SIMULATION AND SENSITIVITY ANALYSIS OF A MIXED FLUID CASCADE LNG PLANT IN A TROPICAL CLIMATE USING A COMMERCIAL SIMULATOR

SIMULATION AND SENSITIVITY ANALYSIS OF A MIXED FLUID CASCADE LNG PLANT IN A TROPICAL CLIMATE USING A COMMERCIAL SIMULATOR Gianfranco Rodríguez 1, Fabiana Arias 1, Maria G. Quintas 1, Alessandro Trigilio 2 and Sabrina Di Scipio 2. 1 Chemical Engineering Students. 2 Thermodynamics and Transfer Phenomena Department. Simón Bolívar University. Valle de Sartenejas, Baruta, Edo. Miranda. Venezuela. AP. 89 e-mail: sdiscipio@usb.ve Abstract At distances greater than 4 km from the source of production, the most profitable way to transport the natural gas (NG) is as liquefied natural gas (LNG). Between years 2-21 the natural gas consumption increased 31.4% and LNG represents 3.5% of the global NG trade in 21 [1]. Venezuela has important proven reserves of NG, therefore the construction of a LNG plant is being considered. The Linde-Statoil Mixed Fluid Cascade process (MFC ) was selected; it consists in three cascades that use different refrigerant blends in each cycle. In the present work a process similar to the MFC, considering cold and tropical temperature for the inlet gas (12 and 3 C) was simulated. The commercial software ProII was used to study the influence on the coefficient of performance () and flow rates of refrigerants of three main operational variables: low and high pressure of the compressors, and outlet temperatures of the main heat exchangers. The following assumptions were made for the simulation: 1).5 bar pressure drop in hot streams and.2 bar in cold ones [3]; 2) The compressors had 8% polytropic efficiency; 3) The cooling stream outlet temperature must be 1 ºC over saturation temperature; 4) The outlet temperature obtained in the main heaters (LNG-HX) must be the same for all the streams and, 5) The minimum internal approach in the LNG-HX s is 2 ºC. It was feasible to simulate a liquefaction process similar to MFC using Venezuelan conditions, by implementation of some changes in the cascades temperatures and employing a different refrigerant mixture in the first cycle (propane and n-butane). The other cascades used the same refrigerants of the original MFC but with different compositions. Tropical thermal conditions, implied the requirement of higher refrigerant flow rates to achieve the same degree of cooling for NG, compared with Norwegian conditions (2.45x1 6 lb/h vs 2.18x1 6 lb/h) and the global decreased 17.4%. Keywords: Liquefaction, Cascade, Simulation, Mixed Refrigerant. Introduction Venezuela has 195.1 TCF of proven reserves of Natural Gas (NG) [2]. The country ranks eighth on the world s NG reserves and first in Latin America, which means NG production could notably increase in the next decades. One of the alternatives to commercialize and transport this gas is applying a liquefaction process. According to PDVSA (the Venezuelan Oil Company), Mariscal Sucre s project consists in a Liquefied Natural Gas (LNG) plant, with a proposed

capacity of 9.4 millions of tons per year (MTPA) distributed in two trains (4.7 MTPA each) using Linde/Statoil technology [3], known also as MFC (Mixed Fluid Cascade) process (see Figure 1a). 1 4 3 2 1 2 3 4 (a) (b) Figure 1. Mixed Fluid Cascade Configuration a) Original Case b) Venezuelan Case (simulation). In 1996, Statoil and Linde, Norwegian and German companies, respectively, created an association in order to improve the available LNG plant technologies, reducing operational cost and its time of building. They developed a new process called MFC [4]. The pre-cooling process (first and second cascade) uses a mixture of Ethane and Propane. For the liquefaction process (third cascade), the blend used is Methane, Ethane and Propane. Finally, the sub-cooling process (fourth and last cascade) includes a mixture of Methane, Ethane and Nitrogen. This technology was first used in Snøhvit LNG plant, in Norway 27. In the Natural Gas liquefaction process, the temperature is decreased from ambient to -164 C (approximately) and the pressure reduction is from 4-6 bar to atmospheric pressure. This process reduces 6 times the volume required to storage and transport the gas, which is one of the most important advantages of LNG. Jensen and Skogestad (29) presented important advances related with the Mixed Fluid Cascade Process, performing the control analysis for such systems [5]. They obtained the specific conditions to reach optimal power consumption in each cycle (cascade). In addition, the authors calculated the refrigerant composition for each cascade, and established estimations of pressure drops in heat exchangers and overheating degree after the compressors, making it possible to establish accurate initial values of importance in the simulations done in the present work. Chang et al. (21) studied the temperature change of the fluids into the LNG heat exchanger [6]. They found that for low temperatures (as used in cooling systems to NG), the entropy produced is proportional to the temperature difference across the heat exchanger. In order to guarantee high

