Thermodynamic and economic optimization of LNG mixed refrigerant processes

Energy Conversion and Management 88 (2014) 947–961

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Thermodynamic and economic optimization of LNG mixed refrigerant processes Mengyu Wang, Rajab Khalilpour, Ali Abbas ⇑ School of Chemical and Biomolecular Engineering, The University of Sydney, NSW 2006, Australia

a r t i c l e

i n f o

Article history: Received 24 July 2014 Accepted 3 September 2014

Keywords: Optimization LNG Mixed refrigerant CAPEX OPEX Exergy

a b s t r a c t Natural gas liquefaction processes are energy and cost intensive. This paper performs thermodynamic and economic optimization of the mid-scale mixed refrigerant cycles including propane precooled mixed refrigerant (C3MR) and dual mixed refrigerant (DMR) processes. Four different objective functions in this study are selected: total shaft work consumption, total cost investment (TCI), total annualized cost (TAC), and total capital cost of compressors and main cryogenic exchangers (MCHEs). Total cost investment (TCI) is a function of two key variables: shaft work (W) and overall heat transfer coefficient and area (UA) of MCHEs. It is proposed for reducing energy consumption and simultaneously minimizing total capital expenditure (CAPEX) and operating expenditure (OPEX). Total shaft work objective function can result in a 44.5% reduction of shaft work for C3MR and a 48.6% reduction for DMR compared to their baseline values, but infinitely high UA of MCHEs. Optimal results show that total capital cost of compressors and MCHEs is more suitable than other objective functions for the objective of reducing both shaft work and UA. It reduces 14.5% of specific power for C3MR and 26.7% for DMR when achieving the relatively lower UA values than their baseline values. In addition, TCI and TAC can also reduce a certain amount of total shaft work at a finite increased UA. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Liquefied natural gas is widely recognized as a clean and economical energy source in recent years, due to its low carbon intensity and relatively low price compared with other fossil fuels. The LNG industry using proven technologies has expanded from small capacities of around one million tonne per annum (MTPA) in 1970s to the current so-called ‘‘mega trains’’ with capacity above 7.8 MTPA [1]. There are a number of the existing liquefaction technologies licensed by different companies (Black & Veatch, ConocoPhillips, Air Products, Shell, Statoil-Linde, etc.) that are available for different capacities of the plants where they will be carried out. These technologies have been reviewed in various studies [2–5]. Natural gas liquefaction processes are energy intensive. The main contribution to energy consumption is shaft work required by compressors which is mainly dependent on the temperature differences in heat exchangers. A common approach in the majority of recent optimization studies is to minimize total shaft work of the liquefaction system. They have encompassed the different optimization techniques, objective functions, and design variables. The ⇑ Corresponding author. Tel.: +61 2 9351 3002; fax: +61 2 9351 2854. E-mail address: [email protected] (A. Abbas). http://dx.doi.org/10.1016/j.enconman.2014.09.007 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.

selection of appropriate design variables, at any given condition, can maximize the overall performance of liquefaction process. Lee et al. [6] presented a synthesis method to optimize a PRICO process with the objective of shaft work reduction. Their method was a combination of non-linear programming (NLP) techniques and thermodynamic approach. A variety of design variables included the condensing and evaporating pressure levels, the refrigerant flowrate, and refrigerant composition. Their proposed NLP techniques were to optimize the refrigerant composition at given refrigerant flowrate and pressures. New refrigerant flowrate and pressures were proposed based on heuristics, judgment, or optimization. Vaidyaraman and Maranas [7] studied the optimal synthesis of MFC cycles by incorporating a non-convex NLP in an optimization model. The selected variables included MR composition, temperature, pressure, vaporization fraction, and compressor pressure ratios. However, only temperature approach at the end of each refrigeration stage was constrained that cannot guarantee no temperature cross in heat exchangers. Aspelund et al. [8] performed an optimization study of PRICO process using a combination of Tabu Search and Nelder–Mead Dowhill Simplex (NMDS) method in Aspen HYSYS and Microsoft Excel Visual Basic for Applications (VBA). They defined three objective functions for optimization: fixed minimum temperature

