A detailed fundamental model of a continuous pulp digester was developed for simulation and control, Most modeling efforts in the past had emphasized either reaction kinetics and. energy transfer assuming a prescribed flow behavior or modeled digester hydraulics with simplified reaction kinetics. The well-known extended Purdue model was augmented by incorporating axial momentum transport, of which an immediate consequence is the ability to simulate chip level and its impact on the Kappa number profile, thus enhancing the ability to model chip compaction. Interaction between digester hydraulics and kinetics is illustrated via simulation examples, including scenarios that show incipient plugging of the digester vessel. Higher-order finite-difference methods were also used to reduce numerical dissipation and dispersion. The ability to describe chip velocities enables rigorous tracking of a transition front within the digester during feedstock grade transitions. The model explains operational difficulties encountered during hardwood to softwood transition.