(538c) The Impact of Problem Formulation On LNG Process Optimization

Liquefaction of natural gas requires energy-intensive low-temperature refrigeration, and the energy efficiency of the refrigeration process is important for the economy of a liquefied natural gas (LNG) plant. In an LNG process, the energy efficiency depends heavily on the irreversibilities in the heat transfer process. As the exergy of heat increases significantly with decreasing temperature below ambient, the heat transfer temperature differences should also be reduced. A consequence of the small temperature driving forces is of course an increased area requirement for the heat exchanger.

The main objective of process design is to minimize total annual cost (TAC), composed of the operating cost and the annualized investment cost. In general, the operating cost decreases with increasing energy efficiency, while the investment cost increases. Reducing the temperature difference in heat transfer processes will reduce the irreversibilities but increase the required heat exchanger area. Thus the purpose of optimization is to find the optimal trade-off between operating and investment costs.

The investment cost is a complex function of the process design, and accurate calculations require detailed data. Therefore, in the initial design phase, the optimization objective is often simplified, by using an approximation for the investment cost. Due to the fact that operating cost is dominating, an alternative to minimizing TAC is to minimize the energy use (power in the compressors). In order to accommodate the trade-off between energy efficiency and heat exchanger area requirements, one or more constraints can be added to the optimization problem.

In heat exchanger network synthesis for above ambient processes, the trade-off between operating cost and investment cost is represented by a specification of a minimum allowed temperature difference (ΔT_min) that is acting as an economic parameter. The value of the specified ΔT_min depends on the application, and may be specified individually for the different heat exchangers in the network. The minimum temperature difference may also be subject to optimization, to find the optimal trade-off [1, 2]. In processes operating above ambient temperature, this minimum temperature difference has proven to be a useful economic trade-off parameter.

A minimum temperature difference is also often used in the design of sub-ambient processes where refrigeration is required. However, as observed by Jensen and Skogestad [3], this may not give the optimal design. By replacing the minimum temperature difference constraint by a maximum area constraint represented by the lumped UA parameter where U is the total heat transfer coefficient and A is the heat transfer area, the process power consumption was found to be reduced for the same heat exchanger area requirement. Minimizing a simplified cost function was also found to give better solutions than specifying a minimum temperature difference constraint [3].

When the optimization problem is formulated with a minimum temperature difference constraint, the optimal solution will favor a constant temperature difference (equal to the minimum allowed) throughout the whole heat transfer process. However, from a power consumption point of view, the heat exchanger area (or UA) should not be uniformly distributed (will be a consequence of having a constant temperature difference in the entire exchanger) along the temperature span of the cooling load. Due to the increasing exergy of heat with decreasing temperature below ambient, the temperature difference in the cold end of the heat exchanger is more important for the irreversibilities than the temperature difference in the warm end. These irreversibilities caused by heat transfer at finite temperature difference then translate proportionally into compressor work in the refrigeration process. As reported in various sources [4, 5], for certain simplifying but quite reasonable assumptions, the heat exchanger area is best utilized if the temperature difference is a linear function of the absolute temperature (Kelvin).

In this work, different formulations of the objective function and the constraints are evaluated and compared. The inadequacy of the minimum temperature difference constraint is found to increase with decreasing temperature level and increasing temperature span of the refrigerant cooling load, indicating its weakness in LNG process design. A challenge associated with several of the alternative formulations of the objective or the constraints is to assign appropriate parameter values. Applied to the design of a simple LNG process, the problem formulation is found to have a significant impact on both the power consumption and the total annual cost of the optimal solution.

References

[1] Towler GP, Sinnott RK. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. 2nd ed. Boston, MA: Butterworth-Heinemann; 2013.

[2] Varbanov PS, Fodor Z, Klemeš JJ. Total Site targeting with process specific minimum temperature difference (ΔT_min). Energy. 2012;44(1):20-28.

[3] Jensen JB, Skogestad S. Problems with specifying ΔT_min in the design of processes with heat exchangers. Industrial and Engineering Chemistry Research. 2008;47(9):3071-3075.

[4] Xu J. Comments on “Equipartition of Forces:  A New Principle for Process Design and Optimization”. Industrial and Engineering Chemistry Research. 1997;36(11):5040-5044.

[5] Chang H-M, Chung MJ, Lee S, Choe KH. An efficient multi-stage Brayton-JT cycle for liquefaction of natural gas. Cryogenics. 2011;51(6):278-286.