948

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

Nomenclature C1 C2 C3 C4 C3MR CAPEX DMR E e

e GA H h HX I JT LMTD LNG MCHE MFC MINLP MR

methane ethane propane i-butane propane pre-cooled mixed refrigerant cycle capital expenditure dual mixed refrigerant exergy specific exergy exergy efficiency genetic algorithm enthalpy, J/mol specific enthalpy, J/mol2 heat exchanger exergy loss Joule-Thomson log mean temperature difference liquefied natural gas main cryogenic heat exchanger mixed fluid cascade mixed integer non-linear programming mixed refrigerant

difference in cryogenic heat exchanger, fixed area of heat exchanger, and the effect of changing heat exchanger area on power consumption and cost. They used mixture of C1–C4 and N2 as MR fluid and set each refrigerant component, refrigerant flow rate, and suction and condenser pressures as an optimization variable. Wahl et al. [9] conducted a similar optimization work to the case studies on the PRICO process in Aspelund et al. [8] using Non-Linear Programming by Quadratic Lagrangian Programming (NLP-QLP) for process simulation and optimization. For the comparison with the previous work of Aspelund et al. [8], the NLP-QLP was more robust and efficient for solving the optimization problems. Shirazi and Mowla [10] developed a genetic algorithm (GA) based mathematical model in MATLAB for optimization of liquefaction process in peak shaving plant. They combined all chosen variables in the objective function of shaft work. The set of variables were condensation, evaporation and intermediate pressures, flowrate and composition of MR. They found that the compressors and LNG heat exchangers made a significantly energy-saving improvement to the liquefaction process. Alabdulkarem et al. [11] carried out a simulation and optimization study of C3MR process with application of GA model in Aspen HYSYSÒ and MATLAB environment. They ran four different pinch temperatures (0.01 K, 1.00 K, 3.00 K, and 5.00 K) in two stages of optimization. The first stage was to optimize the MR cycle followed by optimization of the propane cycle. Their results showed that pinch temperature of 1 K had the significant improvement in power consumption. Wang et al. [12] performed the optimal design and operation of MR system. They used a MINLP methodology with an objective function of power consumption. Although the complexity of optimization was simplified by a thermodynamic function on the basis of rigorous simulation regression, it was still comparatively complex to find the optimal solution. Based on their optimization results, they agreed with Hasan et al. [13] conclusion that the high operational flexibility of heat exchangers depends on processing capacity. Hatcher et al. [14] carried out the identification of the most appropriate formulation of C3MR process. They formulated four objective functions for operation optimization and four objective

MTPA NG NLP NMDS N2 OF OPEX PR P Q R S s SMR T TCF TS UA VBC W

million tonne per annum natural gas non-linear programming Nelder–Mead downhill simplex nitrogen objective function operating expenditure Peng–Robinson pressure, kPa cooling duty, MW gas constant, 8.314 J/(mol K) entropy, J/K specific entropy, J/K/kg single mixed refrigerant temperature, K or °C trillion cubic feet tabu search overall heat transfer coefficient and area of MCHE, MW/°C visual basic code shaft work, MW

