Economic Optimization of Dual Mixed Refrigerant Liquefied Natural

Article pubs.acs.org/IECR

Economic Optimization of Dual Mixed Refrigerant Liquefied Natural Gas Plant Considering Natural Gas Extraction Rate Inkyu Lee and Il Moon* Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea S Supporting Information *

ABSTRACT: This study mainly focuses on the profit optimization of the natural gas liquefaction process considering extraction rate. The target process is the dual mixed refrigerant (DMR) process with 1 million tons per annum (MTPA) capacity. The liquefaction ratio and the amount of boil-off gas (BOG) varies according to the natural gas extraction rate to meet the liquefaction capacity. Therefore, utilizing produced BOG and minimizing wasted BOG is key from an economic point of view. This study performed profit optimization with various extraction rates. Moreover, the energy and cost optimizations are performed to analyze the extraction rate effect. As results for the profit maximization, the total compression energy requirement and the plant cost show optimum values between the energy and cost optimization results. The profit increases by 22.5% with 93.2% liquefaction ratio through the optimization. The result shows that producing BOG as the amount of the fuel requirement for the compression energy supply is the optimal extraction rate. Resultingly, the optimal design of the profit max DMR process is also found through the profit optimization.

1. INTRODUCTION According to the Outlook for Energy (2016), liquefied natural gas (LNG) exports are expected to almost triple from 2014 to 2040 and LNG is expected to remain a highly competitive market because of the abundant gas resources and many aspiring gas exporters.1 The volume of LNG is more than 600 times smaller than that of natural gas of the same mass.2 Generally, LNG is produced by cooling natural gas to −161 °C at atmospheric pressure.3 Therefore, the natural gas liquefaction process is energy intensive due to its cryogenic operation condition.4 LNG plants can be classified by the number of refrigeration cycles and the type of refrigerants used.5 In the past decade, many researches have focused on minimizing compression energy requirement in LNG mixed refrigeration cycles.6 Various optimization methods are applied for the mixed refrigerant cycles in LNG plant. For example, Nogal et al.7 performed the shaft work requirement minimization and capital cost minimization applying a genetic algorithm (GA) in their work. Shirazi and Mowla8 also employed the GA method to minimize energy requirement of the single mixed refrigerant (SMR) process using MATLAB software. Kahn and Lee9 selected the optimization objective as minimizing the compression energy demand employing the particle swarm optimization technique to optimize the SMR process. Wahl et al.10 also focused on the minimizing power consumption of the compressors of the natural gas liquefaction process using sequential quadratic programming (SQP), a deterministic optimization method. Khan et al.11 selected dual mixed refrigerant (DMR) © XXXX American Chemical Society

process and applied GA and Box methodology to minimize specifically the compression energy, which is energy per unit mass of LNG production. Lee et al.12 targeted the propane precooled mixed refrigerant (C3MR) process to minimize specific compression energy with various liquefaction ratios by using the deterministic optimization method. According to the literature survey, most of studies for the natural gas liquefaction process have focused on energy minimization. Few studies have considered the cost for the LNG processes. One of the earliest studies of the cost minimization is adopted to the pure refrigeration system by Barnés and King.13 Cheng and Mah14 developed an interactive synthesis of cascade refrigeration systems. Vaidyaraman and Maranas15 used mixedinteger linear programming to minimize investment and operating cost for the refrigerants selection. Jensen and Skogestad16 developed total annual cost (TAC) equation to minimizing capital and operating cost. However, the capital cost of heat exchanger and operating cost for the compression energy are only considered. Castillo and Dorao17 focused on the cost minimization considering the market cost, power consumption and heat transfer area. Jensen and Skogestad18−20 focused on the minimizing total annualized cost which is the sum of fuel, feed, and operating cost. Wang et al.21 performed optimizations with Received: October 25, 2016 Revised: February 13, 2017 Accepted: February 22, 2017

A

DOI: 10.1021/acs.iecr.6b04124 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Process flow diagram of DMR.

four different objective functions: total shaft work, total cost investment, total annualized cost, and total capital cost of compressors and main cryogenic heat exchangers. However, the cost was calculated by the percentage of component cost of a total capital cost, not the individual equipment cost. Moreover, the extraction rate optimization considering energy selfsufficiency has not been well studied yet. The main purpose of the study is finding optimal extraction rate for the natural gas liquefaction process by cost based optimization. DMR process is targeted because DMR process is one of the most energy efficient LNG processes among various liquefaction processes.22 The liquefaction capacity is set as 1 million tons per annum (MTPA). Thus, the extraction rate have to be exceed 1MTPA and the rest of extracted natural gas which does not liquefied produces boil-off gas (BOG) as the byproduct. To analyze the extraction rate effects, the energy and cost are optimized with fixed and various extraction rate conditions. Moreover, the profit maximization also performed to analyze the natural gas liquefaction process in an economic point of view. The optimizations are mathematically modeled and performed on the basis of deterministic optimization approach. The optimal operating conditions, the equipment capacities, and the extraction rate are found considering energy and plant cost simultaneously.

