Search

The design optimization of heat exchangers is a topic extensively investigated in the literature. The majority of the papers that addressed this problem employed closed-form analytical solutions to...

In a recent study [Parra, A. Ind. Eng. Chem. Res. 2019, 588 3060−3071], the design of reverse osmosis (RO) systems for desalination of water at different concentrations was studied and optimal solu...

In this article, we present for the first time, a globally optimal design procedure of gasketed-plate heat exchangers using a new proposed technique: Set Trimming. Set Trimming is a recently develo...

Separation vessels are traditionally designed based on rules of thumb that guide the designer to a feasible solution. Despite its widespread use, this approach presents important limitations, which...

Shell and tube exchanger design has been formulated as a Mixed Integer Nonlinear Model (MINLM) where area or total annualized cost is optimized. Mixed Integer Nonlinear Programming (MINLP) as well ...

In this article we compare results from different heuristics approaches for the design of VLE separation vessels. In addition, we present an MILP model that embeds the aforementioned heuristics and considers the discrete nature of the geometric variables. We show that different heuristics render different results. In addition, while results from heuristics and MILP often coincide sometime, departures take place. Finally, we show that straight enumeration is viable option for stand-alone design.

Despite the large advances in computational tools attained by the Process Systems Engineering community, industry for the most part still performs basic design of process equipment using trial-and-verification procedures guided by heuristic rules. In this opinion article, we present a discussion on how to depart from the use of these heuristics-based procedures, most step-by-step, sometimes computer-aided. We believe that there are direction changes, some incipient and some in full development already, toward the use of optimization tools for the task. The academic literature is dominated by mixed-integer nonlinear models, solved using different techniques (mostly stochastic or mathematical programming-based). These procedures have practical limitations that have hindered the migration of practitioners away from current heuristics and simplified model-based tools. We discuss these drawbacks and propose solutions. We first show how the use of commercially available discrete values of the design geometrical...

This paper investigates the design optimization of double pipe heat exchanger using mathematical programming. The heat exchanger area is minimized and the thermo-fluid dynamic conditions are consid...

This study presents a globally optimal linear procedure for the simultaneous design of cooling water systems. The optimization entails obtaining optimal pipe diameters, pump selection, and detailed cooler design. For the latter, the Kern model and the linear formulation proposed by Goncalves et al. ( Ind. Eng. Chem. Res. 2017, 56, 5970) were used. The proposed linear model is compared with conventional design procedures, such as optimizing the design of each exchanger first, through area minimization or through area and pressure drop costs. The results illustrate in one of the examples the advantage of using the proposed simultaneous design approach.

In this work, the enumeration algorithms presented in parts I and II for the globally optimal synthesis of heat exchanger networks are extended to consider non-isothermal mixing. The previous models are modified by adding non-isothermal mixing constraints and new models are constructed to target the bounds of the energy consumption and the binding exchanger minimum approximation temperature. These new models are solved using algorithms that involve solving the solution of systems of equations instead of mathematical programming. We also present two alternatives for optimizing each enumerated structure, namely, the use of a global solver, or the use of a golden search with simple resolution of non-isothermal mixing model for fixed energy consumption. The non-isothermal mixing model is reformulated as a convex model, either solved using nonlinear programming or a programming-free methodology, i.e. solving Karush-Kuhn-Tucker equations. A global optimum search algorithm is developed and examples are tested comparing the proposed strategies.

In this work, the enumeration algorithms presented in parts I and II for the globally optimal synthesis of heat exchanger networks are extended to consider non-isothermal mixing. The previous models are modified by adding non-isothermal mixing constraints and new models are constructed to target the bounds of the energy consumption and the binding exchanger minimum approximation temperature. These new models are solved using algorithms that involve solving the solution of systems of equations instead of mathematical programming. We also present two alternatives for optimizing each enumerated structure, namely, the use of a global solver, or the use of a golden search with simple resolution of non-isothermal mixing model for fixed energy consumption. The non-isothermal mixing model is reformulated as a convex model, either solved using nonlinear programming or a programming-free methodology, i.e. solving Karush-Kuhn-Tucker equations. A global optimum search algorithm is developed and examples are tested comparing the proposed strategies.

