(363w) A New MILP Formulation for Scheduling Cleaning in Heat Exchanger Networks Consisting of Multi-Pass Heat Exchangers

Global industrial energy requirement has been increasing due to a continuously growing population and fast economic growth. The process industries, such as refineries, food, and paper industries, are the primary energy consumers, utilizing nearly 30 to 40 % of overall industrial energy consumption worldwide (Conti et al., 2016). Besides this, they contribute a large share of greenhouse gas (GHG) emissions. For instance, globally, refineries contributed 4% of the total GHG (1.3 Gigatons) in 2018 (Lei et al., 2021). Hence, energy-efficient operations in process industries is critical. Process industries widely use heat exchanger networks (HENs) to optimize energy usage. However, the operational efficiency of HENs degrades due to foulant deposition. Fouling has reportedly cost about 0.25% of the GDP of industrialized countries (Macchietto et al., 2011). A study indicated that it leads to ~ 2.5% of global anthropogenic CO2 emissions (Müller-Steinhagen et al., 2009). Hence, mitigating fouling is essential to maintain an optimal energy consumption. This paper proposes an approach to schedule the cleaning of heat exchangers that are susceptible to fouling.

There are two major approaches for fouling mitigation in HENs: The Proactive approach, involves an optimal design and retrofitting of heat exchangers that leads to minimum foulant deposition. The Reactive approach, involves changing the flowrates and cleaning heat exchangers in an optimal fashion such that the impact of foulants that are already deposited would be minimized (Rodriguez and Smith, 2007). This paper seeks to mitigate the impact of fouling using the latter approach. Specifically, a method is proposed to provide optimal schedules for cleaning heat exchangers in a HEN.

Usually, heat exchangers can be modeled using two methods: (1) Mean Temperature Difference (MTD) method, such as Logarithmic Mean Temperature Difference (LMTD), and (2) Effectiveness method, such as ε-NTU, P-NTU (ε:Effectiveness, P:Temperature Effectiveness, NTU: Number of Transfer Units). The methods differ in their mathematical formulations. The MTD method obtains outlet temperatures directly for single pass arrangement and requires multiple iterations for other flow arrangement. Therefore, a MILP based on the MTD method, such as that presented by Lavaja and Bagajewicz (2004), is suitable only for single-pass exchangers; it cannot represent multi-pass heat exchangers adequately within a mathematical program. On the other hand, the effectiveness method results in a set of linear equations for any flow arrangement that can be solved simultaneously to obtain the outlet temperatures directly. MILP with effectiveness method can prove to be adequate in this case and is the approach pursued here.

A MILP based on the effectiveness approach requires linearization of bilinear terms, arising from the product of a continuous variable (temperature) and a binary variable (cleaning heat exchanger). This paper addresses this gap by completely linearizing the MILP with P-NTU model. The proposed approach is flexible and can accommodate different cleaning periods for different heat exchangers. Also, it can represent various fouling behaviors, such as linear and asymptotic that are commonly observed in the industries. In this paper, we first validate our formulation by demonstrating that the schedules obtained by the proposed method are similar to those reported in literature for two examples: a standalone heat exchanger and a small HEN, where all heat exchangers are single pass. Next, we demonstrate the method using multi-pass heat exchangers where existing methods are insufficient. We consider two large HENs with eleven and nineteen multi-pass heat exchangers. Our results show that the proposed method produces more an economical cleaning. In this work we will present the proposed formulation and report results for the above case studies.

Keywords: Heat exchanger networks, fouling, optimal cleaning scheduling, MTD model, Effectiveness model.

References

1. Assis, B. C., Lemos, J. C., Queiroz, E. M., Pessoa, F. L., Liporace, F. S., Oliveira, S. G., & Costa, A. L. (2013). Optimal allocation of cleanings in heat exchanger networks. Applied thermal engineering, 58(1-2), 605-614.
2. Conti, J., Holtberg, P., Diefenderfer, J., LaRose, A., Turnure, J. T., & Westfall, L. (2016). International energy outlook 2016 with projections to 2040(No. DOE/EIA-0484 (2016)). USDOE Energy Information Administration (EIA), Washington, DC (United States). Office of Energy Analysis.
3. Lavaja, J. H., & Bagajewicz, M. J. (2004). On a new MILP model for the planning of heat-exchanger network cleaning. Industrial & engineering chemistry research, 43(14), 3924-3938.
4. Lei, T., Guan, D., Shan, Y., Zheng, B., Liang, X., Meng, J., ... & Tao, S. (2021). Adaptive CO2 emissions mitigation strategies of global oil refineries in all age groups. One Earth, 4(8), 1114-1126.
5. Macchietto, S., Hewitt, G. F., Coletti, F., Crittenden, B. D., Dugwell, D. R., Galindo, A., Jackson, G., Kandiyoti, R., Kazarian, S. G., Luckham, P. F., Matar, O. K., Millan-Agorio, M., Müller, E. A., Paterson, W., Pugh, S. J., Richardson, S. M., & Wilson, D. I. (2011). Fouling in crude oil preheat trains: A systematic solution to an old problem. Heat Transfer Engineering, 32(3–4), 197–215.
6. Müller-Steinhagen, H., Malayeri, M. R., & Watkinson, A. P. (2009). Heat exchanger fouling: environmental impacts. Heat Transfer Engineering, 30(10-11), 773-776.