1. Introduction
During the transportation of sulfur-containing gases in the gathering pipeline, sulfur particles are precipitated from the gas mixture due to changes in fluid temperature and pressure, which can cause serious erosion damage to pipelines, pipe fittings, throttle valves, and other facilities when carried by high-velocity fluids [
1]. Pipeline failures due to erosion formed by sulfur-containing particles account for around 30–40% of the solid particle erosion types each year, which not only reduces the efficiency of the product development and transportation process of sulfur-containing gas reservoirs but also causes significant economic damage and safety hazards. Combined with the current research and development concerning the erosion mechanism of solid particles, the complex variation in erosion behavior of sulfur particles is associated with many influencing factors, such as the characteristics of fluid carrier, the physical properties of erosion particles, the wall materials and the geometry of pipelines [
2]. The variation in these influences can cause huge differences in erosion, for example, it has been found that the degree of erosion damage by particles at the elbow can be more than 50 times higher than that of the straight pipe [
3]. Therefore, understanding the erosion patterns of sulfur-containing particulate gas on gas well-gathering pipelines is a prerequisite to avoid exacerbating the damage caused by the erosion effect and to increase the service life of the pipe column, which is conducive to setting the optimum gas well-gathering pipeline parameters.
Finnie [
4] discovered through erosion experiments that metal and ceramic targets show different erosion patterns at different impact velocities, impact angles, and particle size impacts, and proposed the first erosion theory for plastic materials—the micro-cutting theory, which was later modified to obtain a mathematical formula for the erosion rate at changing incidence angles for calculating the magnitude of volume loss at the wall. Bitter [
5] analyzed the erosion pattern of materials at different erosion angles from the perspective of energy balance and proposes a theory of deformation wear, which explains the total erosion loss as the sum of cutting wear and deformation wear. Levy [
6] used the step-by-step erosion method to carry out extensive experiments to propose a theory of forging and extrusion that restored the evolution of erosion damage. The indentation fracture theory proposed by Evans [
7] described the variation of cracks on the surface of the target material during particle erosion, and these theories have been proposed to better explain the erosion phenomenon on the basis of Finnie’s theory. As the oil and gas industry developed, the phenomenon of solid particle erosion within pipelines came to the fore, based on the development of a preliminary material erosion theory, and early publications by Berger et al. [
8] and Smith [
9] provided an extensive theoretical study of flow in bent pipelines. Ahlert et al. [
10] established erosion models related to pipeline materials, particulate matter properties, and wear angles through various types of pipeline wear experiments. The mathematical model of erosion established by Oka [
11] considers the parameters of particle hardness and material properties and better predicts the erosion behavior of different attributes of particles on different pipes. The E/CRC erosion rate model [
12] uses the laser Doppler velocimeter to measure the flow field distribution and correct the velocity coefficient on the basis of the Finnie model, which can more accurately describe the flow field distribution in the gas-solid two-phase flow model. The DNV RP-0501 model [
13] is established by the DNV Classification Society based on a large number of experimental data. It is proposed that the erosion rate and the particle velocity are a power exponential relationship, which is widely used in actual field applications and is mostly used for erosion prediction of industrial large pipe diameters. Rehan Khan [
14] quantified the influence of different elbow angles on erosion distribution under the condition of sand erosion by a new experimental program, and illustrated three main erosion mechanisms of elbow surface (pitting, ploughing, and cutting), which further perfected the research on erosion and wear mechanism under the condition of multiphase flow. Currently, the DNV and E/CRC erosion models are the most commonly used in pipeline erosion studies, and both models are simple and similar in form for easy comparison in the study of erosion impact parameters.
Today’s computer fluid dynamics (CFD) techniques are widely used in various erosion simulation studies to describe the process of solid particle-wall collisions using the two-phase Euler-Lagrange tracking method, improving the accuracy and applicability of erosion models and parameter corrections and facilitating the development of pipeline erosion studies. Wang [
15] modified some parameters on the basis of Ahlert’s model and established a new erosion prediction model for gas-solid two-phase flow by simulating the erosion phenomenon at the bend location of the pipe through CFD. The accuracy of calculating erosion rates for gas-solid two-phase flows was investigated by McLaury [
16], Edwards [
17] and Haugen et al. [
18] They considered physical variables such as fluid properties, pipe geometry and established relationships between the parameters, although their studies on the effects of secondary flow effects and turbulence effects on solid particles were insufficient. Later, Bozzini et al. [
19] used CFD simulations of erosion in 90° bends to explain the formation of secondary flow in bends and to investigate the effects of factors such as flow velocity and particle content on erosion patterns. Zeng [
20] modified the partial erosion model based on CFD simulations considering the erosion effect of non-spherical particles by introducing a dimensionless constant to explain the effect of secondary flows, vortices and particle trajectories on the formation of partial erosion traces in the elbow. Zhang [
21] used CFD to predict the particle erosion behavior of a 90° elbow under multiphase flow conditions based on Zeng’s study. The effects of secondary collisions, mean curvature, inertial forces, drag forces and Stokes number on the trajectories of sulfur particles were additionally investigated, and the main distribution locations of the severely eroded areas at the elbow were analyzed. Generally speaking, the flow of gas in gas well pipelines presents a high Reynolds number state, if the simulation using a laminar flow state will not truly reflect the movement process of particles; therefore, in recent years, scholars of erosion research have widely used a variety of
k-ε turbulence model of Reynolds-averaged Navier-Stokes (RANS) equations to simulate the fluid flow in the pipeline, which is important to improve the accuracy and reliability of solid particle erosion simulation. For example, Chen [
22], Pei [
23], Peng and Cao et al. [
24] used RNAS of the
k-ε turbulence model to calculate the erosion process of mud on the elbow and analyzed the effect of changes in fluid parameters on the erosion effect. Laín and Sommerfeld et al. [
25] used a stochastic method to calculate a model of particle collisions with rough walls in turbulent transport, and in a subsequent study explained the forces involved, such as drag forces, gravity and lateral lift [
26]. They later calculated the erosion of particles along horizontal to vertical elbows by combining the Euler-Lagrange method with an appropriate turbulence model via a two-way full coupling, considering the effect of inter-particle collisions on erosion [
27]. Laín [
28] has carried out three-dimensional numerical simulations of particle collisions in transportation pipelines by combining the Euler-Lagrange method with an adapted turbulence model to obtain the component streamlines of the gas velocity cross-section and to analyze the particle motion pattern and the variation of the collision frequency.
In general, there are relatively few studies on the erosion of sulfur-containing gases in gathering pipelines. Moreover, sulfur particles have different characteristics compared to other solid particles, such as low density, low hardness and easy rebound, and the erosion distribution pattern caused by most pipelines out of sand is different, especially the distribution difference caused by the change of curvature ratio of the elbow, and it is necessary to carry out research on the erosion distribution pattern of sulfur particles in pipelines under different collision conditions. In this paper, the gas-solid flow simulation model of the pipeline will be developed through the CFD simulation of COMSOL Multiphysics. The relationship between the distribution of erosion traces of sulfur-containing gases at 90° elbows and the variation of secondary vortex flow is investigated without considering chemical corrosion, and the influence law of erosion distribution under different curvature ratio, particle and pipe diameter conditions is analyzed separately to provide a reference for the transportation of sulfur-containing gas gathering pipelines in the industry.