functions for design optimization. They used MR flowrate, outlet pressures of expansion and compression, outlet temperatures of heat exchangers for natural gas stream as variables. The results showed that the most effective objective functions were the minimization of shaft work for operation optimization and minimization of shaft work and UA for design optimization. Wang et al. [1] formulated four different objective functions for operation optimization of C3MR and C3MR with split propane (C3MR-SP) processes. The manipulated variables were same to Hatcher et al. [14]. The exergy efficiency (considering power and cooling duty) was found to be the best objective function for C3MR while the best performance objective function for C3MR-SP was shaft work. OPEX was the second best objective function for both processes. Khan et al. [15] optimized SMR process with nonlinear programming along with exergy efficiency analysis. The process efficiency was improved by using refrigerant composition and flowrate, suction and evaporation pressures, and refrigerant vaporization as design variables. Khan and Lee [16] employed the particle swarm paradigm (PSP) to optimize SMR process. The objective function was to minimize the compression energy requirement using the same variables to Khan et al. [15]. Their results showed that the improvement of the gas for composite curves resulted in the less energy requirement. The stochastic features of PSP are more beneficial to avoid the local optima and find the more feasible solution. Khan et al. [17] developed a knowledge based algorithm for optimization of SMR and C3MR processes. They used a function of maximum heat exchanger exergy efficiency as optimization objective. It was found that the flow fractions of propane and ethane have a noticeable impact on the performance of SMR and C3MR processes respectively. Hwang et al. [18] studied the operation optimization of dual mixed refrigerant (DMR) process. They used a hybrid optimization method of the GA and sequential quadratic programming (SQP) for the minimization of the power consumption. The design variables for optimization were refrigerant flowrate, mole fraction of refrigerant, suction and evaporation pressures, temperature, and flowrate ratio of the tee. There are also some optimization studies which have not presented their objective functions [19–24]. LNG plants are capital

949

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

intensive. Liquefaction processes have relatively high capital cost of equipment required (main cryogenic heat exchangers, massive compressors, and other cryogenic equipment) and high operating cost of energy consumed. The capital cost breakdown for LNG plant ranges from 20% to 50% of the total LNG value chain [25–28]. The cost of liquefaction process accounts for around 30–45% of total capital cost of LNG plant. The objectives of economic optimization is to minimize cost including OPEX and CAPEX. Each expense has individual factors to influence the plant cost. The power consumption is the main factor influencing the operating cost. The capital cost corresponds to the design parameters of heat exchangers. It is well known that there is a trade-off between the OPEX and CAPEX. The power consumption of the compressors can be reduced by using more heat exchangers, large size of heat exchangers or additional cooling cycles. However, it increases the complexity of the process resulting in higher capital costs. Few studies have developed the objective functions associating with both CAPEX and OPEX. One of the earlier studies to attempt the cost minimization of pure refrigeration and gas liquefaction systems is that of Barnés and King [29]. They used a dynamic programing method with heuristics to identify the process configuration with minimum equipment and operating cost. This method could handle the detailed equipment cost correlations and thermodynamic properties. However, it has a limitation on determining the number of stages and their operating temperature ranges. Later, Cheng and Mah [30] developed an interactive synthesis of cascade refrigeration system. They incorporated all the refrigeration features and the cost function identified by Barnés and King [29]. Vaidyaraman and Maranas [31] suggested a systematic methodology to design the refrigeration system and select pure refrigerants for each refrigeration cycle simultaneously. They used mixed-integer linear programming to minimize a weighted sum of investment and operating cost. Some studies have dealt with a simple economic objective function to optimize either CAPEX or OPEX. Nogal et al. [32] developed a GA based model for the optimal design of a SMR cycle to reduce the compression work. They built a mathematical model based on genetic algorithm to search the optimal solution for the objective functions. They considered the capital cost in their objective function and selected the MR flowrate and composition, the inlet and outlet pressures of the compressor, and intermediate temperature between stages as design variables. Jensen and Skogestad [33] proposed a simple TAC equation as the cost function. They only considered the capital cost of heat exchangers, while the capital cost of compressors was included in the operating cost of shaft work. Castillo and Dorao [34] presented a decision-making approach based on game theory. This approach addresses a multiple levels and multi-objective problem simultaneously. A SMR LNG process is an example to examine the robustness and realistic of this approach involving a binary GA. They focused on cost optimization considering the market cost, power consumption and heat transfer area. Shah and Rangaiah [35] and Shah et al. [36] addressed a multiobjective optimization study on a SMR process. An approach was proposed to solve multi-objective optimization for mixed refrigerant processes where the objective functions were the CAPEX and the energy efficiency. The optimization variables included the minimum-temperature-difference and pressure ratio, and the number of refrigeration stages. Jensen and Skogestad [37] used total annualized cost as an objective function. Jensen and Skogestad [38], and Jensen and Skogestad [39] implemented the optimal operation of a mixed refrigerant process to optimize OPEX. In our previous works, Hatcher et al. [14] introduced the basic NPV function so as to maximize the profit of design and operation. However, it is favoured where the area of MCHEs enables to be infinitely large. Later, Wang et al. [1] examined the operation

