Water distribution networks optimization considering unknown flow directions and pipe diameters

Water Distribution Networks (WDN) are present in a large number of industrial processes and urban centers. Reservoirs, pipes, nodes, loops, and pumps compose WDN and their design can be formulated as an optimization problem. The main objective is the minimization of the network cost, which depends on the pipe diameters and flow directions known a priori. However, in the design of new WDN in real industrial problems, flow directions are unknown. In the present paper, a disjunctive Mixed Integer NonLinear Programming (MINLP) model is proposed for the synthesis of WDN considering unknown flow directions. Two case studies are employed to test the model and global optimization techniques are used in its solution. Results show that the global optima WDN cost with the correct flow directions is obtained for the studied cases without the necessity of using additional software to calculate pressure drops and velocities in the pipes.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development —CNPq (Brazil), the Coordination for the Improvement of Higher Education Personnel —Process 88881.171419/2018-01 –CAPES (Brazil) and the Ministério de Economía, Industria y Competitividad CTQ2016-77968-C3-02-P (FEDER, UE)

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

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

The fluctuation in the consumption of treated water is a situation that distribution networks gradually face. In times of greater demand, this consumption tends to suffer unnecessary impacts due to the lack of water. The uncertainty that occurs in water consumption can be mathematically modeled by a finite set of scenarios generated by a normal distribution and attributed to the network design. This study presents an optimization model to minimize network installation and operation costs under uncertainties in water demands. A Mixed Integer Nonlinear Programming model is proposed, considering the water flow directions in the pipes as unknown. A deterministic approach is used to solve the problem in three steps: First, the problem is solved with a nominal value for each uncertain parameter. In the second stage, the problem is solved for all scenarios, with the independent variables of the scenario being fixed and obtained from the solution reached in the first stage, known as the deterministic solution. Finally, all scenarios are solved without fixing any variable values, in a stochastic approach. Two case studies were used to test the applicability of the model and global optimization techniques were used to solve the problem. The results show that the stochastic solution can lead to optimal solutions for robust and flexible water distribution networks, capable of working under different conditions, considering the uncertainties of node demand and variable pipe directions.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development (Brazil), process 309026/2022-9

Optimization of water distribution networks using a deterministic approach

Water distribution networks (WDNs) are the main component of industrial and urban water distribution systems and are currently formed by pipes, nodes and loops. In this article, a deterministic mathematical programming approach is proposed, aiming to minimize the cost of looped WDNs, considering known pipe lengths and a discrete set of commercially available diameters. The optimization model constraints are mass balances in nodes, energy balances in loops and hydraulic equations, in such a way that no additional software is needed to find the appropriate pressure drops and water velocities. Generalized disjunctive programming is used to reformulate the discrete optimization problem to a mixed-integer nonlinear programming (MINLP) problem. The GAMS (General Algebraic Modeling System) environment is used to solve the problem. Four cases are studied to test the applicability of the model and the results show compatibility with the literature.This study was financially supported by 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 428650/2018-0 and 440047/2019-6]; and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

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

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

Water Distribution Networks Optimization Using Disjunctive Generalized Programming

Water Distribution Networks (WDN) are systems of water distribution used in industrial processes and urban centers. The optimal WDN design can be very effective in saving energy, specifically in pumping service, to carry water to nodes of demand, at appropriated velocities and pressures. Indirectly, it can contribute in reducing liquid pollution and accidents caused by pressure overestimation in nodes. The design of WDN can be treated as an optimization problem with a Mixed Integer Nonlinear Programming (MINLP) formulation. The objective function, to be minimized is the WDN cost, given by the product of the pipe diameters and their lengths. The problem constraints are the mass balances in each node, the energy balances in the WDN loops and pressure and velocities limits. A set of commercial diameters is available, with proper costs and rugosity coefficients. The majority of paper published in this research field use external hydraulic simulators and meta-heuristic methods to solve the optimization problem. In the current paper a mathematical model using a deterministic Mathematical Programming approach is proposed and all variables are simultaneously optimized, avoiding the use of external software for pressure and velocities calculations. Two case studies were used to test the model applicability and coded in GAMS, using the global optimization solver BARON. Results showed that for both cases global optima was achieved, proving that it is possible to solve the problem, independently of external hydraulic simulator.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development - CNPq (Brazil), the Coordination for the Improvement of Higher Education Personnel - Process 88881.171419/2018-01- CAPES (Brazil) and the Spanish Ministerio de Economía, Industria y Competitividad CTQ2016-77968-C3-02-P (FEDER, UE)

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