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Solution of SNLAE model of backward feed multiple effect evaporator system using genetic algorithm approach

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Abstract

This paper presents the genetic algorithm approach to solve the highly complex set of fourteen simultaneous nonlinear algebraic benchmark problem for the backward feed seven effect evaporator. Generally, Newton’s method may be considered a better numerical technique to solve such nonlinear problems. However, a higher number of effects (seven in this case) complicates the evaluation of a 14 × 14 Jacobian matrix that involves determining the analytical derivative of all system variables. Also, such a simultaneous nonlinear algebraic equations model exhibits the problem of divergence and instability when initial values have not been chosen appropriately. In this work, genetic algorithm approach has been demonstrated to be very efficient to solve such complex nonlinear models for a large number of effects in evaporative system without any complications. To make the model more realistic and representative of physico-thermal properties of liquor, boiling point elevation of the liquor during evaporation has been incorporated. Finally, the developed models are solved using genetic algorithm to determine the process variables, namely liquor and steam flow rates, which yield process performance parameters of energy efficiency (steam economy and consumption). The results indicate that a maximum steam efficiency may be achieved for a 50 % steam split in the first two effects.

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Abbreviations

A:

Heat transfer area (m2)

C p :

Specific heat capacity (KJ)

h :

Enthalpy of condensate (KJ/kg)

H :

Enthalpy of vapor (KJ/kg)

K :

Fraction of overall steam sent to first effect

L :

Feed flow rate (Kg/hr)

Q loss :

Heat loss

SE:

Steam economy

SC:

Steam consumption (Kg/hr)

U :

Overall heat transfer rate (W/m2 K)

T :

Vapor body temperature (K)

X :

Mass fraction of solute/liquor concentration

λ :

Heat of vaporization (KJ/kg)

τ :

Boiling point elevation (K)

Δ :

Difference in values of a parameters at two consequence points

i :

Effect number

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Acknowledgments

The authors would like to thank Director of Star paper Mill, Saharanpur, India for permissions to visit the mill time to time and collect the real-time plant data. The authors would like to acknowledge Prof. A. K. Ray (Department of Polymer and Process Engineering) and Dr. Millie Pant (Department of Applied Science and Engineering) from IIT Roorkee for some of their useful suggestions and discussions related to the problem solution.

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Authors and Affiliations

  1. Department of Polymer and Process Engineering, IIT Roorkee, Roorkee, 247667, India

    Om Prakash Verma & Gaurav Manik

  2. Computer Science Discipline, DPT, IIT Roorkee, Roorkee, 247667, India

    Suryakant

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  1. Om Prakash Verma
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Correspondence to Gaurav Manik.

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Verma, O.P., Suryakant & Manik, G. Solution of SNLAE model of backward feed multiple effect evaporator system using genetic algorithm approach. Int J Syst Assur Eng Manag 8, 63–78 (2017). https://doi.org/10.1007/s13198-016-0533-0

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