Theoretical Solutions to The Problem of Seepage and Consolidation in Saturated Clay Based on The Spatial Axisymmetric Model

The series solutions to the problem of spatial axisymmetric consolidation are deduced under non-homogeneous boundary conditions. Firstly, differentiable step function is introduced to construct the homogeneous operation function. Secondly, the operation function is used to superimpose the non-homogeneous boundaries to obtain homogeneous boundaries, non-homogeneous fundamental equation and new initial condition. Finally, the method of variables separation is used to construct the eigenfunction, and due to the mathematical justification of complete orthogonality of the eigenfunction, the series expansions of the fundamental equation and initial condition are carried out to obtain solutions for the seepage and consolidation in saturated clay with a borehole boundary. The correctness of the theoretical solutions are verified by the strict mathematical and mechanics derivation and the law of space-time variation in seepage flow.

Thermal Performance of Cemented Paste Backfill Body Considering Its Slurry Sedimentary Characteristics in Underground Backfill Stopes

The combined mine backfill–geothermal (CMBG) system can be used to effectively extract geothermal energy by installing a heat exchange tube (HET) in the underground backfilled stopes of mines, which can be used as the heat supply for buildings in mines and the surrounding areas. The efficient performance of this system strongly depends on the thermal exchange process between the HET and its surrounding cemented paste backfill body (CPB). In this study, a validated simulation model is established to investigate the heat exchange performance of CPB, in which the nonuniformly distributed thermal properties in CPB are fully considered. The results indicate that the increase in the porosity has a negative effect on the heat exchange performance of CPB. With the increase in the porosity, the decreased rate of the conductive heat transfer in CPB could be up to approximately 18%. In conditions with seepage flow, the heat transfer capacity of CPB could be effectively improved. Generally, a higher hydraulic conductivity corresponds to a higher heat transfer performance of CPB. When the seepage velocity rose from 2 × 10−6 to 6 × 10−6 m/s, the thermal conductivity of CPB achieved a 114% increase from 1.843 to 3.957 W/(m·K). Furthermore, it was found that the thermal energy accumulates along the seepage flow direction, enhancing the thermal influencing radius of the HET in this direction. Thus, the arrangement of HETs should fully take into account the seepage flow effect. This proposed simulation model could provide a reference for parameter determination and optimization of CMBG systems.

Stability of a Buoyant Oldroyd-B Flow Saturating a Vertical Porous Layer with Open Boundaries

The performance of several engineering applications are strictly connected to the rheology of the working fluids and the Oldroyd-B model is widely employed to describe a linear viscoelastic behaviour. In the present paper, a buoyant Oldroyd-B flow in a vertical porous layer with permeable and isothermal boundaries is investigated. Seepage flow is modelled through an extended version of Darcy’s law which accounts for the Oldroyd-B rheology. The basic stationary flow is parallel to the vertical axis and describes a single-cell pattern where the cell has an infinite height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. This analysis is performed numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are evaluated for different retardation time and relaxation time characteristics of the fluid. The study highlights the extent to which the viscoelasticity has a destabilising effect on the buoyant flow. For the limiting case of a Newtonian fluid, the known results available in the literature are recovered, namely a critical value of the Darcy–Rayleigh number equal to 197.081 and a corresponding critical wavenumber of 1.05950.

Study on Flow Model and Flow Equation of Shale Gas Based on Micro Flow Mechanism

Shale flow has microscale effects, and the flow is more complex. In this paper, the flow model and flow equation which can be used in the analysis of shale gas flow is established,which is based on the single nanotube model and combined with pore throat test results of the shale core by high-pressure mercury injection, and calculated the contributions of seepage, diffusion, transition flow and free molecular flow to shale gas flow. The contributions of seepage and diffusion were over 95%, and seepage and diffusion were the main flow patterns. Then, a coupled flow model and the coupled flow equation of shale gas with seepage and diffusion were established, which proposed a calculation method of shale permeability and diffusion by relationship between flow pressure and shale gas flow rate, and finally shale gas flow experiments were carried out and analyzed. The results show that the shale gas flow model and the flow equation established in this paper can describe shale gas flow very well. The shale gas flow rate is composed of seepage flow rate and diffusion flow rate, and the seepage flow rate is proportional to the pseudo pressure difference and is proportional to the pressure square difference at low pressure. The diffusion flow rate is proportional to the difference in shale gas density and is proportional to the pressure difference at low pressure. With shale gas reservoir pressure drops, the proportion of diffusion flow increases. The research results enrich the understanding of shale gas flow; they also have certain reference significance to the development of shale gas reservoirs.

The Dynamic Change and Effect of Rainfall Induced Groundwater Flow

This study aims to analyze the groundwater flow changes caused by rainfall and its influence on slope stability. Taking the slope in Dingjiafen, Chuxiong, Yunnan, China as the study area, the study monitored the data of rainfall and drew upon the calculation module of ArcGIS to predict the change of the groundwater flow and water level fluctuation in the soil. In this way, the visual simulation of groundwater flow distribution of the slope was realized; and the influence of groundwater flow distribution caused by rainfall seepage on the slope’s stability was also analyzed. The results indicate that: (1) the rainfall recharge rate is affected by the thickness of the soil layer, the slope, the rainfall intensity, and the initial water content of the soil; (2) the seepage flow of rainfall in per unit time is positively correlated with the soil layer thickness of the slope; (3) the groundwater is repeatedly raised, maintained, and dissipated by periodic rainfall which destroys the structure of the soil; and (4) the rainfall reduces the cohesion and internal friction angle of the soil resulting in the “muddy water softening effect” in the weak zone.