Mechanism Of Multi-scale Gas Flow In Dual-porosity Coal And Numerical Modeling

The prevention and utilization of coal seam gas is an important issue involving the coal mine safty,the high efficient use of clean energy and the emissions of greenhouse gases.It has always been an attractive topic in the fields of energy exploitation,environmental protection and so on.Coal seam gas drainage and coalbed methane exploitation are the key technologies to prevent gas accidents,capture gas energy and control greenhouse gas emissions.The theory of gas flow in coal is the knowledge and understanding what is happening in the process of coal gas storage,gas ad/desorption,gas flow and gas production.The gas flow theory lays foundation and bases for grasping the gas reserves,assessing the risk of gas disasters,calculating gas emission and making prevention and control measures,predicting the gas production,designing gas resources development and other practical engineering problems.Based on the current research results of predecessors,this study explored and attempted the following aspects of coal gas flow theory: calculation of gas content in coal seam,coal matrix gas adsorption and desorption mechanism and theoretical model,multi-scale gas flow mechanism in dual-porosity coal and mathematical modeling,numerical solution and simulator development.This study firstly discusses the approach of calculating gas content in modeling coal seam gas flow.It is well accepted that the Langmuir equation could be used to accurately depicting the relationship between pore pressure and gas content.However,nowdays there are still simplified approaches(e.g.parabolic equation approximation,P.M.??????? approximation)to be used to do gas content calculation in many engineering calculations and academic literatures.By using numerical calculation and theoretical calculation,three approaches of calculating gas content are compared and the error caused by the simplified calculation is quantitatively analyzed.It is found that the gas content curve of Langmuir equation is quite similar to that of a parabolic equation,but the error caused by using P.M.??????? approximation is unacceptable;for accurately predicting gas flow in coal,the gas content should be calculated with the Langmuir equation.Coal is a typical dual-porosity medium composed of fracture and coal matrix.The gas flow mechanism in coal fracture has been widely accepted,while the gas flow mechanism in the coal particle/coal matrix is still controversial.Based on the current academic literature related to gas flow in coal particle/coal matrix,the pore structure of coal is complex and the pore diameter in coal is widely distributed,thus the gas flow should be multi-scale and multi-mechanism behavior,and only using Fick diffusion to describe the gas migration in multi-scale pores is unreasonable and questionable.On the basis of the existing theory,the concept of density-gradient driven flow is proposed to depict gas migration in multi-scale pores in coal particle/ matrix,and the adsorbed gas and free gas in the pores of coal are considered as gas density,and the permeation and diffusion in the pores are integrated as density-difference driven flow based on the concept of mass transfer.A series of coal gas ad/desorption experiment is conducted with multi-scale coal particles under constant pressure boundary and variable pressure boundary,and gas desorption curves are obtain by recorded pressure data throughout the experiments.Camparision of simulated gas desorption curves and measured gas desorption curves are conducted,it shows that the theoretical model proposed in this study is verified to be superior over the classic diffusion model and could be used to accurately predict gas data in the whole process of gas desorption from coal.Based on analyzing the existing mathematical model of coal gas flow and numerical simulation software,it is believed that the simulation technology and numerical solving method for the gas migration in coal matrix need to be improved.Based on the coal gas multi-scale flow mechanism and dual-porosity assumption,considering the coupling effect of coal matrix shrinkage,effective stress and multi-scale flow mechanism,the gas flow model in coal matrix and gas flow model in fracture were derived sperately.The mass transfer term between matrix and fracture was coupled and linked to construct a mathematical model of multi-scale gas flow in dual-porosity coal.Compared with other dual-porosity models the merits of the proposed model are: considering the seepage and diffusion in the coal matrix,the two kinds of flow are unified as the density difference driven flow,and the free gas and adsorbed gas in the matrix are fully considered,which is more consistent to the actual gas migration in coal matrix.The finite difference method was used to discretize the mathematical model of multi-scale gas flow in dual-porosity coal,and efficient numerical software was independently developed based on the Visual Basic programming platform.The advantage of this numerical solution is that the coal matrix blocks are embedded within the fracture network in a mosaic fashion,the matrix blocks and fractures are staggered rather than overlapping each other where fractures create a full separation between adjacent matrix blocks,or matrix blocks could be connected to fractures through coal bridges.Any point in the gas flow field has only one set of parameters,matrix parameters or fracture parameters,and the matrix-fracture mass transfer only occurs at the surface of matrix blocks.This process is different from the solution approach of other existing dual-porosity models and is closer to the actual gas flow.The proposed gas flow model and numerical simulation software in this study was successfully tested against two sets of in situ gas extraction field data.The validated simulator was applied to conduct the parametric sensitivity analysis to evaluate the influencing parameters on the gas flow rate and drainage efficiency.The analysis results demonstrate that the greater the initial fracture permeability,the higher the gas flow rate.The fracture permeability plays a significant role in enhancing gas flow rate at the initial early stage,but it has little influence on gas flow at the late stage.On the other hand,the greater matrix permeability is,the higher gas flowrate at the late stage and the slower decay rate of gas flowrate will be.The mass transfer rate between matrix blocks and fractures varies with the distance from the matrix block to the free coal surface.The shorter the distance between the matrix and free coal surface is,the greater the mass transfer rate will be.Based on the simulated results,the smaller the radius of the matrix is,the higher the cumulative methane desorption amount from the matrix will be.At the same time,the smaller the radius of the matrix is,the greater the flow rate and the slower the decay rate will be.The results demonstrate that the size and permeability of the coal matrix are two key parameters affecting the overall gas deliverability and that they play an important role in gas production at the late stage.These findings also indicate that the mechanism of gas production varies with depletion time: darican flow in fracture system dominates gas rate at the initial stage of gas production,while density gradient driven flow in matrix dominates gas rate at the late stage.