The size of the target process is set as 1 million tons per annum (MTPA). The natural gas feed temperature and pressure is at 37 °C and 5000 kPa while the LNG flow rate is 114 155 kg/h to meet the 1 MTPA design capacity. Table 1 Table 1. Process Design Basis parameters

values

natural gas feed temperature natural gas feed pressure LNG product flow rate LNG product pressure MTD in MSHE cooler discharge temperature pressure drops in MSHE pressure drops in coolers isentropic efficiency of compression units gas turbine calorific power efficiency internal points in MSHE

37 °C 5000 kPa 114 155 kg/h 100 kPa 3 °C 30 °C 100 kPa 0 kPa 75% 38% 40

shows process design basis, and the natural gas feed composition is shown in Table 2. 2.2. Research Objective and Problem Statement. The main objective of this research is finding optimal extraction rate of the natural gas with fixed LNG product flow rate as 1 MTPA to maximize profit. The boil-off gas (BOG) is also produced as the byproduct and the natural gas extraction rate determines the liquefaction ratio and the BOG flow rate. Kurle et al.23 demonstrated that using BOG as fuel gas is the most efficient way to recover BOG on the basis of energy requirement for

2. PROBLEM STATEMENT 2.1. DMR Process Description. The DMR process is the target LNG plant studied in this work. Figure 1 illustrates the process flow diagram of the DMR process. The DMR process uses two mixed refrigerant cycles: the warm mixed refrigerant (WMR) cycle is engaged to precool the natural gas and the cold mixed refrigerant (CMR) is used for the liquefaction of it. Generally, the WMR contains methane, ethane, propane, and butane and the CMR contains nitrogen, methane, ethane, and propane.11 Both mixed refrigerant cycles are compressed and cooled through successive multistage compressors and coolers. The ambient temperature is assumed as 25 and 30 °C for the cooler discharge temperature.

Table 2. Natural Gas Feed Composition

B

component

mole fraction

nitrogen (N2) methane (C1) ethane (C2) propane (C3) isobutane (i-C4) n-butane (n-C4)

0.0020 0.9130 0.0540 0.0210 0.0050 0.0050 DOI: 10.1021/acs.iecr.6b04124 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 2. Problem statement of DMR process.

The unit prices for LNG export and wellhead are obtained from the Energy Information Administration (EIA) data.33 The 10 year average prices from 2003 to 2012 are adopted for the unit natural gas prices in the model. 5.304 USD/Mcf is adopted for the wellhead price and 7.644 USD/Mcf is adopted for the LNG export price. 3.2. Thermodynamic Model. 3.2.1. Compression Unit. The compression units including compressor and pump are modeled as isentropic compression and the energy demands for these units are calculated by following eqs 4−6.

C3-MR process. Therefore, the problem is stated that the produced BOG is first used to provide energy to the compression units in the LNG plant and then the rest of the BOG goes to the flare stack. When the energy produced by the BOG cannot meet the compression energy demand, the rest of the fuel requirement is supplied from the wellhead. The natural gas from wellhead is assumed pretreated. The problem statement of the process is illustrated in Figure 2. The extraction rate is the flow rate of the wellhead natural gas, point (a) in Figure 2, which is the sum of the natural gas flows to power generation and to liquefaction process, point (b) and point (c) in Figure 2 respectively.

3. OPTIMIZATION MODEL DEVELOPMENT The optimization model for the DMR process is developed by using equation oriented optimization software, gPROMS and the Peng−Robinson equation of state is used for the thermodynamic property calculations.24 The deterministic optimization based on the mathematical programming is performed with a successive reduced quadratic programming (SRQPD) solver to find the optimal solutions. The model contains thermodynamic equations as well as capital and operating cost equations. In this chapter, thermodynamic models for the major equipment, cost models, objective functions, optimization variables, and optimization constraints are described. 3.1. Objective Functions. The optimizations with three objective functions are studied for the DMR process optimization: minimizing total compression energy requirement, minimizing total annual cost, and maximizing total annual profit. The objective functions for the optimization model are described as follows in eqs 1-3. Obj1 = min Wttl = min ∑ (Wcomp, i + Wpump) i

(1)

Sout,isen = Sin

(5)

