A review of shale pore structure evolution characteristics with increasing thermal maturities

   Pore structure has a significant effect on the occurrence state of shale hydrocarbons and the hydrocarbon storage capability of shale reservoirs. Consequently, it is quite meaningful to clarify the shale pore structure evolution characteristics for understanding the migration and enrichment mechanisms of hydrocarbons within shale reservoirs during different geological stages. The abundant existence of organic matter within shales complicates the shale pore structure evolution process by hydrocarbon generation, migration and cracking. Many studies have been conducted to reveal the shale pore structure evolution characteristics and the controlling factors. Basically, these studies could be divided into two categories based on the sample source: comparing the pore structure of natural shale samples with different thermal maturities; obtaining shale samples with different thermal maturities by conducting thermal simulation experiments on low-mature shale samples and comparing the pore structure of these simulated shale samples. However, no consistent viewpoint on shale pore structure evolution has been reached. This review presents the state of the art of shale pore structure evolution studies. It is widely recognized in the literature that both the inorganic and organic diagenesis control the shale pore structure evolution process. However, it is found that the shale pore structure evolution models proposed in the literature were largely dependent on the samples used. And it is recommended to conduct the two categories of studies simultaneously in order to obtain more reliable shale pore structure evolution characteristics in future investigations.Cited as: Gao, Z., Fan, Y., Xuan, Q., Zheng, G. A review of shale pore structure evolution characteristics with increasing thermal maturities. Advances in Geo-Energy Research, 2020, 4(3): 247-259, doi: 10.46690/ager.2020.03.0

Entropy and weak solutions in the thermal model for the compressible Euler equations

Among the existing models for compressible fluids, the one by Kataoka and Tsutahara (KT model, Phys. Rev. E 69, 056702, 2004) has a simple and rigorous theoretical background. The drawback of this KT model is that it can cause numerical instability if the local Mach number exceeds 1. The precise mechanism of this instability has not yet been clarified. In this paper, we derive entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method for the KT model. Numerical examples are also given, which are consistent with the above theoretical arguments, and show that the entropy condition is not fully guaranteed in KT model. The negative entropy may be the inherent cause for the non-physical oscillations in the vicinity of the shock. In contrast to these Karlin's microscopic entropy approach, the corresponding subsidiary entropy condition in the LBM calculation could also be deduced explicitly from the macroscopic version, which provides some insights on the numerical instability of the lattice Boltzmann model for shock calculation.Comment: 27 pages,6 figure

Exact solution of the Bose Hubbard model with unidirectional hopping

A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact eigenvalue spectrum can be obtained by solving these equations. The distribution of Bethe roots reveals the presence of a superfluid-Mott insulator transition at the ground state, and the critical point is determined. By adjusting the boundary parameter, we demonstrate the existence of non-Hermitian skin effect even in the presence of interaction, but it is completely suppressed for the Mott insulator state in the thermodynamical limit. Our result represents a new class of exactly solvable non-Hermitian many-body systems, which have no Hermitian correspondence and can be used as a benchmark for various numerical techniques developed for non-Hermitian many-body systems.Comment: 6+8 pages, 2+6 figure