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Exergetic optimization of a refrigeration cycle for natural gas liquefaction Liza Cipolato,a Maria C. A. Lirani,a Thiago V. Costa,a Francine M. Fábrega,a José V. H. d’Angeloa. a

School of Chemical Engineering, University of Campinas, Rua Albert Einstein, 500 – Bloco A, Campinas (SP) – 13083-852, Brazil

Abstract Natural gas is widely use in many industries as fuel and also as raw material. Although gas pipelines present less transportation losses they become impracticable when distances are too long or when demands are highly variable. The liquefaction of natural gas is then necessary to allow its transportation in great volumes, with little loss of material. This also enables its storage in a more stable way. Natural gas consumption is continuously growing worldwide and consequently, the number of exporter terminals (liquefaction industries) and importer terminals (regasification plants) will increase. The natural gas liquefaction process is based on a sequence of refrigeration cycles, which need to work in an optimized way. The exergetic analysis is a very useful thermodynamic tool to evaluate the efficiency of these cycles. This work aims at an exergetic analysis of a multistage cascade refrigeration cycle applied to a natural gas liquefaction process. Firstly, the process was simulated using commercial software and the results obtained from the simulations were validated with literature data, showing a good agreement. After that, different operational conditions, according to a complete factorial design of experiments, were studied, in order to verify the influence of pressure in six specific points of the cycle. The response variable analyzed is the rate of total exergy destroyed in the cycle. The results showed a new set of operational condition to the refrigeration cycle in which the destroyed exergy rate was reduced by approximately 48% in comparison with literature data. Keywords: natural gas, liquefaction, exergy, optimization, refrigeration.

1. Introduction Natural gas consumption is growing worldwide mainly because of its good properties as a fuel. The transportation of natural gas from the producing site to the consumption site is usually done by pipelines, but when the distances are great or the sites are separated by an ocean, the transportation of natural gas in the liquid state is preferred. Natural gas is in liquid state at temperatures around -150 oC or lower and pressures varying up to 500 kPa. In order to reach this low temperature refrigeration cycles are used. The most usual liquefaction processes are: multistage cascade liquefaction; mixed refrigerant and turbine-based. Finn et al. (1999) and Geist (1983) have presented in detail the advantages and disadvantages of each one of these cycles. The classical cascade liquefaction cycle was the first one to be applied in natural gas plants. It is based on a three stage refrigeration cycles, each one operating with a different fluid: methane, ethane (or ethylene) and propane. The mixed refrigeration cycle utilizes only one refrigeration fluid using a mixture of refrigerants, which

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composition is adjusted in order to have its evaporation temperature similar to the natural gas being liquefied, which can change depending on its origin. Because of the high costs involved in construction and operation, the feasibility of an industrial site is strictly related to the efficiency of the process. One possible way of reducing thermodynamic losses of the process is to perform an exergetic analysis, to reduce exergy losses, leading to an optimal operation. The objective of this work is to perform an exergetic analysis of a classical multistage cascade refrigeration cycle applied in the liquefaction of natural gas, in order to propose an optimal operational condition, contributing to reduce the exergy destroyed in the cycle. This analysis will consider the influence of six pressures in different points of the cycle: after the compressor and after the expansion valve of each subcycle.

2. Materials and Methods 2.1. Multistage Cascade Refrigeration Cycle The multistage cascade refrigeration cycle presents lower energy consumption when compared to the other types, enables flexible operation, as each cycle can be independently operated, and requires smaller heat transfer area in the evaporators. This last characteristic implies in a lower thermodynamic efficiency of the process, which requires higher utilities demand. Another disadvantage is the high installation and maintenance costs, as each cycle has its own compressor and refrigeration fluid storage tank. Figure 1 shows the cascade cycle studied in this paper. For simplification of the figure, only one stage is shown per refrigeration fluid. In this cycle, natural gas is cooled and finally liquefied by a three stage process. In the real cycle, each refrigeration stage has multiple expansion and condensation steps, being each of them operated at three different evaporation temperatures. Details of this multicascade cycle can be found in Kanoglu (2002).

