(41a) Modeling of Simultaneous Particle Attrition and Pipe Wear
There are different approaches for coping with this problem: purely empirical, combined computational tools with experimental measurements or fully theoretical modeling. Due to the increase of computational power in the recent years, the most common way to predict these phenomena became computational fluid dynamics coupling with another tool to assess the breakage or erosion. An example for such approach, which is widely used, is the coupling of Discrete Element Method (DEM)-Computational Fluid Dynamics (CFD) simulations with a discrete erosion model. The major advantage of this approach is itâs the straight forward way for saving the collision data (particle impact velocity, angle and specific location) to serve as the input for the erosion model. However, this combination is usually limited to compute the erosion rate at a single pipeline component, which is typically the most vulnerable part in the conveying system, such as contraction or bends, instead of a full system analysis. The reason behind this limitation is the high computational requirements for a full system with huge number of particles. When simulating breakage, the same limitation repeats because of the large amounts of fragments which eventually preventing a full scale prediction of the particle size distribution (PSD).
Regardless of its size, a full scale optimization for the dynamic parameters, e.g. particle velocity and pressure drop, can be done with simplified models. Those models compute the two-phase dynamics with zero dimension (no dependency on the pipe length) or one-dimensional (computing the dynamic parameters in terms of the pipe axial direction) models. The advantage of this method is of course its computation time, nonetheless, 3D effects such as turbulent eddies and swirling flow cannot be accurately computed via this method and therefore 3D evaluation of the particlesâ trajectories is not possible. The consequence of this limitation is the disability to compute explicitly particle-particle and particle-wall interactions, and therefore it cannot express the input needed to breakage or erosion models.
Recently, we developed two models that are combining the advantages of the CFD-DEM and the one-dimensional two phase flow simulations. By doing so, they are capable of predicting erosion or breakage in long-range conveying systems in short computation time. The particle attrition model is solving conventional 1D balance of mass, momentum and energy to compute the two-phase flow dynamics. These set of equations are coupled with the one dimensional breakage algorithm (ODBA) for predicting the alternation of the particlesâ size distribution along the pipeline. The ODBA is combining three essential elements: (i) a tracking procedure, (ii) particle breakage characterization, and (iii) collision characteristics. Tracking is done only on a representative mass which is defined by a chosen number of particles. The particle breakage characteristics defines if a particle would break or not upon impact, and what would be the sizes of its fragments if it does breakage. Those characteristics were adopted from empirical based measurements. The last piece of the puzzle is the collision characteristics that expresses the frequency, location, velocity, and angle of the impact. These characteristics were derived from CFD-DEM data into statistical distribution functions. This complete model allows to forecast the PDS at every desired place in the conveying system, while considering fatigue and p-p as well as p-w interactions.
The second model, for erosion prediction, which is known as one-dimensional erosion model (ODEM), is based on a similar principal like the ODBA. The only fundamental difference from the ODBA is replacing the âparticle breakage characterizationâ with a discrete erosion model that is able to compute the wear depth due to the particle impact. This model needs the input from the collision characteristics in order to give the desired output: erosion rate map of the entire conveying system. Yet, both the ODBA and ODEM have a concealed assumption that is very widely used, but rarely investigated. The energy loss from an impact is attributed only to the investigated phenomena, i.e., when a simulation is after prediction of erosion it is regularly assumed that the particle is rigid, and therefore the energy loss due to the impact is because the surface deformed plastically, or micro cracks were forming. However, many times this is not the case, because the particles are damaged and attrition is well distinguished.
In the current study we address this issue by presenting a new concept for dealing with combined erosion and breakage. The first step toward this cause was to quantify the collision characteristic in terms of the operating conditions, and to prove that those characteristic can be equivalent in both erosion and breakage simulations. The main difference between breakage and erosion CFD-DEM simulations, which the data was collected from, is the materials and the operating conditions. When examining the comparison between breakage or erosion collision characteristics, it turned out that the collision characteristics could be derived as non-dimensional parameters, and they share similar trends for different conveying conditions. One distinct feature that was found is that the non-dimensional impact velocity could be derived as the actual impact velocity divided by the median impact velocity. In addition, the median impact velocity was found to correlate well with the axial velocity of the particles, which means that if the axial velocity is known then so does the median impact velocity. The essence of such analysis is that the actual impact velocity could be predicted in terms of the conveying conditions, without depending on the results from CFD-DEM simulations.
Another contribution of this work is presenting for the first time the methodology of combination between breakage and erosion. When observing at an impact of a discrete particle with a surface, both parties are damaged. The purpose of our analysis is to provide a scheme that recognize which of the bodies was damaged, and what mechanism of erosion or breakage occurs. Furthermore, this recognition allows to quantify with a proper model how much the surface was eroded, if any, or was the particle fractured and broken or not.
Implementing this methodology to the combined ODBA and ODEM, with the analyzed collision characteristics allows a complete modeling of simultaneous breakage and erosion. This features a novel modeling to a phenomenon that was not addressed before for the best of our knowledge.