optimization of C3MR process. They used the OPEX as cost function for the operation study. The findings indicate that it is a good performing objective function to reduce the power consumption. However, it raises the UA value of MCHEs. The additional factor to affect the energy consumption is associated with UA value of MCHEs. It also contributes to the capital cost. However, there is a trade-off between capital cost and operation cost. A few studies revealed their power consumption with the UA value of MCHEs. Aspelund et al. [8] concluded that the higher the UA value the better the thermal performance of the heat exchangers would be for the same LNG production. UA is a function of different refrigerant flow and LMTD. An increase in refrigerant flow resulted in elevation of both power consumption and UA [1,8,9,11,14,40]. Most recent studies have been concerned on reducing the power consumption of compressors in terms of design and operation through minimizing the temperature difference of heat exchanger. It results in an increase in heat exchange area which contributes the most to the capital cost. Only scarce studies assigned both capital cost and size of heat exchangers to the objective function. Therefore, a gap still exists in the literature with regard to the optimization of minimizing capital cost and operation cost considering size of heat exchangers. Most of the dominant baseload LNG plants are mid-scale and use propane precooled mixed refrigerant cycle and dual mixed refrigerant cycle for natural gas liquefaction. This study is focused on two mid-scale processes for optimization namely C3MR and DMR processes. C3MR technology licensed by Air Products and Chemical Inc. (APCI) has been the dominant liquefaction cycle in the current market with nearly 80%. More recently, Shell’s DMR technology has been involved in the Sakhalin II project [41]. C3MR process is a typical propane precooled MR cycle while DMR process is a replacement of precooling cycle on a basis of C3MR process [42]. The major difference is type of refrigerant and number of equipment required (such as MR compressors, MR heat exchangers, and valves) in precooling cycle. The use of mixed refrigerant in precooling cycle can cover a wide temperature range than propane as shown in Figs. 1 and 2. Therefore, it provides more degree of freedom for optimization. The aim of this paper is to investigate the merits of mixed refrigerant based liquefaction processes with a capacity of 3.0 MTPA and evaluate their performances with a focus on energy and cost minimization. We develop a new preliminary economic objective function combining design variable of UA of MCHEs and operating variable of shaft work. Future potential enhancement of the optimized process is evaluated by exergy analysis.

T

Natural Gas

Mixed Refrigerant

Pure Refrigerant

Q Fig. 1. Typical hot and cold composite curves for C3MR process.

950

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

C3MR and DMR plants are assumed to be greenfield onshore projects. The economic analysis was based on the following assumptions.

T

(5) For consistency, C3MR and DMR plants consist of the same CAPEX breakdown for pretreatment, liquefaction, LNG storage, and loading facilities. (6) The cost distribution of main equipment is estimated based on Yin et al. [43]. (7) No loan is made for the total plant investment.

Natural Gas

Mixed refrigerant 2

3.2. Preliminary cost model

Mixed refrigerant 1

The preliminary cost equations below are applied for formulating economic objective functions in Section 3.3.

Q Fig. 2. Typical hot and cold composite curves for DMR process.

