| The special storage method of coalbed methane makes it more unpredictable for the evaluation of total reserves and production history than conventional natural gas resources.In the past,the evaluation of coalbed methane resources,such as coal rank,pressure condition,fracture development,and mineral content,has provided the basic understanding of coalbed methane.However,due to the heterogeneity of macro-scale strata structure,fracture development,and coal composition,many research conclusions are contradictory,and many empirical relationships for the development of specific basins are difficult to apply to other places universally.Moreover,in the late stage of coalbed methane production,the gas production is maintained at a lower level,but it can usually last quite a long time,due to the gas diffusion and desorption in the micro-pores of the matrix control the later production,which forms the tail of the productivity curve.The mining of coalbed methane is closely related to the microstructure and seepage characteristics of coal rock,and the adsorption and desorption law of methane,while macro-scale techniques and methods are difficult to provide help in the above problems.The conventional methods used to study the adsorption behavior of coalbed methane are mainly based on the isothermal adsorption equation for the experimental measurement of pulverized coal particles or their cutting samples.The final result of these experiments is the isothermal adsorption curve of samples at different temperatures and pressure.The isothermal adsorption curve of coal samples has the important reference value for reservoir evaluation and numerical modeling,however,the isothermal data only provides static macroscopic information due to it ignores the dynamic process of adsorption-desorption and adsorption details of the nanopore surface.At the same time,because the wide pore size distribution in coal gas flow is a multi-scale flow process which can be divided as viscous flow,slip flow,transition flow and Knudsen diffusion(free molecular flow).In addition to the macroscopic continuous viscous flow behavior,the microscopic percolation behavior including gas slippage,diffusion,and desorption are also important parts of the flow mechanism.With the development of coalbed methane production,the flow mechanism also changes with the reservoir pressure,which leads to the difficulty of estimating the migration behavior of coalbed methane in the draining process.It is possible to obtain the universal law of gas transport in the coal reservoir by modeling the coal matrix at the micro-and nano-scale base on the microstructure characteristics of the coal.Besides,it is meaningful to deeply analyze the impact of some key factors on coalbed methane diffusion-adsorption process and permeability,which will provide effective guidance for the rational determination of coalbed methane mining mode and improve the recovery of coalbed methane mining.In view of the above problems,we proposed a pore-scale model for dynamic gas diffusion-adsorption,and established a REV-scale model for gas permeability prediction based on the Lattice-Boltzmann method,which will be used to study the dynamic gas diffusion-adsorption characteristics and permeability change law at micro-and nano-scale.The research work in this paper is mainly carried out from the following aspects:(1)First,we introduced the basic principle of Lattice-Boltzmann equation,and then,several fundamental models of the Lattice-Boltzmann method are presented,such as the standard LB model,the passive scalar LB model,and the REV-scale LB model.And with the REV-scale LB model as an example,we showed how the generalized Navier-Stokes equation is recovered by using the Chapman-Enskog technique.Some commonly used boundary condition schemes and the program structure of the Lattice-Boltzmann method are recommended.What's more,the complex boundary recognition and treatment methods of porous media,as well as the mutual conversion between lattice units and physical units,are demonstrated by a simple example.(2)The model of the porous medium gas flow-diffusion-adsorption-coupled LB model is established,which controls the evolution of fluid viscous flow and diffusion by a double distribution function,and the Knudsen diffusion and dynamic adsorption-desorption of gas in the organic matter components of coal are also included in the model.Firstly,the usability of the model was verified by two classic cases,then the impact of the velocity of the fluid,the diffusion rate of gas in the large pore/micro-fracture and the adsorption rate constant on the diffusion-adsorption process were discussed by using 3 dimensionless numbers,namely Re,Pe,Da.Besides,we modified the adsorption layer effect which based on Langmuir isothermal adsorption theory,which makes it more suitable for the adsorption/desorption conditions considering time effect and obtains a dynamic diffusion coefficient model which capable of adaptive change with gas adsorption-desorption.We use the self-developed the Random circle packing(RCP)reconstruction algorithm of porous media to generate the pore-scale coal matrix reconstruction image.And based on the reconstructed coal matrix image,the effect of gas adsorption on the diffusion property of the coal matrix gas was discussed respectively,and the results were compared with the original adsorption layer effect model by the different average pore radii.The results show that the influence of fluid velocity on the diffusion-adsorption process of pore-scale coalbed methane is small and negligible.The gas diffusion coefficient affects the range of gas diffusion and also controls the adsorption process,which determines the position and form of adsorption(whether