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APCI- LNG single mixed refrigerant process for natural gas liquefaction cycle: Analysis and optimization
Journal of Natural Gas Science and Engineering 26 (2015) 470e479
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APCI- LNG single mixed refrigerant process for natural gas liquefaction cycle: Analysis and optimization Peyman Moein a, Mehran Sarmad a, Hadi Ebrahimi a, *, Marziyeh Zare b, Saeed Pakseresht b, Shahrokh Zandieh Vakili b a b
Gas Research Division, Research Institute of Petroleum Industry (RIPI), Tehran 14665-1998, Iran Research & Technology Directorate of National Iranian Gas Company, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 April 2015 Received in revised form 21 June 2015 Accepted 22 June 2015 Available online xxx
In this paper, a typical single mixed refrigerant (SMR) with low energy consumption is analyzed to determine the optimum operating conditions. Genetic Algorithm (GA) tool is used to minimize the total required work by optimizing eleven variables including the outlet pressures of all compressors and throttling valves and the molar flow rate of the MR components. The results of the process simulation show that the total work is varied linearly by the compositions. It is observed that to have a minimum work, when the ambient temperature increases, the compositions of both methane and ethane should be decreased, while those of nitrogen, propane and n-butane should be increased. Moreover, optimized values of the total required work at different ambient temperatures were correlated with a second order polynomial. Increasing feed pressure has small effect on the MR compositions, but significant effect on the total work. © 2015 Elsevier B.V. All rights reserved.
Keywords: LNG Single mixed refrigerant Optimization Genetic algorithm Ambient temperature Feed pressure
1. Introduction The demand for Natural Gas (NG) as a relatively clean fossil fuel has increased in the past years. Although research and development on other fossil fuels mainly oil, coal and their derivatives are going on (Zhang et al., 2014), NG produces approximately less than half the CO2 emissions per unit of generated electricity. Two main ways to transport NG from resources to consumers are pipeline and Liquefied Natural Gas (LNG). The pipeline is most commonly used due to its lower operating cost; however it is inflexible in the case of transmission capacity, and requires enormous initial construction cost. LNG is a liquid form of natural gas with a temperature about 162 C. It has a volume ~1/600 of that of gas at ambient temperature. Although production and transmission of LNG require complex machinery and vehicles, the incremental cost of transport per mile is less than that of pipelines (Cranmore and Stanton, 2000). There are several processes for LNG production such as N2 expander (Yuan et al., 2014), cascade and Mixed Refrigerant (MR) processes. The difference among these processes is related to their
* Corresponding author. E-mail address: [email protected] (H. Ebrahimi). http://dx.doi.org/10.1016/j.jngse.2015.06.040 1875-5100/© 2015 Elsevier B.V. All rights reserved.
capital and operational costs or between hot and cold composite curves (Hatcher et al., 2012). N2 expander processes have several advantages compared to MR ones, including simplicity, less number of equipments, no refrigerant phase change, non-flammability and non-toxicity of N2. However, higher energy consumption per produced LNG tones particularly for large capacity plants is wellknown for N2 expander processes. The cascade cycles contain some refrigeration stages that each stage has its own refrigerant and independent compression system. NG essentially contains mixed hydrocarbons and so its enthalpy with temperature is nonlinearly varied during the liquefaction. Whenever the temperature difference between hot and cold streams in the heat exchangers reaches below a certain value, the entropy generation reduces, but the efficiency increases. This temperature difference in MR cycles could be reduced effectively without need for more auxiliary equipment (Venkatarathnam, 2008). Although the pure refrigerant cycles are simple, a large number of refrigeration stages are required in order to reduce the temperature difference (Andress and Watkins, 2004). Single Mixed Refrigerant (SMR) processes are the simplest MR cycles for liquefaction of natural gas. Compared to mixedrefrigerant cycles (MRC) that have been applied for both large
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
and small-scale systems (Cao et al., 2006), SMR systems have only one series of compressors beside the main cryogenic heat exchangers to cover all range of the liquefaction temperatures (Swenson, 1977). Nevertheless, these MR processes are highly energy intensive, so an optimization procedure is required to minimize energy consumption. Several MR process optimization methods are available in the open literature. Lee et al. (2004) applied a graphical targeting method to optimize a multi-stage MR system by considering minimization of both crossovers and shaft work requirement. Gong et al. (2000) optimized the PRICO process by BOX method. Energy and exergy analysis of SMR, a two-stage expander nitrogen refrigerant and two open-loop expander processes have been evaluated by Remeljej and Hoadley (2006) for LNG production with small-scale LNG. Aspelund et al. (2010) used combination of Tabu Search (TS) and Nelder-Mead Downhill Simplex (NMDS) method linked to AspenHYSYS simulation software to optimize the PRICO process. Mokarizadeh and Mowla (2010) used coded PengeRobinson equation of state and genetic algorithm method to optimize the PRICO process. Alabdulkarem et al. (2011) applied genetic algorithm (GA) for optimization of propane pre-cooled MR (C3MR) and reported MR power consumption at different pinch temperatures. Mortazavi et al. (2012) enhanced the performance of C3MR process by implementing two phase expanders, liquid turbines and gas expanders instead of conventional expansion devices. Xu et al. (2013) optimized the PRICO process using GA under different cold box inlet temperatures and correlated linear regression on the MR composition. Li et al. (2012) also used GA and exergy efficiency to optimize large scale liquefaction systems. Khan and Lee (2013) used particle-swarm optimization methodology coded in MATLAB connected to UniSim simulation software to optimize a SMR process. Wahl et al. (2013) applied sequential quadratic programming (SQP) to optimize the PRICO process. Castillo et al. (2013) compared different precooling cycles for LNG production processes at two different climate conditions, warm (25 C) and cold (6 C). They investigated both power consumption and heat transfer coefficient and found that a three stage propane precooled cycle for warm case and two stage mixed refrigerant cycle for the cold case could be more adequate. Hwang et al. (2013) optimized a dual mixed refrigerant LNG process for different number of refrigerant sub-streams and compression stages using combination of the genetic algorithm and sequential quadratic programming. Jacobsen and Skogestad (2013) used both UniSim and MATLAB softwares for modeling and optimization of a SMR process with disturbances in the flow rate of natural gas and ambient temperature. They expressed that the feasible region of operation could be divided into five sub-regions with different active constraints. Khan et al. (2013) optimized SMR and C3MR processes using knowledge based optimization (KBO) method. By considering boiling point difference of the MR components, they improved energy efficiency of the system. Skaugen et al. (2013) investigated a concept including a detailed heat exchanger model for the optimization of a SMR process. Vatani et al. (2013) considered two mixed refrigerant cycles for design of an LNG production process with integrated natural gas liquids (NGL) recovery. They formulated an optimization problem with minimizing specific power consumption. Wang et al. (2013) optimized two types of C3MR processes by investigating different objective functions including shaft work consumption, exergy efficiency and operating expenditure. They reported that shaft work consumption is the best objective function for the optimization of these processes. Cammarata et al. (2001) used GA for optimization of a modified Collins cycle which was used for liquefaction of helium. Austbo et al. (2014) have presented a detailed review related to the optimization of different LNG processes.
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Because of the nature of nonlinearity and thermodynamic complexity of the LNG processes, optimization of these processes should be performed by global search methods such as GA, Tabu Search (TS), or Simulated Annealing (SA). Due to the fact that GA does not require derivatives and initial points, it was chosen as the optimization method for the current research. In this work a typical APCI (Air Products and Chemicals, Inc.) process (Roberts et al., 2002) as a SMR liquefaction process for LNG production was chosen because of its improved efficiency compared to the other SMR processes. Since special design of this LNG production process, it has low energy consumption. Therefore this process could be a suitable replacement with current LNG production processes due to simplicity, high efficiency and minimum number of existing heat exchangers. The improvements include the compression of vaporized refrigerant at reduced compressor inlet temperatures and the generation of inter-stage liquid refrigerant streams at ambient temperature which could be used beneficially in the refrigeration cycle. On the other hand this APCI process can achieve high thermodynamic efficiency by using a minimum number of heat exchangers to reduce both capital and operating costs (Roberts et al., 2002). The APCI has not been already investigated with the current GA method. Although optimization of several MR components in some special mixed refrigerant processes were investigated in previous studies, but the current APCI process has not been analyzed and optimized in detail yet. Moreover, the pattern of total required work variation at different MR compositions when the other parameters are fixed has not been already presented. On the other hand in open literature in which the effect of MR compositions was considered on the total work, the optimization was performed in different ambient temperatures and at last only the optimized values were presented. So there is a lack of study to show how the total work varies with changing MR compositions by fixing other parameters such as ambient temperature particularly in APCI process. In the present study this pattern was obtained and the results show that the total work will be varied linearly by MR compositions. Also the effect of feed (natural gas) pressure on the total work of refrigeration cycle was investigated. The present APCI single mixed refrigerant cycle which investigated in the present study has some advantages compared to the other SMR cycles which mentioned above. However, this special process has not been investigated yet. So optimization of this cycle can be useful in the case of design of mixed refrigerant liquefaction processes. In this research, the APCI process was simulated in Aspen HYSYS as a base case and optimized by connecting GA MATLAB tool to Aspen HYSYS to minimize the total required work. Then the effects of ambient temperature and feed pressure on the total required work were investigated. Afterwards, the concentrations of the MR components were optimized. In the current paper, not only effects of temperature and pressure are considered as presented in several previous studies, but also change of MR compositions are investigated using the proposed correlations. 2. Simulation and optimization framework 2.1. APCI process The flow sheet of the APCI process modeled by Aspen HYSYS is shown in Fig. 1. As shown in Fig. 1, outlet stream of the last compressor (Compressor-3) is passed through an air cooler (AC-3) divided into two phases (liquid and vapor) in a separator (V-2). Each of them enters the first heat exchanger (HX-1) separately as hot streams. The second cooled liquid stream (stream 16) after passing through a throttling valve returns to the heat exchanger as a cold stream and
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Fig. 1. Process flow diagram of APCI LNG liquefaction process.