This paper is structured as follows: descriptions of selected LNG processes are given in the next section. After that, the optimization framework is introduced for the determination of adjusted variables, constraints, and objective functions. The rest of this paper illustrates and compares the optimal results of the C3MR and DMR processes with literature, following exergy analysis of each process. 2. Process description C3MR and DMR processes consist of precooling cycle and subcooling cycle. The major differences between two processes are the type of refrigerant and number of equipment in their precooling cycle. Figs. 3 and 4 are respectively the flow diagrams of C3MR and DMR processes. The treated natural gas and subcooling refrigerant is cooled to 35 °C in precooling cycle. After precooling, it is subcooled and liquefied by subcooling refrigerant in MCHEs to around 161 °C at atmospheric pressure. The evaporated precooling refrigerant passes through a series of compressors. It is then cooled (using water or fans) and is fully condensed to liquid phase before being recycled back to heat exchangers. The subcooling MR is partially cooled in precooling cycle and is separated into gaseous stream and liquid stream to provide the cooling for natural gas in MCHEs. After that, it is completely vaporized from the exit of MCHE. It is then compressed by a series of compressors to its initial inlet conditions. 3. Optimization formulation 3.1. Assumptions C3MR and DMR processes are simulated under the same conditions including feed gas condition and some other specification listed below. (1) The feed natural gas is assumed as a dry sweet gas prior to processing and treatment. Table 1 lists the feed natural gas composition used in this study. (2) All processes operate at steady state. The potential and kinetic energy effects of steady flow are negligible. (3) The throttle valve and the compressors are considered as adiabatic. (4) Water coolers are used for providing cooling to the system.

3.2.1. Capital cost Natural gas liquefaction process mainly consists of condensers, evaporators, compressors and others. MCHEs and compressors are the major cost of liquefaction processes. However, the limited economic values have been found regarding the facility costs of liquefaction processes. A non-rigorous approach is therefore developed to calculate the cost of compressors and MCHEs. The equation for total capital investment is represented in Eq. (1).

TCI ¼

  m X X Cf X 0 f ¼1

ð1Þ

where TCI is total capital investments ($), X is plant capacity of this study (MTPA), X0 is the basis reference of plant capacity (MTPA), Cf is the equipment cost of a LNG plant for equipment type f ($). Thus, Eq. (2) for each equipment cost is derived from Eq. (1).

C f ¼ af



 X TCI0 X0

ð2Þ

where TCI0 is a baseline value for total capital investment of a LNG plant, af is the percentage of equipment cost of LNG value chain which is expressed in Eq. (3).

af ¼ kbf

ð3Þ

where k is the percentage of capital cost of a LNG plant over total cost of LNG value chain, bf is the percentage of component cost of a LNG plant over total capital cost of a LNG plant, bf values are shown in Table 2. The energy consumption in process operation and purchased equipment are the major costs of power plants. For a LNG plant, the size of MCHEs (UA) contributes to the CAPEX. Compression work (W) contributes to the OPEX which causes the specific requirement in compressor size. It then results in CAPEX variation. According to the capital cost distribution of main equipment for mixed refrigerant cycles given by Yin et al. [43] in Table 2, the equation for capital cost of MCHEs (CMCHE) is defined as a function of reference UA0 value written as below:

C MCHE ¼

a1

Pk

t¼1 UAt

UA0

!

 X TCI0 X0

ð4Þ

where UAt is overall heat transfer coefficient and area at MCHE t in this study (MW/K), UA0 is the reference value for MCHE obtained from the patent given by Jager and Kaart [44], a1 is the ratio of capital cost of cold box to capital cost of LNG value chain. The derivation of the capital cost equation for compressors (Ccomp) is similar to the above. It is a function of operating variable of W:

 Pn   Wi X TCI0 C comp ¼ a2 i¼1 X0 W0

ð5Þ

951

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

S301 E301

C301

C302

E302

E303

HX204

HX205

HX206

C303 CB301 V204

LNG101

V205 T203

T204

T200

V203

V202 V201

V206

V301 T202

T201

HX201

HX202

MCHE

Natural Gas HX203

S302

LNG102 E201

MIX203

MIX202

MIX201

V302

C202 C201

C203

LNG103

V303

Flare

S101 V101 LNG

Fig. 3. The flow diagram of C3MR process (red lines for propane-precooling cycle and blue lines for MR-subcooling cycle). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

where W0 is the referenced shaft work obtained from the patent given by Jager and Kaart [44], a2 is the ratio of capital cost of compressors to capital cost of LNG value chain. Then the new equation for total capital investment consisting of the key operating variable (W) and design variable (the overall UA of MCHEs) is represented as below