Figure 1-Multistage refrigeration cycle (Kanoglu, 2002). 2.2. Process Simulation The multistage cascade refrigeration shown in Figure 1 was simulated using Hysys (Aspen Technology, version 3.2), based on the works of Kanoglu (2002) and Filstead (1965). The fluid package chosen to provide thermodynamic properties was the PengRobinson equation of state, which is adequate for the refrigerants used in the cycles. Steady state operation and adiabatic equipments were assumed in the simulations. Natural gas molar composition used in the simulation was taken from a Brazilian LNG

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plant and is: 90.7% CH4, 6.8% C2H6, 1.3% C3H8, 0.3% C4H10, 0.7% N2 and 0.2% O2. Refrigerants selected were: methane, ethane and propane (all 100% pure). After validation of the simulation by comparison with literature data, obtaining a good agreement, different operational conditions were tested following a full factorial experimental planning. Finally, the results were analyzed by a statistical software, and an optimal operation condition for the process was proposed. 2.3. Exergetic Analysis Details of how to perform an exergetic analysis may be found in Szargut (1980). The aim of this analysis is to locate and evaluate quantitatively the effect of irreversibilities which reduce thermodynamic efficiency of a process, proposing modifications in order to reduce these irreversibilities, by reducing destroyed exergy. In this work only the physical component of exergy for each process stream was analyzed using Equation (1): ex = (h – ho) – To(s – so)

(1)

where h is enthalpy and s is entropy at temperature and pressure of the process stream and the index “o” indicates the value of the variables at the reference state considered, which is To = 298.15 K and Po = 101.3 kPa. The total destroyed exergy of the multistage cascade refrigeration cycle considered in this work is the sum of the destroyed exergy in each control volume of the cycle, which is obtained through an exergy balance. 2.4. Factorial Experiment Design To evaluate the influence of pressures at six different process streams of the cycle (after the compressor and after the expansion valve of each refrigeration subcycle) over total destroyed exergy, a 26 factorial design was applied. Therefore, 6 factors were analyzed, being 2 levels for each one. Following the experimental design, a minimum number of simulations need to be performed for the minimization of the resulting variable, which is the total destroyed exergy of the system. The experimental design resulted in 64 simulations plus the base case, which is the one studied by Kanoglu (2002). In the full factorial design, both the individual and the combined influence of the input factors (pressures) in the total destroyed exergy are analyzed. The basis selection for the different pressure levels for the streams was ±10% over the value of the base case. This choice is due to a limited operational range. Table 1 shows the superior and inferior levels for the tested factors. The results obtained from the full factorial experimental planning were evaluated by a statistical analysis with Minitab 15. Table 1: Planning matrix for the tested factors (pressures, in kPa). Stream 7 10 12 14 16 18

Description after compressor after expansion valve after compressor after expansion valve after compressor after expansion valve

Cycle Methane Methane Ethane Ethane Propane Propane

Base case 3337 170 2069 110 1344 110

Inferior 3003 153 1862 99 1210 99

Superior 3671 187 2276 121 1478 121

*streams numbers correspond to the ones used in the simulations.

3. Results and Discussion After 65 simulations, some combinations of the variables have shown cross temperatures in some heat exchangers. In order to avoid this the pressures of the propane cycle were fixed at the base case value and a new full factorial design was constructed, being 4 factors at 2 levels (24), resulting in 16 experiments plus the base

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case (run #17). Table 2 shows the results obtained for this new experimental design. Run #12 has presented the minimum value for the total destroyed exergy. Table 2: Results of the full factorial design. Process Stream/ Pressure (kPa) Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

7 3003 3671 3003 3671 3003 3671 3003 3671 3003 3671 3003 3671 3003 3671 3003 3671 3337

