Modeling, simulation and control of the dynamics of a Heptads’ effect evaporator system used in the Kraft recovery processes

Abstract

This research article attempts to investigate the dynamic behavior of the heptads’ effect evaporator (HEE) used to concentrate the weak black liquor during the Kraft recovery process in a paper industry. In order to fully characterize the HEE unit, a complete understanding of its performance for steady state and transient conditions is required. For this purpose, a set of first order nonlinear differential equations have been developed for the backward feed flow configuration (BFFC) for an unsteady state. Further, the developed non-linear model is linearized and linear state space equations obtained. The dynamic response of the system in terms of vapor temperature and liquor concentration changes for different changes in input liquor flow rate has been investigated. The rise, delay and settling times for the temperature deviation from steady state have been found to be significantly less as compared with that for the concentration deviation. The results also indicate that each effect of HEE acts as an individual first order system. The placement of such first order systems in series makes both the liquor concentration and vapor temperatures response more sluggish progressively with each subsequent effect. Finally, a Cascade-PID control strategy has been implemented and shown to exhibit differentiated and improved dynamic performance of the HEE system versus open-loop dynamic response.

Water cycle algorithm tuned robust fractional‐order Proportional–Integral–Derivative controller for energy optimization and control of nonlinear Multiple Stage Evaporator: A case study of paper mill

“…This assists in the implementation of a tight and suitable control algorithm by effective utilization of simulation model instead of the real plant. Literature works reveal that the nonlinear dynamic model of MSE has been simulated for designing various controllers such as conventional Proportional–Integral–Derivative (PID), 18,19 Cascade‐PID, 20 model predictive control (MPC), 21,22 linear quadratic regulation (LQR) 23 or flatness‐based control, 24 and Fuzzy‐PID 2,25 . However, some precarious issues in the model simulation and controller design still exist, for instance, the premature convergence of the optimization techniques, computational complexity, and the behavior of the controller to noise and disturbances.…”

Energy optimization of Multiple Stage Evaporator system using Water Cycle Algorithm

“…Evidently, the above-all focus is on optimizing the energy efficiency parameters (SE and SC) by exploring several ESSs proposed for MSE and to delineate erstwhile research accomplishments in the arena of modeling and simulation of MSE under steady-state. Such energy-intensive systems have drawn considerable interest in terms of modeling, simulation, optimization and control ( Bhargava et al., 2008b ; Kaya and Ibrahim Sarac, 2007 ; Verma et al., 2018c , 2018b ). Additionally, there is a considerable amount of literature on simulation of MSE with various ESSs and feed flow configurations via steady and dynamic state modeling ( Bhargava et al., 2008a ; Gautami and Khanam, 2012 ; Khanam and Mohanty, 2010 ; Kumar et al., 2013 ; Verma et al., 2016 , 2017a ).…”