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A model for real gas flow in shale gas matrices is proposed and consists of two main steps: (a) developing a microscopic (single pore) model for a real gas flow by generalizing our previously reported Extended Navier-Stokes Equations (ENSE) method and (b) by using fractal theory concepts, up-scaling the single pore model to the macroscopic scale. A prominent feature of the up-scaled model is a predictor for the apparent permeability (AP). Both models are successfully validated with experimental data. The impact of the deviation of the gas behavior from ideality (real gas effect) on the gas transport mechanisms is investigated. The effect of the structural parameters (porosity Ф, the maximum pore diameter Dmax, and the minimum pore diameter Dmin) of the shale matrix on the apparent permeability is studied and a sensitivity analysis is performed to evaluate the significance of the parameters for gas transport. We find that (1) the real gas transport models for a single pore and porous shale matrix are both reliable and reasonable; (2) the real gas effect affects the thermodynamic parameters of the free gas and the adsorption and transport capacity of the adsorbed gas; (3) the real gas effect decreases the effective permeability for convective flow and surface diffusion; i.e., the derivation degree of the effective permeability for bulk diffusion and Knudsen diffusion increases with increasing pressure but presents a bathtub shape when the pore diameter is smaller than 10 nm; and (4) the apparent permeability increases with Ф, Dmax, and Dmin. It is more sensitive to Dmax, followed by the porosity. Dmin has a minor impact. © 2016 American Institute of Chemical Engineers AIChE J, 2016

An analytical model for gas transport in shale media is proposed on the basis of the linear superposition of convective flow and Knudsen diffusion, which is free of tangential momentum accommodation coefficient. The present model takes into the effect of pore shape and real gas, and is successfully validated against experimental data and Lattice–Boltzmann simulation results. Gas flow in noncircular nanopores can be accounted by a dimensionless geometry correction factor. In continuum-flow regime, pore shape has a relatively minor impact on gas transport capacity; the effect of pore shape on gas transport capacity enhances significantly with increasing rarefaction. Additionally, gas transport capacity is strongly dependent of average pore size and streamline tortuosity. We also show that the present model without using weighted factor can describe the variable contribution of convective flow and Knudsen diffusion to the total flow. As pressure and pore radius decrease, the number of molecule-wall collisions gradually predominates over the number of intermolecule collisions, and thus Knudsen diffusion contributes more to the total flow. The parameters in the present model can be determined from independent laboratory experiments. We have the confidence that the present model can provide some theoretical support in numerical simulation of shale gas production. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2893–2901, 2016

In article number https://doi.org/10.1002/advs.201902043, Quan Xu, Yu Tian, Zhenhai Xia, and co‐workers present how mussel cuticle is a functionally‐graded material with high stiffness, extensibility, and self‐healing capacity and oxygen absorbs on metal ions, weakening the iron‐catecholate bonds in the cuticle and collagen core, but this process can be reversed by sea water.

Metal‐containing polymer networks are ubiquitous in biological systems, and their unique structures enable a variety of fascinating biological behaviors. Cuticle of mussel byssal threads, containing Fe‐catecholate complexes, shows remarkably high hardness, high extensibility, and self‐healing capability. Understanding strengthening and self‐healing mechanisms is essential for elucidating animal behaviors and rationally designing mussel‐inspired materials. Here, direct evidence of Fe3+ and Fe2+ gradient distribution across the cuticle thickness is demonstrated, which shows more Fe2+ inside the inner cuticle, to support the hypothesis that the cuticle is a functionally graded material with high stiffness, extensibility, and self‐healing capacity. The mechanical tests of the mussel threads show that both strength and extensibility of the threads decrease with increasing oxygen contents, but this property degradation can be restored upon removing the oxygen. The first‐principles calculations explain the change in iron coordination, which plays a key role in strengthening, degradation, and self‐healing of the polymer networks. The oxygen absorbs on metal ions, weakening the iron‐catecholate bonds in the cuticle and collagen core, but this process can be reversed by sea water. These findings can have important implications in the design of next‐generation bioinspired robust, highly extensible materials, and catalysis., Evidence of Fe3+ and Fe2+ gradient distribution across the cuticle thickness of bypass thread is provided, which supports that the cuticle is a functionally graded material with high stiffness, extensibility, and self‐healing capacity. The oxygen absorbed on metal ions can weaken the iron‐catecholate bonds in the cuticle and collagen core, but cuticle can heal itself in sea water.