Integration of Optimal Cleaning Scheduling and Control of Heat Exchanger Networks Undergoing Fouling: Model and Formulation

Abstract

The performance and operability of heat exchanger networks (HENs) is strongly affected by fouling, which involves the deposition of unwanted material, which reduces the heat-transfer rate and increases the pressure drop, the operational costs, and the environmental impact of the process. Periodical cleaning and control of the flow rate distribution in the HEN are used to mitigate the effects of fouling and restore the performance of the units. The optimal cleaning scheduling has been formulated as a mixed-integer linear programming (MILP) or mixed-integer nonlinear programming (MINLP) problem and is solved using various approaches. The optimal control has been formulated as a nonlinear programming (NLP) problem and is used to define the flow rate distribution of the network. Both problems share the same objective: minimization of the total cost of the operation. In principle, the simultaneous solution of the optimal control problem and the optimal cleaning scheduling problem should provide greater savings than the independent or sequential solution of the two problems, since the interactions of the two mitigation alternatives are considered. However, these two problems have been typically considered separately, because of modeling and solution challenges. Also, it is not quite clear what additional benefit a simultaneous solution may bring. The challenges for solving the integrated problem are the large scale of the associated optimization problem and the different time scales involved in each operational layer. Here, a general and efficient formulation is proposed, using a continuous time discretization scheme for the integrated problem of scheduling and control of HENs subject to fouling. A dynamic model of the heat exchangers is proposed that is sufficiently detailed to represent the physics of interest with novel modifications to address simultaneously their control and scheduling in a network. The problem is formulated as a MINLP and solved using deterministic optimization algorithms. The flexibility of the model and variations of the formulation are demonstrated with two small case studies. The formulation complexity versus scale and advantages are analyzed. The results show that considering the two problems simultaneously has a very strong synergistic effect, with over a 20% decrease in operational cost achieved, in comparison to using either fouling mitigation alternative individually.

Assessment of a Dynamic Model for the Optimization of Refinery Preheat Trains under Fouling

“…A preheat train model must include individual exchangers and how they are connected in a network. As detailed in [16] a HEN is defined as a multigraph that describes the nodes, the connections between them, and the direction of flow among the nodes for different streams. Nodes are classified as sources ( ), sinks ( ), flow splitters ( ), flow mixers ( ), and exchangers ( ).…”

“…Model B: this simpler, radially-distributed but axially-lumped parameter exchanger model (hence, 1 D-distributed) considers the overall effect of the exchanger inputs on the outputs, without much detail for the heat transfer or deposit distribution inside the unit. The model, detailed in [16] is based on the P-NTU approach [32] and the definition of the P-efficiency (the actual heat transfer in the exchanger with respect to the maximum possible heat transfer), which is related to the number of transfer units and the exchanger geometry. The time evolution of the system is given by the fouling/ageing model, and at every time a steady state algebraic model for the exchangers determines the outlet streams temperature and pressure.…”

“…The result is a rather large number of discrete variables, and a problem complexity directly related to the size and characteristics of the model. A comprehensive complexity analysis is given in [16]. A reformulation of the problem is presented in [35] to reduce the number of discrete variables, together with a solution method based on the sequential solution of nonlinear programming (NLP) problems, instead of the substantially more challenging and problematic MINLP problems.…”

“…This methodology is applied to eight HENs taken from the literature, all at the hot end of refinery preheat trains [13,16,29,30]. The networks range from small (2 exchangers) to relative large ones with 9 exchangers.…”

A Modeling Framework to Investigate the Influence of Fouling on the Dynamic Characteristics of PID-Controlled Heat Exchangers and Their Networks

“…In recent years, various approaches to the mitigation of fouling effects in industrial HEs and HENs have been reported in the literature [3,4]. Fouling leads to the reduction of steady-state heat recovery [5], but also to changes in the transient states of HEs [6] and inefficient control of HEs [7,8] that may have an adverse effect on the overall performance of the HEN [9,10]. In the literature, publications devoted to the effect of fouling on the dynamic behavior of HEs and the role of fouling in control issues are rare and limited in scope [11,12].…”