**Abstract**

The transmission of particle-bearing liquids in pipes has motivated continuing research into erosion mechanisms and the distribution of erosion rates over wetted surfaces. This chapter covers these initiatives with particular reference to erosioncorrosion modelling within bends and straight sections of cylindrical pipes manufactured in a variety of materials and transporting a variety of liquids. Erosion-corrosion modelling techniques such as submerged slurry jets and rotating cylinder electrodes have been used to study factors influencing material degradation. Improvements in computational fluid dynamics (CFD), such as the development of a moving deforming mesh (MDM) have improved the accuracy of CFD models in predicting pipe wall erosion rates. Combined discrete phase tracking approaches such as the CFD-DPM-DEM (discrete phase-discrete element model) have helped improve computational efficiency. Wall impact erosion models are calibrated using laboratory scale tests. Validation of CFD models using full-scale test data is rare, meaning their accuracy is still largely unreported. Material testing has helped to identify the resilience of prospective pipeline materials to erosion-corrosion, while modifications to internal geometry and pipe section have shown potential to improve erosion-corrosion resistance.

**Keywords:** erosion-corrosion, computational fluid dynamics, pipelines, slurry, modelling, state-of-the-art

## **1. Introduction**

Erosion-corrosion (E-C) is recognised as one of the most significant threats to the integrity of pipelines carrying fluids mixed with solid particles. It affects numerous industries including mining, oil and gas, power generation and sediment transport. Marine, aero and food production industries are also affected [1]. Pipework, turbines, pump components and valves can all become heavily damaged by E-C. Improper management can lead to loss of productivity, unplanned downtime, or complete component failure, with obvious environmental and safety concerns. Erosion-corrosion is said to be the primary cause of fluid leakage in pipelines and is estimated to cost the Canadian oil sands industry \$1bn a year in damages [2, 3]. Owing to its importance within industry, the field of erosion-corrosion has enjoyed plentiful research over several decades.


#### **Table 1.**

*Material response to solid particle impact (adapted from [7]).*

Since the first focused work on theoretical mechanisms at least 28 different erosion equations have been proposed, including a total of 33 different parameters [4]. Erosion rate is defined as the rate of mass loss from a surface due to particle impingements. The response of pipeline materials to solid particle impacts depends on the nature of the target material and the treatments to which that material has been subjected. Environmental parameters such as flow velocity [5], pressure [6], temperature, impact angle, solid particle concentration, size and shape are also known to influence erosion [7]. The influence of impact angle depends on the mechanical characteristics of the pipe material. Brittle materials such as ceramics experience maximum erosion at impact angles of 90°. In ductile materials, cutting wear dominates at low impact angles (<20°) while deformation wear is most prominent at high impact angles [7]. This is summarised in **Table 1**.

Finnie [8] suggested that the volume loss due to erosion was proportional to the square of velocity. This comes because kinetic energy is likely the dominant factor governing erosion. Despite this, values of the exponent have been reported between 0.34 and 4.83 [9]. This variation has likely come in part due to difficulties accurately determining the impact velocities of particles in laboratory experiments. Other parameters that affect this number are particle size and its shape. The roundness of particles is often described using the circularity factor (CF). In perfectly spherical particles this factor is equal to 1, reducing as particles become more angular. It has been found that the circularity factor and erosion rate hold an inverse power law relationship [10]. A similar relationship has been found for particle size, with the exponent value quoted ranging between 0.2–4.0 depending on test conditions [9]. The behaviour of particles entrained within a flow is described by the Stokes number. Particles with Stokes numbers close to 1 tend to follow streamlines of the continuous phase. In flows with higher stokes numbers, particle motion is largely inertiadominated and wall collisions are more likely, leading to increased erosion rates [11]. Particles of higher hardness are known to cause higher erosive wear, although the ratio of particle to pipe hardness is perhaps the more important factor governing erosion rate [12].

