Foresight of Collapse if Carbon Steel Side Bagpipe due to Coast Erosion - Research Paper Example

Introduction In the oil and gas industry, the erosion of piping systems is a major concern. When oil or gas is extracted from wells, a combination of water and sand is also extracted. This composition of oil, gas, water and sand traverses large and sometimes intricate piping systems before reaching processing facilities, resulting in sand particles impinging the inside of the pipes. Over the course of time, these impingements will inevitably result in the wearing of the piping walls, eventually causing material degradation. Piping system degradation can be a very dangerous and costly affair, especially due to the explosive nature of the materials under consideration. Therefore, the ability to predict the occurrence of these erosion events is critical before the eventual failure of the piping system takes place. This is done by simulation. Solid particle erosion is a very complicated process, with very varied parameters affecting the erosion rate, thus making simulating the process an even more laborious task. Several studies have been conducted to develop empirical erosion models that can be used to obtain accurate predictions of the erosion process. Most empirical models boil down the erosion process to some of the main parameters, such as impact velocity, impact angle, and particle properties to give a rough estimate of the process. Due to the tremendous analytical and computational requirements of these empirical models, Computational Fluid Dynamics (CFD) has been shown to be a powerful and cost-effective tool to predict complex sand erosion. Previously developed empirical models can be implemented into the software and achieve results that are fairly accurate. However, all these models have inherent discrepancies, dictating the need for better understanding of solid particle erosion, with the knowledge gathered used to develop empirical models that more accurately describe the physical phenomenon. For this paper, the sand erosion for low particle loading cases was modelled by a CFD software, ANSYS Fluent. DNV GL developed a Lagrangian-impact based erosion model, which was implemented into the software and the results achieved compared against previous experiments on erosion rate conducted by [Hus98]. The validation of the model paved the way for more detailed analysis to be conducted for different types of flows and their effect on various piping components. Three types of flow are analysed in this paper, namely; - light crude oil, natural gas, and a composition of light crude oil, methane and water, and their effect on the following pipeline components;- 90 degree short and long radius elbows, S-bend and U-bend. Review of Literature This chapter discusses the theoretical concepts governing solid particle erosion in piping systems, divided into two sections. The first section deals with solid particle erosion, which describes the various mechanisms of solid particle erosion, as well as the parameters affecting the erosion rate. The section also outlines the various numerical and experimental methods for predicting erosion wear. The second section deals with Computational Fluid Dynamics (CFD), which provides a review of the mathematical model applied in the CFD analysis, outlining the governing equations solved by ANSYS Fluent, turbulence models, and discrete phase and multiphase flows modelling Solid particle erosion Background Information [Rev15] defines solid particle erosion as the mechanical removal of materials caused by the impingement of the solid particles on the material surface. In gas and oil systems, the extracted material often has sand particles, which hit, roll or slide the pipe material surface causing degradation. The impact parameters and the pipe material properties affect the mechanism that this degradation will occur. There are several mechanisms that have been proposed in literature through which solid particle erosion occurs, with the most common being abrasion, plastic deformation, fatigue and brittle fracture in oil and gas transportation pipelines [Men95]. The table blow gives a simple definition of these erosion mechanisms. Table 1: Mechanisms of erosion Mechanism of erosion Illustration Definition Abrasion The solid particles hit the surface at low impact angles, penetrating the pipe material with a cutting edge. The material is removed due to cutting, resulting in chippings Plastic deformation The solid particles strike the pipe material at high impact angles and with minimum velocities, causing plastic deformation of the material. The flakes formed detach from the material surface after multiple hits Fatigue The solid particles hit the surface at high impact angles and with low velocities. This leads to the development of cracks in materials with poor plastic deformation ability. Repetitive impingement propagates the cracks, which eventually break into small chips and detach from the surface Brittle fracture The solid particles strike the surface at high impact angles with medium velocities, instantly forming micro-cracks and breaking the material into small chips The mechanisms of abrasion and plastic deformation can only cause erosion in ductile materials, which are able to absorb the impact to some degree, while brittle fracture and fatigue mechanisms normally occur in brittle materials. [Fin58] proposed mathematical models to describe ductile material erosion while [Sri88] proposed mathematical models to represent brittle material erosion. However, despite the significant studies carried out on solid particle erosion, it is not fully understood due to its complex nature, which is partly brought about by large number of parameters influencing erosion, and the associated difficulty of isolating the effect of a single parameter [Kre98]. The parameters of mention include the following;- Table 2: Parameters governing the rate of erosion Parameters Description Particle parameters Size, shape, hardness, brittleness, particle-particle