Tracer transport in naturally fractured reservoirs: Analytical solutions for a system of parallel fractures

摘要

In naturally fractured reservoirs, modeling of mass transfer between matrix blocks and fractures is an important subject during gas injection or contaminant transport. This study focuses on developing an exact analytical solution to transient tracer transport problem along a discrete fracture in a porous rock matrix. Using Gauss-Legendre quadrature, an expression was obtained in the form of a double integral which is considered as the general transient solution. This solution has the ability to account the following phenomena: advective transport in fractures and molecular diffusion from the fracture to the matrix block. Certain assumptions are made which allow the problem to be formulated as two coupled, one-dimensional partial differential equations: one for the fracture and one for the porous matrix in a direction perpendicular to the fracture. Using the obtained analytical solution, tracer concentration in matrix block and fracture was calculated. The advective-diffusive equation in matrix and fracture was used for evaluation of the mass transfer shape factor. The derived analytical solution was used for analyzing early and late time periods of mass transport phenomenon in fractured porous media. Finally, validation of the analytical solution was done by comparing the obtained results with laboratory data adapted from a column tracer test conducted on a fractured till.