Processes 2023 , 11 , 809
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these three phases and the resulting changes in properties at both the macroscopic and microscopic levels.
Figure2. Schematic illustration of a pulp digester composed of three phases (solid, entrapped-liquor, and free-liquor) . Reproduced with permission of the American Automatic Control Council for the conference article [20]. The solid phase of the multiscale model is composed of high and low-reactive lignin, cellulose, xylan, and galactoglucomman. Both the free and entrapped-liquor phases are assumed to consist of six components: active effective alkali (EA), passive effective alkali, active hydrosulfide (HS), passive hydrosulfide, dissolved lignin, and dissolved carbohy- drates (CHO). In this model, the degradation of solid components typically occurs at the boundary between the solid and entrapped-liquor phases. Hardwood species are consid- ered in this study. The details of the mass and energy balance equations, initial conditions, and reaction kinetics of the degradation of solid components are provided in our previous studies [6,7,24,41]. Properties, such as the concentration and temperature, are calculated by applying mass/energy balance equations to the simulation lattice. The simulation lattice consists of a primary wall, a middle lamella, and three secondary wall layers. The wood structure and chemical composition of the cell wall are taken from [6,42]. The length of a single lattice site is set at 3.5 nm, and the size of the two-dimensional lattice is represented by the product of horizontal and vertical lattice sites, L h × L v . The average thickness of wood fibers is 3.8 μ m, L h = 3.8 μ /3.5 nm = 1086, and L v = 800, which is the cell-wall length. The cellulose fibers undergo degradation reactions with an event time step of 0.001–0.01 min. In addition to the bulk dissolution reactions, cellulose fibers also experience further degradation due to depolymerization; this happens in three reactions: peeling-off, stopping, and alkaline hydrolysis with an event time step of 0.0001–0.001 min. It is important to note that dissolution and depolymerization are significantly influenced by the system parameters, such as the temperature and reaction rates. Therefore, these multiscale reactions must be considered together. However, due to the scale difference between degradation and depolymerization (i.e., about 10 times), introducing the molecular scale to the lattice would result in a 100-times larger lattice. To overcome this, the second kMC layer for depolymerization is placed within the existing one for degradation. In this way, micro and nanoscale events are captured by a layered kMC algorithm, and multiple depolymerization events are executed within a single degradation. First, a degradation event is executed. Next, the event time steps Δ t deg are calculated. Then,
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