interaction, concentration, density Impingement parameters Impact angle, coefficient of restitution, impact velocity Material parameters Hardness, coating, ductility, toughness Flow parameters Density, viscosity, velocity Solid particle erosion models Different techniques have been developed to investigate solid particle erosion, with some scholars employing experimental methodologies and others using mathematical models to describe the process. Previous studies proposed different mechanisms and scenarios to describe the observed characteristics of solid particle erosion. These studies resulted in a significant number of physical parameters of solid particles and pipe flow conditions that could be incorporated in mathematical models [And80]. [Fin60] proposed one of the earliest models that fundamentally described solid particle erosion, which stated that erosive wear of a material struck by solid particles depends on the material properties and the particle motion. The model described erosion in ductile materials occurred due to cutting and plastic deformation, while erosion in brittle materials occurred due to crack formation and propagation. This model acted as the basis on which principle assumptions and concepts for subsequent models of solid particle erosion were formulated. Mathematical models primarily used in the oil and gas industry include DNV GL, Tulsa E/CRC, and [Oka05]. DNV GL Det Norske Veritas and Germanischer Lloyd developed RP O501, which is a Recommended Practise for the oil and gas industry providing a comprehensive guideline on erosion assessment in piping systems based on experimental data and CFD simulation results [Det15]. The developed model gives the equation below;- Where; is the erosion rate referred to surface thickness is the material erosion constant from empirical data is the particle impact velocity; equal to fluid velocity is the velocity exponent from empirical data is the impact angle function from empirical data is the particle mass flow rate is the density of target material is the area exposed to erosion Ductile materials experience maximum erosion for particle impact angles between and , while brittle materials are eroded most when the particle impact angle is 90, and reduces as the angle reduces. The plot below shows the relationship between the impact angle function and the particle impact angle for ductile and brittle materials. Figure 1: Plot of against particle impact angle Tulsa E/CRC At the Erosion/ Corrosion Research Centre (E/CRC) in University of Tulsa, [Alh94] proposed an empirical equation to predict erosive wear for carbon steel with a dry or wet surface;- Where;- is the erosion ratio and are empirical constants ( and ) is the Brinell hardness of target material is the particle shape coefficient (1 for sharp, 0.53 for semi-rounded, or 0.2 for fully rounded particles) [Oka05] The Tulsa E/CRC correlation was modified to impact velocity at the normal angle to take into account the effect of target material hardness, particle diameter and other properties, as follows;- Where;- is the erosion damage at normal impact angle is the independent factor denoting particle properties, like shape and hardness is the Vickers hardness of target material is the particle impact velocity is the reference impact velocity is the particle diameter is the reference diameter are the empirical exponent factors is the function of target material hardness and particle properties Experimental methodologies for erosion prediction Despite the rise in the use of CFD techniques for erosion modelling, there is still a significant need for experimental erosion data, which provides data and relationships which are required for the development of erosion models and validation of CFD predictions. In the recent past, increasingly sophisticated equipment has been used to examine the geometry of the eroded surface during experimental procedures, such as laser and physical probe profilers for small scale erosion scars, while 3D laser scanners and coordinate measuring machines for large scale studies. Most experimental erosion data reported are in the form of weight loss of test specimens and photographs of damaged patterns, but quantitative erosion distribution measurements can be of greater use. Quantitative measures capture the actual distribution of the erosion rate across the surface, which can then be compared to the CFD predictions directly. In this study, a reliable sand erosion experiment will be chosen, and the CFD software used to replicate and model the flow to provide a basis for assessing the accuracy of the numerical results when compared to the experimental data. Most experiments are conducted in a pipe loop test rig, but this study will try to find an experiment performed in a pipe, and with low particle mass loading, which is more in line with the focus of this study. An experiment reported by Det Norske Veritas (DNV) is used to validate the DNV GL erosion model. Carbon dioxide gas is pumped through a reducer, entering the pipe at a subsonic velocity, though a contraction, and flows through a pipe of smaller diameter. The reduction in pipe diameter increases the flow velocity, which affects the particle dynamics, and as a result, the erosion rate. The floe and particle parameters, and the pipe geometry for this experiment are as shown below [Hus98];- Figure 2: Pipe geometry, particle and flow parameters Computational Fluid Dynamics (CFD) Background information Computational Fluid Dynamics is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows. It is the use of applied mathematics, physics and computational software to visualize how a gas or liquid flows, and its effect on the objects it flows past. CFD is based in the Navier-Stokes equations, which describe how the parameters of a flowing liquid, such as pressure, velocity, density and temperature, are related [Rou142]. However, the Navier-Stokes equations are complex and cannot be solved analytically, except in special circumstances. An