Steady-state simulation of a continuous moving bed reactor in the pulp and paper industry

Abstract

This paper is concerned with the mathematical modeling and simulation of the steady-state operation of an industrial moving bed heterogeneous reactor for the kraft pulping of Eucalyptus globulus. The cooking takes place in a single-vessel hydraulic digester adapted for isothermal cooking (ITC), a further development of the modi"ed continuous cooking (MCC) process. A heterogeneous model is used to take into account the di!erent phases, each with distinct pro"les of temperature and concentration of organic (lignin, cellulose and hemicellulose) and inorganic (e!ective alkali and sul"de) compounds. The numerical solution of the model is based on a non-uniform discretization strategy to cope with special geometric and operational features of the digester. The decrease in bulk porosity caused by the compaction of the bed and the progressive increase in the voidage of chips as a result of chemical reactions are incorporated into the model as well as the resulting implications in the entrapped and free liquor #ows. The model presented here can be used in optimization studies and has been validated with data from an industrial mill.

The use of splitting methods in the numerical simulation of reacting flows

“…The results obtained for the evolution problem present physical evidence. The stationary results agree with the numerical results in [1]. …”

“…In this section we consider the system of hyperbolic partial differential equations that describes the behaviour of a moving bed reactor -the digesterused in the paper and pulp industry ( [1]). …”

“…In system (27), the velocity u F is positive for i = 1, 2, 3 -the liquid phase flows downwards -and is negative for i = 4, 5, and z ≥ EXT -because the liquid phase flows upwards countercurrently. The reaction terms R i are represented by exponential functions depending on y i and are experimentally established in [1]. The boundary and initial conditions as well as the values of the parameters used in the model were obtained experimentally and are established in [1].…”

“…The reaction terms R i are represented by exponential functions depending on y i and are experimentally established in [1]. The boundary and initial conditions as well as the values of the parameters used in the model were obtained experimentally and are established in [1].…”

“…Recent literature ( [2], [4], [6]) has provided several ways of dealing with operator splitting as far as the sequence of these physical phenomena and also the possible coupling between some of them are concerned. Numerical simulations in [0,1] pointed out that the coupling of reactions with diffusive transport in a sequence composed by a convection problem in a certain interval [0, t/2], a diffusion-reaction problem in [0, t] and a final convection problem in [t/2, t] perform notably better than an uncoupled splitting. In this paper we present a theoretical justification of this numerical evidence by studying the splitting errors and the stability properties of some numerical methods, based on different sequences and couplings of physical phenomena.…”