Synthesis of heat-integrated complex distillation systems via Genetic Programming
Introduction
The synthesis of complex distillation system is a problem of multi-hierarchy combinatorial optimization. The out layer of this problem is to find the optimal distillation sequence, the middle layer is to identify the heat integration strategy and the inside layer is to confirm the optimal operation parameters for every unit included in the flowsheet. The complexity and combinatorial explosion of this kind of problem leads to the high difficulty for solving it. Recently, some new progress is made for the synthesis of complex distillation system.
Some distinct thermally coupled configurations were searched and for each of the distinct configuration, all the thermodynamically equivalent configurations can be easily drawn (Agrawal, 1999, Agrawal, 2000a, Agrawal, 2000b). Then, a systematic procedure was presented by Agrawal (2003), which can synthesize all feasible basic configurations using N − 1 distillation columns with each column having only a condenser at the top and a reboiler at the bottom. It also generates all feasible thermally coupled schemes with classical two-way liquid and vapor communication between the distillation columns. Rong, Kraslawski, and Turunen (2003a) studied the synthesis of the functionally distinct thermally coupled distillation configurations for quaternary mixtures, which contain some new feasible configurations that are not included in the known superstructures. Then, some new distillation systems that can employ the thermal coupling and heat-integration principles simultaneously have been found and a simple experiential procedure was given to obtain these practical configurations for an N-component mixture (Rong, Kraslawski, & Turunen, 2003b). Afterward, Rong, Kraslawski, and Turunen (2004) presented the synthesis and optimal design of thermodynamically equivalent thermally coupled systems for multicomponent distillations and heuristics and a simple procedure have been approached to find an optimal such configuration. Based on the previous works, some new strategies for simultaneous thermal coupling and heat integration have been approached by Rong and Turunen (2006), where heat integrations are performed between heat exchangers associated with both single middle components and submixtures of middle components and a large number of new heat-integrated thermally coupled distillation systems are synthesized.
Meanwhile, superstructure optimization methods have got some obvious progress. As an example of recent work, Caballero and Grossmann (2001) proposed the Generalized Disjunctive Programming (GDP) model for the optimal synthesis of thermally linked distillation columns. Grossmann (2002) gave a general comment about the non-linear mixed-integer and disjunctive programming techniques and Caballero and Grossmann (2002) have presented a systematic approach for generating all the thermodynamic equivalent structures for a given sequence, then, this method could be integrated in the framework of Disjunctive Programming to exact the best solution for a given objective function (Caballero & Grossmann, 2003). Afterward, a two stage decomposition procedure was described that gave a novel superstructure for designing sequences of distillation columns, which ranges from conventional to fully thermally coupled systems and goes through all the alternative intermediate possibilities (Caballero & Grossmann, 2004) and the optimal synthesis of complex distillation columns using rigorous models was given (Grossmann, Aguirre, & Barttfeld, 2005). Recently, Caballero and Grossmann (2006) improved a superstructure approach for synthesizing heat-integrated thermally coupled distillation sequences, which was based on a state-task approach instead of an equipment-based system. The model was formulated as a Generalized Disjunctive Programming (GDP) problem and solved as a modified mixed integer non-linear programming (MINLP) model. The above works can create a large number of new distillation configurations, which has formulated a large new search space for the optimization work.
The stochastic optimization algorithms are widely adopted in recent years, which have no special requirement on the form of the objective function. The searching process of these algorithms can be achieved along many different ways by using some stochastic rules and can converge to the global optimum with high probability. Genetic Programming (GP) (Koza, 1992, Koza, 1994) is one of the stochastic optimization algorithms that can express the complex structure problems with its hierarchy and can determine the feasible solving space automatically without giving any superstructures. Then, the global optimum can be searched automatically in the genetic evolutionary process. Because other algorithms do not possess the feature of GP, a set of solution strategy based on GP is proposed in this paper to study the synthesis of complex distillation systems.
Section snippets
Introduction for GP
The principles and operations of GP are very similar to Genetic Algorithm (GA) that starts its calculation from the initializing populations and generates some new populations using a variety of operations including reproduction, crossover and mutation, so the optimal solution is achieved according to the biological evolution rules finally. The difference between the two methods in nature is that GA uses the length-fixed character to represent every problem while GP adopts the dendriform code
Problem statement
The complex distillation system addressed in this paper can be stated as follows.
A single feed stream of N-component mixture is given with the known conditions (i.e. composition, flow rate, temperature and pressure) and the problem is to synthesize a minimum total annual cost separation flowsheet that can separate the multicomponent mixture into pure components. The flowsheet can be formed by N − 1 or more than N − 1 columns including conventional column, thermally coupled (linked) side stripper,
Conventional column sequence encoding method
At first, the conventional column sequence with sharp separation is studied in this work and only one kind of node i.e. column node is defined. It can be shown by Fig. 2 that GP tree-like code (for the left part of Fig. 2) can express the corresponding distillation separation flowsheet (for the right part of Fig. 2) directly. The symbol C in the GP code is called column node that corresponds to a distillation column in the actual distillation flowsheet. Every column node has two branches that
The cost model
According to the above definition for GP encoding method and evolutionary operations, the algorithm can generate numerous dendriform codes that apart correspond to various actual separation structures. The next step is to optimize various parameters of every column such as the operation pressure etc.; and then the diameters and sizing of all columns for every flowsheet are confirmed in order to calculate the total cost of every separation flowsheet.
Calculation steps for GP algorithm
The GP-based synthesis algorithm includes the following steps:
- (1)
The initial population is generated randomly and the size of population is set to D while the maximal evolutionary generation is set to F where D and F will be assigned according to every actual problem. For every column node, the operation pressure is dispersed according to the method described in Section 5.2, that is to say, the pressure rank Z is selected randomly between the upper and lower operation pressure limitation (i.e. Pmax
Examples
The calculation software of GP algorithm is programmed using C++ language and the effectiveness of this algorithm is validated by the following two typical separation problems on a Pentium 4/3.0 G computer. The data for the two problems are given in Table 2 and the available utilities are shown in Table 1.
Example 1 is a five-component mixtures separation problem with the operation pressure ranging from 0.1 to 0.3 MPa and the size of population for GP is set to 60 while the maximal evolutionary
Conclusion
GP is adopted to study the problem of heat-integrated complex distillation system synthesis and a series of unique encoding method and solution strategy is proposed in this paper. The structure feature of such complex system is abstracted for three parts including the separation sequence, the connection pattern between different separation missions and the heat integration structure. Meanwhile, the non-sharp separation that can contain two middle distribution components between the light and
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