Hout = (Hout,isen − Hin)/ηisen + Hin

(6)

Q̇ = ṁcold ·(Hcold,in − Hcold,out) =

(2)

∑ {ṁ hot, j ·(Hhot,out,j − Hhot,in,j)} j

(7)

where Q̇ is heat flow, the subscript j refers to the jth hot stream, hot refers to the hot stream, and cold refers to the cold stream in the MSHE. To check the feasibility of the MSHE, the temperature range inside the MSHE is divided into 40 points. The temperature difference between the hot and cold streams must be larger than the minimum temperature difference at each point. 3.2.3. Cooler. The cooler is modeled on the basis of the heat balance as follows:

where Obj2 is objective function 2 and C is cost. The subscript plant, ann, cap, and op refers to plant, annual, capital, and operating, respectively. Obj3 = max Prfann = max(PrfLNG,ann − C NG,ann − Cplant,ann)

(4)

where ṁ is mass flow rate, H is enthalpy, S is entropy, and η is efficiency. The subscripts out, in, and isen represent the outlet stream, the inlet stream, and isentropic compression conditions, respectively. The isentropic efficiency is assumed to be 0.75 on the basis of industrial experience. The enthalpy and entropy are the function of the temperature, pressure, and composition. For the compression units, the compositions of the inlet and outlet of the compression unit are the same. Therefore, the temperature and the pressure are the variables of the compression unit. When the temperature and pressure of the inlet and the outlet pressure are given, the outlet temperature is calculated by the entropy balance, eq 5. The outlet enthalpy is decided by eq 6, and then the compression work requirement of the compressor and pump is calculated by eq 4. 3.2.2. Multistream Heat Exchanger. The multistream heat exchanger (MSHE) contains multiple hot streams and the MSHE model is developed on the basis of heat balance as follows:

where Obj1 is objective function 1 and W is energy requirement. The subscript ttl is total, comp is compressor, pump is pump, and i refers to the ith compressor. Obj2 = min Cplant,ann = min Ccap,ann + Cop,ann

W = ṁ ·(Hout,isen − Hin)/ηisen

(3)

where Obj3 is objective function 3 and Prf is profit. The subscript LNG is LNG export and NG is wellhead of natural gas. C


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Industrial & Engineering Chemistry Research Q̇ cooler = mcw ̇ (Hcw,in − Hcw,out) = ṁ hot (Hhot,out − Hhot,in)

where N is number of required compression units, M is number of required gas turbines during the plant life, and PL is plant life; the subscript turb is gas turbines, MSHE is multistream heat exchanger, and k is the kth cooler. The total plant life is assumed to be 20 years because the average life cycle of a natural gas liquefaction plant is known to be around 20− 25 years.30 Because the equipment life for the compression units are known as under 50 000 h, approximately 5 years, the compressors are needed four times during the plant life.31 For the gas turbines, the equipment lifetime is known as 100 000− 160 000 h, approximately 11−18 years.32 Therefore, the gas turbines are required two times each, during the plant life. The equipment investment cost calculation is mainly based on the six-tenths-factor rule:26 the cost of a unit can be approximated by an exponent of 0.6 times of the capacity ratio from the cost of the initial unit. The six-tenth-factor rule is described as follows:

(8)

where the subscripts cooler and cw denote the cooler and cooling water, respectively. 3.2.4. Separator Model. The vapor fraction of stream has to be calculated in the separator model to calculate the flow rate of the vapor and liquid streams. The vapor fraction is calculated using Hin = VF·Hv ,out + (1 − VF) ·Hl ,out

(9)

where the VF is vapor fraction, subscript v is vapor, and subscript l is liquid. 3.2.5. Gas Turbine. The gas turbine models are described as follows in eqs 10-14. WBOG = kJkcal ·ηturb ·CVCH4·(ṁ BOG ·nBOGCH4)

(10)

Wttl = WBOG + WFNG

(11)

WFNG = kJkcal ·ηturb ·CVCH4· (ṁ FNG,calc · nNGCH4)

(12)

ṁ FNG = MAX(ṁ FNG,calc , 0)

(13)

ṁ ENG = ṁ FNG + ṁ NGFeed

(14)

Ca = C b·(Xa /Xb)exp

where X is equipment capacity and exp is the exponent factor; the subscripts a and b represent equipment a and b, respectively. Different types of equipment have different exponential values for the investment cost calculation. The exponent factors for compressor, pump, and cooler are 0.69, 0.33, and 0.60, respectively.26 The reference size and cost of equipment are obtained by using the commercial software, Aspen Economic Evaluation, and pilot plant experience. For the MSHE cost, the B-value cost calculation method is applied.27 The models for the B-value method are described as follows in eqs 17−19.

