Framework for Embedding Process Simulator in GAMS via Kriging Surrogate Model Applied to C3MR Natural Gas Liquefaction Optimization

Rigorous black-box simulations are useful to describe complex systems. However, it cannot be directly integrated into mathematical programming models in some algebraic modeling environments because of the lack of symbolic formulation. In the present paper, a framework is proposed to embed the Aspen HYSYS process simulator in GAMS using kriging surrogate models to replace the simulator-dependent, black-box objective, and constraints functions. The approach is applied to the energy-efficient C3MR natural gas liquefaction process simulation optimization using multi-start nonlinear programming and the local solver CONOPT in GAMS. Results were compared with two other meta-heuristic approaches, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), and with the literature. In a small simulation evaluation budget of 20 times the number of decision variables, the proposed optimization approach resulted in 0.2538 kW of compression work per kg of natural gas and surpassed those of the PSO and GA and the previous literature from 2.45 to 15.3 %.The authors acknowledge the National Council for Scientific and Technological Development – CNPq (Brazil), processes 148184/2019-7, 440047/2019-6, 311807/2018-6, 428650/2018-0, and Coordination for the Improvement of Higher Education Personnel – CAPES (Brazil) for the financial support

MINLP model for work and heat exchange networks synthesis considering unclassified streams

The optimal synthesis of work and heat exchange networks (WHENs) is deeply important to achieve simultaneously high energy efficiency and low costs in chemical processes via work and heat integration of process streams. This paper presents an efficient MINLP model for optimal WHENs synthesis derived from a superstructure that considers unclassified streams. The derived model is solved using BARON global optimization solver. The superstructure considers multi-staged heat integration with isothermal mixing, temperature adjustment with hot or cold utility, and work exchange network for streams that are not classified a priori. The leading advantage of the present optimization model is the capability of defining the temperature and pressure route, i.e. heating up, cooling down, expanding, or compressing, of a process stream entirely during optimization while still being eligible for global optimization. The present approach is tested to a small-scale WHEN problem and the result surpassed the ones from the literature.The authors LFS, CBBC, and MASSR acknowledge the National Council for Scientific and Technological Development – CNPq (Brazil), processes 148184/2019-7, 440047/2019-6, 311807/2018-6, 428650/2018-0, and Coordination for the Improvement of Higher Education Personnel – CAPES (Brazil) for the financial support. The author JAC acknowledge financial support from the “Generalitat Valenciana” under project PROMETEO 2020/064

A pinch-based method for defining pressure manipulation routes in work and heat exchange networks

Aiming for more energetically efficient and sustainable solutions, academic attention to work and heat integration (WHI) has grown in the last decade. Simultaneous models for work and heat exchanger network (WHEN) synthesis often derive from heat integration (HI) frameworks. However, it can be noted that simultaneous optimization models for WHI are considerably more complex to solve than in the HI case. The design of efficient pressure manipulation routes (i.e., allocation and sizing of compression and expansion machinery) in process streams prior to heat exchange match allocation can make the optimization procedure more efficient. This work proposes a systematic procedure based on a model that employs Pinch Analysis concepts for defining these routes based on capital and operating cost targets. The solution approach is a hybrid meta-heuristic method based on Simulated Annealing (SA) and Particle Swarm Optimization (PSO). The obtained routes are then converted into a HI problem by fixing pressure manipulation unit sizes. The detailed HI solution is finally transferred into a WHI optimization model as initial design. In the two tackled examples, the total annual costs (TAC) predicted by the Pinch-based model differed by 0.5% and 1.2% from the final optimized WHEN obtained in the detailed WHI framework.The authors gratefully acknowledge the financial support from the Coordination for the Improvement of Higher Education Personnel – Processes 88887.360812/2019–00 and 88881.171419/2018–01 – CAPES (Brazil) and the National Council for Scientific and Technological Development – Processes 305055/2017–8, 428650/2018–0 and 311807/2018–6 – CNPq (Brazil)

Multi-objective simulation optimization via kriging surrogate models applied to natural gas liquefaction process design

