The paper presents a mathematical model for the study of the advective transport problem where gravity-induced entry of chemicals takes place from open regions of lined boreholes and fracture-type cavities that are deeply located in porous geological media. A characteristic feature of a gravity driven deep geological disposal concept is the presence of time-dependent advective flow velocities in the system. It is shown that certain exact closed-form solutions can be developed to describe the gravity-driven transport of a contaminant into a fluid-saturated host porous geologic medium.