In this work, we propose a methodology to solve a nonlinear mathematical model for the optimal design of reverse osmosis (RO) networks, which ameliorates the shortcomings of the computational performance and sometimes convergence failures of commercial software to solve the rigorous mixed integer nonlinear programming (MINLP) models. Our strategy consists of the use of a genetic algorithm to obtain initial values for a full nonlinear MINLP model. In addition, because the genetic algorithm based on the rigorous model equations is insurmountably slow, we use metamodels to reduce the mathematical complexity and considerably speed up the run. We explore the effects of the feed flow, seawater concentration, number of reverse osmosis stages, and the maximum number of membrane modules in each pressure vessel on the total annualized cost of the plant.

This article addresses the globally optimal design of kettle vaporizers. Established procedures are heuristics-based trial and verification as well as optimization-based that do not guarantee global optimality. The proposed optimization formulation aims at minimizing heat transfer area; the optimal set of the design variables are the tube length and diameter, number of tube passes, tube layout and pitch, and shell diameter. The problem is solved using Set Trimming, an optimization technique that employs the inequality constraints to gradually reduce the search space until only the feasible candidates remain. After the Set Trimming is performed, the globally optimal solution can be readily found through a simple inspection along the set of remaining viable candidate solutions. This approach has important advantages: it attains the global optimum solution without the need of initial values, there is no convergence drawbacks and it is fast. The performance of the proposed approach is illustrated by its comparison with four different stochastic methods.

In a recent article, Goncalves et al.,11,12 introduced a linear and rigorous methodology for equipment design, in particular shell and tube heat exchanger. Here, we explore its application to air coolers, a problem that we solve globally for the first time. Because the approach is linear, results are globally optimal. The objective function is the total annualized cost. The constraints include the thermal and hydraulic modeling of the process stream flow in the tube bundle and the air flow through the finned surface. In addition, we worked on reducing computing time, through an analysis of different alternatives for the description of the original discrete variables organized in sets of binary variables. The performance of the proposed approach is illustrated through its comparison with an air cooler described in the literature. This article is protected by copyright. All rights reserved.

Typical heat exchanger design procedures are based on the use of fixed values of fouling factors, mostly based on estimates coming from practice. However, fouling depends on thermofluidynamic conditions (e.g. flow velocity) which values are consequence of the selection of design variables (e.g. baffle spacing). Therefore, the inclusion of fouling models into an optimal design procedure may yield better solutions. In this article, we extend a recent globally optimal linear formulation for the design of shell and tube heat exchangers (Goncalves et al., 2017). Our extension leads to a linear model and consists on adding velocity dependent fouling factors. A comparison with design examples based on fixed fouling factors indicates that the linear problem can identify better design solutions, without involving any external convergence loop.

In a recent article (Goncalves et al., AIChE J. 2017. DOI: 10.1002/aic.15556), we presented a mixed-integer linear programming formulation for the detailed design of shell and tube heat exchangers based on the Kern approach (Kern, D. Q. Process Heat Transfer; McGraw Hill, 1950). The formulation relies on the use of standardized values for several mechanical parts, which we express in terms of discrete choices. Because we aim at having this model used as part of more complex models (i.e., heat exchanger networks synthesis), we identified a need to improve its computational efficiency. In this article, we explore several different modeling options to speed up solutions. These options are based on different alternatives of aggregation of the discrete values in relation to the set of binary variables. Numerical results show that these procedures allow large computational effort reductions.

We solve globally an extension of the isothermal mixing stages model (Synheat) proposed by Yee and Grossmann, later extended to nonisothermal mixing by Bjork and Weterlund and solved globally by Faria et al. This new extension of that model was recently presented in a conference proceedings. The model allows specific structures that are more commonly accepted in industry than generalized complex structures that suffer from somewhat disorganized branched and sub-branches which present several practical challenges. This stages/substages superstructure has limited branching and several matches in series in each branch. Our industrial experience shows us that these are acceptable in practice. The novel contribution of this article is then solving such a model globally, adding the control of temperature differences upon mixing

Fouling is a major problem in the operation of heat exchangers, resulting in increased capital, operational, and maintenance costs. Shell-and-tube heat exchangers are traditionally designed using fixed values of fouling resistances, ignoring that fouling rates depend on the exchanger geometry, rendering different fouling resistances for the same thermal service. This article discusses the use of fouling rate models in the design of shell-and-tube heat exchangers. We link a heat exchanger design algorithm to a dynamic simulation of the fouling rate. The proposed procedure is explored for the design of heat exchangers where fouling occurs in the tube side due to crude oil flow. Four examples illustrate how the utilization of the fouling rate model alters the solution of the design problem, including aspects related to a “no fouling” condition in the design, the impact of the duration of the operational campaign in the results, and how the uncertainty in the fouling prediction can be handled.

