(171h) A Superstructure-Based Model for Multistream Heat Exchanger Design within Flow Sheet Optimization

A multistream heat exchanger (MHEX) is a special heat-transfer equipment that allows multiple streams to exchange heat simultaneously. Its typical applications include air separation, natural gas (NG) processing, liquid hydrogen, petrochemicals, and liquefied natural gas (LNG).¹ Most processes employing MHEXs are capital- and energy intensive, and often involve phase changes of multicomponent mixtures. Consequently, modeling and optimization of such processes require efficient models for MHEXs that can ensure the feasibility of all heat exchanges, accommodate arbitrary phase changes, use phase-dependent nonlinear stream properties, and enable seamless and simultaneous optimization of the overall process. The design targets (e.g. flows and exchange areas) for MHEXs and operational (e.g. flows, temperatures, pressures, etc.) targets for the flowsheet are obtained from such optimization.²

While commercial process simulators have MHEX models, these models are generally proprietary, and do not inherently impose ensure minimum driving force for heat transfer.^3,4 Considering these problems, Kamath et al.³ proposed a pinch-based equation-oriented formulation for MHEXs that ensures minimum driving force during flowsheet optimization. Their model is a special case of simultaneous optimization and heat integration of chemical processes without utilities. They presented a disjunctive formulation to handle phase changes, and approximated the non-differentiable max function, inherent in a pinch-based model, by a smoothing function. Watson et al.⁴ revised the equation describing the pinch locator from Kamath et al.³, and suggested a non-smooth solution strategy for the design and simulation of MHEXs. However, their study primarily focused on the simulation of MHEXs outside of an optimization framework. On the other hand, Pattison and Baldea² introduced a pseudo-transient framework for the equation-oriented modeling of MHEX avoiding Boolean variables. Their formulation involves ordinary differential and algebraic equations (DAEs), ensures feasible heat exchange, handles phase changes, and is suitable for flowsheet optimization applications. MHEXs can also be modeled as a network of two-stream exchangers as opposed to the composite-curve approach. Yee et al.⁵proposed a stage-wise superstructure for simultaneous heat integration along with area and energy targeting, and presented its application to model an MHEX. However, they assumed constant heat capacities, and did not account for phase changes. Furthermore, they assumed isothermal mixing and neglected pressure drops.

In this work, we propose an equation-based model for MHEX design that guarantees the feasibility of heat exchanges, and allows seamless and simultaneous overall process optimization. This model accommodates arbitrary and unknown phase changes of streams during the optimization process without the need to use any Boolean variables. Similar to Yee et al.⁵, we treat the MHEX as a network of simple two-stream exchangers, but with a novel single-stage superstructure. Since we address overall process optimization and MHEX design, the state variables (flows, compositions, inlet/outlet temperatures, and inlet/outlet pressures) of MHEX streams may be unknown optimization variables. Our formulation is novel, uses exact physical properties from a process simulator, and offers three advantages for MHEX design. First, it provides heat transfer areas for each pair of heat-exchanging streams in the MHEX. Second, it allows the user to impose constant-phase two-stream heat exchanges, if desired. This enables better estimation of heat transfer coefficients (HTCs). Third, the use of precise HTCs and simulator-based physical properties result in accurate heat exchange areas. Lastly, our formulation uses a new form of the LMTD constraints to eliminate the numerical problems arising due to non-positive arguments in a logarithmic function.

We use the two most complex case studies in the literature^2-4 to illustrate the capabilities of our model to optimize processes employing MHEXs. The first study (Liquefied Energy Chain or LEC) is a transport chain to produce LNG from stranded natural gas using liquid inert nitrogen (LIN) and liquid carbon dioxide (LCO2). It was first suggested by Wechsung et al.⁶, and subsequently simulated by Watson et al.⁴. The second study (PRICO®) is an industrial natural gas liquefaction process discussed by Kamath et al.³ and Pattison and Baldea.² For the first case study, we consider more variables for optimization than the literature⁶, minimize LIN flow and report a comparable solution (0.8979 kg/s vs 0.898 kg/s⁶). For the second study on the highly non-linear PRICO® process, we reduce the compressor power by 5.16% over the best-reported solution in the literature.²

References:

1. Hasan MMF, Karimi IA, Alfadala HE, Grootjans H. Operational modeling of multistream heat exchangers with phase changes. AIChE Journal. 2009;55(1):150-171.

2. Pattison RC, Baldea M. Multistream heat exchangers: Equation-oriented modeling and flowsheet optimization. AIChE Journal. 2015;61(6):1856-1866.

3. Kamath RS, Biegler LT, Grossmann IE. Modeling multistream heat exchangers with and without phase changes for simultaneous optimization and heat integration. AIChE Journal. 2012;58(1):190-204.

4. Watson HAJ, Khan KA, Barton PI. Multistream heat exchanger modeling and design. AIChE Journal. 2015;61(10):3390-3403.

5. Yee TF, Grossmann IE, Kravanja Z. Simultaneous optimization models for heat integration—I. Area and energy targeting and modeling of multi-stream exchangers. Computers & Chemical Engineering. 1990/10/01 1990;14(10):1151-1164.

6. Wechsung A, Aspelund A, Gundersen T, Barton PI. Synthesis of heat exchanger networks at subambient conditions with compression and expansion of process streams. AIChE Journal. 2011;57(8):2090-2108.