Numerical Simulation Study of Proppant Transport in Cross Fractures

Hydraulic fracturing technology is an important means to stimulate unconventional reservoirs, and the placement morphology of proppant in cross fractures is a key factor affecting the effect of hydraulic fracturing. It is very important to study the proppant transport law in cross fractures. In order to study the proppant transportation law in cross fractures, based on the CFD-DEM method, a proppant transport model in cross fractures was established. From the two aspects of the flow field in the fractures and the morphology of the proppant dune, the influence of the natural fracture approach angle, the fracturing fluid viscosity and injection rate on the proppant transport is studied. Based on the principle of hydropower similarity, the conductivity of proppant dune under different conditions is quantitatively studied. The results show that the natural fracture approach angle affects the distribution of proppant and fracturing fluid in natural fractures, and further affects the proppant placement morphology in hydraulic fractures and natural fractures. When the fracturing fluid viscosity is low and the displacement is small, the proppant forms a "high and narrow" dune at the entrance of the fracture. With the increase of the fracturing fluid viscosity and injection rate, the proppant settles to form a "short and wide" placement morphology. Compared with the natural fracture approach angle, the fracturing fluid viscosity and injection rate have a more significant impact on the conductivity of proppant dune. This paper investigated the proppant transportation in cross fractures, and quantitatively analyzes the conductivity of proppant dunes with different placement morphology. The results of this study can provide theoretical guidance for the design of hydraulic fracturing.

Study of Interactions between Induced and Natural Fracture Effects on Hydraulic Fracture Propagation Using a Discrete Approach

The interaction mode of induced fracture and natural fracture plays an important role in prediction of hydraulic fracture propagation. In this paper, a two-dimensional hydromechanical coupled discrete element model is first introduced in the framework of particle flow simulation, which can well take into account mechanical and hydraulic properties of rock samples with natural fracture. The model’s parameters are strictly calibrated by conducting numerical simulations of uniaxial compression test and direct tensile and shear tests, as well as fluid flow test. The effectiveness of coupled model is also assessed by describing hydraulic fracture propagation in two representative cases, respectively, rock samples with and without preexisting fracture. With this model in hand, the effects of interaction between induced and natural fractures with different approach angles and differential stresses on fluid injection pressure and fracture propagation patterns are investigated and discussed. Results suggest that the interaction modes mainly involve three basic behaviors including the arrested, captured with offset, and directly crossing. For a given differential stress, the captured offset of hydraulic fracture by natural fracture gradually decreases with the approach angle increase, while for a fixed approach angle, that captured offset increases with differential stress decrease.

EXPERIMENTAL STUDIES ON A PLOW WITH A DISK DISINTEGRATOR

Studies were conducted on the operation of a plow with a disk disintegrator in a unit with an MTZ-82 tractor on black soil with a flat relief on soybean stubble with the amount of plant residues from 300 to 400 g/m2. During the research, the following parameters were changed: the disk approach angle, the disk section installation height, and the tractor speed. As a result of the study, it was found that at the speed of a plow with a disk disintegrator from 4 to 5 km/h, the depth of plant residues embedding is maximum and ranges from 15 to 19 cm, while fuel consumption becomes minimal in the range from 18 to 30 kg/ha.

Obtaining Experimental Values of the Uniformity of Seed Distribution by Multivariate Regression Analysis

One of the key factors affecting agricultural productivity is the availability of technical means that include machine and tractor units of agricultural enterprises. The production volume of the plant growing industry depends on high yields that can be achieved by high-quality sowing, which implies the optimal seed placement and sowing depth. Thus, the modernization of existing seeding machines and the creation of new ones that ensure the optimal seed placement is an urgent task. This study aimed to develop a coulter for uniform seed distribution along the furrow length. The object of the study was uniform sowing patterns for grain crops based on the optimal parameters of the proposed working unit of the seeding machine obtained by multivariate regression analysis. A symmetric orthogonal compositional plan of the second order was chosen as a model. The criterion for optimization of the geometric parameters of the developed coulter was the uniformity of seed distribution along the furrow length. The following parameters of the proposed coulter were changed: the cut length of the outer side of the rectilinear profile of the lower edge of the rack varied within 20–80 mm (L), and the approach angle in the horizontal plane (α) and the roll angle in the vertical plane (β) varied within 3–28 deg. The study yielded the regression equation for constructing the response surfaces. The analysis of the response surfaces showed that the optimal parameters for uniform seed distribution along the furrow length can be achieved at the approach angle α=250, the roll angle β=150, and the cut length of the lower edge of the rack L=50 mm. Keywords: Coulter, sowing, grain, quality, distribution uniformity, multivariate experiment

Numerical Simulation Research on the Interactive Propagation of Hydraulic Fractures and Natural Fractures

In order to study the fracture propagation behavior after the interaction between hydraulic fractures and natural fractures, the cohensive unit of Abaqus finite element software is used to simulate the influence of natural fractures in the rock on the propagation behavior of hydraulic fractures. The simulation results show that when the approach angle is kept constant, as the in-situ stress difference increases, hydraulic fractures are more likely to penetrate the natural fractures and expand along the direction of the maximum horizontal principal stress; while the stress difference remains the same, as the approach angle increases, hydraulic fractures are easier to penetrate natural fractures and expand along the direction of maximum horizontal principal stress. When the approach angle is kept constant, as the tensile strength of natural fractures increases, hydraulic fractures are more likely to penetrate the natural cracks and expand along the direction of the maximum horizontal principal stress; while the tensile strength of natural cracks remains unchanged, as the approach angle increases, the probability of forming a complex fracture network between hydraulic fractures and natural fractures is reduced, and it is easier to penetrate the natural fractures and expand along the direction of the maximum horizontal principal stress.

Proposing a New Evaluation Method in Si Wafer Rotary Grinding

Although there have been several studies on machining of semiconductor materials, most of them are concerned with abrasive finishing (such as chemical-mechanical polishing, mechanical polishing and lapping), and only a few have reported on optimizing rotary grinding conditions (such as the grinding wheel rotational speed, wafer rotational speed, wheel diameter, wafer diameter, and feed rate). In this study, to gain further insight, we define a dimensionless number and use it to evaluate our experimental results. This dimensionless number — called the “grain approach angle” — is the ratio of the grain running length of the machined wafer surface and the depth of cut due to grain during the grain running time. For this study, our evaluation coefficients are taken to be surface roughness, grinding force, and grinding ratio. We found it more suitable to use the grain approach angle rather than a previously defined dimensionless number (which was evaluated as the ratio of the wheel rotational speed to the wafer rotational speed). We also found that, by using the grain approach angle, trends in surface roughness exhibited invariant similarities under varying conditions.