# Computer 3D Simulation of Proppant Particles
## 1 Introduction  
Currently, the mainstream idea in research on the physical properties of proppants is physical experiments or a combination of physical experiments and numerical simulation. The simulation of proppant particles is generally implemented using auxiliary software such as DEM (Altair EDEM v2.7) and CFD (Autodesk CFD 2021). However, there is almost no one focused on the computer simulation of hydraulic fracturing proppant particles. [PERSON] et al. [1] used DEM software to simulate the compaction state of proppant particles under pressure. The pore structure of the proppant filling layer simulated by DEM was extracted and inputted into the LB (Lattice Boltzmann) simulator as an internal boundary condition for fluid flow. Therefore, the transport and precipitation mechanisms of proppant particles within the numerical framework of DEM-LB were studied. A continuous medium-fine particle deposition model was used to fit the numerical results of pore-scale particle tracking deposition, thereby determining the macro deposition coefficient. The effects of fine particle size, proppant particle size heterogeneity, and effective stress on the macro deposition coefficient were studied. Similarly, scholars have conducted research on the properties of particles such as heat conduction, force conduction, and particle breakage under effective stress and microstructure through DEM [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. As early as 1611, [PERSON] began to study the arrangement of spheres and proposed the densest accumulation of spheres, known as the [PERSON] conjecture [13]. This conjecture is about the best sphere-loading method in three-dimensional Euclidean space. That is, the sphere-loading method with the smallest gap left. This conjecture holds that under the condition that each sphere has the same size, the density of the sphere without any loading method is greater than face-centered cubic and hexagonal densest packing methodwith a density slightly greater than 74%. The microstructure of the proppants studied in this paper is similar to the [PERSON] conjecture, but there are also significant differences. In order to simulate the placement of particles, it is assumed that the particles are circular and are not intersecting, overlapping, or suspended. There are three main paving methods shown in Figure 1. Figure 1a shows the entire two-dimensional space that starts from the center circle and gradually diffuses outward by placing new circles tangent to it [14]. This method can avoid the intersection, overlap, and suspension of particles. However, the effect simulated by this method is not suitable for the given two-dimensional rectangular space. Figure 1b shows placing a circle inside the boundary of the two-dimensional space and gradually advancing towards the middle until the entire space is filled [15; 16; 17]. This method can obtain a two-dimensional rectangular space with good filling effect. However, there will be large pores in the middle of the space, making the particles in this part appear linear in suspension. The stacking method shown in Figure 1c is to place particles at the bottom of the two-dimensional space, filling the bottom space from left to right. In addition to the bottom layer, particles are gradually stacked in the same manner from bottom to top until they fill the entire two-dimensional space [17; 18; 19; 20]. However, this method does not take into account the principle that the placement of particles is based on the minimum distance from the bottom edge. Although it is possible to ensure that there is no intersection, overlap, or suspension between particles, there will be large residual space at the top. The intuitive result is that the entire two-dimensional space is not fully filled with particles. Due to the complexity of particle accumulation, most scholars mainly use simulation software for the two-dimensional simulation of particles. There are very few studies on the three-dimensional simulation of proppant particles.