An Overview of the Application of Harmony Search for Chemical Engineering Optimization
Table 9
Problem description of distillation design and optimization.
Application
Type of optimization problem
Objective function
Optimization variables
Constraints
Reference
Design of three distillation sequences
Global optimization
For multi-component distillation: minimize , where is the column heat duty, is the reflux ratio, is the pressure of the column, is the temperature of the feed, is the feed stage number, and is the number of column stages.
Discrete and continuous variables: and .
, where is the resulting purity vector and is the required purity vector.
For thermally coupled reactive distillation: minimize , where is the reflux ratio, is the pressure of the column, is the distillate flux, is the side flux, is the interconnection flow, represent the numbers of the feed stages, is the first reaction tray location, is the last reaction tray location, is the location of the interconnection flow, is the location of the vapor stream, is the number of stages of the main column, and is the number of stages of the stripper.
Discrete and continuous variables: and .
, where is the resulting purity vector and is the required purity vector.
For dividing wall distillation: minimize , where is the reflux ratio, is the pressure of the column, is the distillate flux, represent the side fluxes, is the liquid interconnection flow, is the vapor interconnection flow, is the feed stage number, is the first prefractioner tray location, is the last prefractioner tray location, represent the side stream tray locations, and is the number of column stages.
Discrete and continuous variables: , and .
, where is the resulting purity vector and is the required purity vector.
Minimize TAC, TAC = min , where TAC is the total annual cost, is the cost, is the set containing all possible sequences, is the set containing all possible column pressures, is a distillation sequence, and is the pressure of the column.
Water and energy minimization in the thermal cracking process
Global optimization
Minimize  + ,,, where EC is the energy consumption, WU is the water use, is the gas energy consumption at the boiler, is the oil energy consumption at the boiler, is the amount of produced product, is the feed water for the cooling tower and steam grid, min is the minimum value, and max is the maximum value.
Naphtha mass flow rate, ratio of steam dilution, temperature in the transfer line exchange, temperature of high-pressure steam, steam induction to turbines, distillate to feed ration column, temperature after transfer line exchange, and total naphtha mass flow rate.
Process and utility constraints related to production and quality requirements, equipment performance, and resource characteristics.
Separation cascade design for multi-component mixtures
Global optimization
Minimize , where is the total flow rate of the cascade, is the minimum concentration in the product, is the maximum concentration in the waste, is the actual concentration in the product, is the actual concentration in the waste, and are problem-related coefficients.
Number of centrifuges and feed stage.
Minimum concentration of component k in the product . Maximum concentration of component k in the waste .
Maximize , where is the final product flow rate and is the total number of products.
Component flow rates .
(1) Quantity conservation constraints: ,,, where is the feed flow rate of unit u, is the flow rate of stream from unit , is the flow rate of stream coming from units reaching unit , is the flow rate of stream coming from unit reaching unit , is the yield level of stream from unit , is the set of streams from unit , is the set of streams leaving units and reaching unit, is the set of units with destination, and max is the maximum value. (2) Quality constitutive relation constraints: ,, where is a component property, is a final product property, is the number of component streams, is the number of final products, and is the number of linear properties. (3) Non-linear quality constitutive relation constraints: ,,.