The literature about heat exchanger design optimization encompasses a large number of papers, but only a small fraction is dedicated to phase change systems. This article presents for the first time a linear design optimization approach for horizontal shell and tube condensers that guarantees global optimality. Area is minimized using an integer linear model. This model is obtained from a mathematical reformulation of the original nonlinear thermofluid dynamic equations and it is solved using integer linear programming (ILP). Because of the linear nature of the proposed model, the global optimum is always attained, without the need of using specialized global solvers, selection of good initial estimates or drawbacks related to convergence issues. Numerical results indicate that the proposed approach can present solutions with lower heat transfer areas than two design procedures presented in chemical process design textbooks.

This work presents a new superstructure for refinery hydrogen networks synthesis. The superstructure eliminates the need to have the pressures of compressors as variables, while both dedicated and shared compressors can be included. As a result of considering the pressures as the parameters known a-priori, the constraint of compression power is expressed by using linear equation. Hydrogen networks synthesis is then formulated as a new mixed integer nonlinear model whose nonlinearities are only attributed to the bilinear and concave terms. The proposed model is a simple optimization problem that could be solved to global optimality. Four literature examples and an industrial case are tested for illustration purpose. The obtained solution results exhibit 3.1–4.5 % reduction in the total annualized cost compared with those of literature ones.

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non-linear and non-convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well-known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. This article is protected by copyright. All rights reserved.

Gas lift technology is one of the most common methods used for wells with insufficient reservoir pressure. It makes use of gas reinjection to enhance individual well production. When several wells are used to produce a reservoir, a problem arises regarding the selection about how to produce each well so that overall production can be maximized. To accomplish it, one needs to determine the optimal production of each well and how much gas ought to be injected. In this article, we revise previous efforts and present a new MINLP model, which we solve globally using RYSIA, a recently developed global optimization algorithm (Faria and Bagajewicz, AICHE J. 58 (8) 2320–2335).

We present an extension of a previously presented superstructure (Floudas et al., 1986) for heat exchanger network grassroots design. This extension is such that it includes several matches between two streams, activates splitting control and allows for mixing temperature control. We solve this model globally using RYSIA, a recently developed method bound contraction procedure (Faria and Bagajewicz, 2011a, 2011b, 2011c; Faria et al., 2015). We also add a new RYSIA feature called Lifting Partitioning. Results show structures that cannot be obtained using the stages model (Yee and Grossmann, 1990) or other similar restrictive models.

This paper presents a mathematical programming approach for the design of counter current gasketed plate heat exchangers. The objective function corresponds to the minimization of the heat transfer area and the set of constraints includes the thermofluid-dynamic equations for evaluation of film coefficients and pressure drops, the heat transfer rate equation, and bounds on velocities and pressure drops. We also consider discrete geometric options. The expressions of the objective function and constraints are reformulated into a linear form, without loss of rigor, i.e. the solution of the linear problem is exactly the same of the original one. Therefore, problems related to nonconvergence or multiple local optima with different values of objective function are avoided. An example of a typical design task is employed to illustrate the performance of the proposed approach.

In this article, the water source diagram (WSD) ( Gomes et al., 2007 ) is extended to the design of water networks involving both fixed flowrate and fixed contaminant load, as well as water loss/gain operations. The algorithm targets minimum external water consumption while simultaneously synthesizing the corresponding water system structure. In addition, it is shown that the WSD can be applied to water allocation problems (WAP) based only on water sources and sinks, maintaining its good performance. To illustrate the methodology, case studies handling hybrid water system are presented, including a zero wastewater discharge discussion and data from a Brazilian pulp mill.

Even though the last decades have seen an explosion of simulation and optimization tools in Process Systems Engineering, this has not had a significant impact in the basic design of equipment such as heat exchangers, condensers, reboilers, distillation columns, absorption, adsorption columns, etc. To this date most mainstream textbooks advocate the use of trial and error procedures, while scattered work has been done using MINLP methods. In addition, these methods are most of the time local and/or do not converge if no good initial points are provided. We provide here alternatives to formulate global and robust rigorous models, sometimes linear. In this paper, we discuss the challenges that this quest is presenting.

We modify our recently introduced bound contraction methodology for global optimization of bilinear MINLP models1 to solve the stage-wise superstructure model for heat exchanger networks.2 Because the problem has nonlinearities that are not bilinear or quadratic instead of converting the problem into a fully quadratic one, which would add much more variables and equations, we use a different relaxation approach that takes advantage of monotonicity. Aside from the original bound contraction method, we also use branch and bound combined with bound contraction at each node.