A surrogate-based multi-objective optimization framework is employed in the design of natural gas liquefaction processes using reliable, black-box process simulation. The conflicting objectives are minimizing both power consumption and heat exchanger area utilization. The Pareto solutions of the single-mixed refrigerant (SMR) and propane-precooled mixed refrigerant (C3MR) processes are compared to determine the suitability of each process in terms of energy consumption and heat exchanger area. Kriging models and the ɛ-constraint methodology are used to sequentially provide simple surrogate optimization subproblems, whose minimizers are promising feasible and non-dominated solutions to the original black-box problem. The surrogate-based ɛ-constrained optimization subproblems are solved in GAMS using CONOPT. The Pareto Fronts achieved with the surrogate-based framework dominate the results from the NSGA-II, a well-established meta-heuristics of multi-objective optimization. The objective functions of non-dominated solutions go as low as 1045 and 980.3 kJ/kg-LNG and specific UA values of 212.2 and 266.9 kJ/(°C kg-LNG) for SMR and C3MR, respectively. The trade-off solutions that present the minimum sum of relative objectives are analyzed as well as the dominance of C3MR over SMR at low power consumption values and conversely at low heat exchanger area utilization.The authors LFS, CBBC, and MASSR acknowledge the National Council for Scientific and Technological Development–CNPq (Brazil), processes 200305/2020-4, 148184/2019-7, 440047/2019-6, 311807/2018-6, 428650/2018-0, 307958/2021-3 and Coordination for the Improvement of Higher Education Personnel–CAPES (Brazil) for the financial support. The author JAC acknowledges financial support from the “Generalitat Valenciana” under project PROMETEO 2020/064 and the Ministerio de Ciencia e Innovación , under project PID2021-124139NB-C21

Optimal synthesis of multiperiod heat exchanger networks: A sequential approach

Heat exchanger network (HEN) synthesis is an important research field in industrial processes. It is possible to minimize utilities usage as well as pollutant emissions by an optimal HEN synthesis. In multiperiod HENs, the same heat transfer devices must be able to operate under different operating conditions. The synthesis of multiperiod HEN can be formulated as an optimization problem. In the present paper it is used a sequential approach to solve the problem of synthesizing multiperiod HEN, considering heat capacities and stream temperatures variations into different operation periods. In this approach, multiperiod HEN synthesis is decomposed into three sequential steps, considering three optimization models. The novelties of the proposed approach are a modification in a well-known superstructure from the literature, with the inclusion of new by-pass streams, and an improvement in the NLP model of the third step. Two benchmark literature examples are studied and the obtained results prove the approach applicability, showing better values and network topologies.The authors acknowledge the support provided by CAPES (Coordination for the Improvement of Higher Education Personnel) – Brazilian Education Ministry

Heat Exchanger Network Optimization for Multiple Period Operations

In this paper an optimization model is presented for the synthesis of a heat exchanger network (HEN) for multiperiod operations. A literature very well-known stagewise superstructure is used, but isothermal mixing assumption is not made and a timesharing procedure is adopted. A MINLP problem is solved separately for each period of operation. The final multiperiod HEN is synthesized automatically considering the greatest areas and not fixing matches in each device in different periods, which avoids excessive heat exchange areas. Heat exchangers are designed to be feasible in practice, with a minimum acceptable area. Three literature problems were used to test the applicability of the proposed model. The objective function aims to minimize the total annualized cost (TAC). During implementation of the model, inconsistencies found in the literature were corrected. Results indicate that lower TACs were obtained in the present paper and each heat transfer device is feasible in practice.The authors acknowledge the support provided by CAPES (Coordination for the Improvement of Higher Education Personnel)−Brazilian Education Ministry

An extended method for work and heat integration considering practical operating constraints

The development of methodologies for the simultaneous work and heat integration has increasingly been the focus of recent research. Approaches may vary among optimization and heuristic-based methods considering direct and indirect work exchange, in addition to, or with the development of new strategies for heat recovery. This work presents a strategy for the synthesis of work and heat exchange networks (WHEN) considering the use of single-shaft-turbine-compressor (SSTC) units. The method is based on a meta-heuristic approach and aims fundamentally at synthesizing WHEN that may operate within industrial-like conditions, which are often narrower than those considered in the literature due to simplification assumptions. Therefore, in the present work, practical temperature upper/lower-bound constraints are considered for pressure manipulation units, and the number of coupled units per shaft is limited. Evidently, these constraints yield additional difficulties for the optimization method. The method considers inlet and outlet temperatures as decision variables in the units of a block-based model, making the maintenance of solutions within feasible range more efficient during the optimization runs. Moreover, a new Simulated Annealing (SA) based strategy is developed for deciding optimal compressor/turbine couplings in a model that considers a preset number of “slots” per shaft. The method aims at minimizing total annual costs (TAC) and is tested over four case studies. The first two are used both as benchmark for TAC comparison to those reported in the literature as well as for testing the new constraints. The other two cases are investigated for TAC and energy-wise improvements to original designs. Considerable economic improvements and better use of energy are attained in all cases. For the two benchmark studies, solutions with TAC 1.5% and 4.3% lower than literature designs were found. For the industrial cases, energy requirements were overall reduced. For instance, in example 3, no external power source is required, while literature solutions present power shortage. In example 4, compression power requirements were reduced by 9.9%. The method also proved efficient in maintaining solutions within practical operating ranges.The authors acknowledge the financial support from the National Council for Scientific and Technological Development – Processes 150500/2018-1, 305055/2017-8 and 311807/2018-6 – CNPq (Brazil) and the Coordination for the Improvement of Higher Education Personnel – Processes 88887.360812/2019-00 and 88881.171419/2018-01 – CAPES (Brazil)

