, rheological parameters, flow rates, casing and hole sizes, and annulus eccentricity. The flow regime was considered laminar. Numerical model capability to reproduce accurately flow patterns in these conditions was assured by comparison with others analytical-numerical solutions for concentric systems. Results show that local Reynolds number Re, shear stress τw and pressure gradient predictions G, under local eccentricity variations, differ from those under constant eccentricity. Differences in Re and τw show a maximum for eccentricity ranging from 60% to 80%, for all flow conditions whereas for G, this difference increases as casing deflection does it. When variable eccentricity models are compared to constant eccentricity one, the latter approach underestimates Re and τw along the narrowest section of the annuli, whereas overestimates the same features along the widest clearance. Additionally, considerably higher variations between these two models are taking place along the narrowest section compared to the variations arising on the widest annular section. When applied to well cementing processes, these results show that considering the most realistic scenario may impact significantly the flow pattern prediction on the annulus during primary cementing operations. Therefore, the quality of the cement job may be greatly compromised.