Om Prakash Verma

Mathematical Modeling of Multistage Evaporator System in Kraft Recovery Process

In order to reduce the energy consumption of the concentrating the black liquor in Kraft recovery process in paper mill, a mathematical models is developed and proposed for the analysis of multi stage evaporator (heptad’s effect evaporator system). These multistage evaporator is modeled based on the flow of black liquor and steam operation option. In the present study, live steam split, liquor feed split, pre-heaters and hybrid of these energy saving scheme are coupled with backward, forward and mixed feed multi stage evaporator system. The systematic material balance and heat balance equations are described as the form of matrix equation to realize the generality of the mathematical models. The advantage of these models are its simplicity, representation of equations in matrix form and linearity. The proposed mathematical models can be easily solved by numerical methods combining with the iteration method, which has one more advantages of less sensitive to its initial values, high convergence speed and stability. The developed models can also be easily simulate under different operating strategies once knowing the liquor, steam and effects parameters.

Optimization of steam economy and consumption of heptad’s effect evaporator system in Kraft recovery process

Mathematical models have been studied and solved for evaluating an optimized process configuration for the energy intensive black liquor concentrating Kraft recovery process in paper mills. In the present study, a heptads effect evaporator system is considered and modeled first on the basis of three possible flow directions of black liquor feed and heating steam, i.e. backward, forward or mixed feed. Further, live steam split, liquor feed split, feed preheating and a hybrid of these energy saving schemes are coupled with the basic backward, forward and mixed feed arrangements. The systematically evaluated material and heat balance equations evolve into main model equations that are then represented in matrix forms, thereby, to generalize the models mathematically. The advantage of the studied models are their simplicity in linear representation of equations in matrix form and ease of numerical solution. The proposed mathematical models are iteratively solved using different numerical techniques: Gauss-Jordan, Gauss-elimination, Gauss–Seidel, Jacobi, successive over-relaxation and interior-point methods. The simulation results indicate that amongst the 15 simulated models, backward feed with the added arrangements of feed split, steam split and feed preheating showed the best steam economy. The studied models can be applied and easily extended to solve problems with different operating conditions as well once the liquor, steam and other evaporator effects parameters are known.

Simulation and control of a complex nonlinear dynamic behavior of multi-stage evaporator using PID and Fuzzy-PID controllers

Abstract The dynamic model of heptads’ stage evaporative unit employed in concentrating black liquor in paper industry show tremendous complexity. In this work, linearization of such a complex nonlinear model consisting of 14 first order nonlinear differential equations and determination of the system transfer functions has been explored through an exhaustive state space representation technique. The transfer functions that relate the product concentration change to liquor flow rate deviation have been evaluated and presented through this work for the first time. These serve as an input to design a PID controller and study its response for a set point change in product concentration. The response analysis indicated a noticeable overshoot, undershoot and Integral Square Error (ISE), that may collectively influence the product quality. To overcome this issue and to make controlling of product concentration more robust, an intelligent Mamdani type Fuzzy Logic-Proportional-Integral-Derivative (FLC-PID) controller has been additionally designed and its response simulated. A comparison of response of FLC-PID and PID indicated that the rise time of former is larger than the latter. However, FLC-PID response settles faster with ∼49% smaller settling time than PID, possesses zero undershoot, a ∼93% reduced overshoot and 21% reduced ISE. The results demonstrate improved tracking capability, and hence, better control performance of FLC-PID for transient changes in product concentration.

Analysis of Hybrid Temperature Control for Nonlinear Continuous Stirred Tank Reactor

Classical controllers usually require a prior knowledge of mathematical modeling of the process. The inaccuracy of mathematical modeling degrades the control performance of the continuous stirred tank reactor (CSTR), which shows nonlinearity to some extent. It is very necessary to attain desired temperature within a specified period of time to avoid overshoot and absolute error, with better temperature tracking capability, else the process is disturbed in the nonlinear CSTR system. This paper studies the output (temperature) tracking and disturbance rejection problem of nonlinear CSTR control systems with uncertainties via classical control PID, cascade control, and hybrid intelligent controller that includes FLC, adaptive control, and adaptive neuro-fuzzy inference system (ANFIS). This paper evaluates change in an adaptive controller response with varying adaptive gain. It has been observed that OLTF of CSTR is stable, and adaptive controller is best suitable for temperature control for ISE, and also has much better temperature tracking capability. Adaptive controller and ANFIS both have observed zero overshoot.

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

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.

Energy management in multi stage evaporator through a steady and dynamic state analysis

Increasing energy demand, high cost of energy and global warming issues across the globe require energy-intensive industries, such as paper mills to improve energy efficiency. Multi-stage evaporators used to concentrate the black liquor in such mills form its most energy consuming unit and require a strong understanding of steady and unsteady state behavior to ensure energy savings. The modeling of nonlinear heptads’ effect system yielded a set of complex nonlinear algebraic and differential equations that are analyzed using Interior-point method and state space representation. Dynamic response of product concentration and system vapor temperatures along with system stability and controllability have been explored by disturbing the flow rate, concentration and temperature of feed, and fresh steam flow rate. Simulations predict that steam flow rate, feed flow rate and its concentration invariably are major controlling factors (in decreasing order) of vapor temperature and product concentration. The interactive behavior between different effects translates into slower responses of the effects with increasing separation from disturbance source. This steady state and transient study opens many new explanations to this relatively less explored area and helps to propose and implement industrial PID controllers to reduce steam consumption and control product quality.