Synthesis And Optimization Of Work And Heat Exchanger Networks

With the rapid growth of the world’s population and the development of the process industry,energy demand is continuously increasing,while fossil fuels as the main energy source are gradually depleting.To solve this contradiction,China calls for promoting energy conservation and emission reduction while developing renewable energy to achieve its carbon peak and carbon neutral targets.Work and heat are the two dominant forms of energy in the process industry.The former is consumed or generated in the pressure equipment,and the latter is transferred to or absorbed from process streams through heat exchangers.Heat can be transformed into work and vice-versa.If the process units for the two forms of energy are integrated as one system(i.e.,work and heat exchange network,WHEN),the utilization and recovery of work and heat can be considered simultaneously,and the overall energy utilization rate of the system can be greatly improved.In addition,the traditional heuristic and simulation-based process design method can no longer meet the current needs of high-quality development in the manufacturing industry.A new generation of WHEN synthesis methods are urgently needed to realize the simultaneous optimization of network structures and operational parameters.The superstructure-based model method is capable to consider various possible structures of WHENs through the combination problem,and the relationship between variables in networks can be represented by model constraints.The optimal WHEN can be determined by solving the model.Based on the mathematical programming method,we analyze and discuss the computational difficulty and accuracy problem in the WHEN synthesis.Then we solve the above problems from the aspects of model development and algorithm design.Several efficient WHEN synthesis methods are proposed.The main research contents are as follows:(1)In the previous work,the models for the WHEN synthesis have high complexity and can only be applied to small-scale problems.To address the computational difficulty,we analyzed and found that the largest challenge in the WHEN synthesis is that the thermodynamic paths of process streams are unknown.To synthesize such a complicated system,we propose a two-phase strategy:targeting and design.In the targeting phase,the optimal thermodynamic paths of process streams are determined by optimizing the utility consumption and estimated capital investments.To represent possible thermodynamic paths of unclassified process streams,we propose a novel stage-wise superstructure where the utility consumption and heat exchanger area of the heat exchanger network(HEN)part are estimated by an extended pinch analysis method under the assumption of vertical heat transfer.With the obtained thermodynamic paths,the HEN synthesis problem in the design phase is carried out by solving the well-known stage-wise superstructure(SWS)model.Two literature examples are presented to illustrate the effectiveness and applicability of the proposed method.In two case studies,our approach yields WHENs with 30.7 and 28.3%lower total annual cost,respectively.(2)To address the inefficiency problem of commercial solvers in solving WHEN models,an efficient optimization method is presented in this work.Based on the two-phase strategy mentioned above,specific optimization algorithms are designed for each phase.In the targeting phase,a novel targeting model is introduced to identify the optimal thermodynamic paths of process streams.The genetic algorithm in the outer level is applied to adjust the streams’temperatures,and the golden section search method in the inner level is used to adjust the hot utility consumption.With the obtained thermodynamic paths,the detailed HEN is determined using an enumeration-based global optimization algorithm in the design phase.The proposed method is applied to four examples.Results show a decrease of 4.26%in the total annual cost(TAC)for the liquefied natural gas(LNG)example,48.7%in the TAC for the postcombustion CO2 capture example,and 1.05%in the TAC for the two-stage membrane separation process example.Then the model and algorithms are extended to the multi-objective optimization,and turboexpanders are considered for the work exchange.The Pareto curve in the case study shows that there is a strong coupling relationship between the economic objective and environmental impact objective,which reflects the significance of the multi-objective optimization.(3)To address the low accuracy problem of the WHEN models applying ideal assumptions,the PR equation of state is used in this work to estimate stream properties.To maintain the solution efficiency,the concept of Minimal WHEN structures is introduced.Minimal structures feature one compression/decompression task and one heat exchange task per stream.The thermodynamic paths of streams can only be pressure-change after temperature-change or pressure-change before temperature-change.Therefore,the suction and discharge temperatures of pressure equipment can be pre-calculated once the thermodynamic paths of streams are fixed.The work exchange network(WEN)and the HEN,as the sub-networks of the WHEN,can be optimized individually.An enumeration-based optimization framework is developed based on this feature.By enumerating all Minimal WHEN structures and optimizing the sub-networks to globally optimal,the global optimality of the solution can be assured.Finally,the approach allows the use of turboexpanders and single-shaft-turbine-compressors for work exchange.Four examples are presented to show the effectiveness and accuracy of the proposed method.(4)The Minimal WHEN synthesis method is extended to the Non-minimal WHEN synthesis method.Non-minimal structures feature one compression/decompression task and at most two heat exchange tasks per stream.Compared with Minimal structures,streams in Non-minimal WHEN structures have one more possible path:temperature-change,followed by pressure-change,and temperature-change again.Therefore,the suction temperature of pressure equipment is a continuous variable,which is defined as Tcut.The lower and upper bounds of Tcut can be obtained by the pressure equipment calculation based on boundary conditions.Then each Tcut can be discretized between its bounds.For each discrete temperature point,the corresponding discharge temperature of pressure equipment can be pre-calculated.In this way,WHENs can be split into WENs and HENs for independent optimization,thereby reducing the computational complexity.It is found that the TAC of WHENs in the targeting model,tacWHI,is unimodal over each Tcut.Based on the assumption that tacWHI is unimodal in the variable space of all Tcut and qHU,we design a search algorithm to quickly find the optimal solution.Case studies demonstrate the effectiveness of the proposed method.All targeting models are solved within 10 seconds and shown to be globally optimal.(5)To improve the solving efficiency of the WHEN synthesis problem,a decomposition algorithm based on distributed computing is proposed to solve the HEN sub-problem.First,the range of HEN input energy and possible stream matching are determined by the composite curvebased method.Then the matching groups are enumerated by the transshipment model to further narrow down the optimization space.The matching groups are assigned to multiple threads,where the structure optimization models with the highest complexity are solved in parallel to obtain the optimal HEN structure of each matching group.After summarizing the results of each thread,the optimal structure among all match groups can be determined.In addition,full connections of the streams between different heat exchangers are considered in the structure generation step,which can generate HEN structures that cannot be represented by the SWS model.Eleven examples ranging from small-scale to large-scale problems validate the effectiveness of our method.