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In lots of reports, improvement of shale percolation ability by shale-hydration has been reported, some researchers even regard low hydraulic fluid flowback rate as an advantage; they mainly focused on inorganic pores and fractures because brittleness of inorganic minerals decides the fracturing effects, but organic pores occupy large proportion of shale pores. In order to discover the moisture influence on organic pores, we prepare 4 samples by adjusting water content reaching 9.37%, 35.97%, 61.6%, and 80.45% and observe and quantitatively analyze 10,343 pore changes before and after processing of the 4 samples through SEM and image processing software, respectively, meanwhile, match the incremental water invasion rate curve with the dry pore size distribution curve. We also compare the water invasion mass of normal shale sample and organic partially removed sample. This paper first visually observes and counts the influence of hydration on organic shale pores through analysis of pore number, diameter, kurtosis, median, area, and characteristic lengths; discovers hydration and dehydration jointly cause the expected changes; the whole procedure contains two opposite mechanisms, pore closure or deformation caused by squeeze and enlarged pores or newborn fractures caused by water flush. Based on experimental and analysis results, conclusions are drawn that organic pores can be influenced by moisture, water flush and clay hydration expansion work jointly, and water flush function is weak when moisture is low, but it becomes stronger with the sufficient moisture. Therefore, sufficient soak time is beneficial to development.

In order to estimate relative permeabilities of brine–gas, a semi-analytical model based on fractal theory is proposed. The model simplifies porous media as treelike nanotubes, the single nanotube’s flow has been branched out into whole pore network of core sample through treelike fractal theory. Two-phase flow description in sole nanotube, based on a setting of gas bubbles pushing continuous water phase ahead, solves pressure drop around brine and gas bubbles by Stokes’ viscous force, Laplace equation and Fairbrother–Stubbs bubble film thickness formula, Bretherton bubble pressure drop. By substituting the other three classic formulas into Bretherton expression, the iteration equation of pressure drop around a single gas bubble is acquired, the number of gas bubbles is multiplied and the gas phase pressure drop is calculated. Through merging small bubbles into a large bubble, the relative permeabilities of two phases can be solved by introducing Poiseuille’s law and Darcy’s law. After getting the fundamental data, pore size distribution data and viscosity of two phases, relative permeability curves can be drawn, revealing comprehensive elements including wettability, fluid viscosity, saturation, morphological characteristics. The calculated curves cross each other on the right half of the [Formula: see text]-axis, meet the features of real production, flowback difficulties of hydraulic liquid and well production dropping quickly, also show identical trend with experimental data. Through a series of sensitivity analysis, to some extent, the influence on relative permeabilities is compared of different fractal models, different film thickness, bubble length, water sorption layer thickness, elastic deformation of pores.

Understanding gas transport in shale matrix is of great significance for reservoir evaluation and gas well productivity. Up to now, numerous transport models were developed based on the hypothesis of homogeneous confined cylindrical nanopores by coupling with multiple mechanisms. In this work, a new transport model is proposed by coupling different transport mechanisms employing the volume fraction of organic matter (OM) instead of the total organic carbon content (TOC). The signature that the OM density is generally lower than the bulk matrix is also considered. The porosity of OM and inorganic matter (iOM) is determined by rock pyrolysis analysis, respectively. Water distribution in OM and iOM pores in the form of water clusters and adsorbed water films is quantified by water adsorption experiments. Gas transport model in moisturized shale matrix pores is then established considering the difference in water distribution. Meanwhile, both of the proposed models are analytical solutions with the hypothesis that the OM and iOM are arranged parallelly. The impacts of different factors on gas transport capacity are analyzed and discussed. Results indicate that the apparent permeability of the shale matrix decreases with the decline of pore radius. For the same pore diameter, the gas transport capacity of OM pores is much greater than that of iOM pores. The apparent permeability decreases with the increasing OM fraction. The irreducible water within the shale matrix can reduce the gas flow capacity considerably, and the apparent permeability is more sensitive to the change of irreducible water saturation at low pressure comparing with that at high pressure. This study sheds fundamental light on the gas transport distinctions in dry and moisturized shale matrix, which provides insights into the development of water-bearing shale gas reservoirs.

This paper presents a new Monte Carlo technique called the equilateral triangular mesh random walk. A major advantage of the method over the classical Monte Carlo techniques, such as the fixed random walk and the floating random walk, is that it is capable of handling Neumann problems which the classical Monte Carlo methods cannot handle. However, the presentation in this paper is limited to the application of the triangular mesh random walk to Dirichlet problems of Laplace's and Poisson's equations. Numerical experiments involving two-dimensional problems confirm the accuracy of the triangular mesh random walk.

The Monte Carlo methods (MCMs) have been applied with great success to the solution of the elliptic differential equation, but none of them in their present form can be used when a mixed boundary condition is involved. To overcome this limitation existing in classical MCMs, a new fixed random walk method, known as the triangular mesh random walk method, is presented for the elliptical problem with mixed boundary condition. This method can be used to solve many electromagnetic field problems. The numerical calculation involving some two-dimensional problems confirms the efficiency of triangular mesh random walk method.

Monte Carlo methods are generally known for solving field problems one point at a time unlike other numerical methods such as the finite difference and finite element methods which provide simultaneously the solution at all of the grid nodes. This work presents an absorbing Markov chain method to solve Poisson's equation with Dirichlet boundary conditions for intractable inhomogeneous problems.

The Markov chain method for solving Laplace's equation with Dirichlet boundary condition has been discussed in a few papers. This paper presents an absorbing Markov chain method to solve Possion's equation with Dirichlet boundary condition. In the Markov chain, the fundamental matrix N defines the transient relationships for a randomly walking particle from state s/sub j/ passing through state s/sub i/ before it reaches the absorbing state. From the fundamental matrix N and the probability matrix R from non-absorbing states to absorbing states, the contributions of boundary points and interior points to the potential of internal points are defined. The absorbing Markov chain method overcomes a major disadvantage of classic Monte Carlo methods that they are only capable of calculating the potential at a single point at a time unlike other numerical methods such as finite difference and finite element methods which provide simultaneously the solution at all the grid nodes. This paper presents an example to show the accuracy of the absorbing Markov chains solution.

With double revolving fields theory and frame transformation both α– βaxis and d–q axis, this paper presents a new equivalent circuit for a single–phase reluctance motor in steady state and discusses various negative sequence circuits. Since there is a new rotor structure with a magnetic bridge, a magnetic barrier and a special rotor magnetic circuit, the variance of two–axis parameters xd, xq with load is considered emphatically while analysing steady state performance. Since each phase parameter on the rotor is not equivalent, this paper presents a method for calculating equivalently concentrated two–axis parameters x2d, x2q, r2d, r2q. The theoretical results presented have been confirmed by experimental work on tested sample machines. The method for studying steady state performance can be generally adapted to any single–phase reluctance motor for all types of rotors.