Advanced Mathematical Models & Applications

A problem of anomalous solute transport in an element of a fractured-porous medium (FPM), consisting of a single fracture and an adjacent porous block (matrix), is considered. The solute transport in the fracture, which is considered as a one-dimensional object, is carried out on the basis of convective and diffusion phenomena, and in the porous block - on the basis of only diffusion phenomena. In the porous block, the diffusion process occurs anomalously, which means that Fick’s law is violated. The solute mass transfer through the common boundary of the fracture and the porous block is also accounted. The mathematical model consists of two differential equations of fractional order for the fracture and the porous block, respectively. A problem of injection of a liquid, containing solute, into a fracture is considered. The problem is numerically solved and the fields of solute concentration and relative mass transfer through the common boundary of the fracture and the porous block are determined. The effect of anomalies on the distribution of solute concentration and relative mass transfer is estimated.