where the kJkcal is conversion factor of kJ/kcal, CV is the calorific value which has units kcal/kg, nBOG is component mass fraction of the BOG, nNG is component mass fraction of the natural gas feed, and MAX is the function of choosing maximum value; the subscripts are turb for the gas turbine, CH4 for methane, BOG for the BOG, FNG for the fuel from the natural gas, calc for the calculation value, ENG for the extracted natural gas, and NGFeed for natural gas feed to the liquefaction process. Note that the generated power from the gas turbine is calculated by the calorific value and the concentration of the methane and the efficiency of the gas turbine is adapted as 0.38.25 From the separator model, the amount of BOG is calculated and then the generated power using BOG as the fuel is decided with calculated BOG mass flow rate by eq 10. As described in eq 11, the total required power is supplied by the BOG and natural gas fuel. To meet the power requirement of the liquefaction process, the amount of the power from the natural gas fuel is calculated. If the amount of BOG fuel is enough to provide the power to the compression units, the amount of the power using natural gas fuel has the negative value, and if not, the amount of power using natural gas fuel has the positive value. Through eq 12, the required amount of natural gas fuel is calculated. When the amount of natural gas fuel has the negative value, it means the natural gas fuel is not required. Thus, the amount of the natural gas fuel get the value of 0 by eq 13 when the calculated value of it is negative. 3.2.6. Other Equipment. The expansion valve is modeled on the basis of isenthalpic expansion. The inlet enthalpy and the outlet enthalpy of the valve is same; thus the outlet temperature of the valve can be calculated by the outlet pressure. The mixer and splitter are modeled by mass and heat balance. 3.3. Cost Model. 3.3.1. Capital Cost. The annual capital cost is the sum of major equipment investment costs as follows: Ccap,ann =

V = 1.15·∑ Vz

(17)

z

Vz =

Q̇ z /LMTDz

LMTD =

Bz

(18)

(Thot,in − Tcold,out) − (Thot,out − Tcold,in) ln[(Thot,in − Tcold,out)/(Thot,out − Tcold,in)] (19)

where V is volume, LMTD is the log mean temperature difference, B is the B-value, and T is temperature; subscript z refers to the zth zone inside the MSHE. The active volume of the MSHE can be calculated from the log mean temperature difference (LMTD), heat flow, and the B-value. The B-value and the cost for the MSHE can be read from published data.28 Note that the interest rate is considered for every equipment from the reference data published in a year to set the standard costs of equipment at the same point of year because the reference data are published in different years. The installation cost for the gas turbine is modeled by the amount of the energy supply, 230 USD/kW.25 The unit of work is kJ/h; thus the unit conversion for time have to be performed in the gas turbine cost model. Thus, the gas turbine investment cost is described as follows: C turb = 828000·Wttl

(20)

The capital costs for other equipment such as the separator, valve, and mixer are considered negligible because these costs are relatively low. 3.3.2. Operating Cost. The operating cost can be classified into three categories: electricity cost, maintenance cost, and

∑ {N ·Ccomp,i + Cpump + M·Cturb + CMSHE + Ccooler, k}/PL

(16)

(15) D


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Industrial & Engineering Chemistry Research Table 3. Objective Functions and Natural Gas Flow Rate Constraints for Different Optimization Cases units objective function constraints NG feed flow rate LNG flow rate

Opt1

Opt2

Obj1: min total energy Obj1: min total energy million ton/year million ton/year

1.05 1.00

≥1.00 1.00

(21)

where the subscript mt and water are refers to the maintenance and the cooling water for the coolers, respectively. The amount of energy production from fuel is calculated by the multiply of the calorific value and the concentration and of methane. The energy is self-sufficiency by the turbine and fuel, the maintenance cost, and cooling water cost are considered for the operating cost. The maintenance cost is modeled to take a 3% portion of the total capital cost annually.26 The annual maintenance cost is described as follows:

1.05 1.00

≥1.00 1.00

≥1.00 1.00

(24)

where the subscript MTD is the minimum temperature difference. MSHEs in LNG plants are associated with a large amount of heat exchange at 1−3 °C MTD for the efficiency enhancement.34 Therefore, the MTD in the MSHE is set as 3 °C.