after heat exchanging, enters the second stage of compression (Compressor-2). The cooled vapor phase goes to a phase separator (V-3) and the same operation occurs in the second heat exchanger (HX-2). The outlet cold stream of the third heat exchanger (stream 26) mixes with that of the second exchanger (stream 25) and after heat exchanging enters the first stage of compression (Compressor1). The temperature of natural gas after three steps decreases to about 155 C and after passing through throttling valve (Valve-4), LNG is produced at 162 C and atmospheric pressure. In this paper the properties of natural gas and outlet temperature of LNG from the last heat exchanger (HX-3) are fixed and only the properties of MR can vary during the optimization. The simulation assumptions are listed in Table 1.
fitness function. On the other hand, all generated data from the simulation case of HYSYS are exported to the MATLAB code. There is a continuous linking between the MATLAB optimization code and HYSYS simulation case. During data acquisition, the optimization by GA is going on until the minimization of the objective function is performed. 2.3. Optimization formulation In the current optimization problem, minimization of the total work of the plant (for all compressors and a pump) was defined as an objective function expressed as:
Minimize f ðXÞ ¼
2.2. Optimization problem In order to optimize the process by GA method, MATLAB was connected to Aspen HYSYS process simulator. In this situation the GA method acts as a controller and the Aspen HYSYS model is a server. A MATLAB program code adapted from a previous work (Behroozsarand et al., 2009) was prepared to call the Aspen HYSYS simulation and transfer the data produced by GA. Calculated total required work by Aspen HYSYS is sent to MATLAB to be used in
Table 1 Assumptions of the APCI plant simulation. Parameter
Value
Adiabatic compressor efficiency Minimum temperature approach of cold box ( C) Pressure drop in heat exchangers (bar) Pressure drop in air coolers (bar) Heat leakage of cold box Flow rate of natural gas(kg mole/h) Pressure of natural gas entering cold box (bar) Temperature of hot stream at cold box inlet ( C) Temperature of natural gas at cold box outlet ( C) Composition of natural gas (% mole) N2 CH4 C2H6 C3H8 n-C4H10 i-C4H10
75% 2 0.1 0.2 0% 26700 66.5 32 155 0.90 94.00 3.10 1.30 0.40 0.30
X WCompressors þ WPump
(1)
In the above equation X is an adjusted variable vector including MR molar flow rates of components, the outlet pressure of MR compressor stages and the MR pressure after each throttling valve. Nitrogen, methane, ethane, propane and n-butane are used as the components of the mixed refrigerant. PengeRobinson equation of state is applied to calculate the properties of both MR and NG. GA optimization of this process is limited to three constraints. First, the minimum approach temperature in the heat exchangers should be greater than 2 C to satisfy reliability and feasibility of the process. Second, the temperature of MR in the inlet of compressors should be greater than the dew temperature of the fluid in that pressure to prevent formation of liquid in the suction part of the compressors. Third, the pressure of streams entering to a mixer should be equal. These constraints are formulated as follow:
DTmin;HXi 2 C Ti Tdew;i Pi;in ¼ Pj;in
ðfor MixersÞ
where DTmin;HXi represents the minimum approach temperature in heat exchanger i, Ti and Tdew;i refer to operating temperature and dew point temperature of the stream i and Pi;in and Pj;in illustrate the mixer pressure of inlet streams (i and j).
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479 Table 2 Tuning parameters of GA. Tuning parameters
Value
Population size Selection method Tournament size Mutation method Crossover fraction Crossover function Stopping criteria Maximum number of generations Objective function tolerance
300 Tournament 4 Adaptive feasible 0.8 Two-point 200 106
composite curves in the heat exchangers should be greater than 2 C while the temperature of compressors inlet streams should be greater than the dew point of these streams. This figure is obtained when the other variables are assumed to be fixed while only the composition of MR can be varied. According to Fig. 2, the total required work extremely depends on the MR composition. It is shown that in this process, the relationship between work and composition is linear. Additionally, the effects for all components do not have the same trend. For instance, rising nitrogen mole fraction causes the required work to be increased, while increase in methane mole fraction decrease the work. As illustrated in Fig. 2, ethane and n-Butane behave similar to methane and the behavior of propane is similar to nitrogen. The regressed linear equations are listed below:
8 9 1:7616 xN2 þ 1:1856 105 > > 0:058 < x < 0:07 > > N 2 > > > > > > 105 < 0:274 0:267 < x < 2:668 xCH4 þ 2:0177 = CH4 5 WT ¼ j 0:324 < xC2 H6 < 0:334 1:9899 xC2 H6 þ 1:9512 10 > > > > 0:258 < xC3 H8 < 0:265 > > 2:9399 xC3 H8 þ 0:52886 105 > > > > : 5 0:0745 < xnC4 H10 < 0:0775 ; 7:7894 xnC4 H10 þ 1:8907 10
The last limitation is defined as a linear constraint for GA optimization while the first and second constraints are defined as the penalties for the objective function as shown below:
Minimize PðX; rÞ ¼ f ðXÞ þ r
P i
g1 ðxÞ ¼ 2 DTmin;HXi g2 ðxÞ ¼ Tdew;i Ti
! 2
½maxf0; gi ðxÞg
(2)
where r is the penalty factor, assumed here as 10þ14 . If all the constraints are satisfied, the second term in the right hand side of Eq. (2) would be zero (PðX; rÞ ¼ f ðxÞ). Otherwise the second term will be a large value that GA modifies the penalty function in the next generation. The tuning parameters of GA are listed in Table 2. 3. Results and discussion 3.1. The base case solution Design and control of a MR process is extremely related to the total required work. This work depends on not only amount of mixed refrigerant composition, but also the amount of increase or decrease in compositions. Knowing total required work at different mixed refrigerant compositions could give a good view about the design of a new MR process or control of the current processes. Analyzing the results obtained from the simulation could present the relationship between total required work and MR composition in APCI and predict the system performance before the optimization. However, only a few researches are found in open literature about it for other MR processes. For considering the effect of compositions, all other parameters such as temperature and pressure are assumed constant. Effect of MR composition on the total required work is shown in Fig. 2. The hot stream enters to the cold box at a temperature of 32 C. The range of each MR component mole fraction was selected as follow: a minimum approach temperature between hot and cold
473
(3)
where WT is total required work in kW and xN2 , xCH4 , xC2 H6 , xC3 H8 and xnC4 H10 represent the molar composition of nitrogen, methane, ethane, propane and n-butane, respectively. Therefore, it is important to find the best values for MR compositions in addition to the other variables to minimize the total required work. The base case solution was performed when the inlet hot stream of the cold box was at 32 C. The search convergence process is shown in Fig. 3. As shown in Fig. 3 the optimization was terminated before maximum 200 generations which indicates that the average change in the objective function (total required work) value is less than 106 after about 66 generations according to Table 2. The adjusted variables and the range of each one used in the optimization solution are presented in Table 3. The lower and upper bounds were selected as 50% less and 50% more than each variable value in the base case, respectively. The values of adjusted variables and the total required work in the base and optimized case are presented in Table 4. As shown in Table 4 after the optimization, the total required work decreases about 14% compared to the base case. Fig. 4 illustrates the hot and cold composite curves of the cold box for the base and optimized cases. In fact, the composite curves of all three heat exchangers are collected in a figure. As shown in Fig. 4(a) there is a gap between composite curves that causes low process efficiency due to considerable thermodynamic irreversibility and exergy loss during heat exchange. After the optimization temperature difference between hot and cold composite curves became smaller than that of the base case (Fig. 4(b)). The total required work decreases about 14% due to the decrement in temperature difference. Fig. 5 shows the temperature approach of the cold box in different heat duties. The approach temperature is based on minimum approach temperature of all three heat exchangers. For each heat exchanger a hot composite curve is obtained by combination of all hot streams and at the same way a cold composite curve is obtained by combination of all cold streams. The aim of optimization is minimizing the difference temperature (approach temperature) between these two composite curves (hot and cold streams) for LNG heat exchangers.
