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The percolation properties and permeability of a group of anisotropic three-dimensional fracture networks are studied numerically. Finite-size scaling is used to extrapolate the percolation thresholds of infinite networks in three spatial directions, i.e., X , Y , and Z directions. The influence of the angular dispersion parameter of fracture orientations on percolation thresholds is analyzed. In this analysis, we considered a family of fractures in a three-dimensional space that are oriented around the Z axis based on the Fisher distribution. We revealed that increased anisotropy leads to decreased percolation thresholds in both X and Y directions, and in these two directions percolation thresholds in anisotropic networks demonstrate a declining trend as anisotropy goes up. However, in the Z direction the trend is the opposite. The fracture networks are triangulated via an advancing front technique and the macroscopic permeability of the networks is determined by solving the two-dimensional Darcy equation in each fracture. We found that the macroscopic permeability in the X and Y directions is higher than the associated permeability of isotropic fracture networks, and this property for anisotropic networks in the Z direction is lower compared with that of the isotropic case. Furthermore, as the anisotropy of networks increases the differences become more remarkable.

A systematic approach is proposed to design an optimal batch water-using network with centralized regeneration in order to deal with coordination of discontinuous water-using operations with one central continuous regeneration unit during multiple repeated batch cycles. The mathematical formulation in weak forms that readily induces process dynamic expressions is established under the framework of continuous time representation, in which a rigorous dynamic model of a tank is embedded. The freshwater consumption and the regeneration flow rates are minimized by a two-stage optimization approach. The integration of the batch water-using system highlights fixed regeneration flow rates and transitional behaviors from the start-up phase to steady state in multiple batch cycles. Optimal network structures and evolution characteristics of residual water and contaminant concentrations in buffer tanks can be achieved through solutions to the nonlinear programming problems (NLP). Four scenarios, including truly batch and semicontinuous water-using systems in both multiproduct and multipurpose batch plants, are presented to demonstrate the applicability of the proposed approach.

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During running-in period, the friction coefficient and roughness profile of contacting elements experience drastic changes as a result of asperities deformation and wear. These transient changes affect the steady-state performance of mechanical elements such as gears, cam followers, and bearings. An experimental study on the effect of running-in operating conditions on the properties of a tribosystem is conducted using a pin-on-disk test rig. Curve-fit relationships are developed based on the experimental data to relate running-in duration, friction coefficient, and running-in weight loss to load, speed, and surface roughness. A model to predict the steady-state friction coefficient in the lubricated contact of pin and disk is developed based on the load-sharing concept.

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