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.

In almost all previous approaches for the design optimization of shell-and-tube heat exchangers, global optimality was not guaranteed. Recognizing that the geometric components are discrete due to its physical nature (e.g., number of baffles) or commercial standards (e.g., tube diameter), purely integer linear models or mixed integer linear models using the Kern or the Bell-Delaware models were developed in previous work and solved globally using mathematical programming. The time used to solve these models was relatively small but still too large when repeated calculations are needed. We show in this article that the use of Set Trimming avoids using mathematical programming (MINLP or MILP) and reduces the computational time by at least 2 orders of magnitude.

No abstract

No abstract

This article presents a method for the mathematical optimization of the design of heat exchangers including fouling rate modeling for the tube-side. The description of the fouling rate in crude preheat trains of petroleum distillation units is commonly based on threshold models (Ebert-Panchal model and its variants). Our formulation of the design problem employs a mixed-integer linear programing approach; therefore the solution is the global optimum and common nonconvergence drawbacks of mixed-integer nonlinear programming models are totally avoided. Three different examples are employed to compare the proposed approach with an optimization procedure using fixed fouling resistances. The results indicate that in two problems was possible to obtain design solutions associated to smaller heat exchangers. Additionally, three case studies are also explored to discuss how fouling is related to crude types, pressure drop manipulation, and energy integration.In heat exchanger design, it is common to consider some constraints regarding relations between geometric variables. The baffle spacing must be limited between 20 and 100% of the shell diameter 22 and also the ratio between the tube length and shell diameter must be between 3 and 15 23