Synthesis Of Nonsharp Heat Integrated Thermally Coupled Distillation Sequences Based On Stochastic Optimization

The synthesis of distillation sequences is a large-scale combinatorial optimization problem.Simultaneously involving heat integration and thermal coupling between distillation columns in the distillation sequence synthesis can further improve the energy efficiency of the distillation system,but it exponentially enlarges the scale of the optimization problem,dramatically complicates the flowsheet representation,and brings a greater difficulty in solving the problem.In this paper,a novel stochastic optimization method was proposed to effectively and automatically synthesize simultaneously heat integrated and thermally coupled distillation sequences(HITCDSs),which allow nonsharp splits to significantly improve the thermodynamic efficiency of the separation procedure and further reduce the energy consumption of the distillation system.To effectively implement the stochastic optimization strategies,a new binary tree encoding method was proposed to equivalently represent the distillation sequences.The encoding method places no limit on the number of middle components distributed in nonsharp splits,and hence can generate a complete search space of nonsharp distillation sequences.Further,the method avoids decomposing the synthesis problem to realize the automatic synthesis of large-scale distillation systems.For an arbitrary distillation sequence represented by the binary tree encoding method,its thermally coupled structures can be represent by a set of 0-1 binary variables.Pinch-based energy integration strategies were proposed to determine the optimal heat integrated structure for a randomly generated distillation flowsheet.Hence,there is no need to adopt integer variables to encode and represent heat integrated structures.In the stochastic optimization,a series of evolutionary rules was developed to randomly generate neighboring solutions of the distillation configurations.A distillation sequence can be evolved to a neighboring one by randomly pruning and generating its binary tree branches and a thermally coupled structure is evolved by randomly transforming the 0-1 variables.Starting from a randomly given initial distillation sequence and its corresponding thermally coupled structure,all feasible distillation sequences and thermally coupled structures can be randomly generated through a continuous evolutionary procedure.To obtain the HITCDS with minimum total annual cost(TAC),the distillation sequences,thermally coupled structures,heat integrated networks and the operating parameters of the distillation columns(operating pressures,reflux ratios,and key component recoveries)should be optimized simultaneously,which is a large non-convex optimization problem.To solve this problem,an optimization framework was proposed by combining the simulated annealing(SA)algorithm and particle swarm optimization(PSO)algorithm,wherein the SA algorithm was used to update and optimize distillation sequences and thermally coupled structures;for an arbitrary distillation configuration randomly generated by SA algorithm,the operating parameters of the distillation columns were optimized using PSO algorithm.To evaluate a randomly generated distillation configuration,the separation tasks involved in the distillation configuration were designed based on the Fenske-Underwood-Gilliland(FUG)shortcut method first.Thereafter,the optimal heat integrated network was automatically determined by the pinch method.Finally,the TAC of the HITCDS was calculated.The method proposed in this paper can deal with the separation problem of an arbitrary N-component(N ≥ 3)zeotropic mixture.To validate the correctness and effectiveness of the proposed method,the method was applied to solve nonsharp distillation system synthesis problems with different scales,including the more complex six-and seven-component nonsharp HITCDS synthesis problems,which have hardly been investigated.The results prove that the proposed method could achieve the automatic synthesis of complex distillation systems,and the solution efficiency was high.In the case studies,the probability of obtaining the optimal solution by the proposed method was tested.The testing results indicated that the proposed method could obtain the optimal and several sub-optimal distillation configurations with high probabilities(i.e.,>80%),which verified the robustness of this new stochastic optimization method when solving large-scale distillation system synthesis problems.The obtained sub-optimal distillation configurations had close TAC to the best one,and they shared structural similarities to the best one.Hence,the sub-optimal solutions are valuable alternatives for the designer.Additionally,compared to the previously reported method that limited the number of middle components in nonsharp splits,our proposed method could obtain optimal distillation configurations with lower TACs,which further verified the advantage of the proposed method to ensure a complete search space of nonsharp distillation sequences.Finally,the optimization results proved that the optimal HITCDS could further reduce the TAC of the distillation system compared to the optimal conventional distillation sequence,distillation sequence employing only energy integration and distillation sequence employing only thermal coupling.