compressor efficiency, the temperature difference in the LNG main heat exchanger streams has to be set at the minimum possible, then, it is necessary to use a specification to solve the cycle and satisfy this condition. Linde-Statoil LNG technology has been selected to Mariscal Sucre Project in Venezuela, as mentioned before; in consequence, the objective of the present study is to determine the operational conditions and composition of refrigerant blends to suit the requirements of the Venezuelan NG composition and environmental weather. First of all, it is necessary to determine the cycle s conditions of the process carried out in Norway, where natural gas enters at an average temperature of 12 C, and adapt it to Venezuelan conditions where NG is fed at 3 C. Using the known temperature and pressure conditions it is possible to simulate the Norwegian cycle and determine the composition of the refrigerant blend used in each cycle. Once the base case is settled, the process is evaluated under Venezuelan natural gas conditions, developing a sensitivity analysis. After that, the results of both cycles (Norwegian and Venezuelan case) are compared based on the total work, and the coefficient of performance, (defined as the heat absorbed by the refrigerant among the total work required in the cycle). All the case studies were evaluated using PRO/II, a commercial simulating package which is a widely used program for property estimation and processes design, including multiple thermodynamics methods. Previous works reported the use of commercial simulators to analyze refrigeration cycles. Berit et al. (212) used PRO/II for energy estimation in each stream of the heat exchanger to evaluate exergy losses of the LNG plant in Norway [7]. Also Chang et al. (212) reported the frequent application of commercial simulation packages for simulating natural gas refrigeration cycles in a similar study about the multi stream heat exchangers, which are the main equipment of the MFC process simulated in this study [8]. Methods The simulation of a Mixed Fluid Cascade process (see Figure 1b), similar to the MFC LNG was done using the PRO/II process simulation software. The Peng-Robinson equation of state was used for thermodynamic calculations due to its proved modeling process effectiveness with NG streams [9]. API method was selected to determine liquid densities. The following assumptions were made for the simulation: 1).5 bar pressure drop in hot streams and.2 bar in cold ones [4]. 2) The compressors had 8% polytrophic efficiency. 3) The cooling stream outlet temperature must be 1 ºC over the stream saturation temperature. 4) The outlet temperature obtained in the main heaters (LNG-HX) must be the same for all the streams and, 5) The minimum internal approach (MITA) in the LNG-HX s is 2 ºC. A 2 MTPA flow rate of NG was considered with a 52 bar inlet pressure. The operational conditions for the Norwegian MFC case were obtained by oral communication with engineers related with the Snøhvit Project, and the conditions for the Venezuelan case had to be calculated. The refrigerants compositions for each case were determined. The equation 1 was used to determine the of the whole cycle.

C removed H final H initial comp comp2 comp comp In order to solve the system, valves v1, v2, v3 and v4 were treated separately, first simulating the temperature and pressure change for each one. In the cycles with a binary refrigerant blend a range of values for the composition of one of the compounds was established. For the ternary blends the procedure was similar, for the first component it was established a variation range starting from and ending in 1%, for the second the variation was in the inverse direction, and the amount of the third component was calculated by difference. To fix the final composition of each blend, the outlet temperature of the valve that requires lower mass refrigerant was searched. In both cases the first component of the blend was selected by being the heaviest component of the mixture. The results from this calculation were used as first guest value in a controller on the software. This restrained device was used as an additional component of the cycle in the simulation in order to achieve a fast convergence to the solution values. The controller allows manipulating a variable, until reaching a specific convergence in conjunction with another fixed specification. This convergence is led by the given tolerance (deviation of the outcome value) for the fixed parameter. These devices were used to obtain results for refrigerant s flow mass and refrigerant s blend composition in each cycle. Considering all the parameters mentioned above, and mantaining the pressures in each cycle, it was studied the possibility to apply the same simulation under Venezuelan requirements. The following modifications for the MFC process were analyzed in order to meet the requirements for Natural Gas liquefaction in a tropical weather: 1) Keep all the same process units and operational conditions regarding to the Norwegian case, just changing the gas inlet temperature. 2) Add an additional heat exchanger for cooling down the NG from 3 to 12 C at the beginning of the process. 3) Based on the heat load distribution for each cycle in the Norwegian case, determine new temperature limits for each cycle in the Venezuelan case and simulate. The first 2 cases did not require any previous calculation as they were just based on the same conditions of the Norwegian cycle (previously simulated). In the third case, in order to define the outlet temperatures of the main heat exchangers (LNG-HX), the heat load for each cycle of the Norwegian case was calculated and these values were taken as percentage of heat removed per cycle. Then these results were transferred to the Venezuelan case based on the concept of

