Study on an Analytical Solution of Gas Seepage Equation Considering the Adsorption Effect

2015 ◽  
Vol 744-746 ◽  
pp. 1654-1661
Author(s):  
Zhi Gang Zhang
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Gas Adsorption ◽  
Development Planning ◽  
Practical Significance ◽  
Coal Bed ◽  
Adsorption Effect ◽  
Gas Seepage ◽  
Standard Solution ◽  
Adsorption Quantity

The functional relationship between rock and coal permeability and gas adsorption quantity has been determined, based on earlier experimental results. Then, by method of mathematical physics, the authors derived an analytical solution for a gas seepage equation in which the adsorption effect has been considered. This analytical solution could be used for developing the theory of Seepage Mechanics and Computational Fluid Dynamics, and for checking and correcting various numerical solutions as a standard solution, and for inspiring various calculating techniques such as difference schemes, grid generation, and others as well. The analytical solution derived in this paper has extremely important practical significance in conducting the arrangement of gas extraction operation in coal mine and the CBM (coal bed methane) development planning.

scholarly journals Experimental Analysis of Pore Structure and Fractal Characteristics of Soft and Hard Coals With Same Coalification

2021 ◽  
Author(s):  
Barkat Ullah ◽  
Yuanping Cheng ◽  
Liang Wang ◽  
Weihua Yang ◽  
Izhar Mithal Jiskani ◽  
...  
Keyword(s):  
Pore Structure ◽  
Adsorption Capacity ◽  
Gas Adsorption ◽  
Hysteresis Loops ◽  
Control Measures ◽  
Practical Significance ◽  
Coal Bed ◽  
Hard Coal ◽  
Pore Surface ◽  
Soft Coal

Abstract Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical significance for coal bed methane and the prevention of dynamic disasters such as coal and gas outbursts. This study investigates the pore structure and fractural characteristics of soft and hard coals using nitrogen and carbon dioxide (N2/CO2) adsorption. Coal samples from Pingdingshan Mine in Henan province of China were collected and pulverized to the required size (0.2-0.25mm). N2/CO2 adsorption tests were performed to evaluate the pore size distribution (PSD), specific surface area (SSA), and pore volume (PV). The pore structure was characterized based on fractural theory. The results unveiled that the strength of coal has a significant influence on pore structure and fracture dimensions. The obvious N2-adsorption isotherms of the coals were verified as Type IV (A) and Type II. The shape of the hysteresis loops indicates the presence of slit-shaped pores. There are significant differences in SSA and PV between both coals. The soft coal showed larger SSA and PV than hard coal that shows consistency with adsorption capacity. The fractal dimensions of soft coal are respectively larger than that of hard coal. The greater the value of D1 (complexity of pore surface) of soft coal is, the larger the pore surface roughness and gas adsorption capacity is. The results enable us to conclude that the characterization of pores and fractures of soft and hard coals is different, tending to different adsorption/desorption characteristics and outburst sensitivity. In this regard, results provide a reference for formulating corresponding coal and gas outburst prevention and control measures.

scholarly journals Effect of temperature on gas seepage characteristic based on coal-gas interaction model

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 661-667
Author(s):  
Yi Xue ◽  
Zhengzheng Cao ◽  
Faning Dang ◽  
Yang Liu ◽  
Mingming He
Keyword(s):  
Gas Adsorption ◽  
Coupled Model ◽  
Interaction Model ◽  
Coal Bed ◽  
Effect Of Temperature ◽  
Coal Gas ◽  
Numerical Result ◽  
Matrix Deformation ◽  
Gas Seepage ◽  
Fully Coupled

The temperature has a significant impact on the coal seam gas extraction. A fully coupled model is established in this study, which takes into account the coal-gas interaction characteristic. The numerical result shows that the coalbed CH4 migratio and transport evolution coal bed CH4 reservoir is not only dependent on the coal matrix deformation, gas pressure and gas adsorption, but also closely related to temperature.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

scholarly journals Changes in Pore Structure of Coal Caused by CS2 Treatment and Its Methane Adsorption Response

