The Fractional Order Mathematical Models For Fractured Rock Medium Well Flow Problems And Their Analytical Solutions

Fractured rock medium well flow problem is one of the important contents in the groundwater dynamics in fractured rock.The heterogeneity,direction and roughness of fracture distribution enable the fracture flow with high degree of heterogeneity and anisotropic.The groundwater flow in fractured rock medium can be classified into two categories;one is flow along the fracture and the other is flow along the fault zone and the pipeline.By studying the law of the groundwater flow in the fracture,the classical Cubic Law,which described the groundwater flow in the fractured rock medium is obtained.Up to now,the models of fracture seepage flow are mainly divided into two classes of models: fracture-porous double porosity medium model and non-double porosity model.Firstly,the fractured rock media will be divided into horizontal single fractured rock medium,inclined single fractured rock medium,vertical single fractured rock medium and mixed single fractured rock medium to describe the groundwater flow in fractured rock media.Next,assuming that the groundwater only moves in the fracture,the water bearing layer of the fractured rock medium with same thickness is infinite,the occurrence is horizontal,the water flow obeys the cubic law and pumps with the constant Q,we establish the fractional order mathematical models of unsteady flow in a horizontal single fractured rock medium with a full well flow in the radial anisotropy,unsteady flow in a radial anisotropic fractured medium with a single fractured rock medium,the unsteady flow in a vertical fractured rock medium with a radial anisotropy,the unsteady flow in a radial anisotropic fractured rock medium with a fractured medium,and the non-steady flow in the radial anisotropy of the fractured rock medium,respectively.Finally,through fractional order differential-integral theory,definitions of Laplace transform,Fourier transform,Wright function,Mittag-Leffler function,we obtain the analytical solution of each model and the formula of the permeability coefficient tensor of the fractured rock aquifer.