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Fig. 2. The variation of total work with Nitrogen, Methane, Ethane, Propane and n-Butane content of MR at 32 C cold box inlet hot stream.
As shown in Fig. 5 the minimum approach temperature in all heat duties is greater than 2 C that satisfies the feasibility of the process. In the case of optimized process the approach temperatures along three heat exchangers are smaller than that of the base case and close to the minimum allowable approach temperature (2 C) that causes decreasing in energy consumption.
3.2. Effect of ambient temperature One of the most important variables that affect the required work of the LNG plants is ambient temperature. When the ambient temperature varies, in order to keep the process in an optimum condition the composition of MR should be changed. In fact, the variation of ambient temperature affects basically the outlet
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
xNitrogen ¼ 5 104 Ta þ 0:0151 xMethane ¼ 4:3 103 Ta þ 0:4826 xEthane ¼ 4:3 103 Ta þ 0:3572 xPropane ¼ 7:2 103 Ta þ 0:1457 xnButane ¼ 9 104 Ta 0:0006
Fig. 3. Search convergence process at 32 C cold box inlet hot stream.
Table 3 The adjusted variables and optimization range. Adjusted Variable
Unit
Lower bound
Upper bound
Flow rate of NitrogenðX1 Þ Flow rate of Methane ðX2 Þ Flow rate of Ethane ðX3 Þ Flow rate of Propane ðX4 Þ Flow rate of n-Butane ðX5 Þ Compressor-1 outlet pressure ðX6 Þ Compressor-2 outlet pressure ðX7 Þ Compressor-3 outlet pressure ðX8 Þ valve-1 outlet pressure ðX9 Þ valve-2 outlet pressure ðX10 Þ valve-3 outlet pressure ðX11 Þ
(kmol/h) (kmol/h) (kmol/h) (kmol/h) (kmol/h) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
2000 10000 12000 8000 3000 650 2000 5000 600 150 150
9000 41000 50000 34000 13000 2000 4000 7000 2000 450 450
Case
Variables MR components flow rate (kmol/h)
Base Optimized Case
Base Optimized
X1
X2
X3
X4
X5
4388 4461
20557 21206
25470 25965
17223 19937
6478 6112
Variables
Obj. Function
Pressures (kPa)
Total work (kW)
X6
X7
X8
X9
X10
X11
1061 1325
3197 2719
6040 6021
1051 1315
224 339
234 349
149188 128325
temperature of the air coolers. Due to changing ambient temperature, outlet temperature of air coolers is varied from 20 C to 40 C with 0.5 C intervals. Hence, the optimization process was performed at different ambient temperatures to find the best composition of MR. Finally linear regression curves are obtained for each component of MR that shows the variation of concentration with ambient temperature to keep the process in an optimum condition. Fig. 6 shows the variation of MR composition and its linear regression to keep the system in the optimized condition at different ambient temperatures. The regressed equations are listed below.
(4)
where Ta is ambient temperature in C. xNitrogen , xMethane , xEthane , xPropane and xnButane represent the molar composition of nitrogen, methane, ethane, propane and n-butane, respectively. In this study the ambient temperature has been considered equal to cold box inlet MR temperature. As shown in Fig. 6 when ambient temperature increases from 20 C to 40 C, the concentration of nitrogen, propane and n-butane should be increased about 40%, 50% and 103%, respectively. Also the concentration of methane and ethane should be decreased about 22% and 32%, respectively. Furthermore as illustrated in Fig. 6 and Eq. (4), the variation slope of propane concentration versus ambient temperature is greater than that of other components and the amount of n-butane concentration was increased more than that of other components (about 2 times). Fig. 7 shows the variation of total required work versus ambient temperature and its second order polynomial regression. The regressed equation is presented below:
WT ¼ 0:0003Ta2 0:0221Ta þ 1:8772
Table 4 The values of adjusted variables in the base and optimized process.
475
(5)
where WT is total required work in MW. As shown in Fig. 7 when ambient temperature increases, the total required work decreases to about 33 C. After 33 C increasing the ambient temperature causes the total required work increases too. Therefore the base design of this APCI process should be performed at ambient temperature of about 33 C and the operating temperature should be kept at about 33 C to minimize the total required work. When ambient temperature increases it is required to provide more refrigeration capacity to liquefy natural gas. In comparison to lighter hydrocarbons such as methane and ethane, heavier hydrocarbons with higher boiling points such as propane and n-butane could produce this refrigeration capacity in higher ambient temperatures. So the concentration of propane and n-butane in mixed refrigerant should be increased at higher ambient temperatures. There are two factors that affect the total required work at different ambient temperatures. The first one is increment of mixed refrigerant temperature at the suction part of the compressors. The compressors work will be increased by increasing fluid temperature at the suction part. The second factor is related to the type of fluid which will be compressed. Since the compressor work varies by fluid molecular weight inversely (because the outlet pressure of all compressors are fixed), heavier hydrocarbons require less work for compression rather than that of light hydrocarbons. As mentioned above the amount of propane and n-Butane should be increased by increasing ambient temperature. So, the required work for compression of this fluid will be decreased. Fig. 8 shows that MR molecular weight varies linearly by ambient temperature. Variation of the total required work by MR molecular weight is shown in Fig. 9. As shown in Fig. 9 when MR molecular weight value is equal to about 31.5 (kg/k mol) which is corresponding to ambient temperature of about 33 C, the total required work is at minimum value. Fig. 10 shows variation of total required work by both effective parameters: MR molecular weight and ambient temperature. According to this figure, the ambient temperature and MR molecular weight have opposite effects on the total required work. From 20 C to about 33 C the effect of fluid type (MR molecular weight) is more significant and causes the work to be decreased. For
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
320
320
300
300
280
280
260
260 Temperature (K)
Temperature (K)
476
240 220 Cold Stream
200
Hot Stream
180
240 220 200
Cold Stream
180
Hot Stream
160
160
140
140
120
120
100 0
50
100
150 200 250 Heat Flow (MW)
300
100
350
0
50
100
(a)
150 200 250 Heat Flow (MW)
300
350
(b)
Fig. 4. Hot and cold composite curves of three heat exchangers in the cold box (a) the base case, (b) the optimized case.
12
16
App.Temp.
10 Approach Temperature (K)
Approach Temperature (K)
14
12 10 8 6
App. Temp.
4
Min. App. Temp.
Min. App. Temp.
8 6 4 2
2 0 0
50
100
150
200
250
300
350
0 0
50
100
Heat Flow (MW)
150
200
250
300
350
Heat Flow (MW)
(a)
(b)
Fig. 5. Approach temperature curves of three heat exchangers in the cold box (a) the base case, (b) the optimized case.
0.5
159
0.45
158
Nitrogen Methane
0.3
Ethane
0.25
Propane
0.2
n-Butane
0.15
157
Total Work (MW)
Molar Composition
0.4 0.35
156 155 154 153 152
0.1
151
0.05
150 149
0 18
20
22
24
26
28
30
32
34
36
38
40
42
Ambient Temperature (°C)
Fig. 6. Optimized MR molar composition in various ambient temperatures.
20
22
24
26
28
30
32
34
36
38
Ambient Temperature (°C) Fig. 7. The total required work in various ambient temperatures.
40
33.5
0.45
33
0.4
32.5
0.35 MR Molar Composition
MR Molecular Weight
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
32 31.5 31 30.5 30
477
0.3 N2
0.25
CH4 0.2
C2H6 C3H8
0.15
n-C4H10
0.1
29.5
0.05
y = 0.187x + 25.296 29
0 5500
28.5 20
22
24
26
28
30
32
34
36
38
40
5900
6300
6700
7100
7500
Feed Pressure (kPa)
Ambient Temperature (°C) Fig. 11. Optimized MR molar composition in various feed pressures. Fig. 8. Variation of MR molecular weight with ambient temperature.
3.3. Effect of feed pressure 159 158
Another parameter which affects the total required work of the LNG plants is the pressure of natural gas. In this section optimization of the APCI process was performed by considering the molar flow rates of MR components as adjusted variables and minimization of the total required work as an objective function. Also the other variables used in the optimization of the base case were kept constant. Feed pressure was changed from 55 bar to 75 bar with a 0.5 bar pressure step size. The linear regressions of MR mole fractions at various feed pressure levels are indicated in Fig. 11. The regressed equations are listed below:
y = 0.7755x - 49.165x + 930.06
Total Work (MW)
157 156 155 154 153 152 151 150 149 29
29.5
30
30.5
31
31.5
32
32.5
33
MR Molecular Weight Fig. 9. Variation of total required work with MR molecular weight.