Pressure [bar] removing the same amount of heat (in percentage) on each cycle and with a simple energy balance it was possible to determine new outlet temperatures for heat exchangers. In these cases, the refrigerant blend composition for each cycle was kept the same as the results obtained for the Norwegian simulation. Additionally, a sensitivity analysis was developed evaluating the effect of low and high pressures, and outlet temperatures of the main heat exchangers (LNG-HX s) on the total work, refrigerant compositions and,. Low pressures were varied in the range 2 to 4 bar. High pressures were varied considering that each cycle has a different value for the compressor outlet pressure; it was varied in the approximate range of ± 25% around the base case. Heat exchangers outlet temperatures (except the last cascade) were modified maximum 5 C above and below the base case value. Each change was made separately in each cycle and the reported results are shown for individual and global effects. Results Considering the three modifications on the original MFC process mentioned before, it was not possible to meet the Venezuelan heat transfer requirements for the NG to be liquefied. In consequence, the following 2 variations were included to achieve convergence of the cycle: 1) Separate the first two cycles, which in the original case used the same refrigerant blend. Employ a new refrigerant composition in the first cycle. The proposed refrigerant is composed by propane and butane since this mixture appears to cover the temperature variation range for the gas in this particular cycle (3 to -7 ºC). The previous mixture of ethane and propane at 3 bar covered a temperature range of about -1 to -6 C. The operating range of refrigeration was determined based on the refrigerant vapor pressure curves shown in Figure 2. 1 N2 C1 1 C2 C3 C4 1-25 -2-15 -1-5 5 1 15 Temperature [ C] Figure 2. Cooling curves for the considered refrigerants.

2) Set all the low pressures at 3 bar in order to achieve the conditions set on the previous variation. In Figure 2 can be noticed that for 8 bar, propane and butane do not cover the desired temperature range. Table 1 is shown the conditions that represents the operation of a MFC process for Norwegian (N) and Venezuelan (V) cases. Table 2 contains the refrigerant composition of each cascade cycle in the MFC process under Venezuelan weather conditions. It was necessary to include relevant differences in composition of the first cycle as a consequence of feeding gas at higher temperature. Table 1. MFC operational conditions for Norwegian (N) and Venezuelan (V) cases. Cycle 1 Cycle 2 Cycle 3 Cycle 4 T gas ( C) T P LNG-HX out (bar) gas ( C) T P LNG-HX out (bar) gas ( C) T P LNG-HX out (bar) gas ( C) LNG-HX P out (bar) In Out Comp Valv Out Comp Valv Out Comp Valv Out Comp Valv 4 Valv 5 N 12-17 2 8-23 2 3-77 19 3-155 54 3 1 V 3-1.9 2 3-39.3 2 3-72.1 19 3-155 54 3 1 Table 2. Composition of refrigerant mixture for Venezuelan conditions. Component Cycle 1 Cycle 2 Cycle 3 Cycle 4 N 2.117 C 1.57.476 C 2.3295.8837.4223 C 3.6528.675.593 nc 4.3472 In Table 3 is shown a first comparison for each cycle work and for the obtained parameters at tropical conditions and the ones calculated for the original system. As it was expected, the Norwegian case presented a higher value of due to the NG feed temperature. Table 3. Work required for each cycle and total work, NG removed heat and global. Compressor Power Total Q per Cycle (kw) Power removed C 1 C 2 C 3 C 4 (kw) (kw) Norway 9522 787 9767 17984 4436 43311,976 Venezuela 8997 17569 9672 2783 5721 45954,86 With the Venezuelan thermal conditions, higher flow rates of refrigerants were required to achieve the same degree of cooling for NG, compared with Norwegian conditions (2.45x1 6 lb/h

