The mechanical and transport properties of a Bentheim sandstone are studied both experimentally and numerically. Three classical classes of loads are applied to a sample whose permeability is measured. The elasticity and the Stokes equations are discretized on unstructured tetrahedral meshes which precisely follow the deformations of the sample. Numerical results are presented, discussed, and compared to the available experimental data.

Stimulated and propped fractures provide the conductive pathways in low matrix permeability rocks. We study the impact of fracture aperture and proppant size and fraction on the effective transmissivity of a stimulated fracture filled with a partial monolayer of proppant grains. The proppant grains are treated as circular cylindrical obstacles, and the fracture walls are planar. The key geometric parameters are the obstacle fraction f and the ratio between the fracture aperture and the obstacle diameter α. We use three‐dimensional Stokes flow numerical simulations to demonstrate that the fracture flow model given by the Reynolds equations may largely overestimate the flow rate. To circumvent the inability of the Reynolds model to fulfill the no‐slip boundary condition at the rims of the obstacles, we use the Brinkman flow model adapted to the case of fracture flow. The relative difference between the effective transmissivities computed with the Stokes and Brinkman models for systems with multiple obstacles is below 10% for fractions up to 0.5. We use the Brinkman model to study the effective transmissivity of a plane‐walled fracture with circular cylindrical obstacles. Systematic numerical simulations show that the normalized effective transmissivity is predominantly dependent on f and α, and the effects of obstacle ordering are minor. The presented numerical results can be used by petroleum engineers for estimating transmissivities of propped fractures under in situ conditions. The model can also be applied to microfluidic systems and for deriving first‐order estimates of the effective transmissivity of rough‐walled, natural fractures with load‐bearing contact areas.

We use Lattice Boltzman Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two-and three-dimensional Stokes equations, and a 2.5D Stokes-Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes-Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes-Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes-Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8%. The differences between the 3D Stokes and 2.5 Stokes-Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes-Brinkman model.

This article describes the influence of dynamic bridging in the unloading of a hopper at a processing plant on the grain flow homogeneity in a convective-microwave zone. In accordance with calculation methods for unloading hoppers, the parameters of the hopper unit and those of the outlet hole insuring that grain flows without static bridging formation is defined. It was found that moisture content fluctuations do not affect the process of grain transport. The equation for dynamic bridging rise depending on its position on the vertical axis of the unloading hopper has been deduced that enables the definition of the inhomogeneity of grain flow from its outlet hole. Calculations show that a certain inhomogeneity occurred between the right and the left parts of the unloading hopper in relation to its vertical axis in the course of grain discharging. This effect underlies the inhomogeneity of grain processing and reduction of its effectiveness in convective-microwave zones. An experimental model of unloading the hopper has been manufactured in order to perform investigational studies. The results of studies have completely confirmed the hypotheses. It has been found that dynamic bridge formation in unloading of the hopper results in the inhomogeneity of grain flow in convective-microwave zone.