Mathematical Modeling of Gas Concentration Profiles in Modified Atmosphere Bulk Packages

A three-dimensional mathematical model was developed to predict gas distribution as a function of time insidea perforation-generated modified atmosphere bulk package using the principle of diffusion in a ternary gas mixture.Product and air space layers in the package were considered. The model incorporates simultaneous oxygen consumption,carbon dioxide generation and porosity in the product layer. An implicit-explicit finite difference numerical technique wasused to solve the transient three-dimensional equations. The mathematical model closely predicted measured gasconcentrations in different types of packages. The results show package CO2 concentration increased; whereas, O2concentration decreased with increasing distance from the perforation. Higher gas concentration gradients were obtainedin packages with thin air space thickness. Thus the effective distance from the perforation is an important parameter forgas concentrations in perforation-generated modified atmosphere bulk package.