Accumulation process in the environment for a generalized mass transport system

In last decades, there have been drastic environmental transformations and mutations happening all around the world. Due to the continuous mass transfer process, for example, CO 2 {{\rm{CO}}}_{2} mass transfer, which in this case, takes the form of greenhouse gas emissions, unusual and extreme kinds of phenomena have been occurring here and there, disturbing our ecosystems and causing damage and chaos on their paths. Reducing or stopping these gas emissions has become one of the major topics in our planet. We investigate the solvability of a mathematical model describing the mass transport process in nature and where additional perturbations parameters have been considered. Besides addressing the stability of the model, its convergence analysis is also given with the use of Crank–Nicholson numerical method, in order to assess its efficiency and perform some numerical simulations. The results obtained show that the model’s dynamic is characterized by many grouping (accumulation) zones, where mass (of CO 2 {{\rm{CO}}}_{2} , for instance) accumulates in an increasing way. This result is important in controlling how CO 2 {{\rm{CO}}}_{2} can be stored in this growingly perturbed environment that surrounds us.