MR Molecular Weight
Total Work (MW)
28
28.5
29
29.5
30
30.5
31
31.5
32
32.5
33
33.5
34
159
159
158
158
157
157
156
156
155
155
154
154
153
153
152
152
151
151
150
150
149
149 20
22
24
26
28
30
32
34
36
38
40
Ambient Temperature (°C) Amb. Temperature
Molecular Weight
Fig. 10. Variation of total required work by MR molecular weight and ambient temperature.
temperatures above 33 C the effect of fluid temperature at compressor suction is more significant and causes the required work for compression to be increased.
xNitrogen ¼ 1 106 Pf þ 0:034 xMethane ¼ 7 106 Pf þ 0:3995 xEthane ¼ 1 105 Pf þ 0:1311 xPropane ¼ 8 106 Pf þ 0:4257 xnButane ¼ 3 106 Pf þ 0:0096
(6)
where Pf is the feed pressure in kPa. xNitrogen , xMethane , xEthane , xPropane and xnButane represent the molar composition of nitrogen, methane, ethane, propane and n-butane, respectively. As shown in Fig. 11 when the feed pressure increases from 55 to 75 bar, the concentration of nitrogen, methane and propane should be decreased to about 7%, 4% and 4%, respectively. Also the concentration of ethane and n-butane should be increased to about 11% and 23%, respectively. According to Fig. 11 and Eq. (6) the slope of ethane concentration versus feed pressure is greater than that of other components while the concentration of n-butane concentration was increased more than that of other components. On the other hand the feed pressure has not an effective influence on the optimization variables including compositions of mixed refrigerant. Variation of ambient temperature affects directly the efficiency of compressors (at different inlet temperatures) and the mixed refrigerant conditions. This is due to changing temperature and phase condition (liquid/gas ratio) of outlet streams of air coolers (12 and 13) and operation of HX-1, HX-2, and HX-3. So for the optimization of this new condition, the composition of MR must be changed clearly to minimize the gap between composite curves of HXs. Feed stream (natural gas) is independent and its pressure variation has an indirect effect on mixed refrigerant conditions. Although the feed pressure affects the total required work of mixed refrigerant compression, its amount is less significant than those of ambient temperature on the mixed refrigerant compositions. Also,
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Pf T Ta DTmin W WT x X
156
154
Total Work (MW)
152 150 148 146 144
142 140 5500
5900
6300
6700
7100
7500
Feed Pressure (kPa) Fig. 12. The total required work in various feed pressures.
the variation of Feed pressure has a negligible effect on HX composite curves. Fig. 12 shows the variation of total required work versus feed pressure and its linear regression. The regressed equation is presented below:
WT ¼ 0:0047Pf þ 179:26
feed pressure (kPa) temperature ( C) Ambient temperature ( C) minimum approach temperature ( C) work (kW) total required work (kW, MW) molar composition adjusted variable vector
Subscripts dew dew point i stream i in inlet stream j stream j Abbreviations APCI Air Products and Chemicals, Inc GA Genetic Algorithm LNG Liquefied Natural Gas MR Mixed Refrigerant NG Natural Gas SMR Single Mixed Refrigerant
(7) References
where WT is the total required work in MW and Pf is the feed pressure in kPa. As shown in Fig. 12 when the feed pressure increases, the total required work decreases continuously. According to Eq. (7) by increasing the feed pressure from 55 bar to 75 bar, the total required work decreases about 6%. 4. Conclusion The APCI LNG process was simulated and optimized by coupling of Aspen HYSYS as the process simulation software and MATLAB as the optimizing software. GA optimization method was chosen in order to make sure a global optimum condition would be reached. The optimized value of each variable was obtained and reported. The total required work was reduced by 14% compared to the base case. Also, the effect of ambient temperature on the process performance was investigated. The optimization was performed in the range of 20 Ce40 C with 0.5 C step sizes by variation of molar flow rate of MR components only. When the ambient temperature increases, to keep the process in the optimum condition the concentration of nitrogen, propane and n-butane should increase and methane and ethane should decrease. When the ambient temperature increases, the total required work behavior follows a second order polynomial with about 33 C minimum point which is corresponding to MR molecular weight of about 31.5 kg/kmol. In addition, the optimization was performed in various feed pressures from 55 bar to 75 bar. The results showed that there is not a significant change in MR compositions in this range of pressure. Moreover the total work decreases linearly by increasing the feed pressure. Acknowledgements We gratefully acknowledge the support of Research & Technology Directorate of National Iranian Gas Company. Nomenclature
Symbols P pressure (kPa)
Alabdulkarem, A., Mortazavi, A., Hwang, Y., Radermacher, R., Rogers, P., 2011. Optimization of propane pre-cooled mixed refrigerant LNG plant. Appl. Therm. Eng. 31 (6e7), 1091e1098. Andress, D.L., Watkins, R.J., 2004. Beauty of simplicity: phillips optimized cascade LNG liquefaction process. Adv. Cryogen. Eng. 49, 91e98. Aspelund, A., Gundersen, T., Myklebust, J., Nowak, M.P., Tomasgard, A., 2010. An optimizationesimulation model for a simple LNG process. Comput. Chem. Eng. 34 (10), 1606e1617. Austbo, B., Lovseth, S.W., Gundersen, T., 2014. Annotated bibliographyduse of optimization in LNG process design and operation. Comput. Chem. Eng. 71, 391e414. Behroozsarand, A., Ebrahimi, H., Zamaniyan, A., 2009. Multiobjective optimization of industrial autothermal reformer for syngas production using nonsorting genetic algorithm II. Ind. Eng. Chem. Res. 48, 7239e7529. Cammarata, G., Fichera, A., Guglielmino, D., 2001. Optimization of a liquefaction plant using genetic algo rithms. Appl. Energy 68 (1), 19e29. Cao, W., Lu, X., Lin, W., Gu, A., 2006. Parameter comparison of two small-scale natural gas liquefaction processes in skid-mounted packages. Appl. Therm. Eng. 26 (8), 898e904. Castillo, L., Dahouk, M.M., Di Scipio, S., Dorao, C.A., 2013. Conceptual analysis of the precooling stage for LNG processes. Energy Convers. Manag. 66, 41e47. Cranmore, R.G., Stanton, E., 2000. Natural gas. In: Dawe, R.A. (Ed.), Modern Petroleum Technology, Upstream Volume. Institute of Petroleum, John Wiley and Sons Ltd, Chichester, pp. 337e382. Gong, M.Q., Wu, J.F., Luo, E.C., Zhou, Y., Liang, J.T., Zhang, L., 2000. Optimum composition calculation for multicomponent cryogenic mixture used in JeT refrigerators. Adv. Cryo. Eng. 45, 283e290. Hatcher, P., Khalilpour, R., Abbas, A., 2012. Optimisation of LNG mixed-refrigerant processes considering operation and design objectives. Comput. Chem. Eng. 41, 123e133. Hwang, J.H., Ku, N.K., Roh, M.I., Lee, K.Y., 2013. Optimal design of liquefaction cycles of liquefied natural gas floating, production, storage, and offloading unit considering optimal synthesis. Ind. Eng. Chem. Res. 52 (15), 5341e5356. Jacobsen, M.G., Skogestad, S., 2013. Active constraint regions for a natural gas liquefaction process. J. Nat. Gas. Sci. Eng. 10, 8e13. Khan, M.S., Lee, M., 2013. Design optimization of single mixed refrigerant natural gas liquefaction process using the particle swarm paradigm with nonlinear constraints. Energy 49, 146e155. Khan, M.S., Lee, S., Rangaiah, G.P., Lee, M., 2013. Knowledge based decision making method for the selection of mixed refrigerant systems for energy efficient LNG processes. Appl. Energy 111, 1018e1031. Lee, G.C., Smith, R., Zhu, X.X., 2004. Optimal synthesis of mixed-refrigerant systems for low temperature process. Ind. Eng. Chem. Res. 41, 5016e5028. Li, Y., Wang, X., Ding, Y., 2012. An optimal design methodology for large-scale gas liquefaction. Appl. Energy 99, 484e490. Mokarizadeh Haghighi Shirazi, M., Mowla, D., 2010. Energy optimization for liquefaction process of natural gas in peak shaving plant. Energy 35, 2878e2885. Mortazavi, A., Somers, C., Hwang, Y., Radermacher, R., Rodgers, P., Al-Hashimi, S., 2012. Performance enhancement of propane pre-cooled mixed refrigerant LNG plant. Appl. Energy 93, 125e131. Remeljej, C.W., Hoadley, A.F.A., 2006. An exergy analysis of small-scale liquefied
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479 natural gas (LNG) liquefaction processes. Energy 31 (12), 2005e2019. Roberts, M.J., Agrawal, R., Daugherty, T.L., 2002. Single Mixed Refrigerant Gas Liquefaction Process. US Patent 6,347,531. Skaugen, G., Walnum, H.T., Hammer, M., Wahl, P.E., Wil-helmsen, Ø., Kolsaker, K., 2013. Design and optimization of compact heat exchangers in process used for liquefaction of natural gas. In: 5th International Conference on Applied Energy ICAE 2013. 2013 July 1e4, Pretoria, South Africa. Swenson, L.K., 1977. Single Mixed Refrigerant, Closed Loop Process for Liquefying Natural Gas. US Patent 4,033,735. Vatani, A., Mehrpooya, M., Tirandazi, B., 2013. A novel process configuration for coproduction of NGL and LNG with low energy requirement. Chem. Eng. Process: Process Intensif. 63, 16e24. Venkatarathnam, G., 2008. Cryogenic Mixed Refrigerant Processes. Springer, New York.
