A computational fluid dynamics investigation of the flow behavior near a wellbore using three-dimensional Navier–Stokes equations

Mohammad Jalal Ahammad,Stephen Butt,Jahrul Alam,Mohammad Azizur Rahman

doi:10.1177/1687814019873250

Abstract

The analysis of fluid flow near the wellbore region of a hydrocarbon reservoir is a complex phenomenon. The pressure drop and flow rates change in the near wellbore with time, and the understanding of this system is important. Besides existing theoretical and experimental approaches, computational fluid dynamics studies can help understanding the nature of fluid flow from a reservoir into the wellbore. In this research, a near wellbore model using three-dimensional Navier–Stokes equations is presented for analyzing the flow around the wellbore. Pressure and velocity are coupled into a single system which is solved by an algebraic multigrid method for the optimal computational cost. The computational fluid dynamics model is verified against the analytical solution of the Darcy model for reservoir flow, as well as against the analytical solution of pressure diffusivity equation. The streamlines indicate that the flow is radially symmetric with respect to the vertical plane as expected. The present computational fluid dynamics investigation observes that the motion of reservoir fluid becomes nonlinear at the region of near wellbore. Moreover, this nonlinear behavior has an influence on the hydrocarbon recovery. The flow performance through wellbore is analyzed using the inflow performance relations curve for the steady-state and time-dependent solution. Finally, the investigation suggests that the Navier–Stokes equations along with a near-optimal solver provide an efficient computational fluid dynamics framework for analyzing fluid flow in a wellbore and its surrounding region.

Highlights

In the petroleum industry, the fluid flow phenomena at the vicinity of a wellbore are very important since most of the important quantities such as pressure drop, flow rate, formation damage, and so on are expected in this region.[1]
This study investigates modeling of fluid flow phenomena around the near wellbore of a reservoir using 3D Navier–Stokes equations (NSE)
We study the nature of the fluid flows around the near wellbore for a steady-state and time-dependent solution

Summary

Introduction

The fluid flow phenomena at the vicinity of a wellbore are very important since most of the important quantities such as pressure drop, flow rate, formation damage, and so on are expected in this region.[1]. Advances in Mechanical Engineering permeable formation or perforation tunnels.[2,3] Darcy’s equation describes reservoir fluid flow in the regions where the flow phenomena are linear. Forchheimer equation describes nonlinear fluid flow through porous media.[4,5,6,7] Nonlinear flow behavior in the near wellbore regions may have a significant influence on oil and gas production of the hydrocarbon reservoir.[7,8,9] Holditch and Morse[10] investigated the near wellbore fluid flow using a model of fractured porous media, and concluded that over prediction of the flow rates happened when the linear equation was considered. Their study showed that the hydrocarbon production had a 50% decline over the life of the well when the nonlinearity of the flow was neglected. Further research can be performed using three-dimensional (3D) Navier–Stokes equations (NSE) toward the study of near wellbore fluid flow

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