10 153 153 187 187 153 153 187 187 153 153 187 187 153 153 187 187 170

12 1862 1862 1862 1862 2276 2276 2276 2276 1862 1862 1862 1862 2276 2276 2276 2276 2069

14 99 99 99 99 99 99 99 99 121 121 121 121 121 121 121 121 110

Total destroyed exergy (kJ/h) 132262 10750 250836 10290 134099 10916 254631 10461 130182 10563 246560 10096 131957 10723 250215 10262 19494

Figure 2 shows the main effects plot for the full factoril design 24. From Figure 2, one can see that the factors which individually influence the destroyed exergy are the pressures of streams 7 and 10. As the slope seen in the plot of stream 7 is higher than that of stream 10, it is possible to conclude that the influence of the pressure of stream 7 on the response variable is higher. The pressures of streams 12 and 14 are not statistically significant, when analyzed individually, as the plots of these streams show practically horizontal lines. Figure 3 is the Pareto diagram of the full factorial design and presents the influence of the factors, individually and combined, on the response variable. Figure 3 shows that the destroyed exergy was influenced by factors A, B and AB. That means that the pressures of streams 7, 10 and also the combined effect of these two pressures together influence the destroyed exergy of the cycle. The thin line at 0.05 represents the confidence interval (95%), which is the limit to the significance of the estimated effects.

Figure 2: Main effects plot over the total destroyed exergy.

Figure 3: Pareto diagram for total destroyed exergy.

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The independent variables and the interactions are statistically significant if the value of the effect is at right side of p = 0.05. Thus the significant effects are the pressures of streams 7, 10 and the combination of pressures 7 and 10. Figure 4 shows the response surface for the relation between the total destroyed exergy and pressures of streams 7 and 10. Lower values for total destroyed exergy are achieved for high pressure values of streams 7 and 10. It is important to notice that when analyzing the independent influence of the factors on the response variable, Figure 2, one would suggest that the pressure of stream 10 should operate at its minimum value. Nevertheless, when the factors are analyzed together the combined influence of the pressures is higher than the influence of pressure of stream 10 alone, as shown in the Pareto diagram. Therefore, the influence of the pressure of stream 10 alone is disguised by the influence of combined pressures of streams 7 and 10 and as a result, the optimal operation point is at both higher points of streams 7 and 10. Using the optimization tool of Minitab 15, the optimal operation point was determined, which is the one shown in run #12 at Table 2.

Figure 4: Response surface - relation between destroyed exergy and pressures at streams 7 and10.

4. Results and Discussion The classical multistage cascade refrigeration cycle applied in the liquefaction of natural gas was studied using an exergetic analysis. The influence of six pressures at six different points of the cycle was evaluated: after the compressor and after the expansion valve of each refrigeration subcycle. The base case scenario has presented a rate of total destroyed exergy of 19494 kJ/h. Through a full factorial design and a statistical analysis a new set of operational conditions based on the analyzed factors resulted in a reduction of 48% of this rate, obtaining a new rate of total destroyed exergy of 10096 kJ/h. Using a thermoeconomic analysis it is possible to check the final benefit of this reduction in the total destroyed exergy. Technically, the modifications proposed are feasible.

References C.G. Filstead, 1965, Camel LNG Plant: world`s largest, Hydrocarbon Processing, v. 44, n.7, 135138 pp. A.J. Finn, G.L. Johnson, T.R. Tomlinson, 1999, Gas processing developments: a special report – developments in natural gas liquefaction, Hydrocarbon Processing, v. 78, n. 4, 47-60 pp. J.M. Geist, 1983, The role of LNG in energy supply, International Journal of Refrigeration, v. 6, n. 5, 283-297 pp. M. Kanoglu, 2002, Exergy analysis of multistage cascade refrigeration cycle used for natural gas liquefaction, International Journal of Energy Research, v. 26, 763-774 pp. J. Szargut, 1980, International progress in second law analysis, Energy, v. 5, 709-718 pp.