Is adding charcoal to soil a good method for CO2 sequestration? Modeling a spatially homogeneous soil

Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools. We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g. type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2. Keywords: Modeling chemical kinetics in fertile soils; Solvability of a nonlinear ODE system; Equilibria and steady states; Simulation; Biochar; CO2 sequestration