Corrosion is an electrochemical process, caused by the interaction of the conveying fluid with the pipe material. As was the case with erosion, corrosion strongly depends on the nature of the pipe material. It has been found that the combined effects of erosion and corrosion can lead to significantly higher material loss rates than the summation of both processes separately [13, 14]. In the past decade, most erosion-corrosion research has been driven by the oil and gas industry. However, additional sectors have also been subject to investigation. In recent years, erosioncorrosion has been studied in concentrating solar power systems [15], engine cooling systems [16], fertiliser/mineral processing [14, 17] and geothermal power generation *Erosion-Corrosion in Pipe Flows of Particle-Laden Liquids DOI: http://dx.doi.org/10.5772/intechopen.107231*

[18] to name a few. The focus of research in these fields has been varied. Influencing factors such as pipe material, geometry and flow conditions have been studied. Methods of studying E-C due to particle-laden fluids can be broken down into pipeline tests, laboratory simulations and numerical simulations. The first two methods were reviewed in by Vahid Javaheri et al. [9]. Numerical simulation using computational fluid dynamics (CFD) was reviewed in 2014 by Mazdak Parsi et al. [19], and later by Messa et al. [20] in 2021. Recent developments in erosion-corrosion research were reviewed in 2017 [1]. This chapter will review developments in the modelling and management of erosion-corrosion subsequent to these works. The scope of this work will be limited to E-C of pipelines containing liquid-solid flows. Three-phase, gas-liquid or gas-solid flows will not be considered.

### **2. Numerical and laboratory scale modelling**

#### **2.1 Laboratory techniques**

After the review in [1], various researchers have published work in which the erosion-corrosion behaviour of pipeline materials has been tested. Owing to their existing popularity, pipeline steels have been the focus of the majority. Due to their low cost, compact size, easy setup and short test durations, bench-scale laboratory tests are the most popular method for investigating E-C. Of these, the jet impingement test and slurry pot testers are the most popular techniques used today [9]. Other techniques used include the submerged jet impingement test [17, 21], pin-on-disk test [22], electrode cells [23] and rotating cylinder electrode [24] to name a few. Aside from the latter two techniques, these experimental methods have been recently reviewed in [9, 25].

Submerged jet impingement tests are a popular means of testing different materials. Results from jet tests are commonly used to calibrate erosion models in CFD packages, as will be discussed later in this chapter. While the high velocities required make the method unsuitable for simulating erosion in real pipelines, they are a valuable tool for evaluating material performance [9]. For example, Karafyllias et al. [17] used a submerged direct impact jet to investigate the performance of two stainless steels (UNS S31600 and UNS S42000) and two white cast irons (27WCI and 37WCI). Tests were carried out in a neutral and acidic (pH 3) environment. They found that the austenitic grain structure of the UNS S31600 and WCI37 samples better-resisted corrosion at pH 3. At neutral pH, the increased hardness of both WCI alloys led to increased erosion resistance over the softer stainless steels. Their tests were carried out at 90° impact angles and 21 m/s jet velocities. This limits the applicability of the results to real-world scenarios where a wide range of slurry velocities and impact angles are common. Using a similar methodology, Brownlie et al. [18] investigated the performance of various engineering materials for use in geothermal power generation. The performance of three grades of stainless steel, a carbon and low-alloy steel, Inconel 625 and Ti-6Al-4 V were evaluated. They found that low-carbon and low-alloy steels are especially vulnerable to erosion-corrosion at shallow impingement angles. Inconel 625 and super austenitic stainless steel UNS S31254 exhibited the greatest E-C resistance. Cathodic protection was employed and found to have a profound effect on erosion rate, reducing volume loss due to E-C of low alloyed ATSM A470 Grade C steel by nearly 6 times. Mostafa et al. [26] investigated the wear rate of HDPE as a function of impact velocity and angle using slurry impingement tests.

Impact angles between 30 and 90° were studied at velocities of 4, 5 and 6 m/s. The erodent particles were silica sand. Mass change measurements were used to quantify material loss from target samples. Erosion was found to peak at impact angles around 45–50° and increased proportionally with slurry velocity.

The popularity of the slurry pot apparatus is owed to the ease at which the influence of slurry velocity, concentration and impact angle can be studied on sample materials. By substituting test specimens, the performance of different materials can be easily evaluated. However, hydrodynamic differences limit this method's ability to predict erosion rates within real-world pipe flows [9].

