Dynamic Optimization of the Flow Rate Distribution in Heat Exchanger Networks for Fouling Mitigation Bruna C. G. Assis, ‡ Julia C. Lemos, † Fa ́ bio S. Liporace, ‡ Se ́ rgio G. Oliveira, ‡ Eduardo M. Queiroz, § Fernando L. P. Pessoa, § and Andre ́ L. H. Costa* ,† † Instituto de Química, Rio de Janeiro State University (UERJ), Rua Sã o Francisco Xavier, 524, Maracanã , Rio de Janeiro, RJ, CEP 20550-900, Brazil ‡ Petrobras Research & Development Center (CENPES/PETROBRAS), Cidade Universita ́ ria, Avenida Hora ́ cio Macedo, 950, Rio de Janeiro, RJ CEP 21949-900, Brazil § Escola de Química, Federal University of Rio de Janeiro (UFRJ), Avenida Athos da Silveira Ramos, 149, Ilha do Fundã o, Rio de Janeiro, RJ CEP 21949-900, Brazil ABSTRACT: Heat exchanger networks are structures composed of a set of heat exchangers interconnected in order to reduce utilities consumption. During the network operation, heat exchangers may present a decrease of their thermal effectiveness caused by fouling, which corresponds to the undesirable accumulation of deposits over their thermal surface. In this context, this paper presents a proposal to increase the energy recovered in heat exchanger networks affected by fouling through the optimization of the distribution of the flow rates of the process streams. The problem corresponds to a dynamic optimization problem, because the flow rate optimization affects the surface temperature and velocity, which modifies the fouling rate, thus demanding the simultaneous analysis of the entire time horizon. The objective function is represented by the integral of the utility consumption during the operational time horizon. The main constraints include mass and energy balances, heat exchangers equations (P-NTU method), and fouling rate modeling. The mathematical structure of the problem corresponds to a nonlinear optimization. The utilization of the optimization scheme is illustrated by the analysis of two examples of heat exchanger networks. 1. INTRODUCTION Heat exchanger networks (HENs) are structures composed of a set of interconnected heat exchangers which promote the heat transfer between process streams, therefore allowing a reduction in the utility consumption in process plants. Because of the increase of energy costs, the design of these systems has attracted considerable attention since the 1980s of the last century. 1 However, the energy efficiency increase obtained through a HEN may be severely disturbed by fouling. Heat exchanger fouling is the undesirable accumulation of deposits over the heat exchange surface. This phenomenon introduces extra resistances in the thermal circuit, bringing a reduction of the overall heat transfer coefficient. As a consequence, there is a diminution of the heat exchanger effectiveness. The literature presents several approaches for fouling mitigation based on the utilization of computational resources. Considering the operation of a HEN, a subject widely investigated corresponds to the optimization of the cleaning schedule of the heat exchangers. This mitigation technique was explored using mixed-integer nonlinear programming (MINLP), 2-4 mixed-integer linear programming (MILP), 5-7 and stochastic methods. 4,8 More recently, additional aspects were explored together with the cleaning schedule: manipu- lation of by-passes, 8 desalter control, 9 and hydraulic behavior. 10 Fouling mitigation can also be considered during the design of individual heat exchangers, 11,12 HEN synthesis/retrofitting, 13,14 or the utilization of heat transfer enhancement devices in the HEN synthesis. 15,16 Another approach for fouling mitigation involves the optimization of the distribution of the flow rates in HENs. This approach was proposed for fouling management in crude preheat trains by Oliveira Filho et al., 17 based on a steady-state modeling of the system using a given set of fouling resistances. The extension of this formulation also considering the hydraulic behavior of HENs through a constrained mathemat- ical programming problem was explored in Assis et al. 18 The flow split optimization associated with the cleaning of parallel heat exchangers was studied in Ishiyama et al. 19 A previous work involving the operational optimization of the flow rate distribution in HENs, not linked to fouling issues, can be found in Lid et al. 20 However, the redistribution of the flow rates along the heat exchangers in a network may have a strong effect on the fouling rate. In these cases, the application of the optimal solution found for a given instant may bring a potential loss of the energy recovery in the future, due to the impact of the modification of the fouling rates; that is, the set of adopted flow rates can determine an increase of fouling in certain heat exchangers which may cause an opposite effect in the energy recovery when considering the entire operational horizon. An additional discussion about the impact of flow rate distribution Received: May 30, 2014 Revised: May 4, 2015 Accepted: May 12, 2015 Published: May 12, 2015 Article pubs.acs.org/IECR © 2015 American Chemical Society 6497 DOI: 10.1021/acs.iecr.5b00453 Ind. Eng. Chem. Res. 2015, 54, 6497-6507