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Wahl, P.E., Løvseth, S.W., Mølnvik, M.J., 2013. Optimization of a simple LNG process using sequential quadratic programming. Comput. Chem. Eng. 56, 27e36. Wang, M., Khalilpour, R., Abbas, A., 2013. Operation optimization of propane precooled mixed refrigerant processes. J. Nat. Gas. Sci. Eng. 15, 93e105. Xu, X., Liu, J., Jiang, C., Cao, L., 2013. The correlation between mixed refrigerant composition and ambient conditions in the PRICO LNG process. Appl. Energy 102, 1127e1136. Yuan, Z., Cui, M., Xie, Y., Li, C., 2014. Design and analysis of a small-scale natural gas liquefaction process adopting single nitrogen expansion with carbon dioxide pre-cooling. Appl. Therm. Eng. 64 (1), 139e146. Zhang, X., Myhrvold, N.P., Caldeira, K., 2014. Key factors for assessing climate benefits of natural gas versus coal electricity generation. Environ. Res. Lett. 9, 114022.
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APCI- LNG single mixed refrigerant process for natural gas liquefaction cycle: Analysis and optimization Peyman Moein a, Mehran Sarmad a, Hadi Ebrahimi a, *, Marziyeh Zare b, Saeed Pakseresht b, Shahrokh Zandieh Vakili b a b
Gas Research Division, Research Institute of Petroleum Industry (RIPI), Tehran 14665-1998, Iran Research & Technology Directorate of National Iranian Gas Company, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 April 2015 Received in revised form 21 June 2015 Accepted 22 June 2015 Available online xxx
In this paper, a typical single mixed refrigerant (SMR) with low energy consumption is analyzed to determine the optimum operating conditions. Genetic Algorithm (GA) tool is used to minimize the total required work by optimizing eleven variables including the outlet pressures of all compressors and throttling valves and the molar flow rate of the MR components. The results of the process simulation show that the total work is varied linearly by the compositions. It is observed that to have a minimum work, when the ambient temperature increases, the compositions of both methane and ethane should be decreased, while those of nitrogen, propane and n-butane should be increased. Moreover, optimized values of the total required work at different ambient temperatures were correlated with a second order polynomial. Increasing feed pressure has small effect on the MR compositions, but significant effect on the total work. © 2015 Elsevier B.V. All rights reserved.
Keywords: LNG Single mixed refrigerant Optimization Genetic algorithm Ambient temperature Feed pressure
1. Introduction The demand for Natural Gas (NG) as a relatively clean fossil fuel has increased in the past years. Although research and development on other fossil fuels mainly oil, coal and their derivatives are going on (Zhang et al., 2014), NG produces approximately less than half the CO2 emissions per unit of generated electricity. Two main ways to transport NG from resources to consumers are pipeline and Liquefied Natural Gas (LNG). The pipeline is most commonly used due to its lower operating cost; however it is inflexible in the case of transmission capacity, and requires enormous initial construction cost. LNG is a liquid form of natural gas with a temperature about 162 C. It has a volume ~1/600 of that of gas at ambient temperature. Although production and transmission of LNG require complex machinery and vehicles, the incremental cost of transport per mile is less than that of pipelines (Cranmore and Stanton, 2000). There are several processes for LNG production such as N2 expander (Yuan et al., 2014), cascade and Mixed Refrigerant (MR) processes. The difference among these processes is related to their
* Corresponding author. E-mail address: [email protected] (H. Ebrahimi). http://dx.doi.org/10.1016/j.jngse.2015.06.040 1875-5100/© 2015 Elsevier B.V. All rights reserved.
capital and operational costs or between hot and cold composite curves (Hatcher et al., 2012). N2 expander processes have several advantages compared to MR ones, including simplicity, less number of equipments, no refrigerant phase change, non-flammability and non-toxicity of N2. However, higher energy consumption per produced LNG tones particularly for large capacity plants is wellknown for N2 expander processes. The cascade cycles contain some refrigeration stages that each stage has its own refrigerant and independent compression system. NG essentially contains mixed hydrocarbons and so its enthalpy with temperature is nonlinearly varied during the liquefaction. Whenever the temperature difference between hot and cold streams in the heat exchangers reaches below a certain value, the entropy generation reduces, but the efficiency increases. This temperature difference in MR cycles could be reduced effectively without need for more auxiliary equipment (Venkatarathnam, 2008). Although the pure refrigerant cycles are simple, a large number of refrigeration stages are required in order to reduce the temperature difference (Andress and Watkins, 2004). Single Mixed Refrigerant (SMR) processes are the simplest MR cycles for liquefaction of natural gas. Compared to mixedrefrigerant cycles (MRC) that have been applied for both large
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
and small-scale systems (Cao et al., 2006), SMR systems have only one series of compressors beside the main cryogenic heat exchangers to cover all range of the liquefaction temperatures (Swenson, 1977). Nevertheless, these MR processes are highly energy intensive, so an optimization procedure is required to minimize energy consumption. Several MR process optimization methods are available in the open literature. Lee et al. (2004) applied a graphical targeting method to optimize a multi-stage MR system by considering minimization of both crossovers and shaft work requirement. Gong et al. (2000) optimized the PRICO process by BOX method. Energy and exergy analysis of SMR, a two-stage expander nitrogen refrigerant and two open-loop expander processes have been evaluated by Remeljej and Hoadley (2006) for LNG production with small-scale LNG. Aspelund et al. (2010) used combination of Tabu Search (TS) and Nelder-Mead Downhill Simplex (NMDS) method linked to AspenHYSYS simulation software to optimize the PRICO process. Mokarizadeh and Mowla (2010) used coded PengeRobinson equation of state and genetic algorithm method to optimize the PRICO process. Alabdulkarem et al. (2011) applied genetic algorithm (GA) for optimization of propane pre-cooled MR (C3MR) and reported MR power consumption at different pinch temperatures. Mortazavi et al. (2012) enhanced the performance of C3MR process by implementing two phase expanders, liquid turbines and gas expanders instead of conventional expansion devices. Xu et al. (2013) optimized the PRICO process using GA under different cold box inlet temperatures and correlated linear regression on the MR composition. Li et al. (2012) also used GA and exergy efficiency to optimize large scale liquefaction systems. Khan and Lee (2013) used particle-swarm optimization methodology coded in MATLAB connected to UniSim simulation software to optimize a SMR process. Wahl et al. (2013) applied sequential quadratic programming (SQP) to optimize the PRICO process. Castillo et al. (2013) compared different precooling cycles for LNG production processes at two different climate conditions, warm (25 C) and cold (6 C). They investigated both power consumption and heat transfer coefficient and found that a three stage propane precooled cycle for warm case and two stage mixed refrigerant cycle for the cold case could be more adequate. Hwang et al. (2013) optimized a dual mixed refrigerant LNG process for different number of refrigerant sub-streams and compression stages using combination of the genetic algorithm and sequential quadratic programming. Jacobsen and Skogestad (2013) used both UniSim and MATLAB softwares for modeling and optimization of a SMR process with disturbances in the flow rate of natural gas and ambient temperature. They expressed that the feasible region of operation could be divided into five sub-regions with different active constraints. Khan et al. (2013) optimized SMR and C3MR processes using knowledge based optimization (KBO) method. By considering boiling point difference of the MR components, they improved energy efficiency of the system. Skaugen et al. (2013) investigated a concept including a detailed heat exchanger model for the optimization of a SMR process. Vatani et al. (2013) considered two mixed refrigerant cycles for design of an LNG production process with integrated natural gas liquids (NGL) recovery. They formulated an optimization problem with minimizing specific power consumption. Wang et al. (2013) optimized two types of C3MR processes by investigating different objective functions including shaft work consumption, exergy efficiency and operating expenditure. They reported that shaft work consumption is the best objective function for the optimization of these processes. Cammarata et al. (2001) used GA for optimization of a modified Collins cycle which was used for liquefaction of helium. Austbo et al. (2014) have presented a detailed review related to the optimization of different LNG processes.
