Scaling, Complexity, and Design Aspects in Computational Fluid Dynamics

Sheldon Wang

doi:10.3390/fluids6100362

Abstract

With the availability of more and more efficient and sophisticated Computational Fluid Dynamics (CFD) tools, engineering designs are also becoming more and more software driven. Yet, the insights in temporal and spatial scaling issues are still with us and very often imbedded in complexity and many design aspects. In this paper, with a revisit to a so-called leakage issue in sucker rod pumps prevalent in petroleum industries, the author would like to demonstrate the need to use perturbation approaches to circumvent the multi-scale challenges in CFD with extreme spatial aspect ratios and temporal scales. In this study, the gap size between the outer surface of the plunger and the inner surface of the barrel is measured with a mill (one thousandth of an inch) whereas the plunger axial length is measured with inches or even feet. The temporal scales, namely relaxation times, are estimated with both expansions in Bessel functions for the annulus flow region and expansions in Fourier series when such a narrow circular flow region is approximated with a rectangular one. These engineering insights derived from the perturbation approaches have been confirmed with the use of full-fledged CFD analyses with sophisticated computational tools as well as experimental measurements. With these confirmations, new perturbation studies on the sucker rod leakage issue with eccentricities have been presented. The volume flow rate or rather leakage due to the pressure difference is calculated as a quadratic function with respect to the eccentricity, which matches with the early prediction and publication with comprehensive CFD studies. In short, a healthy combination of ever more powerful modeling tools along with the physics, mathematics, and engineering insights with dimensionless numbers and classical perturbation approaches may provide a balanced and more flexible and efficient strategy in complex engineering designs with the consideration of parametric and phase spaces.

Highlights

In oil industry, artificial lift methods are often utilized to transfer the oil and gas from the formation to the surface, especially during the later phase of a petroleum reservoir’s productive life due to the diminishing fluid pressure [1]
For the purpose of illustrating the need for perturbation studies before full-fledged computational fluid dynamics (CFD) simulations, we focus on the so-called leakage issue related to the necessary gap between the plunger and the barrel for the smooth operation of the pump mechanisms [15,16]
The Reynolds number is a clear indication about the quasi-static nature of the Couette and Poiseuille flows within the narrow annulus region, in order to have some guidance with respect to the selection of the sampling time in the experimental measurements of the pressure and the displacement within the sucker rod pump unit, we must investigate further the inertia effects and other time dependent issues

Summary

Introduction

Artificial lift methods are often utilized to transfer the oil and gas from the formation to the surface, especially during the later phase of a petroleum reservoir’s productive life due to the diminishing fluid pressure [1]. We would like to demonstrate, through the analytical studies of the so-called leakage issues in sucker rod pumps prevalent in petroleum industries, the need for in-depth understanding of contributions of the geometries with extreme spatial ratios and the flow characteristics with specific relaxation time These insights will help to understand the complexity and many design aspects and enable more efficient use of computational resources with challenging spatial aspect ratios and temporal scales. The temporal scales, namely relaxation times, are estimated with both expansions in Bessel functions for the annulus flow region and expansions in Fourier series when such a narrow circular flow region is approximated with a rectangular one These engineering insights derived from the perturbation approaches have been confirmed with the use of full-fledged CFD analyses with sophisticated computational tools. A healthy combination of ever more powerful modeling tools along with the physics, mathematics, and engineering insights with dimensionless numbers and classical perturbation approaches may provide a balanced and more flexible and efficient strategy in complex engineering designs with the consideration of parametric and phase spaces

Analytical Approaches

Eccentricity Issues

Computational Approaches

Findings

Conclusions