1.0 ≤ CR i ≤ 3.5

(25)

where CR is the compression ratio, which cannot be larger than 3.5.35

(22)

Vi̇ ≤ 380000 (m 3/h)

The heat flow for the cooler is calculated by the heat exchanger model to meet cooler discharge temperature at 30 °C. The unit cost of cooling water is 0.354 USD/GJ.29 The annual cooling water cost is described as follows: Cwater,ann = 3.101·∑ ṁ j ·{Hcooler,out, j − Hcooler,in, j}

Opt5 Obj3: max specific profit

TMSHE,hot, z − TMSHE,cold, z ≥ TMSHE,MTD

Cmt,ann = 0.03·∑ {Ccomp, i + Cpump + C turb + C MSHE + Ccooler, j}

Opt4 Obj2: min total cost

CMR and the WMR, five for the compression ratio of each compressor (the pump compression ratio is assumed as equal to the compression ratio of the WMR compressor2), two for the CMR temperature of the MSHE outlet, two for the WMR temperature of the MSHE outlet, four for the CMR compositions, and five variables for the WMR compositions. 3.5. Optimization Constraints and Optimization Cases. Several physical constraints involved in this model are described as follows in eqs 24−29.

cooling water cost for the coolers. The electricity cost is not included because the energy is modeled that the natural gas fuel for the compression energy is supplied by the BOG first, and the rest of energy is supplied by the wellhead. The annual operating cost is described as follows: Cop,ann = Cmt,ann + Cwater,ann

Opt3 Obj2: min total cost

(26)

where V̇ is the volumetric flow rate of a single flow centrifugal compressor must be less than 380 000 m3/h.18

(23)

The unit of the mass flow rate is kg/h, and the unit of the enthalpy is kJ/kg; thus the conversion factor from second to hour is considered in eq 23. 3.4. Optimization Variables. The objective of this work is finding the optimal natural gas extraction rate; the optimization model controls the natural gas feed flow rate. The energy objective function, Obj1, is directly affected by required power of the compression units. As described in eqs 4−6, the required power of the compression unit is directly affected by the mass flow rate of the refrigerant and enthalpy difference. The inlet and outlet pressure of the compressor is the key variable for the compression power requirement with given temperature and composition because the enthalpy is a function of the temperature, pressure, and composition. Therefore, the optimization model controls the compression ratios for the compressors, the CMR and the WMR flow rate, the discharge pressure for the refrigerants. The main purpose of the natural gas liquefaction process is heat exchanging, thus the flow rates of the refrigerants are affected by the heat exchanging efficiency. The composition of the mixed refrigerant also affects to the heat exchanging efficiency. Therefore, the outlet temperatures of the CMR and the WMR through MSHE, and the compositions of the CMR and the WMR are controlled by the optimization model to obtain the optimal solution. The model contains 23 optimization variables: one variable for the natural gas feed flow rate, two for the flow rate of the CMR and the WMR, two for the discharge pressure of the

ṁ LNG = 1.0(MTPA)

(27)

ṁ NG = 1.05(MTPA)

(28)

ṁ NG ≥ 1.00(MTPA)

(29)

To meet the design capacity, the LNG product flow rate is fixed as 1.0 MTPA. Equation 21 represents the liquefaction ratio is set as 95% with same as the base case. For the constraint eq 22, the liquefaction ratio can be changed depending on the natural gas extraction rate. To find optimal extraction rate of the natural gas, the constraints for the natural gas feed flow rate, eqs 21 and 22, are differently adopted to five optimization cases: Opt1 to Opt5. The objective function for Opt1 and Opt2 is minimizing the total energy consumption, which is one of the most general objective functions in previous researches for LNG plant design and optimization.36 Opt1 minimizes the total energy consumption with fixed natural gas feed flow rate at 1.05 MTPA. Opt2 minimizes the total energy with various natural gas feed flow rates that are larger than 1.0 MTPA. Because the LNG product flow rate is fixed in this model, the minimizing total energy means the same as the minimizing specific energy, which is the energy demand for the unit mass of LNG product. Opt3 minimizes the total cost with a fixed natural gas feed flow rate of 1.05 MTPA, and Opt4 minimizes the total cost with various natural gas feed flow rates, larger than 1.0 MTPA. The last optimization case, Opt5, maximizes the annual profit with various natural gas feed flow rates as larger than 1.0 MTPA. The objective functions for the five optimization cases and the natural gas feed and product constraints for these cases are shown in Table 3. E


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Figure 3. MSHE composite curves: (a) base case, (b) Opt1, (c) Opt2, (d) Opt3, (e) Opt4, and (f) Opt5.

