The gasification of sugarcane cutting residues (RAC) is a process that occurs in a gasifier where the transformation of this raw material into a solid-state and a gasifying agent with a moderate calorific value occurs, thanks to the application of heat. And under restricted oxygen levels, we can say that there are several styles of gasifiers for air, steam, oxygen, and hydrogen, all of which have a performance that can be analyzed and categorized by their performance to avoid damage to the environment. (1) The objective of this article is based on the mathematical development using simulation of the gasification of cane cutting residues. (2) In the methodology, the simulation of the gasification and CO₂ capture process was developed from the biomass residues of the sugarcane cutting residues; it was carried out as a transformation of the primary fuel into a gas stream whose main components are CO₂ and H₂, which can be separated relatively easily by their concentrations, available pressures and in some cases, their temperatures; (3) According to the kinetic data obtained, the second-order reaction in the transformation and improvement of the process was identified; applying to the optimization of development in the capture of CO₂, contributing to the reduction of greenhouse gases. (4) The gasification simulation process results in a biomass conversion corresponding to 93% of its feed and the formation of volatiles whose molar fraction corresponds to 37% H₂, 12% CH₄, 37% CO and 12 % CO₂.