The migration process of radionuclide and the factors affecting the process behaviour are of crucial importance for the performance and safety assessment of geological repository. The advection-diffusion equation for description of radionuclide migration in porous media is developed via the conformable derivative approach. The radionuclide migration from liquid to solid phase due to adsorption and the radioactive decay are also considered. The advective-diffusive systems are subject to source concentrations that vary exponentially with time and the analytical solutions of conformable advection-diffusion equation are presented.

1 Introduction

Nowadays, nuclear power generation, radioactive materials utilization and nuclear weapons production have produced significant amount of high level radioactive wastes (HLW). Therefore, a reliable technological and societal system is necessary for management of these radioactive wastes that assure safety, for both current and future generations. Consequently, deep geological disposal has been recommended, developed, and implemented as the safest and most effective final disposition approach for radioactive wastes. The concept of geological disposal is generally provided by a combination of engineered and natural barriers, called a multi-barrier system, to prevent the radionuclide from reaching the human environment. Over the long timescales, radionuclides will migrate through the host rocks of the multi-barrier system. Thus, it is of great significance to understand the migration processes altering radionuclides depth distributions in host rocks to predict how they will evolve over time and to evaluate countermeasures against the contamination. Nuclides transfer from a flowing fracture to the rock matrix is a combination of many complex processes, among them advection and diffusion are the two main processes. Various predicted models have been proposed for the evolution of radionuclide distributions within the host rocks, in which the traditional advection-diffusion equation (ADE) is the most popular one. Adsorption plays an important role in radionuclides migration in adsorbing porous media. Another safety-important characteristic of radioactive waste is that radioactive decay acts to reduce the total radiological hazard over time. Moreover, advection and diffusion in low permeability porous media generally exhibit time-dependent behavior (Zhou et al. 2018; Yang et al.2019). As a consequence, the present work will develop the traditional ADE via the popular conformable derivative approach, meanwhile, take the adsorption and radioactive decay factors into account.

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