471
Because of the nature of nonlinearity and thermodynamic complexity of the LNG processes, optimization of these processes should be performed by global search methods such as GA, Tabu Search (TS), or Simulated Annealing (SA). Due to the fact that GA does not require derivatives and initial points, it was chosen as the optimization method for the current research. In this work a typical APCI (Air Products and Chemicals, Inc.) process (Roberts et al., 2002) as a SMR liquefaction process for LNG production was chosen because of its improved efficiency compared to the other SMR processes. Since special design of this LNG production process, it has low energy consumption. Therefore this process could be a suitable replacement with current LNG production processes due to simplicity, high efficiency and minimum number of existing heat exchangers. The improvements include the compression of vaporized refrigerant at reduced compressor inlet temperatures and the generation of inter-stage liquid refrigerant streams at ambient temperature which could be used beneficially in the refrigeration cycle. On the other hand this APCI process can achieve high thermodynamic efficiency by using a minimum number of heat exchangers to reduce both capital and operating costs (Roberts et al., 2002). The APCI has not been already investigated with the current GA method. Although optimization of several MR components in some special mixed refrigerant processes were investigated in previous studies, but the current APCI process has not been analyzed and optimized in detail yet. Moreover, the pattern of total required work variation at different MR compositions when the other parameters are fixed has not been already presented. On the other hand in open literature in which the effect of MR compositions was considered on the total work, the optimization was performed in different ambient temperatures and at last only the optimized values were presented. So there is a lack of study to show how the total work varies with changing MR compositions by fixing other parameters such as ambient temperature particularly in APCI process. In the present study this pattern was obtained and the results show that the total work will be varied linearly by MR compositions. Also the effect of feed (natural gas) pressure on the total work of refrigeration cycle was investigated. The present APCI single mixed refrigerant cycle which investigated in the present study has some advantages compared to the other SMR cycles which mentioned above. However, this special process has not been investigated yet. So optimization of this cycle can be useful in the case of design of mixed refrigerant liquefaction processes. In this research, the APCI process was simulated in Aspen HYSYS as a base case and optimized by connecting GA MATLAB tool to Aspen HYSYS to minimize the total required work. Then the effects of ambient temperature and feed pressure on the total required work were investigated. Afterwards, the concentrations of the MR components were optimized. In the current paper, not only effects of temperature and pressure are considered as presented in several previous studies, but also change of MR compositions are investigated using the proposed correlations. 2. Simulation and optimization framework 2.1. APCI process The flow sheet of the APCI process modeled by Aspen HYSYS is shown in Fig. 1. As shown in Fig. 1, outlet stream of the last compressor (Compressor-3) is passed through an air cooler (AC-3) divided into two phases (liquid and vapor) in a separator (V-2). Each of them enters the first heat exchanger (HX-1) separately as hot streams. The second cooled liquid stream (stream 16) after passing through a throttling valve returns to the heat exchanger as a cold stream and
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Fig. 1. Process flow diagram of APCI LNG liquefaction process.
after heat exchanging, enters the second stage of compression (Compressor-2). The cooled vapor phase goes to a phase separator (V-3) and the same operation occurs in the second heat exchanger (HX-2). The outlet cold stream of the third heat exchanger (stream 26) mixes with that of the second exchanger (stream 25) and after heat exchanging enters the first stage of compression (Compressor1). The temperature of natural gas after three steps decreases to about 155 C and after passing through throttling valve (Valve-4), LNG is produced at 162 C and atmospheric pressure. In this paper the properties of natural gas and outlet temperature of LNG from the last heat exchanger (HX-3) are fixed and only the properties of MR can vary during the optimization. The simulation assumptions are listed in Table 1.
fitness function. On the other hand, all generated data from the simulation case of HYSYS are exported to the MATLAB code. There is a continuous linking between the MATLAB optimization code and HYSYS simulation case. During data acquisition, the optimization by GA is going on until the minimization of the objective function is performed. 2.3. Optimization formulation In the current optimization problem, minimization of the total work of the plant (for all compressors and a pump) was defined as an objective function expressed as:
Minimize f ðXÞ ¼
2.2. Optimization problem In order to optimize the process by GA method, MATLAB was connected to Aspen HYSYS process simulator. In this situation the GA method acts as a controller and the Aspen HYSYS model is a server. A MATLAB program code adapted from a previous work (Behroozsarand et al., 2009) was prepared to call the Aspen HYSYS simulation and transfer the data produced by GA. Calculated total required work by Aspen HYSYS is sent to MATLAB to be used in
Table 1 Assumptions of the APCI plant simulation. Parameter
Value
Adiabatic compressor efficiency Minimum temperature approach of cold box ( C) Pressure drop in heat exchangers (bar) Pressure drop in air coolers (bar) Heat leakage of cold box Flow rate of natural gas(kg mole/h) Pressure of natural gas entering cold box (bar) Temperature of hot stream at cold box inlet ( C) Temperature of natural gas at cold box outlet ( C) Composition of natural gas (% mole) N2 CH4 C2H6 C3H8 n-C4H10 i-C4H10
75% 2 0.1 0.2 0% 26700 66.5 32 155 0.90 94.00 3.10 1.30 0.40 0.30
X WCompressors þ WPump
(1)
In the above equation X is an adjusted variable vector including MR molar flow rates of components, the outlet pressure of MR compressor stages and the MR pressure after each throttling valve. Nitrogen, methane, ethane, propane and n-butane are used as the components of the mixed refrigerant. PengeRobinson equation of state is applied to calculate the properties of both MR and NG. GA optimization of this process is limited to three constraints. First, the minimum approach temperature in the heat exchangers should be greater than 2 C to satisfy reliability and feasibility of the process. Second, the temperature of MR in the inlet of compressors should be greater than the dew temperature of the fluid in that pressure to prevent formation of liquid in the suction part of the compressors. Third, the pressure of streams entering to a mixer should be equal. These constraints are formulated as follow:
DTmin;HXi 2 C Ti Tdew;i Pi;in ¼ Pj;in
ðfor MixersÞ
where DTmin;HXi represents the minimum approach temperature in heat exchanger i, Ti and Tdew;i refer to operating temperature and dew point temperature of the stream i and Pi;in and Pj;in illustrate the mixer pressure of inlet streams (i and j).
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479 Table 2 Tuning parameters of GA. Tuning parameters
Value
Population size Selection method Tournament size Mutation method Crossover fraction Crossover function Stopping criteria Maximum number of generations Objective function tolerance
300 Tournament 4 Adaptive feasible 0.8 Two-point 200 106
composite curves in the heat exchangers should be greater than 2 C while the temperature of compressors inlet streams should be greater than the dew point of these streams. This figure is obtained when the other variables are assumed to be fixed while only the composition of MR can be varied. According to Fig. 2, the total required work extremely depends on the MR composition. It is shown that in this process, the relationship between work and composition is linear. Additionally, the effects for all components do not have the same trend. For instance, rising nitrogen mole fraction causes the required work to be increased, while increase in methane mole fraction decrease the work. As illustrated in Fig. 2, ethane and n-Butane behave similar to methane and the behavior of propane is similar to nitrogen. The regressed linear equations are listed below:
8 9 1:7616 xN2 þ 1:1856 105 > > 0:058 < x < 0:07 > > N 2 > > > > > > 105 < 0:274 0:267 < x < 2:668 xCH4 þ 2:0177 = CH4 5 WT ¼ j 0:324 < xC2 H6 < 0:334 1:9899 xC2 H6 þ 1:9512 10 > > > > 0:258 < xC3 H8 < 0:265 > > 2:9399 xC3 H8 þ 0:52886 105 > > > > : 5 0:0745 < xnC4 H10 < 0:0775 ; 7:7894 xnC4 H10 þ 1:8907 10
The last limitation is defined as a linear constraint for GA optimization while the first and second constraints are defined as the penalties for the objective function as shown below:
Minimize PðX; rÞ ¼ f ðXÞ þ r
P i
g1 ðxÞ ¼ 2 DTmin;HXi g2 ðxÞ ¼ Tdew;i Ti
! 2
½maxf0; gi ðxÞg
(2)
where r is the penalty factor, assumed here as 10þ14 . If all the constraints are satisfied, the second term in the right hand side of Eq. (2) would be zero (PðX; rÞ ¼ f ðxÞ). Otherwise the second term will be a large value that GA modifies the penalty function in the next generation. The tuning parameters of GA are listed in Table 2. 3. Results and discussion 3.1. The base case solution Design and control of a MR process is extremely related to the total required work. This work depends on not only amount of mixed refrigerant composition, but also the amount of increase or decrease in compositions. Knowing total required work at different mixed refrigerant compositions could give a good view about the design of a new MR process or control of the current processes. Analyzing the results obtained from the simulation could present the relationship between total required work and MR composition in APCI and predict the system performance before the optimization. However, only a few researches are found in open literature about it for other MR processes. For considering the effect of compositions, all other parameters such as temperature and pressure are assumed constant. Effect of MR composition on the total required work is shown in Fig. 2. The hot stream enters to the cold box at a temperature of 32 C. The range of each MR component mole fraction was selected as follow: a minimum approach temperature between hot and cold
473
(3)
where WT is total required work in kW and xN2 , xCH4 , xC2 H6 , xC3 H8 and xnC4 H10 represent the molar composition of nitrogen, methane, ethane, propane and n-butane, respectively. Therefore, it is important to find the best values for MR compositions in addition to the other variables to minimize the total required work. The base case solution was performed when the inlet hot stream of the cold box was at 32 C. The search convergence process is shown in Fig. 3. As shown in Fig. 3 the optimization was terminated before maximum 200 generations which indicates that the average change in the objective function (total required work) value is less than 106 after about 66 generations according to Table 2. The adjusted variables and the range of each one used in the optimization solution are presented in Table 3. The lower and upper bounds were selected as 50% less and 50% more than each variable value in the base case, respectively. The values of adjusted variables and the total required work in the base and optimized case are presented in Table 4. As shown in Table 4 after the optimization, the total required work decreases about 14% compared to the base case. Fig. 4 illustrates the hot and cold composite curves of the cold box for the base and optimized cases. In fact, the composite curves of all three heat exchangers are collected in a figure. As shown in Fig. 4(a) there is a gap between composite curves that causes low process efficiency due to considerable thermodynamic irreversibility and exergy loss during heat exchange. After the optimization temperature difference between hot and cold composite curves became smaller than that of the base case (Fig. 4(b)). The total required work decreases about 14% due to the decrement in temperature difference. Fig. 5 shows the temperature approach of the cold box in different heat duties. The approach temperature is based on minimum approach temperature of all three heat exchangers. For each heat exchanger a hot composite curve is obtained by combination of all hot streams and at the same way a cold composite curve is obtained by combination of all cold streams. The aim of optimization is minimizing the difference temperature (approach temperature) between these two composite curves (hot and cold streams) for LNG heat exchangers.