4. OPTIMIZATION RESULTS AND DISCUSSION The base case conditions for the CMR and WMR compositions, suction and discharge pressures, flow rates, and natural gas feed and LNG flow rate are adapted from the base case conditions (intercooled at 38 °C and feed at 38 °C) in the work of Khan et al.11 To find other operation conditions, the compression ratios and MCHE outlet temperatures are set as the optimization variables and obtained by the energy minimizing optimization. 4.1. Energy Minimization. The total compression work, specific compression work, and operation conditions for the base case and optimal cases are shown in Table S1. Total energy minimization with fixed natural gas feed flow rate, Opt1 result shows 39.4% energy saving compared to the base case. The WMR precools the natural gas more than the base case, until −24.92 °C, and the final liquefaction temperature which is caused by the CMR is almost same, −155.05 °C. The WMR flow rate increases by 40.8% and the CMR flow rate decreases by 46.0%, which means the cooling portion of the WMR is increased. The LMTDs for the CMR and WMR also decrease by 59.5% and 65.4%, respectively. To find the optimal extraction rate, the Opt2 optimization is performed with the optimization variable of the natural gas feed flow rate. The open variable of the natural gas feed flow rate causes another improvement in terms of the compression energy. The Opt2 result shows 46.9% of total energy saving compared to the base case. The cooling portion of the WMR increases more than it does for Opt1, precooling the natural gas by −32.24 °C. The liquefaction ratio of the Opt2 result is 72.0%, which produces 0.39 MTPA of BOG. As the liquefaction ratio decreases, the final liquefaction temperature can be increased and it leads energy saving. The final liquefaction temperature for the Opt2 case is −119.09 °C. Therefore, the nitrogen which has the lowest boiling point among the CMR components is removed and the methane and ethane fraction is highly increased from

the base case to the Opt2 case. On the contrary, the methane, which has the lowest boiling point among the WMR components, is increased. It is caused by the increase of the cooling portion of the WMR cycle. The CMR and the WMR compositions for the base case and optimal cases are shown in Table S2. The composite curves for heat exchanging are very efficient tools for chemical processes.37 In general, the distance between hot and cold streams decreases after optimization.12 The improvement of the heat exchanging efficiency is caused by the irreversibility reduction and it also causes decreasing of the temperature difference.38 Figure 3 represents the MSHE composite curves for the hot and cold streams for the base and optimal cases; the right side of the dashed line shows natural gas precooling by the WMR cycle and the left side shows the liquefaction by the CMR cycle. It can be checked that the temperature differences of the optimal cases are decreased than the base case. When the results of Opt1 and the Opt2 are compared, the cooling portion for the WMR cycle is increased and the final liquefaction temperature is increased also in the Opt2 result. The increase of the liquefaction temperature leads to a decrease of the compression energy requirement. On the contrary, the increase of the liquefaction temperature leads to an increase of the BOG. 4.2. Cost Minimization. Even though the energy requirement takes the largest portion in LNG plant cost, energy minimization cannot guarantee the minimum cost because of the capital costs.39 Therefore, the cost optimizations are performed. To analyze the effect of the natural gas feed flow rate in terms of the cost for the 1 MTPA DMR process, the cost optimizations are performed in Opt3 and Opt4. Figure 4 shows the total cost for the base and optimal cases. The result of Opt3, total cost minimization with 1.05 MTPA natural gas feed flow rate, shows 15.3% cost saving compared to the base case. For the optimization result of Opt4, which is the total cost minimization F


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Figure 4. Total annual costs for the base case and optimal cases.

Figure 5. Compression energy supply for the base case and optimal cases.

with various natural gas feed flow rates, the total cost saved by 36.8% from the base case. When the results of Opt3 and Opt1 are compared, the total compression work increases by 18.1% but the total cost decreases by 7.8%. It shows that the plant cost can be reduced even though the plant is not operated at minimum energy operation conditions. The same tendency occurs for Opt4 in comparison to the result of Opt2, where the total compression energy requirement increases by 19.6% and the total cost decreases by 26.0%. Figure 5 shows the amount of compression energy supplying sources for the base case and optimal cases. The cases with the fixed natural gas feed flow rate, base and Opt1 and Opt3 cases, show that the energy from the BOG cannot supply the whole energy demand from the

compression units. Thus, the rest of the compression energy demand has to be supplied by additional fuel from the wellhead. Figure 5 shows that the compression energy requirements for Opt3 and Opt4 are higher than those for Opt1 and Opt2, respectively. However, the operating cost and the capital costs show opposite results: Opt3 and Opt4 are lower than Opt1 and Opt2, respectively. The annual operating costs for the base case and optimal cases are shown in the Table S3 and Figure 6. The capital cost shows that the compressors take largest portion in the capital costs. The compression ratio and the flow rate of mixed refrigerant are mainly determines the compression energy requirement. The capital costs for all cases are shown in the Table S4 and Figure 7. As shown in Table S1, the energy G


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Figure 6. Annual operating costs for the base case and optimal cases.

