Abstract

Stokes flow of a Newtonian fluid through oil and gas production tubing of uniform diameter is studied. Using a direct simulation on computer-aided design of discretised conduits, velocity profiles with gravitational effect and pressure fields are obtained for production tubing of different inner but uniform diameter. The results obtained with this new technique are compared with the integrated form of the Hagen–Poiseuille equation (i.e., lubrication approximation) and data obtained from experimental and numerical studies for flow in vertical pipes. Good agreement is found in the creeping flow regime between the computed and measured pressure fields with a coefficient of correlation of 0.97. Further, computed velocity field was benchmarked againstANSYS Fluent; a finite element commercial software package, in a single-phase flow simulation using the axial velocity profile computed at predefined locations along the geometric domains. This method offers an improved solution approach over other existing methods both in terms of computational speed and accuracy.

Highlights

  • Fluid flow through pipes has attracted a great deal of scientific and engineering discipline interests due to their prevalence in biological systems such as blood flow in human body and multi-phase in flow in oil and gas producing wells

  • A rigorous numerical workflow for the direct simulation of fluid flow in oil and gas production tubing was developed. This method is embedded into a novel simulation approach that begins with Computer-Aided Design (CAD) modelling and discretisation of the geometry and ends with an efficient numeric solution of momentum and conservation equations in a non-commercial package

  • The 2D and 3D single phase flow code based on Stokes equation was formulated and tested

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Summary

Introduction

Fluid flow through pipes has attracted a great deal of scientific and engineering discipline interests due to their prevalence in biological systems such as blood flow in human body and multi-phase in flow in oil and gas producing wells. Approximate solutions have been obtained using the Hagen–Poiseuille (i.e., lubrication approximation) for flow in pipes by integrating the equation at each axial location along the pipe to obtain the overall pressure drop (e.g., Al-Atabi et al [9]) This has allowed for modelling and simulation of Newtonian and non-Newtonian fluid flow in networks of interconnected pipes for oil transportation, production tubing design or a. Laboratory experiments usually give a detailed structural behaviour of flow in production tubing, but, numerical approaches are cheaper and preferable in preliminary investigation and analysis These aforementioned DNS methods have focussed mainly on the modelling of flow structure and less on the actual engineering of the physical problem in the numerical evaluation of the velocity fields within realistic geometries. The developed model is verified against analytical solution and validated against experimental and numerical results

Methodology
Governing equations
Discretisation of the momentum equation
Numerical solution and code set-up
SAMG set-up parameters
Geometric model construction
FEM discretisation of geometric models – meshing
Numerical simulation
Verification of the single-phase flow model in 2D vertical pipes
Boundary and initial conditions in 2D geometries
Comparison with analytical solution
Verification of the single-phase flow model in 3D vertical pipes
Model validation and benchmarking with commercial software package
Model validation – comparison with experimental measurements
Discussions
Conclusion

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