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Fig. 2. The variation of total work with Nitrogen, Methane, Ethane, Propane and n-Butane content of MR at 32 C cold box inlet hot stream.
As shown in Fig. 5 the minimum approach temperature in all heat duties is greater than 2 C that satisfies the feasibility of the process. In the case of optimized process the approach temperatures along three heat exchangers are smaller than that of the base case and close to the minimum allowable approach temperature (2 C) that causes decreasing in energy consumption.
3.2. Effect of ambient temperature One of the most important variables that affect the required work of the LNG plants is ambient temperature. When the ambient temperature varies, in order to keep the process in an optimum condition the composition of MR should be changed. In fact, the variation of ambient temperature affects basically the outlet
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
xNitrogen ¼ 5 104 Ta þ 0:0151 xMethane ¼ 4:3 103 Ta þ 0:4826 xEthane ¼ 4:3 103 Ta þ 0:3572 xPropane ¼ 7:2 103 Ta þ 0:1457 xnButane ¼ 9 104 Ta 0:0006
Fig. 3. Search convergence process at 32 C cold box inlet hot stream.
Table 3 The adjusted variables and optimization range. Adjusted Variable
Unit
Lower bound
Upper bound
Flow rate of NitrogenðX1 Þ Flow rate of Methane ðX2 Þ Flow rate of Ethane ðX3 Þ Flow rate of Propane ðX4 Þ Flow rate of n-Butane ðX5 Þ Compressor-1 outlet pressure ðX6 Þ Compressor-2 outlet pressure ðX7 Þ Compressor-3 outlet pressure ðX8 Þ valve-1 outlet pressure ðX9 Þ valve-2 outlet pressure ðX10 Þ valve-3 outlet pressure ðX11 Þ
(kmol/h) (kmol/h) (kmol/h) (kmol/h) (kmol/h) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
2000 10000 12000 8000 3000 650 2000 5000 600 150 150
9000 41000 50000 34000 13000 2000 4000 7000 2000 450 450
Case
Variables MR components flow rate (kmol/h)
Base Optimized Case
Base Optimized
X1
X2
X3
X4
X5
4388 4461
20557 21206
25470 25965
17223 19937
6478 6112
Variables
Obj. Function
Pressures (kPa)
Total work (kW)
X6
X7
X8
X9
X10
X11
1061 1325
3197 2719
6040 6021
1051 1315
224 339
234 349
149188 128325
temperature of the air coolers. Due to changing ambient temperature, outlet temperature of air coolers is varied from 20 C to 40 C with 0.5 C intervals. Hence, the optimization process was performed at different ambient temperatures to find the best composition of MR. Finally linear regression curves are obtained for each component of MR that shows the variation of concentration with ambient temperature to keep the process in an optimum condition. Fig. 6 shows the variation of MR composition and its linear regression to keep the system in the optimized condition at different ambient temperatures. The regressed equations are listed below.
(4)
where Ta is ambient temperature in C. xNitrogen , xMethane , xEthane , xPropane and xnButane represent the molar composition of nitrogen, methane, ethane, propane and n-butane, respectively. In this study the ambient temperature has been considered equal to cold box inlet MR temperature. As shown in Fig. 6 when ambient temperature increases from 20 C to 40 C, the concentration of nitrogen, propane and n-butane should be increased about 40%, 50% and 103%, respectively. Also the concentration of methane and ethane should be decreased about 22% and 32%, respectively. Furthermore as illustrated in Fig. 6 and Eq. (4), the variation slope of propane concentration versus ambient temperature is greater than that of other components and the amount of n-butane concentration was increased more than that of other components (about 2 times). Fig. 7 shows the variation of total required work versus ambient temperature and its second order polynomial regression. The regressed equation is presented below:
WT ¼ 0:0003Ta2 0:0221Ta þ 1:8772
Table 4 The values of adjusted variables in the base and optimized process.
475
(5)
where WT is total required work in MW. As shown in Fig. 7 when ambient temperature increases, the total required work decreases to about 33 C. After 33 C increasing the ambient temperature causes the total required work increases too. Therefore the base design of this APCI process should be performed at ambient temperature of about 33 C and the operating temperature should be kept at about 33 C to minimize the total required work. When ambient temperature increases it is required to provide more refrigeration capacity to liquefy natural gas. In comparison to lighter hydrocarbons such as methane and ethane, heavier hydrocarbons with higher boiling points such as propane and n-butane could produce this refrigeration capacity in higher ambient temperatures. So the concentration of propane and n-butane in mixed refrigerant should be increased at higher ambient temperatures. There are two factors that affect the total required work at different ambient temperatures. The first one is increment of mixed refrigerant temperature at the suction part of the compressors. The compressors work will be increased by increasing fluid temperature at the suction part. The second factor is related to the type of fluid which will be compressed. Since the compressor work varies by fluid molecular weight inversely (because the outlet pressure of all compressors are fixed), heavier hydrocarbons require less work for compression rather than that of light hydrocarbons. As mentioned above the amount of propane and n-Butane should be increased by increasing ambient temperature. So, the required work for compression of this fluid will be decreased. Fig. 8 shows that MR molecular weight varies linearly by ambient temperature. Variation of the total required work by MR molecular weight is shown in Fig. 9. As shown in Fig. 9 when MR molecular weight value is equal to about 31.5 (kg/k mol) which is corresponding to ambient temperature of about 33 C, the total required work is at minimum value. Fig. 10 shows variation of total required work by both effective parameters: MR molecular weight and ambient temperature. According to this figure, the ambient temperature and MR molecular weight have opposite effects on the total required work. From 20 C to about 33 C the effect of fluid type (MR molecular weight) is more significant and causes the work to be decreased. For
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479
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Fig. 4. Hot and cold composite curves of three heat exchangers in the cold box (a) the base case, (b) the optimized case.
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Fig. 5. Approach temperature curves of three heat exchangers in the cold box (a) the base case, (b) the optimized case.
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Fig. 6. Optimized MR molar composition in various ambient temperatures.
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3.3. Effect of feed pressure 159 158
Another parameter which affects the total required work of the LNG plants is the pressure of natural gas. In this section optimization of the APCI process was performed by considering the molar flow rates of MR components as adjusted variables and minimization of the total required work as an objective function. Also the other variables used in the optimization of the base case were kept constant. Feed pressure was changed from 55 bar to 75 bar with a 0.5 bar pressure step size. The linear regressions of MR mole fractions at various feed pressure levels are indicated in Fig. 11. The regressed equations are listed below:
y = 0.7755x - 49.165x + 930.06
Total Work (MW)
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Fig. 10. Variation of total required work by MR molecular weight and ambient temperature.
temperatures above 33 C the effect of fluid temperature at compressor suction is more significant and causes the required work for compression to be increased.