Figure 7. Total capital costs for the base case and optimal cases.

minimizations favor the reducing compression ratio over the cost minimization results. It shows that the compression ratio affects results more than the flow rate in terms of the energy demand. However, the flow rate mainly affects the cost of the compression unit. Thus, the cost minimizations are performed by decreasing the flow rate of the mixed refrigerant. It means the compression ratio and refrigerant flow rate are under a trade-off relationship. Figure 8 illustrates the compressor trade-off relationship on the total compression work and total annual cost. The total mixed refrigerant flow rate of Opt3 is 38.9% lower than that of Opt1, and 26.9% lower for Opt4 than for Opt2. Another cost saving is highly achieved in the MSHE cost. The trade-off relationship in the heat exchanger is well-known

between capital cost (favored by a large temperature difference) and operating cost (favored by a small temperature difference).19 In this model, the MSHE cost is function of the heat exchanger active volume, and the active volume is proportional to the heat flow and inversely proportional to the LMTD. Thus, the MSHE cost is decreased when the heat flow is decreased or the LMTD is increased. Simply, it can be said that the reducing of the area between hot and cold stream in the composite curve leads the increase of the MSHE cost; meanwhile, it leads to the improvement of the heat exchanging efficiency. Therefore, the optimal MSHE design has to be found in terms of the cost. Back to Figure 3, the temperature difference between hot and cold stream for the Opt3 and Opt4 cases H


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Figure 8. Compression ratio and refrigerant flow rate effects for the total compression work and total annual cost.

cannot meet the whole compression energy requirement. On the contrary, the required energy is decreased as the liquefaction ratio decreases. However, the fuel from BOG is far exceeds the energy requirement. Therefore, finding the optimal extraction rate under this trade-off relationship is needed from an economic point of view and it can be found through the profit maximization. These trade-off relationships are simultaneously considered by the profit optimization. As a result of the Opt5 case, the annual profit is 84.90 million USD per year with 93.2% of liquefaction ratio. The wellhead extraction rate is 1.07 MTPA with producing 1.00 MTPA of LNG and 0.07 MTPA of BOG. To reduce the wellhead extraction, the compression power is only supplied by the BOG and the wasted BOG is minimized. It can be explained by two reasons. First, the energy saving through decreasing liquefaction ratio is highly affected by the cost saving. Therefore, the profit optimization is performed in the direction of reducing the liquefaction ratio. At the same time, the amount of fuel has to satisfy the energy requirement. Second, the natural gas extraction rate increase leads to the cost increase. Thus, the optimization is performed in the direction of decreasing the natural gas extraction rate. The natural gas extraction rate is the sum of the natural gas to the power generation and the natural gas to the liquefaction process. To satisfy the two reasons above, the natural gas to the power generation has to be minimized to decrease the natural gas extraction rate. On the contrary, the BOG to the power generation has to be maximized to decrease the liquefaction ratio. Therefore, it is the optimal operating condition in terms of profit that the compression power is only supplied by the BOG.

is increased compared to the Opt1 and Opt2 cases, but the heat flow is decreased. As the result of cost minimization, the Opt4 case shows the minimum costs among all cases with 71.4% liquefaction ratio, which produces 1.00 MTPA LNG product and 0.40 MTPA BOG byproduct. The final liquefaction temperature is −118.95 °C for the Opt4 optimization. The results of energy and cost optimizations with various extraction rate show the huge amount BOG flow rate and the large amount of BOG could lead to economic loss. 4.3. Profit Maximization. To overcome the limitation of the energy and the cost optimization that cannot consider effect of the BOG byproduct, the optimization of annual profit is performed with various extraction rates in Opt5. As defined in eq 8, the total profit is the profit of LNG and pipeline BOG export subtract the wellhead price and the plant cost. The annual profit maximization contains the meaning of minimizing BOG flow rate, meanwhile minimizing plant cost. To reduce the BOG flow rate, the liquefaction ratio has to be increased to meet the plant capacity, 1MTPA. However, the liquefaction ratio have to be decreased to reduce the energy and the cost. Therefore, the profit optimization could find the optimal liquefaction ratio, which means the optimal extraction rate for the 1MTPA DMR process. The total compression energy requirement for the Opt5 case is 34.25 MW, which is higher than the energy minimization (Opt2) and lower than the cost minimization (Opt4). The plant cost shows the opposite result, Opt5 is lower than Opt2 and higher than the Opt4 case. The main variables for the compressor, compression ratio, and the refrigerant flow rate show the same tendency. Back to Figure 8, the total compression ratios of the CMR and WMR cycle for the Opt5 case are higher than Opt2 and lower than Opt4, and the total refrigerant flow rate vice versa. Another trade-off relationship in the liquefaction ratio is found by the optimizations. The energy and cost are favored by a lower liquefaction ratio but the profit favored a higher liquefaction ratio. The annual plant cost and annual profit for the base case and optimal cases are shown in Table S5. The energy and cost optimization with various extraction rates, Opt2 and Opt4, show lots of natural gas loss because of the low liquefaction ratio. Thus, the annual profit is extremely smaller than the optimizations with fixed natural gas extraction rate, Opt1 and Opt3. When the liquefaction ratio is higher, the required energy is higher but the gas turbine fuel from BOG

