The primary objectives of this study are (i) to provide easy-use equations for field engineers to estimate the sand erosion rate of ESP systems, and (ii) to provide recommendations to minimize sand erosion. The overall goal is to minimize the ESP impeller erosion rate to increase its run lifetime; this will directly benefit operators because it implies a reduction in non-productive time due to equipment replacement, service, and workover. The performance of an ESP system under sand production conditions is a crucial issue for operators and service oil companies. Potential and aggressive sand production in oil wells, for example from unconsolidated formations or fractured oil shale, will be an issue for an ESP system even if it was the best economical and technical option among the existing artificial lift systems. Production with solids entrainment significantly affects the reliability of an ESP system and thus results in reduced ESP run lifetime and company revenue.

The approach to accomplish the above study objectives involves analytical formulations and numerical CFD (Computational Fluid Dynamics) simulations. Numerous CFD simulations carried out allowed verifying the validity of the newly developed analytical equation to estimate the solid particle velocity. The methodology follows Finnie's (1960) analytical erosion model, which provides a versatile solution approach to achieve the erosion rate by estimating the kinetic energy of the solid particle and the plastic deformation of the eroded material analytically. The newly developed solid particle velocity equation is a function of liquid density, solid density, impeller radius and angular velocity, blade angles, liquid velocity, solid concentration, and solid impingement angle.

Conclusions from both analytical and numerical studies indicate key results: a) the lower the particle velocity, the lower the erosion rate, b) increasing solids concentration increases erosion rate, and c) increasing solids density decreases the erosion rate. Until now there is no guidance on how to operate an ESP system under liquid-solid flow conditions. The new analytical modeling approach delivers significant reduction of time and effort required to estimate the erosion rate since CFD needs complex pump geometry and mesh construction. A field example shows how to calculate the pump stage erosion rate using the new equation, and to estimate the ESP run life.

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