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Nonlinear modeling of batch digester discharge dynamics with rheology-driven hydraulic transport and drainability coupling, TAPPI Journal September 2026

ABSTRACT: Batch digester blowdown constitutes a strongly nonlinear transient transport process governed by the coupled evolution of pulp consistency, slurry density, hydraulic resistance, liquid inventory, and discharge line dynamics. A control-oriented nonlinear formulation is developed by coupling dry fiber and free liquor mass balances with phase volume reconstruction, consistency-dependent hydraulic resistance, channeling and drainability effects, and a power law head flow relationship derived within a lumped hydraulic inertance framework. A fixed-gain PI con troller obtained from local linearization is employed as the conventional benchmark, whereas an integral sliding mode controller (SMC) explicitly compensates the nonlinear time-varying hydraulic structure and bounded disturbances. Both strategies are evaluated under identical actuator constraints and sequential perturbations involving oppos ing head, hydraulic resistance, channeling, drainability, and dilution. Numerical results demonstrate lower root mean-square error, integral absolute error, and peak flow-tracking error for the SMC, with rapid recovery toward the prescribed sliding boundary layer and improved robustness to variations in the nonlinear flow exponent n. Cumulative electrical energy and batch-specific specific energy consumption remain comparatively similar, indicat ing that the principal SMC benefit is enhanced hydraulic regulation rather than substantial batch energy reduction. Specific energy consumption is an established metric for energetic assessment of slurry transport. Model-based hydraulic demand, electrical power, and sliding manifold surfaces further characterize the nonlinear operating domain. The resulting framework provides a computational proof-of-concept for modeling and control of transient batch digester discharge systems.