uniform adsorption).The magnitude of adsorption constant determines the strength/rate of adsorption,the increase of diffusion coefficient and adsorption constant can effectively enhance the adsorption rate of gas,and the trend of gas concentration-adsorption change is closer to Langmuir isothermal adsorption curve.In the adsorption process,the gas diffusion rate in the solid particles is controlled by the gas diffusion rate and the matrix adsorption property of the large pore/micro-fracture,and the gas diffusion rate or adsorption rate in the large pores can accelerate the adsorption of the gas effectively,but the gas diffusion property in the solid particles will decrease rapidly.During the adsorption-desorption process,if unconsidering the adsorption layer effect of gas in micropores,the prediction of diffusion coefficient may be wrong.For a size-fixed coal matrix,due to the adsorption amount of the gas is limited,the results of the dynamic adsorption-desorption model will eventually return to the analytic solution of the static isothermal adsorption equation when the time is sufficient.However,the intermediate process is greatly different under different diffusion coefficient and the adsorption/desorption constant.As coal are usually tight and low permeability,when the gas diffusion,adsorption/desorption is not sufficient,the direct use of static constants will produce a great error.(3)We proposed a generalized Lattice Boltzmann model(GLBM)for the REV-scale coalbed methane transport in coal matrix is established,and the gas-solid dynamic adsorption-desorption are also included.In this model,the generalized Navier-Stokes equation and the convection-diffusion equation are controlled by a double-distributed LB equation,and the process of gas-solid dynamic adsorption-desorption is considered by using a source/sink term.Based on the microscopic image of coal,a binary algorithm of solid matrix and micro-fracture is developed,and a two-dimensional scanning image can be binary and imported into LBM for calculation.The effects of specific surface area,porosity and adsorption properties of coal on the adsorption process were analyzed based on the regular distribution matrix model and the reconstructed image of microscopic coal.The results show that the adsorption effect is enhanced with the increase of surface area and micro-fracture porosity,or the decrease of matrix size.As the adsorption rate increases with the difference between the saturation adsorption capacity and the difference of adsorption amount.And the effect of saturated adsorption amount on the adsorption process decrease with the increase of specific surface area and micro-fracture porosity,or increases with the decrease of matrix size,while the Langmuir pressure presents the opposite trend.The simulation results of the coal micro-reconstruction model show that the adsorption of methane-coal is affected by matrix porosity/permeability,Langmuir pressure,and geometrical complexity.Higher matrix porosity/permeability or lower Langmuir pressure increases the adsorption rate and the corresponding affected area.The appearance of the diffusion peak curve shows that geometric complexity,including matrix size,shape,and distribution,plays an important role in the adsorption-desorption process.(4)A GLBM model for predicting the coalbed methane permeability at the REV-scale coupled with the viscous flow,slip flow,transition flow and Knudsen diffusion is then built.The model also includes the effect of adsorption layer and surface adsorption,and the contribution of viscous flow and Knudsen diffusion to total gas flow is automatically adjusted by the weighting factor.In addition,the random generation algorithm of three-component porous media was developed according to the morphology and distribution of organic matter,inorganic components and micro-fracture of coal.Before starting the calculation,the correctness of the LB model was verified based on the experimental data of the published literature.The results show that the pore size of the coal matrix is the key factor affecting the gas permeability.The effect of Knudsen diffusion,surface diffusion,and the adsorption layer is smaller with the increase of pore size and can be negligible in the large pore.The Knudsen diffusion and surface diffusion are the main flow mechanisms in nanopores,and the presence of the adsorption layer weakens the contribution of Knudsen diffusion and surface diffusion to total gas flow.When the average pore size is less than 10nm,the permeability will be severely underestimated if the effect of Knudsen diffusion or surface diffusion is neglected.Reservoir pressure plays a significant role in the permeability of gas in the coal seam,and permeability is a function of reservoir pressure.Knudsen diffusion and surface diffusion contribute more to the total flow at low pressure.Gas migration in IOM is mainly controlled by Knudsen diffusion at the low reservoir pressure,while in the OM Knudsen diffusion and surface diffusion dominate the mass transfer.Because of a wider range of pore size distribution means the appearance of meso-and macro-pores is relatively more frequent,therefore,the contribution of IOM to gas flux is greater.The permeability of the coal matrix itself is very low.It is the fracture which contributes very much to the enhancement of gas permeability in the coal seam.With more fracture branches(the larger the fractal dimension,or the larger the volume fraction),the gas permeability of coal will be greater,and gas flow will be more effective.The use of hydraulic fracturing and other reservoir stimulation techniques in the CBM development process is necessary. |
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