Simulation of the transient behaviour of a digester used in the pulp and paper industry

The development of mathematical models that describe industrial processes is playing an increasing role in industrial context, because such models can replace, in some cases, experimental simulation, in a more inexpensive and flexible way. In this paper is presented a preliminary study of a transient model of a continuous moving bed reactor - the digester - used in the pulp and paper industry. In this complex and heterogeneous digester a moving bed of wood chips, containing cellulose, hemicellulose and lignin, reacts with sodium hydroxide and sodium sulfide - dissolved in a liquid phase - to remove the lignin from the cellulose fibers. The mathematical model studied here has been developed by Fernandes in a forthcoming Ph.D Thesis. The model is derived from the fundamental principles of mass and energy balance and is represented by a system of 15 partial differential equations (PDE) of convection-reaction type. The numerical methods used in the discretization of this PDE system are based on operator splitting which essentially consists in considering separately convection and reaction phenomena. This approach allows the use of methods with different properties - explicitness, implicitness and order - for each subprocess. The final global class of methods represents in some sense a “patching of tailored methods” well adapted to the feature of individual phenomena. Numerical simulations of the concentrations of organics and inorganics are presented.