Detailed numerical evaluation of diffusion convection equation in layered reservoirs during tracer injection

Characterization of heterogeneous reservoirs such as multilayered or fractured systems is an important issue in different disciplines such as hydrology, petroleum and geothermal systems. One of the popular methods that can be used for this purpose is tracer tests. Better understanding of the mechanisms of mass transfer (convection–diffusion process) is essential for having a proper test interpretation. In this study, the solutions of different scenarios of tracer flow in a pair of high and low-permeable layered reservoirs including convection and diffusion mechanisms are discussed. Although analytical solutions generally provided exact solutions, they involve several assumptions and might be hard to use for complex problems. As a result, numerical methods are selected for the investigation of different scenarios and addressing cases that are beyond access of analytical methods. In this study, several scenarios of considering diffusion and convection in low and high permeable zones and effective parameters on tracer concentration are investigated. According to the results of this study, the higher the porosity ratio of low to high permeable layer, the more time is needed to get the final concentration value. Also, by increasing the value of the dispersivity coefficient, the time needed to increase the concentration decreases. In other words, the sharp increase in concentration for lower times is seen in higher dispersivity values. The concentration profile variation is affected by Peclet number. The difference among concentration profiles in different cases is considerable, especially in low Peclet numbers where the diffusion mechanism is dominant. This behavior is more common in low permeable mediums such as multilayered tight or shale reservoirs.