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Run Chen ◽  
Yong Qin ◽  
Pengfei Zhang ◽  
Youyang Wang
Keyword(s):  
Pore Structure ◽  
Adsorption Capacity ◽  
Gas Adsorption ◽  
Recovery Process ◽  
Micropore Volume ◽  
Methane Adsorption ◽  
Coal Bed ◽  
Methane Recovery ◽  
Before And After ◽  
Key Issues

The pore structure and gas adsorption are two key issues that affect the coal bed methane recovery process significantly. To change pore structure and gas adsorption, 5 coals with different ranks were treated by CS2 for 3 h using a Soxhlet extractor under ultrasonic oscillation conditions; the evolutions of pore structure and methane adsorption were examined using a high-pressure mercury intrusion porosimeter (MIP) with an AutoPore IV 9310 series mercury instrument. The results show that the cumulative pore volume and specific surface area (SSA) were increased after CS2 treatment, and the incremental micropore volume and SSA were increased and decreased before and after Ro,max=1.3%, respectively; the incremental big pore (greater than 10 nm in diameter) volumes were increased and SSA was decreased for all coals, and pore connectivity was improved. Methane adsorption capacity on coal before and after Ro,max=1.3% also was increased and decreased, respectively. There is a positive correlation between the changes in the micropore SSA and the Langmuir volume. It confirms that the changes in pore structure and methane adsorption capacity due to CS2 treatment are controlled by the rank, and the change in methane adsorption is impacted by the change of micropore SSA and suggests that the changes in pore structure are better for gas migration; the alteration in methane adsorption capacity is worse and better for methane recovery before and after Ro,max=1.3%. A conceptual mechanism of pore structure is proposed to explain methane adsorption capacity on CS2 treated coal around the Ro,max=1.3%.

scholarly journals Complex Variable Meshless Manifold Method for Elastic Dynamic Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Analytical Solution ◽  
Complex Variable ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Least Square ◽  
Dynamic Problems ◽  
Finite Covering ◽  
Moving Least Square ◽  
Elastic Dynamics ◽  
Good Agreement

Combining the finite covering technical and complex variable moving least square, the complex variable meshless manifold method can handle the discontinuous problem effectively. In this paper, the complex variable meshless method is applied to solve the problem of elastic dynamics, the complex variable meshless manifold method for dynamics is established, and the corresponding formula is derived. The numerical example shows that the numerical solutions are in good agreement with the analytical solution. The CVMMM for elastic dynamics and the discrete forms are correct and feasible. Compared with the traditional meshless manifold method, the CVMMM has higher accuracy in the same distribution of nodes.

scholarly journals Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

2021 ◽  
Author(s):  
Thomas TJOCK-MBAGA ◽  
Patrice Ele Abiama ◽  
Jean Marie Ema'a Ema'a ◽  
Germain Hubert Ben-Bolie
Keyword(s):  
Analytical Solution ◽  
Linear Function ◽  
Dispersion Equation ◽  
Source Term ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Liouville Problem ◽  
Finite Domain ◽  
Advection Dispersion ◽  
Sink Term

Abstract This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Numerical Simulation for Migration of the Pollutants in Soil

2010 ◽  
Vol 113-116 ◽  
pp. 1684-1687 ◽  
Author(s):  
Ge Hu ◽  
Shu Ai Peng ◽  
Wei Wang
Keyword(s):  
Numerical Solutions ◽  
Scientific Basis ◽  
Practical Significance ◽  
Time Space ◽  
Calculation Results ◽  
Pollutant Migration ◽  
Volatile Pollutant ◽  
General Mathematical Model ◽  
Diffusion Convection ◽  
Pollutant Concentration Distribution

In the soil environment，through analyzing the numerical solutions of pollutant migration, the time-space law of the transmission of organic pollutants in soil can be mastered, which has both theoretical and practical significance. The general mathematical model of the migration of volatile pollutant in soil was established; and typical models of pollution sources emission were calculated, and the influence of various parameters in model on calculation results were compared, such as diffusion, convection, adsorption and degradation parameters; finally a correlation analysis and discussion was made on calculation results of the pollutant concentration distribution. The calculation results show that the convection is the main reason causing pollutants migration, and the influence of volatility to migration process cannot be ignored. It provides the scientific basis and approach for the pollution forecasting and prevention.

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