A three-dimensional numerical simulation model that predicts biogas production from a plug-flow anaerobic digester is developed. The model is based on the principles of conservation of mass, conservation of energy, and species transport. A first-order kinetic model is used to predict the forward reaction rate in the digestion process. A user defined function for computing the source terms of the reaction rate in the species transport is developed. CFD (computational fluid dynamics) simulations are conducted using Fluent 6.1 to predict the temperature profiles and concentration distributions in the digester. Model prediction is checked against measured biogas production obtained from the literature. The predicted and measured results agree within 5%. Biogas production sensitivity to chemical reaction rates is numerically determined. This simplified first-order kinetic model is part of an overall effort to develop a three-dimensional numerical model that can link digester-process controls, fluid flow conditions and anaerobic digestion for different digester design, climatic conditions and manure compositions.