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The prediction of important control properties is a challenging task for shell and tube heat exchangers design. Dynamic models, which include fouling effects, are still poorly investigated in the recent literature. To study the behavior of variable conditions over time and its influence on the dynamic aspects of the system, a design approach based on TEMA standards has been proposed, aiming to analyze the process in a more realistic equipment. To study the behavior of time-varying conditions and its influence in the system dynamics, the model considered in this work is based on the idea of heat exchanger cells as the basic modeling element. This kind of approach has some advantages over the distributed model, such as continuous variables in time and discrete in space, leading to ordinary differential equations (ODE) and also providing the possibility of controlling the model complexity by adjusting the number of modeling cells. The ratio between output and input signals in each cell generates eight operator transmittances that describe the dynamic of the system. The influence of fouling in the dynamic behavior is evaluated by considering its resistance (R f) as a function of time. The model was implemented in MATLAB/Simulink and simulations have been carried out for different R f values with a step change in three input variables. Open loop responses showed that as R f increases, the quality of response is deteriorated and the system is affected mainly by the inertia and thermal exchange inefficiency.

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Fouling is one of the main causes of industrial problems regarding operation and control of shell and tube heat exchangers. Although fouling is a time dependent phenomenon, most papers in the literature focus on fouling mitigation in steady-state heat recovery. In this work, a lumped parameter model to describe time-varying conditions and their influence in controller tuning is presented. For each modeling cell, there are four input variables (inlet temperatures and flow rates for shell and tube sides), which generate two output signals (outlet temperatures for shell and tubes). The influence of fouling in process control is evaluated by considering intermediate values of thermal resistance of fouling (R f), simulating its variation with time. The model was implemented in MATLAB/Simulink, and simulations have been carried out for different periods of operation. A step change was applied in the shell flow rate to evaluate the response in the tube outlet temperature. Results show that periodic fitting in proportional integral derivative (PID) parameters are needed to keep the tube outlet stream at the desired temperature. Moreover, two optimization strategies are presented for tuning controller gains constrained by some step response performance indicators. Three case studies have been taken as benchmarks, and results show that this strategy is promising.

Water Distribution Networks (WDN) are the main component of industrial and urban water distribution systems and are currently formed by pipes, nodes, and loops. In the present paper a deterministic Mathematical Programming approach is proposed, aiming to minimize the cost of looped WDN, considering known pipe lengths and a discrete set of available commercial 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 appropriated pressure drops and water velocities. Generalized Disjunctive Programming is used to reformulate the discrete optimization problem to a Mixed Integer Non-Linear Programming (MINLP) problem. GAMS (General Algebraic Modeling System) environment is used to solve This is a previous version of the article published in

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