Mass [lb/hr] vs 2.18x1 6 lb/h); in addition, the power required in the compressor of Cycle 2 increases notably (see Table 3), and the total is 17.4% lower for the tropical climate. Sensitive analysis considering Venezuelan conditions a. Effect of change in the low pressure of each cycle. The initial outlet pressure in every valve, except for the one of the main gas line, was established in 3 bar. This value was varied in a ±33,33% respecting the initial set value. For the first cycle where refrigerant mixture consists on propane and butane, the pressure and the refrigerant flow increased proportionally. The flow rate was maintained constant in the other cycles. The Figures 3a and 3b show the results found. A 3% change in low pressure produces a maximum percentage variation of 16,8% for flow rate in 1st cycle, 69% for the mass of propane and 1,1% for the. Ciclo Cycle 4 4 5 Propano Propane 1.5 2 2.5 3 3.5 4 4.5 5 Pressure V1 [bar].845.84.835.83.825.82.815.81.85 1.5 2 2.5 3 3.5 4 4.5 Pressure V1 [bar] Figure 3. Effect of low pressure change in valve 1 on a) Mass flow, b) Global. For the second cycle, the flow rate rose as the low pressure did. It produced a change in the flow rate of 1 st and 2 nd cycle. The proportion of ethane increases with the pressure. For the value the curve showed a maximum near the pressure established initially. The results of the change in the 2 nd cycle are showed in Figures 4a and 4b. As a consequence of increase 3% the outlet pressure in the 2 nd cycle, the refrigerant flows augmented 87.9 and 8.7% for the first and second cycle, respectively, the ethane content in the mixture of the second refrigerating cycle increased 61.2%. The global varied 21.1 %. The change of low pressure in the 3 rd cycle affects the refrigerant mass requirements of cycles 1,

Mass [lb/hr] Mass [lb/hr] 2 and 3, while the fourth cycle remain unchanged. The methane flow and the increased proportionally to the pressure (see Figure 5 and b). The increment of the light component allows the refrigerant to reach the same cooling temperatures at the LNG-HX outlet system to compensate the reduction in the decompression range. The increment of the light component also produces a bigger flow rate requirement in the system as consequence of a lower Cp (specific heat at constant pressure), which affects the energy balances. The mass increased 13.3, 2.3 and 9.2% in 1 st, 2 nd and 3 rd cycles, respectively. The methane flow rate changes 121% and the global changes 1.4% from the base case. Ciclo Cycle 4 4 5 Etano Ethane 1.5 2.5 3.5 4.5 Pressure V2 [bar].86.84.82.8.78.76.74.72 1.5 2.5 3.5 4.5 Presión V2 [bar] Figure 4. Effect of low pressure change in valve 2 on: a) Mass flow, b) Global. 5 1.5 3.5 Pressure V3 [bar] Ciclo Cycle 4 4 Metano Methane.85.8.795.79.785.78.775 1 2 3 4 5 Pressure V3 [bar] Figure 5. Effect of low pressure change in valve 3 on: a) Mass flow, b) Global. For the 4 th cycle it can be observed an increment in every mass flow rate, and the same tendency for the increment of the lighter component in the mixed refrigerant. Results are shown in Figure 6a and 6b. The refrigerant flow increased 2.6, 2.3, 5.3 and 1%, for the cycles 1, 2, 3 and 4, respectively. Nitrogen s mass in the last cycle varies in 41.4%, while the changes 3%.

Mass [lb/hr] Mass [lb/hr].795 5 1 3 5 Pressure V4 [bar] Ciclo Cycle 4 4 Nitrógeno Nitrogen.79.785.78.775.77.765 1.5 2.5 3.5 4.5 Pressure V4 [bar] Figure 6. Effect of low pressure change in valve 4 on: a) Mass flow, b) Global. b. Effect of cycles intermediate temperatures variations In each case, the variation was applied to the heat exchanger cooling requirement at the NG outlet. The NG conditions (including temperatures) at the system s inlet and output remained constant so the total heat removed is also constant. The variation also considers that the rest of the streams through the heat exchanger change their temperature at the outlet. The temperature between cycles 1 and 2 has been changed ±2% of its initial value (-1.9 C). The results are shown in Figures 7a and 7b. The required refrigerant mass increased 3 and 14.9% in cycles 1 and 2, respectively, and variation reached 8.9%. Figure 7b shows the presence of a maximum value near the initial point which coincides with a minimum value for cycle refrigerant s mass flow (Figure 7a). 35 Ciclo 4 Cycle 4 5 265 27 275 28 Temperature [K].8.78.76.74.72.7 265 27 275 28 Temperature [K] Figure 7. Effect of first and second cycles intermediate temperature changes on: a) Refrigerants mass flow, b) Global. The temperature between cycles 2 and 3 has been changed ±2% of its initial value (-39.3 C). The

