In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field. 相似文献
This paper presents gas compositions and H-, O-isotope compositions of sulfide- and quartz-hosted fluid inclusions, and S-, Pb-isotope compositions of sulfide separates collected from the principal Stage 2 ores in Veins 3 and 210 of the Jinwozi lode gold deposit, eastern Tianshan Mountains of China. Fluid inclusions trapped in quartz and sphalerite are dominantly primary. H-and O-isotopic compositions of pyrite-hosted fluid inclusions indicate two major contributions to the ore-forming fluid that include the degassed magma and the meteoric-derived but rock 18O-buffered groundwater. However, H- and O-isotopic compositions of quartz-hosted fluid inclusions essentially suggest the presence of groundwater. Sulfide-hosted fluid inclusions show considerably higher abundances of gaseous species CO2, N2, H2S, etc. than quartz-hosted ones. The linear trends among inclusion gaseous species reflect the mixing tendency between the gas-rich magmatic fluid and the groundwater. The relative enrichment of gaseous species in sulfide-hosted fluid inclusions, coupled with the banded ore structure indicating alternate precipitation of quartz with sulfide minerals, suggests that the magmatic fluid has been inputted to the ore-forming fluid in pulsation. Sulfur and lead isotope compositions of pyrite and galena separates indicate an essential magma derivation for sulfur but the multiple sources for metallic materials from the mantle to the bulk crust.
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