Yingke Liu

Unsteady Flows of a Generalized Fractional Burgers’ Fluid between Two Side Walls Perpendicular to a Plate

The unsteady flows of a generalized fractional Burgers’ fluid between two side walls perpendicular to a plate are studied for the case of Rayleigh-Stokes’ first and second problems. Exact solutions of the velocity fields are derived in terms of the generalized Mittag-Leffler function by using the double Fourier transform and discrete Laplace transform of sequential fractional derivatives. The solution for Rayleigh-Stokes’ first problem is represented as the sum of the Newtonian solutions and the non-Newtonian contributions, based on which the solution for Rayleigh-Stokes’ second problem is constructed by the Duhamel’s principle. The solutions for generalized second-grade fluid, generalized Maxwell fluid, and generalized Oldroyd-B fluid performing the same motions appear as limiting cases of the present solutions. Furthermore, the influences of fractional parameters and material parameters on the unsteady flows are discussed by graphical illustrations.

An investigation of the key factors influencing methane recovery by surface boreholes

The paper deals with key factors influencing surface borehole gas drainage. Herein, the surface borehole drilled through the overburden of gobs, which was commonly operated in China, has been investigated. By building a mathematical model, the literature probed into the issue that how such factors as permeability coefficient and pressure of coal seams affected the flow of pure methane under standard conditions. The results indicated that a key factor was the distance between mining face and borehole (reflecting the gas permeability coefficients of overlying coal seams and gobs). The data measured from surface gas drainage practice at Wulan Coal Mine verified the conclusions of the theoretical research.

An anomalous subdiffusion model with fractional derivatives for methane desorption in heterogeneous coal matrix

Methanedesorption in coal matrix is one of the fundamental gas transport processes during coalbed methane extraction, the mechanism of which is commonly described by Fickian diffusiontheory. Here, an anomalous subdiffusion model with fractional derivatives is developed to explore the methanedesorption in coal matrix with a highly heterogeneous pore structure. Numerical simulations reproduce the volume fraction of gas desorbed over the entire timescale of experimental desorption. It is suggested that the diffusion of methane in heterogeneous coal matrix may obey the anomalous time and space subdiffusion, rather than Fickian second law. The physical reason is perhaps due to the basic topological complexity inherent to porous coal matrix and the strong adsorption effect of coal on methane molecules.

Numerical modeling of gas flow in deformed well casing for the prediction of local resistance coefficients pertinent to longwall mining and its engineering evaluation

During gob gas venthole (GGV) drainage, the borehole casing is to withstand various forces induced by the movement of overlying strata of the longwall panel so as to become deformed. Tensile deformation, compressive deformation and shear deformation are the most typical deformation modes of the casing. Once deformation of the casing occurs, the flow resistance of gas in casing increases sharply, which causes the volumetric flow of gob gas recovery to decrease. Through an analysis of the cross-sectional shapes of three typical casing deformations, the characteristic parameters of each kind of deformation were determined. In addition, a numerical simulation of the gas flow field was carried out using the four casing models, i.e., one without deformation and three with typical deformations. The changing characteristics of the local resistance coefficient of the deformed casing with varying characteristic parameters of corresponding deformation were analyzed. In addition, this study compared the local resistance coefficient of casings for the three deformation models and deduced that the local resistance coefficient resulting from shear deformation is the largest. Furthermore, by considering the flow field characteristics of gas in the three models, this study determined that the vortex induced by the separation of the boundary layer in the areas of deformation was a major cause of local resistance. Finally, a method for predicting the characteristic parameter values of casing deformation was proposed, and a case study was performed. The research results provide a theoretical basis for predicting the influence of casing deformation on GGV drainage.

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

Thermal convection at the steady state for high Rayleigh number in a rotating porous half space is investigated. Taking into account the effect of rotation, Darcy equation is extended to incorporate the Coriolis force term in a rotating reference frame. The velocity and temperature fields of thermal convection are obtained by using the homotopy analysis method. The influences of Taylor number and Rayleigh number on the Nusselt number, velocity profile, and temperature distribution are discussed in detail. It is found that the Nusselt number decreases rapidly with the increase of Taylor number but tends to have an asymptotic value. Besides, the rotation can give rise to downward flow in contrast with the upward thermal convection.

Effect of magmatic intrusion on coal pore characteristics and fractal research

The pore characteristics in magmatic intruded coals are closely related to the absorption-desorption and the flow of Coalbed Methane (CBM) in coal seams. Coal samples with different degrees of magmatic intrusion are tested using the method of mercury intrusion porosimetry (MIP). A number of parameters, such as the pore diameter, the volume, the connectivity and the specific surface area, are investigated. In addition, the fractal theory is introduced as a new approach to characterize the pore characteristics in intruded coals by calculating the fractal dimensions. The correlation between the fractal dimension and the inherent moisture content is also discussed. The results indicate that 1) when the coal approaches the magma, the pore size, the pore volume, the open pores and pore connectivity increase, but the total specific surface area exhibit decline trends; 2) the calculated fractal dimension can demonstrate the above characteristics; 3) a significant relationship between the inherent moisture content and the fractal dimension can be established. The research findings in this paper provide a useful fundamental knowledge to guide future studies of CBM development or gas outburst for intruded coals.