5. CONCLUSION Natural gas liquefaction processes are highly energy intensive due to the high compression power demand. Thus, energy requirement minimization is a major concern in the design and optimization of an LNG plant. However, the optimization should consider not only the energy but also plant cost from an economic point of view. Moreover, the natural extraction rate can be affected by the compression energy requirement as well as the plant cost. This research focuses on the profit optimization of the 1MTPA capacity DMR process considering the extraction rate. First, energy optimization with fixed and various extraction rates is performed to analyze liquefaction ratio effects. I


Article

Industrial & Engineering Chemistry Research ṁ M MAX N nBOG nNG Obj1 Obj2 Obj3 PL Prf Q̇ S T V V̇ VF W X η

The result shows that the energy can be saved by decreasing the liquefaction ratio to 72.0%, which means increasing the extraction rate and the amount of BOG. Second, cost optimization with fixed and various extraction rates is performed. The result shows a similar tendency with the energy optimization; the plant cost also can be saved by decreasing the liquefaction ratio to 71.4%. The energy requirement and the amount of BOG production are on the trade-off relationship. In the optimization results for the profit maximization, the total compression energy requirement decreases by 38.6% and the annual profit increases by 22.5% with a 93.2% liquefaction ratio and 1.07 MTPA extraction rate. The result shows that producing BOG as an amount of the fuel requirement for the compression energy supply, 0.07 MTPA, is the optimal extraction rate. Through the profit optimization, it is figured out that the liquefaction ratio has to be minimized and the natural gas extraction rate has to be minimized. Therefore, the natural gas to power generation is minimized and the BOG to power generation is maximized. As a result, the compression power is only supplied by the BOG and is the optimal operating condition in terms of the profit. Moreover, other operation conditions considering the energy requirement and the plant cost are also found through the profit optimization. This study is novel because it finds the optimal extraction rate by considering energy and plant cost simultaneously in the profit optimization of the natural gas liquefaction process.

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Subscripts

a ann b BOG cap calc CH4 cold comp cooler ENG FNG hot i in isen j k l LNG MSHE NG NGFeed mt MTD op out plant pump ttl turb v water z

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b04124. Compression work and operating conditions, refrigerant compositions, annual operating costs, capital costs, and annual plant costs and annual profit (PDF)

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AUTHOR INFORMATION

Corresponding Author

*I. Moon. Tel.: +82 2 2123 2761. Fax: +82 2 312 6401. E-mail: [email protected]. ORCID

Il Moon: 0000-0003-1895-696X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by a grant from the LNG Plant R&D Center, funded by the Ministry of Land, Infrastructure, and Transport (MOLIT) of the Korean Government, and also by the BK 21 Program, funded by the Ministry of Education (MOE) of Korea.

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NOMENCLATURE

Variables

B C CR CV exp H kJkcal LMTD

mass flow rate (kg/h) number of turbines function of choosing maximum value number of compression units component mass fraction of BOG component mass fraction of natural gas objective function 1 objective function 2 objective function 3 plant life (year) annual profit (USD) heat flow (kJ/h) mass entropy [kJ/(kg·K)] temperature (K) volume (m3) volumetric flow rate (m3/h) vapor phase fraction power (kJ/h) equipment capacity compression efficiency

coefficient for B-value method cost (USD) compression ratio calorific value (kcal/kg) exponent factor mass specific enthalpy (kJ/kg) conversion factor from kcal to kJ (kJ/kcal) log mean temperature difference (°C)

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equipment a annual equipment b boil off gas capital calculation value methane cold stream compressor cooler extracted natural gas fuel from natural gas hot stream ith compressor inlet stream isentropic condition jth hot stream in MSHE kth cooler liquid liquefied natural gas multistream heat exchanger natural gas natural gas feed to liquefaction process maintenance minimum temperature difference (°C) operation outlet stream plant pump total turbine vapor cooling water zth point in the multistream heat exchanger

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Economic Optimization of Dual Mixed Refrigerant Liquefied Natural

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