Mass [lb/hr] cycle s mass flow changes reached 51, 5.6 and 21.1% for the 1 st, 2 nd and 3 rd cycle, respectively (see Fig. 8a). The varies 6.6% as consequence of the intermediate temperature changes (Fig. 8b). 5 225 23 235 24 Temperature [K] Ciclo 4 Cycle 4.8.79.78.77.76.75.74.73 225 23 235 24 Temperature [K] Figure 8. Effect of second and third cycles intermediate temperature changes on: a) Refrigerants mass flow, b) Global. The variation of the intermediate temperature between the 1 st and 2 nd refrigeration cycles shows a maximum for the near to -37.15 C. The mass variation shows that reducing the second cycle s refrigerant mass produces a diminution in first cycle s refrigerant mass and a consequent increase in the third cycle s mass because of the increment in the temperature in the second heat exchanger outlet. The temperature between cycles 3 and 4 has been changed ±2% of its initial value (-72.1 C). Temperature increase between 3 rd and 4 th cycles produces an increment in the refrigerant flow rate in the 4 th cycle and a consequent reduction in the 3 rd cycle s mass while refrigerant mass in 1 st and 2 nd cycles remain almost constant. The flow refrigerant varied 1.2, 2.2, 12 and 19.5% in the 1 st, 2 nd, 3 rd and 4 th cycle, respectively (Fig. 9a). The value decrease with the temperature increase, it varied 1.5% (Fig. 9b). c. Effect of cycles high pressure levels variations For the 1 st cycle the compressor outlet has been varied ±25% from its initial value (2 bar). As expected, the refrigerant flow in each cycle remains constant (see Figure 1a). This is because the compressor pressure doesn t affects the energy balance in the heat exchangers. The decreases inversely with the outlet pressure increase. The of the whole system varies 2.6% because of the changes made in the first cycle s compressor outlet (Fig. 1b).

Mass [lb/hr] Mass [lb/hr] Ciclo 2 Cycle 2 Ciclo 3 Cycle 3 Ciclo 4 Cycle 4 5 195 2 25 21 Temperature [K].85.8.795.79.785.78.775.77 196 198 2 22 24 26 28 Temperature [K] Figure 9. Effect of third and fourth cycles intermediate temperature changes on: a) Refrigerants mass flow, b) Global. 26 24 22 18 16 14 12 Ciclo Cycle 4 4 1 2 3 Pressure C1 [bar].81.85.8.795.79.785.78.775.77 1 15 2 25 3 Pressure C1 [bar] Figure 1. Effect of first cycle s high pressure change on a) Refrigerants mass flow, b) Global. The 2 nd cycle s compressor outlet was modified ± 5% of its initial value (2 bar). Between 5 to 21 bar, the refrigerant flow required in the 1 st cycle reduced progressively while the showed an increment in this zone (Figure 11a and 11b). The mixed refrigerant condensates at different temperatures depending on the high pressures level in the cycle. When the dew point temperature is reached at the outlet of each partial condenser in the system, the flow of refrigerant and presented changes. The limits of the range above mentioned corresponds to values close to the dew point temperatures in the 1 st and 2 nd cooler of this cycle variation reaches 14.3% and the requirement of refrigerant mass in 1 st cycle changes 127% from the lowest value reached. The 3 rd cycle s compressor outlet was modified ± % of its initial value ( 9 bar). Cycles and 2 showed changes in their refrigerant mass requirement meanwhile the 3 rd and 4 th cycles refrigerant mass remain constant (Figure 12a). The global present maximums and minimums in different points of the studied ranges, depending on the stage where the dew point

Mass [lb/hr] Mass [lb/hr] was reached in each cooling phase (Figure 12b). varies 1.9%, the refrigerant flow increased 33.7 % and decreased 35% for the 1 st and 2 nd cycle, respectively. 35 5 1 2 3 Pressure C2 [bar] Ciclo Cycle 11 Ciclo Cycle 22 Ciclo Cycle 33 Ciclo Cycle 4 4.82.8.78.76.74.72.7.68.66 1 15 2 25 3 Pressure C2 [bar] Figure 11. Effect of second cycle s high pressure change on: a) Refrigerants mass flow, b) Global. 5 14 24 Pressure C3 [bar] Ciclo Cycle 3 3 Ciclo 4 Cycle 4.84.82.8.798.796.794.792.79.788.786.784 14 16 18 2 22 24 26 28 3 Pressure C3 [bar] Figure 12. Effect of third cycle s high pressure change on: a) Refrigerants mass flow, b) Global. Finally the 4 th cycle s compressor outlet was modified ±9% of its initial value (5 bar). The refrigerant flow changed 1.6% for the 1 st and 2 nd cycle and 6.7% for the 3 rd cycle (Figure 13a). The global varies.8% (Figure 13b), it reached a maximum near base case pressure. Refrigerant flows remained without great changes because the variation of the 4 th compressor outlet (9%) was not as extended as the previous variations in the rest of the cycles (4%).

