Advection-diffusion mass transfer behavior of solutes transfer in fractal capillary bundles

Jin Yi; Huang Huan; Song Huibo; Zheng Junling; Dong Jiabin; Dong Wenhao

doi:10.16186/j.cnki.1673-9787.2023040005

Abstract：It is very crutial to explore the migration law of coalbed methane in coal reservoir for its efficient development and productivity evaluation.The migration of coalbed methane in reservoir channels belongs to the coupling of advection and diffusion,which is constrained by the intricate morphological complexity of pore structures.However,the conventional continuum-based theories fail to rigorously characterize the gov-erning influence of multiscale fractal features of pore structures on coupled advective-diffusive transport pro-cesses.Objectives To fuether elobrate the intrinsic mechanisms of coupled advection-diffusion mass transfer of coalbed methane in complex multiscale pore structures,this study employs a systematic approach.Meth-ods Firstly,the fractal capillary bundle model is constructed based on the fractal topology theory to quanti-tatively characterize the geometric heterogeneity and topological connectivity of pore structures;secondly,building upon the classical Taylor-Aris equation,the mathematical mass transfer equation for solute advection-diffusion is derived,incorporating the scale-invariant characteristics of pore structures;finally,the lattice Boltzmann method is employed to simulate the advection-diffusion process of solutes in fractal capillary bundles,elucidating the influence mechanism of fractal characteristics of pore structures on solute transport.Results The results show that the advection-diffusion mathematical mass transfer model can accu-rately predict the effective diffusion coefficient of solute and has good adaptability.The pore structure char-acteristic parameters such as fractal dimension of pipe tortuosity,scaling lacunarity and maximum pipe di-ameter restrict the solute advection-diffusion behavior.Specifically,the fractal dimension of pipe tortuosity is inversely proportional to the effective diffusion coefficient,while the scaling lacunarity and the maximum pipe diameter have a good positive correlation with the effective diffusion coefficient,and affect the solute advection-diffusion process in the form of controlling the fluid flow rate.Conclusions The research results can provide theoretical and methodological references for the study of the complex migration laws of coal-bed methane in coal reservoirs,and further provide theoretical and decision support for the accurate predic-tion of coalbed methane production capacity and the optimization of reservoir fracturing and modification schemes.