In this paper, we show the implementation of the Generalized Likelihood Ratio (GLR) method to detect and also identify the size and location of leaks in pipelines. We introduce the use of accurate hydraulic models for hypothesis testing and the use of economics to determine the thresholds of detection and identification. We compare the leak detection power and costs to those of other simple leak detection methods. The economic comparison includes computing the losses for not detecting the leaks (false negatives) and detecting leaks that do not exist (false positives). We also illustrate the improvement in the power of our method by using more-accurate instrumentation.

When there was a lack of computing power, several approximate formulas (Weymouth, Panhandle, AGA, etc.) were developed to obtain pressure drop in gas pipelines, which are in many instances still be...

We review the performance of different technologies published in a recent patent by Ji and Bagajewicz (2007) aimed at increasing distillates yield. We also present different implementation schemes composed of various combinations of the two technologies and compare both distillate yield and energy expenditure to the current conventional distillation process for light, intermediate, and heavy crudes. We demonstrate sizable increases of yield as well as significant profit. The criteria for analysis were yield, energy savings, gross margin, and potential extra revenue for each scheme. While the comparisons are made on the basis of grassroots design, we took one technology and assumed a retrofit of an existing column via simple change in the heat recovery, to assess the extra investment needed.

Design optimization of air coolers is often presented limiting fan calculations to the required power, without considerations of fan capabilities or commercial viability. In this article, new design optimization procedures are presented to include the selection of a commercial-type fan and, thus, the air flow rate as a variable. The resulting model is a mixed integer nonlinear programming (MINLP) problem, which is solved globally, using three different enumeration procedures, and the performance among them is compared. The proposed approaches are illustrated by two case studies. Results showed that the smart enumeration scheme can provide the global solution in an acceptable computational time even when considering large problems.

The minimum number of units in a network has been proposed to be obtained using a very simple formula using graph theory (Hohmann, E. C. Ph.D. Thesis, University of Southern California, Los Angeles, CA, 1971.; Linnhoff, B. et al. Comput. Chem. Eng. 1979, 3, 295). This is done, usually, assuming that thermodynamic feasibility holds, especially in Pinch technology, where it is applied above and below the pinch, but also for cases where the pinch is ignored. While the failure of this formula is informally known in the community, to our knowledge no realistic counterexample was presented before. We provide such an industrial counterexample. In addition, we propose to use a recently developed MILP model (Barbaro, A., and Bagajewicz, M. Comput. Chem. Eng. 2005, 29, 1945) that guarantees finding the global minimum number of exchangers. Finally, we point out the large number of alternative solutions that real industrial problems may exhibit.

This paper presents a comparison of two heat exchanger network retrofit methods as they are applied to crude units: the well-known and widely used Pinch Design Method (PDM) and a recently developed...

In heat exchangers, fouling is the undesired accumulation of deposits over the equipment thermal surface. This phenomenon causes a gradual reduction of the overall heat transfer coefficient. The traditional approach to handle the fouling problem during the design consists in the introduction of fouling factors in the evaluation of the (dirty) overall heat transfer coefficient. However, this approach ignores the fact that the fouling rate is dependent on the flow velocity and temperature. Aiming to fill this gap, this paper investigates the optimization of the design of heat exchangers including fouling modelling. Among the many fouling manifestations, this investigation focuses on chemical reaction fouling in crude oil streams associated to the presence of asphaltenes, modelled by a threshold model (Ebert Panchal model and its variants). According to this model, there are conditions of surface (or film) temperature and flow velocity where there is no fouling. The developed formulation of the design problem employs a mixed integer linear programing approach, where the geometry-related design variables are defined based on standard values. The results are compared with a traditional approach with fixed fouling factor, which indicates a potential reduction of capital costs.

In this paper, we address the strategic planning of integrated bioethanol–sugar supply chains (SC) under uncertainty in the demand. The design task is formulated as a multi-scenario mixed-integer linear programming (MILP) problem that decides on the capacity expansions of the production and storage facilities of the network over time along with the associated planning decisions (i.e., production rates, sales, etc.). The MILP model seeks to optimize the expected performance of the SC under several financial risk mitigation options. This consideration gives a rise to a multi-objective formulation, whose solution is given by a set of network designs that respond in different ways to the actual realization of the demand (the uncertain parameter). The capabilities of our approach are demonstrated through a case study based on the Argentinean sugarcane industry. Results include the investment strategy for the optimal SC configuration along with an analysis of the effect of demand uncertainty on the economic performance of several biofuels SC structures.