Masa [lb/hr] 5 47 52 57 62 Pressure C4 [bar] Ciclo Cycle 4 4.792.791.79.789.788.787.786.785.784 47 52 57 Pressure C4 [bar] Figure 13. Effect of fourth cycle s high pressure change on: a) Refrigerants mass flow, b) Global. Conclusions Norwegian climate conditions (gas inlet temperature of 12⁰C) decrease the cooling required in the condensers, obtaining a higher. Under Venezuelan climate conditions (gas inlet temperature of 3⁰ C) the system requires higher flow rates of refrigerants to achieve the same degree of cooling for NG. Trough the simulation of the MFC process, it was obtained different data related with operational conditions and the refrigerant flow and compositions required in each cycle. This data could be used as first approximation for the design of a LNG plant in a tropical and cold weather. The sensitivity analysis of the MFC process, under Venezuelan conditions, provided the following information of different operational variables: Low pressure effect: The increase of the ligther refrigerant mass is proportional to the outlet pressure of the valve. When higher values of low pressures were used, a higher flow rate of refrigerant was required. Nevertheless, the composition was maintained and they all had the same tendency of increase. An increase of 3% in the low pressure, produced an increment of 69, 61, 121 and 42 % in the composition of the lighter refrigerant in the 1 st, 2 nd, 3 rd and 4 th cycle, respectively. High pressure effect: The of the 1 st cycle was inversely proportional to the high pressure. The in the 2 nd and 3 rd cooling stages presented maximums and minimum values corresponding to the proximity of the dew points temperatures of refrigerant blends in each partial condenser of each cycle. In the last cooling step the maximum value obtained corresponded to the saturated liquid temperature of the refrigerant mixture reached in the previous cooling phase. The high pressure do not have a significant influence on refrigerant flows and compositions required in each cycle.

Intermediate temperature effect: The variation is proportional to the required refrigerant of the following cycle, but it was inversely proportional to the flow rate in all the preceding cycles. These changes in the flow rate, kept compositions constant and produce maximum and minimum values in the curve. References [1] British Petroleum. Natural Gas. In: BP Statistical Review of World Energy, June 211, <http://www.bp.com/statisticalreview>. (Accesed Aug 3, 212). [2] Resolution Nº 91, Official Gazette Nº 39716, July 19 th, 211. Venezuela. [3] DVSA Construction & Engineering (28) Mariscal Sucre s LNG Project (Venezuela). <http://www.slideshare.net/energia/proyecto-gnl-venezuela-mariscal-sucre>. (Accesed Jun 16, 211). [4] World-Scale Baseload LNG Production. MFC (Mixed Fluid Cascade Process) (21). <http://zaf.engineering.preview.linde.com/en/index.html>. (Accesed May 5, 211). [5] Jensen, J.B and S. Skogestad, S. Optimal Operation of a Mixed Fluid Cascade LNG Plant. Comput. Aided Chem. Eng. Vol. 21 (26) 1569-1574. [6] Chang, H.M., Chung, M., Lee, S., and Choe, K. An efficient multi-stage Brayton JT cycle for liquefaction of natural gas. Cryogenics Vol. 38 Issue 6 (June 211) 278-286. [7] Berit, A. and Erstvag, I. Exergy Evaluation of the Artic Shnohvit Liquefied Natural Gas Processing Plant in Northern Norway-Significance of Ambient Temperature. Energy Fuels Vol. 26 (212) 259 267. [8] Chang, H.M., Su Lim, H., Hyung, K. (in press). Effect of multi-stream heat exchanger on performance of natural gas liquefaction with mixed refrigerant. Cryogenics (212) http://dx.doi.org/1.116/j.cryogenics.212.5.14. [9] Nasrifar, Kh. and Moshfeghian, M. Vapor liquid equilibria of LNG and gas condensate mixtures by the Nasrifar Moshfeghian equation of state. Fluid Phase Equilib. Vol. 2 (22) 23 216.