{"title":"多孔岩石基质中具有径向扩散作用的溶质沿单一通道传输:简单解析解与时域随机行走算法的实现","authors":"Shuo Meng , Xinyuan Mo , Longcheng Liu","doi":"10.1016/j.jhydrol.2024.131527","DOIUrl":null,"url":null,"abstract":"<div><p>Numerous field observations show that the channels in one fracture are narrow and the solute penetration depth might be larger than the width. For this case, the diffusion from a channel into the matrix is more realistic to be modeled as radial diffusion than one-dimensional. In present work, the single channel model with radial diffusion is revisited and a simple and robust analytical solution is developed. This solution takes a convolution form of two functions, in which different transport mechanisms are accounted for. The statistical interpretations of the two functions and the analytical solution aid to develop a simple Time Domain Random Walk (TDRW) algorithm and an extension is made to improve its accuracy, efficiency and applicability. To demonstrate the accuracy and efficacy of the extended algorithm, three groups of simulations are performed and it is found that the results of all approaches are identical. The TDRW algorithm, having the same performance as that of inverse Laplace transform solution, is superior to Gaussian quadrature method in computational time. However, due to Monte Carlo nature of the algorithm, the computational burden of TDRW algorithm is dependent on the number of particles applied, which also influences the calculation accuracy. Therefore, a trade-off between computational burden and calculation accuracy should always be made, once the TDRW algorithm is used.</p></div>","PeriodicalId":362,"journal":{"name":"Journal of Hydrology","volume":null,"pages":null},"PeriodicalIF":5.9000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022169424009235/pdfft?md5=6885296a4cbe23ed799d0b27f606f25b&pid=1-s2.0-S0022169424009235-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Solute transport along a single channel with radial diffusion in the porous rock matrix: A simple analytical solution and the implementation of time domain random walk algorithm\",\"authors\":\"Shuo Meng , Xinyuan Mo , Longcheng Liu\",\"doi\":\"10.1016/j.jhydrol.2024.131527\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Numerous field observations show that the channels in one fracture are narrow and the solute penetration depth might be larger than the width. For this case, the diffusion from a channel into the matrix is more realistic to be modeled as radial diffusion than one-dimensional. In present work, the single channel model with radial diffusion is revisited and a simple and robust analytical solution is developed. This solution takes a convolution form of two functions, in which different transport mechanisms are accounted for. The statistical interpretations of the two functions and the analytical solution aid to develop a simple Time Domain Random Walk (TDRW) algorithm and an extension is made to improve its accuracy, efficiency and applicability. To demonstrate the accuracy and efficacy of the extended algorithm, three groups of simulations are performed and it is found that the results of all approaches are identical. The TDRW algorithm, having the same performance as that of inverse Laplace transform solution, is superior to Gaussian quadrature method in computational time. However, due to Monte Carlo nature of the algorithm, the computational burden of TDRW algorithm is dependent on the number of particles applied, which also influences the calculation accuracy. Therefore, a trade-off between computational burden and calculation accuracy should always be made, once the TDRW algorithm is used.</p></div>\",\"PeriodicalId\":362,\"journal\":{\"name\":\"Journal of Hydrology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.9000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022169424009235/pdfft?md5=6885296a4cbe23ed799d0b27f606f25b&pid=1-s2.0-S0022169424009235-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Hydrology\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022169424009235\",\"RegionNum\":1,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, CIVIL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Hydrology","FirstCategoryId":"89","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022169424009235","RegionNum":1,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
Solute transport along a single channel with radial diffusion in the porous rock matrix: A simple analytical solution and the implementation of time domain random walk algorithm
Numerous field observations show that the channels in one fracture are narrow and the solute penetration depth might be larger than the width. For this case, the diffusion from a channel into the matrix is more realistic to be modeled as radial diffusion than one-dimensional. In present work, the single channel model with radial diffusion is revisited and a simple and robust analytical solution is developed. This solution takes a convolution form of two functions, in which different transport mechanisms are accounted for. The statistical interpretations of the two functions and the analytical solution aid to develop a simple Time Domain Random Walk (TDRW) algorithm and an extension is made to improve its accuracy, efficiency and applicability. To demonstrate the accuracy and efficacy of the extended algorithm, three groups of simulations are performed and it is found that the results of all approaches are identical. The TDRW algorithm, having the same performance as that of inverse Laplace transform solution, is superior to Gaussian quadrature method in computational time. However, due to Monte Carlo nature of the algorithm, the computational burden of TDRW algorithm is dependent on the number of particles applied, which also influences the calculation accuracy. Therefore, a trade-off between computational burden and calculation accuracy should always be made, once the TDRW algorithm is used.
期刊介绍:
The Journal of Hydrology publishes original research papers and comprehensive reviews in all the subfields of the hydrological sciences including water based management and policy issues that impact on economics and society. These comprise, but are not limited to the physical, chemical, biogeochemical, stochastic and systems aspects of surface and groundwater hydrology, hydrometeorology and hydrogeology. Relevant topics incorporating the insights and methodologies of disciplines such as climatology, water resource systems, hydraulics, agrohydrology, geomorphology, soil science, instrumentation and remote sensing, civil and environmental engineering are included. Social science perspectives on hydrological problems such as resource and ecological economics, environmental sociology, psychology and behavioural science, management and policy analysis are also invited. Multi-and interdisciplinary analyses of hydrological problems are within scope. The science published in the Journal of Hydrology is relevant to catchment scales rather than exclusively to a local scale or site.