approximation of the exact solution to the equations can be obtained by numerical approach, which has an advantage over other analytical and experimental methods on aspects such as universality, flexibility, and cost [Wil061]. Governing equations There are three equations that govern fluid flow and heat transfer, that are generally variations of the physics laws of conservation [Zin99];- a) Conservation of mass The continuity equation is given by;- Where;- rate of change of density with respect to time net flow of mass out of the element across its boundaries (convective term) This is the general form of the unsteady, 3D mass conservation equation that is valid for both compressible and incompressible flows. b) Conservation of momentum (Newton’s second law of motion) The momentum conservation equations in the Cartesian coordinate system is given by;- Where;- is the source of momentum c) Conservation of energy (1st law of thermodynamics) The energy conservation equation only applies if there’s heat transfer within the fluid, or if flow is compressible. However, none of these applies in this study, thus this equation is not considered. Turbulence Turbulent flow is a flow regime in fluid dynamics characterized by chaotic changes in pressure and flow velocity [Bat00]. Turbulence increases the complexity of engineering processes due to its effect on dynamic properties, thus there have been several numerical methods developed to describe its effects, such as;- a) Reynolds-averaged Navier-Stokes equations (RANS) The Navier-Stokes equations are time averaged prior to numerical analysis, where the flow variables in the instantaneous continuity and the equations are decomposed into the mean (corresponding upper case letter) and fluctuating components (prime letter), as shown in the equation below;- These expressions are substituted into the Navier-Stokes equations and averaged to give the equations below [Ver07];- These equations are referred to as Reynolds-averaged Navier-Stokes (RANS) equations. b) Direct numerical simulation (DNS) c) Large eddy simulation (LES) Standard and Realizable k-epsilon model The k-epsilon model is a two equation turbulence model for the RAS equations to compute Reynolds stresses. It includes two transport equations for turbulent kinetic energy (k), and the turbulent dissipation (ε), which is the dissipation rate of (k) [Moh94]. The Standard k-epsilon is the most widely used turbulence model, as it provides reliable solutions for a wide variety of industrial flows without changing the model constants. The model provides accurate results for wall-bounded and internal flows with small mean pressure gradients, as well as free-shear layer flows with relatively small pressure gradients. However, this model has limited capacity when dealing with large adverse pressure gradients [Ver95]. The Realizable k-epsilon is an improvement over the standard k-epsilon model, with two distinctive features; a new formulation for turbulent viscosity, and a new turbulent dissipation equation. This model has an advantage over the previous for flows involving strong adverse pressure gradients. The CFD simulations done in this study are for flows over curved surfaces, and as such, the realizable k-epsilon is used. Near-wall treatments Turbulent flow is significantly affected by the presence of walls, which affect the velocity field through the no-slip condition. The velocity varies from zero at the wall surface, to free stream velocity further away from the wall. The near-wall region can be subdivided into the following layers;- a) Viscous sublayer – also referred to as the laminar sublayer, this is the innermost layer where the viscosity has the greatest influence since the flow approximately resembles laminar flow b) Buffer layer – also known as the blending region, this is an interim region where the effects of turbulence and viscosity on the flow are both equally important c) Fully turbulent region – also known as the log-law region, turbulence has the dominant effect to flow in this region Figure 3: Layers of the near-wall region Due to the significant velocity variations in the near-wall region, accurate representations of the flow is difficult since numerical solution variables will have high gradients. Nonetheless, ANSYS Fluent utilizes semi-empirical formulas, known as ‘wall functions’, to link the region between the wall and the fully turbulent region. This approach reduces the demand that the model will have on the CPU and memory, as a coarser mesh can be used. However, the viscous sublayer and buffer regions are not resolved [ANS09]. The standard wall function in the software are based on the [Lau74] methodology, which has the following steps;- a) The momentum equations are solved with a modified wall viscosity b) The turbulent kinetic energy is solved with modified integrated production and dissipation terms c) The predicted turbulent kinetic energy, k, sets the turbulent dissipation, ε The wall law for the mean velocity parallel to the wall is given by;- Where;- is the dimensionless velocity is the velocity parallel to the wall is the friction velocity is the Von Karman constant () is the dimensionless distance from the wall is an empirical constant depending on wall roughness ( for smooth walls) is the distance from the wall is the kinematic viscosity of fluid is the wall shear stress is the fluid density References Hus98: , (Husern & Kvernvold, 1998), Rev15: , (Revie, 2015), Men95: , (Meng & Ludema, 1995), Fin58: , (Finnie, 1958), Sri88: , (Srinivasan & Scattergood, 1988), Kre98: , (Kreith, 1998), And80: , (Andrews, 1980), Fin60: , (Finnie, 1960), Oka05: , (Oka, et al., 2005), Det15: , (Det & Germanischer, 2015), Alh94: , (Alhert, 1994), Rou142: , (Rouse, 2014), Wil061: , (Wilcox, 2006), Zin99: , (Zinng, 1999), Bat00: , (Batchelor, 2000), Ver07: , (Versteeg & Malalasekera, 2007), Moh94: , (Mohammadi & Pironneau, 1994), Ver95: , (Versteeg & Malalasekera, 1995), ANS09: , (ANSYS, 2009), Lau74: , (Launder & Spalding, 1974), Read More