Chung et al. [27] used a slurry pot tester to study E-C in a variety of different pipeline steels. API 5 L X65, X70 and X80 steels were compared with ASTM A1053 dual phase stainless steel and AR400 hard plate. Tests were carried out at two speeds and dissolved oxygen levels. The steels were characterised using electron microscopy, X-ray, micro-mechanical probing, and electrochemical testing techniques. At the lowest oxygen level (0.6 ppm) corrosion was mainly suppressed. At high oxygen levels and slurry velocities, dual-phase stainless steel suffered enhanced damage to its passive film and E-C resistance decreased. They concluded that E-C resistance is a function of a combination of mechanical properties including hardness, strain hardening capability, ductility, toughness, and deformation before failure. The high E-C resistance exhibited by AR400 was attributed to its finer microstructure (when compared to the X series steels) obtained after the tempering and quenching process. The author recommended the use of fine micro-structured steels for slurry transport.

A slurry pot tester was also used by Singh et al. [28]. They investigated the influence of particle type and circularity factor on erosion wear of stainless steel (SS 316L). Samples of fly ash, bottom ash and sand were compared. Particle characteristics were measured using digital image processing on SEM images. It was discovered that the value of erosion wear decreased with the circularity factor. The relationship between erosion rate and circularity factor appeared to follow the inverse power law. The exponent value was predicted as 2.668 for multisized slurry.

Rotating disk/cylinder electrode systems are a popular choice for those wishing to establish the effect of flow velocity and solid concentration on corrosion in pipeline steels. Aguirre et al. [24] used a rotating cylinder electrode (RCE) to investigate the mechanism of corrosion-accelerated erosion in carbon steel API 5 L X65 in alumina slurry doped with mineral quartz. Tests were carried out at different fluid velocities and dissolved oxygen (DO) concentrations. SEM and electron backscatter diffraction (EBSD) inspection was used to analyse surface wear patterns. DO availability increased the wear rate of steel. It was proposed that plastic deformation due to particle impingements increased the formation of anodic/cathodic sites to an order of magnitude larger than the original impact site. This led to further increases in corrosion rate.

A multifactorial study by the same author [29] used similar apparatus to investigate the influence of velocity, particle concentration, temperature, pH, dissolved oxygen, and copper ion content on E-C in pipes of the same material. Sample degradation was measured using a combination of gravimetric techniques and surface morphology measurement using SEM imaging and energy dispersive X-Ray spectroscopy (EDX). Also using an RCE, Molina et al. [30] assessed the directionality of wear scars at different velocities when API 5 L X65 steel is exposed to quartz slurry. This was done by applying Fast Fourier Transform (FFT) to SEM images. They found that patterns in erosion wear scars could be successfully identified. Implementation of this technique could be used to enhance understanding of erosion wear.

Using combined wire beam and coupon electrodes, Xu et al. [23] investigated the influence of pre-corrosion on E-C in X65 pipeline steel. Pre-corrosion is common in pipelines where residual moisture is present following pressure testing. While they found that the E-C rate was similar in pre-corroded and non-pre-corroded samples, their findings cannot be extended beyond X65 steel.

### **2.2 Numerical methods**

Computational fluid dynamics (CFD) is a popular method of wall impact erosion modelling in particle-laden fluids. Erosion modelling procedures generally follow three steps: First, the continuous phase is resolved. The motion of elements within the discrete phase is then calculated. Finally, by using element motion in the near wall region estimates of material removal due to collisions can be generated at each wall node. By following this procedure, detailed erosion maps can be generated for geometry analysis [2]. While CFD simulations can yield highly detailed results, their accuracy has come under scrutiny in many papers [31]. The main sources of uncertainty lie within accurately modelling particle wall impact behaviour and estimating the material loss due to particle wall impingement. Particle tracking has also proven difficult and computationally expensive. Two main methods of multiphase modelling exist in CFD packages today. An overview of each is provided below.

### *2.2.1 Eulerian-Eulerian approach*

The Eulerian-Eulerian methodology, often referred to as the two-fluid model, treats both phases equally. This approach is computationally efficient and allows models containing numerous phases to be resolved. The downside of the Eulerian approach is that individual particle motion cannot be calculated. This limits the use of the Eulerian-Eulerian approach in erosion modelling. Despite this, the approach remains useful in applications where high solid concentrations are present or when the coupling between the fluid-particle or particle-particle is important [3].