xNitrogen ¼ 1 106 Pf þ 0:034 xMethane ¼ 7 106 Pf þ 0:3995 xEthane ¼ 1 105 Pf þ 0:1311 xPropane ¼ 8 106 Pf þ 0:4257 xnButane ¼ 3 106 Pf þ 0:0096
(6)
where Pf is the feed pressure in kPa. xNitrogen , xMethane , xEthane , xPropane and xnButane represent the molar composition of nitrogen, methane, ethane, propane and n-butane, respectively. As shown in Fig. 11 when the feed pressure increases from 55 to 75 bar, the concentration of nitrogen, methane and propane should be decreased to about 7%, 4% and 4%, respectively. Also the concentration of ethane and n-butane should be increased to about 11% and 23%, respectively. According to Fig. 11 and Eq. (6) the slope of ethane concentration versus feed pressure is greater than that of other components while the concentration of n-butane concentration was increased more than that of other components. On the other hand the feed pressure has not an effective influence on the optimization variables including compositions of mixed refrigerant. Variation of ambient temperature affects directly the efficiency of compressors (at different inlet temperatures) and the mixed refrigerant conditions. This is due to changing temperature and phase condition (liquid/gas ratio) of outlet streams of air coolers (12 and 13) and operation of HX-1, HX-2, and HX-3. So for the optimization of this new condition, the composition of MR must be changed clearly to minimize the gap between composite curves of HXs. Feed stream (natural gas) is independent and its pressure variation has an indirect effect on mixed refrigerant conditions. Although the feed pressure affects the total required work of mixed refrigerant compression, its amount is less significant than those of ambient temperature on the mixed refrigerant compositions. Also,
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Pf T Ta DTmin W WT x X
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the variation of Feed pressure has a negligible effect on HX composite curves. Fig. 12 shows the variation of total required work versus feed pressure and its linear regression. The regressed equation is presented below:
WT ¼ 0:0047Pf þ 179:26
feed pressure (kPa) temperature ( C) Ambient temperature ( C) minimum approach temperature ( C) work (kW) total required work (kW, MW) molar composition adjusted variable vector
Subscripts dew dew point i stream i in inlet stream j stream j Abbreviations APCI Air Products and Chemicals, Inc GA Genetic Algorithm LNG Liquefied Natural Gas MR Mixed Refrigerant NG Natural Gas SMR Single Mixed Refrigerant
(7) References
where WT is the total required work in MW and Pf is the feed pressure in kPa. As shown in Fig. 12 when the feed pressure increases, the total required work decreases continuously. According to Eq. (7) by increasing the feed pressure from 55 bar to 75 bar, the total required work decreases about 6%. 4. Conclusion The APCI LNG process was simulated and optimized by coupling of Aspen HYSYS as the process simulation software and MATLAB as the optimizing software. GA optimization method was chosen in order to make sure a global optimum condition would be reached. The optimized value of each variable was obtained and reported. The total required work was reduced by 14% compared to the base case. Also, the effect of ambient temperature on the process performance was investigated. The optimization was performed in the range of 20 Ce40 C with 0.5 C step sizes by variation of molar flow rate of MR components only. When the ambient temperature increases, to keep the process in the optimum condition the concentration of nitrogen, propane and n-butane should increase and methane and ethane should decrease. When the ambient temperature increases, the total required work behavior follows a second order polynomial with about 33 C minimum point which is corresponding to MR molecular weight of about 31.5 kg/kmol. In addition, the optimization was performed in various feed pressures from 55 bar to 75 bar. The results showed that there is not a significant change in MR compositions in this range of pressure. Moreover the total work decreases linearly by increasing the feed pressure. Acknowledgements We gratefully acknowledge the support of Research & Technology Directorate of National Iranian Gas Company. Nomenclature
Symbols P pressure (kPa)
Alabdulkarem, A., Mortazavi, A., Hwang, Y., Radermacher, R., Rogers, P., 2011. Optimization of propane pre-cooled mixed refrigerant LNG plant. Appl. Therm. Eng. 31 (6e7), 1091e1098. Andress, D.L., Watkins, R.J., 2004. Beauty of simplicity: phillips optimized cascade LNG liquefaction process. Adv. Cryogen. Eng. 49, 91e98. Aspelund, A., Gundersen, T., Myklebust, J., Nowak, M.P., Tomasgard, A., 2010. An optimizationesimulation model for a simple LNG process. Comput. Chem. Eng. 34 (10), 1606e1617. Austbo, B., Lovseth, S.W., Gundersen, T., 2014. Annotated bibliographyduse of optimization in LNG process design and operation. Comput. Chem. Eng. 71, 391e414. Behroozsarand, A., Ebrahimi, H., Zamaniyan, A., 2009. Multiobjective optimization of industrial autothermal reformer for syngas production using nonsorting genetic algorithm II. Ind. Eng. Chem. Res. 48, 7239e7529. Cammarata, G., Fichera, A., Guglielmino, D., 2001. Optimization of a liquefaction plant using genetic algo rithms. Appl. Energy 68 (1), 19e29. Cao, W., Lu, X., Lin, W., Gu, A., 2006. Parameter comparison of two small-scale natural gas liquefaction processes in skid-mounted packages. Appl. Therm. Eng. 26 (8), 898e904. Castillo, L., Dahouk, M.M., Di Scipio, S., Dorao, C.A., 2013. Conceptual analysis of the precooling stage for LNG processes. Energy Convers. Manag. 66, 41e47. Cranmore, R.G., Stanton, E., 2000. Natural gas. In: Dawe, R.A. (Ed.), Modern Petroleum Technology, Upstream Volume. Institute of Petroleum, John Wiley and Sons Ltd, Chichester, pp. 337e382. Gong, M.Q., Wu, J.F., Luo, E.C., Zhou, Y., Liang, J.T., Zhang, L., 2000. Optimum composition calculation for multicomponent cryogenic mixture used in JeT refrigerators. Adv. Cryo. Eng. 45, 283e290. Hatcher, P., Khalilpour, R., Abbas, A., 2012. Optimisation of LNG mixed-refrigerant processes considering operation and design objectives. Comput. Chem. Eng. 41, 123e133. Hwang, J.H., Ku, N.K., Roh, M.I., Lee, K.Y., 2013. Optimal design of liquefaction cycles of liquefied natural gas floating, production, storage, and offloading unit considering optimal synthesis. Ind. Eng. Chem. Res. 52 (15), 5341e5356. Jacobsen, M.G., Skogestad, S., 2013. Active constraint regions for a natural gas liquefaction process. J. Nat. Gas. Sci. Eng. 10, 8e13. Khan, M.S., Lee, M., 2013. Design optimization of single mixed refrigerant natural gas liquefaction process using the particle swarm paradigm with nonlinear constraints. Energy 49, 146e155. Khan, M.S., Lee, S., Rangaiah, G.P., Lee, M., 2013. Knowledge based decision making method for the selection of mixed refrigerant systems for energy efficient LNG processes. Appl. Energy 111, 1018e1031. Lee, G.C., Smith, R., Zhu, X.X., 2004. Optimal synthesis of mixed-refrigerant systems for low temperature process. Ind. Eng. Chem. Res. 41, 5016e5028. Li, Y., Wang, X., Ding, Y., 2012. An optimal design methodology for large-scale gas liquefaction. Appl. Energy 99, 484e490. Mokarizadeh Haghighi Shirazi, M., Mowla, D., 2010. Energy optimization for liquefaction process of natural gas in peak shaving plant. Energy 35, 2878e2885. Mortazavi, A., Somers, C., Hwang, Y., Radermacher, R., Rodgers, P., Al-Hashimi, S., 2012. Performance enhancement of propane pre-cooled mixed refrigerant LNG plant. Appl. Energy 93, 125e131. Remeljej, C.W., Hoadley, A.F.A., 2006. An exergy analysis of small-scale liquefied
P. Moein et al. / Journal of Natural Gas Science and Engineering 26 (2015) 470e479 natural gas (LNG) liquefaction processes. Energy 31 (12), 2005e2019. Roberts, M.J., Agrawal, R., Daugherty, T.L., 2002. Single Mixed Refrigerant Gas Liquefaction Process. US Patent 6,347,531. Skaugen, G., Walnum, H.T., Hammer, M., Wahl, P.E., Wil-helmsen, Ø., Kolsaker, K., 2013. Design and optimization of compact heat exchangers in process used for liquefaction of natural gas. In: 5th International Conference on Applied Energy ICAE 2013. 2013 July 1e4, Pretoria, South Africa. Swenson, L.K., 1977. Single Mixed Refrigerant, Closed Loop Process for Liquefying Natural Gas. US Patent 4,033,735. Vatani, A., Mehrpooya, M., Tirandazi, B., 2013. A novel process configuration for coproduction of NGL and LNG with low energy requirement. Chem. Eng. Process: Process Intensif. 63, 16e24. Venkatarathnam, G., 2008. Cryogenic Mixed Refrigerant Processes. Springer, New York.
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Wahl, P.E., Løvseth, S.W., Mølnvik, M.J., 2013. Optimization of a simple LNG process using sequential quadratic programming. Comput. Chem. Eng. 56, 27e36. Wang, M., Khalilpour, R., Abbas, A., 2013. Operation optimization of propane precooled mixed refrigerant processes. J. Nat. Gas. Sci. Eng. 15, 93e105. Xu, X., Liu, J., Jiang, C., Cao, L., 2013. The correlation between mixed refrigerant composition and ambient conditions in the PRICO LNG process. Appl. Energy 102, 1127e1136. Yuan, Z., Cui, M., Xie, Y., Li, C., 2014. Design and analysis of a small-scale natural gas liquefaction process adopting single nitrogen expansion with carbon dioxide pre-cooling. Appl. Therm. Eng. 64 (1), 139e146. Zhang, X., Myhrvold, N.P., Caldeira, K., 2014. Key factors for assessing climate benefits of natural gas versus coal electricity generation. Environ. Res. Lett. 9, 114022.