A Novel Sequential Approach for the Design of Heat Exchanger Networks

This paper presents a new algorithm for the design of heat exchanger networks (HEN) that tries to take advantage of the strengths of the sequential and simultaneous approaches. It is divided into two sequential parts. The first one is an adaptation of the transportation model (TransHEN). It maintains the concept of temperature intervals and considers the possibility of heat transfer between all the hot and cold streams inside those intervals, and at the same time it allows the a priori calculation of the logarithmic mean temperature difference between all possible heat exchanges, and therefore it maintains the area estimation linear in the model. The second step (HENDesign model), uses a superstructure that contains all the possible alternatives in which the matches predicted by the first stage model can exchange heat to design the final heat exchanger network. Unlike the sequential approach, in this model, all heat flows, temperatures, areas, etc. are reoptimized maintaining the set of matches predicted in the first stage. The model is highly nonlinear and nonconvex, however, it is relatively easy to get good results, because the model starts with the values predicted by the TransHEN model. The algorithm has been tested using fifteen benchmark problems commonly used in literature to compare the performance of heat exchanger network algorithms. In eleven out of the fifteen cases present better or equal results than the best ones reported in the open literature. In three the results presented only marginal differences in total annualized cost (lower than 0.5%) and only a difference of 2.4% in the largest one.The authors gratefully acknowledge financial support from the «Generalitat Valenciana: Conselleria de Educación, Investigación, Cultura y Deporte-Spain» under project PROMETEO 2020/064 and from the “Conselho Nacional de Desenvovimento Científico e Tecnológico-CNPq–Brazil, under projects 428650/2018-0 and 311807/2018-6.

Synthesis and optimization of work and heat exchange networks using an MINLP model with a reduced number of decision variables

Integrating the energy available in industrial processes in the form of heat and work is fundamental to achieve higher energy efficiencies as well as to reduce process costs and environmental impacts. To perform this integration, a new framework for the optimal synthesis of work and heat exchange networks (WHEN) aiming to reduce capital and operating costs is presented. The main contribution of this paper is the elaboration of a new WHEN superstructure and mixed-integer nonlinear programming (MINLP) derived model. Strategies of changing variables are applied to reduce the number of decision variables from the model. The MINLP problem with a reduced number of decision variables is solved with a two-level meta-heuristic optimization approach, using Simulated Annealing in the combinatorial problem and Particle Swarm Optimization in the nonlinear programming problem. For the sake of validation, this methodology is applied to three case studies comprising two, five, and six process streams. Economic savings achieved outperform results reported in the literature from 1.0 to 7.2%. Also, the solutions obtained present non-intuitive WHENs that shows the importance of using superstructure-based mathematical programming for such a difficult decision-making task.The authors would like to acknowledge the Coordination for the Improvement of Higher Education Personnel - CAPES (Brazil), processes 88887.217374/2018-00 and 88881.171419/2018-01, and the National Council for Scientific and Technological Development – CNPq (Brazil), processes 148184/2019-7, 305055/2017-8, 428650/2018-0 and 440047/2019-6, for the financial support

Synthesis of Heat-Integrated Distillation Sequences with Nonsharp Splits Using a Sequential Metaheuristic Method

Distillation is an energy-intensive process, and it is vital that strategies are developed to improve these processes’ sustainability. Synthesis of heat-integrated distillation sequences (HIDiS) plays a vital role in such a task. By identifying and integrating heat sources and sinks within distillation sequences, these configurations enable effective heat recovery and utilization, leading to reduced energy consumption and environmental impacts. The present work presents a new superstructure-based model with a Pinch-based operator for implicit heat integration (i.e., prediction of heat integration costs) and a stochastic solution approach for developing efficient HIDiS. Explicit heat integration (definition of heat exchanger matches) is then performed in the second part of the method. Two examples in the literature were used to validate the method. In both cases, the strategy presented was able to attain solutions with better total annual costs than those from the literature (15.8 and 11.5% lower). Solutions found with the present approach presented a greater degree of heat integration than those from the literature: more heat recovery units are present with considerably greater total heat duty (about twice greater in example 1, for instance).The authors gratefully thank the National Council for Scientific and Technological Development─CNPq (Brazil), processes 311807/2018-6, 428650/2018-0, 307958/2021-3, 309026/2022-9, from the Coordination for the Improvement of Higher Education Personnel─CAPES (Brazil) and from the Spanish ‘Ministerio de Ciencia y Educación’ under the project PID2021-124139NB-C21 for financial support