Discrete Element Method (DEM) is attracting increasing interest for the simulation of Drilling fluid flow, much of the previous DEM modelling has considered two-dimensional (2D) flows and used circular solids particles in drilling fluid. The flow of particulate materials plays a critical role in dilling mud processes.

The Discrete Element Method (DEM) derives from the 1970s, which is a kind of highly non-linear numerical method. It can describe the movement on a particle scale, which can help the researchers have an insight into understanding the complex screening process and developing the motion law of particles on the screen. DEM has been applied widely in the study of particle flow in mining industry and agriculture vibration screen and turned out to be very useful in understanding the fundamentals of the screening process But the differences between these kinds of vibration screens and shale shakers are huge, which include structural characters, particle content and sizes, work

environment and working parameters and so on. So the research results on vibration screens used in the other fields are not suitable for petroleum shale shaker. In this work, we adapt the DEM model for this specific shale shaker used in petroleum industry. The mathematical model of solid particles moving on the screen has been built, based on which the simulation conditions are proposed. The changing laws of particles conveying speed and filter ratio of shale shakers had been achieved, which will be helpful in the structural design and practical work of shale shaker.

In discrete element simulation of granular flows the collisional interactions of particles with each other and with their environment are detected and modelled using a suitable contact force law. Equations of motion are then solved for the particle motions and for the motion of any boundary objects with which the particles interact.

The three key parts of the DEM algorithm are:

- A search grid is occasionally used to construct a particle near-neighbour interaction list. Using only particle pairs in the near neighbour list reduces the force calculation to an OðnÞ operation, where n is the total number of particles. Using such methods allows very large problems to be solved. Depending on the size distribution problems with up to 250,000 particles are now easily solved on single processor workstations.
- The collisional forces for each collision are estimated using the spring-dashpot model for each pair of particles in the near-neighbour list.
- All the collisional and other forces acting on the particles are summed and the resulting equations of motion.

## Size separation by a vibrating screen

Vibrating screens are commonly used to separate particles according to their size. Separation is a critical step in most mineral processing operations and the efficiency of this separation has direct implications for both mineral recovery levels and costs.

Particle segregation by one level of a screen is presented here. We consider an 800 mm square section of a screen,10 mm thick,containing a 12 × 12 array of 40 mm square holes. The screen is covered by a mixture of 8000 spherical particles,with sizes uniformly distributed between 10 and 60 mm,to a depth of 400 mm. Periodic boundaries have been applied at each of the sides of the

screen to simulate a screen having a much larger area. The screen is oscillated upwards and to one side with a frequency of 3 Hz,a vertical amplitude of 50 mm,and a sideways amplitude of 20 mm. The oscillations in the two directions are in phase so that the screen moves sinusoidally in a straight line inclined at 22 to the vertical.

Fig. 1 shows the screen at two times during the vibration cycle. As it moves upwards,smaller particles move freely through the holes in the screen. The flow of small particles continues throughout the screen’s upward movement, although the rate declines slightly. As the screen moves down,the particles lag behind and loose contact with the screen. The flow of small particles through the screen abates until the screen reaches its lowest point and the particles crash back into the screen producing a surge of smaller particles through the screen. This behaviour leads to a regular pulsing flow of fines from the screen. Also observed in Fig. 1 is the well-defined size segregation of the material on top of the screen,with the larger (dark grey) particles being dominant near the upper surface. The progressive percolation of small particles from the upper

regions to the region adjacent to the screen ensures a continual supply of fines to flow through the screen. The ability of DEM to simulate this type of flow demonstrates the method’s potential for use as a design tool for such industrial particle handling equipment.

## Influence of Screen Slope

The screen slopes was important feature of shale shaker while keeping the other parameters unchanged. The influence results are shown in (Fig. 2). On the one hand, the screen slopes up gradually as screen slope α varies from

-2° to 2°. Particles will accumulate around the inlet, and the filter ratio will increase. On the other hand, the angle change is very small, so the variation of filter ration is very slight.

Among the three parameters, vibration frequency has the greatest impact on filter ratio. Increasing vibration frequency can not only improve the conveyance velocity of particles but also decrease the filter ratio. However it’s restricted by the strength requirement. The vibration intensity increases sharply along with vibration frequency, which puts forward higher requirements on the strength of the shale shaker. Therefore, when the workers want to improve the working performance of shale shakers by increasing the vibration frequency, the structure strength requirement of shale shaker should be taken into consideration.