TCI ¼

a1

Pk

t¼1 UAt

UA0

þ a2

Pn

i¼1 W i

W0

þ a3 þ a4 þ a5 þ a6

!

 X TCI0 X0 ð6Þ

where TCI is the total capital investment ($), a3, a4, a5, and a6 are the proportion of capital cost of instrument and control system, assistant equipment, construction engineering, and MR confection system in LNG value chain respectively. 3.2.2. Operating cost The operating cost includes natural gas cost and utility costs (cooling water and electricity). The equation for cost of natural gas is

C NG ¼ F NG PNG HPA

ð7Þ

where FNG is the flowrate of feed natural gas (kg/h), PNG is the price of feed natural gas ($/MMBtu), HPA is hours per annum (h). The equation for cost of utilities is

C UT ¼ Pelectricity

n m X X W i HPA þ P cooling Q j HPA i¼1

j¼1

ð8Þ

where Pelectricity is the electricity price ($/GJ), Pcooling is the price of cooling water ($/GJ), Qj is the cooling duty at heat exchanger j (MW). 3.3. Objective functions There are two types of objective functions used for optimization in this study: shaft work and cost. Objective function 1 (OF1) is minimization of total shaft work. It is a well-known objective function found in literature for design and operation optimization. It is represented as:

min W total ¼

n X Wi

ð9Þ

i¼1

where Wi is the shaft work used at compressor i (MW). Objective function 2 (OF2) is minimization of total capital cost of liquefaction equipment. The expression for this objective function is same to Eq. (6).

minTCI ¼ a1

Pk

t¼1 UAt

UA0

þ a2

Pn

i¼1 W i

W0

þ a3 þ a4 þ a5 þ a6

!

 X TCI0 X0 ð10Þ

where TCI is the total capital investment ($). The above OF2 is substituted into total annualized cost (TAC) equation. The general form of TAC equation is given in Eq. (11).

min TAC ¼ f ðCAPEX þ OPEXÞ

ð11Þ

952

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

Natural Gas

E201 CB301

C201

LNG101

E202

C202

V201

S301

E301

LNG102

C301

E302

C302

E303

C303

V301

LNG103 Flare

V302 S101 V101 LNG Fig. 4. The flow diagram of DMR process (red lines for MR-precooling cycle and blue lines for MR-subcooling cycle). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 1 Feed natural gas composition. Components

Mole fraction (%)

Methane Ethane Propane n-Butane Nitrogen

96.92 2.94 0.06 0.01 0.07

where 0.1TCI is depreciation cost ($/year), TAC is the total annual cost per tonne LNG ($/tonne-LNG), CNG is cost of natural gas ($/ year), CUT is cost of utilities ($/year). To simplify the expression of OF2, a3, a4, a5, a6 are eliminated as capital costs of the equipment remain constant during optimization. They include the costs of instrument and control system, assistant equipment (including cycle water, boiler, fire protection, etc.), construction engineering, and MR confection system. This simplified function is called objective function 4 (OF4). It is minimization of MCHEs and compressors cost.

Table 2 Capital cost distribution of a LNG plant’s main equipment. Item

Million RMB

bf (%)

Cold box (including pipeline, heat exchangers) Compression system Instrument and control system Assistant equipment Construction engineering Mixed refrigerant confection system Sum

2.30 1.50 1.40 0.70 0.50 0.20 6.6

34.85 22.73 21.21 10.61 7.58 3.03 100

1 min TAC ¼ ð0:1TCI þ C NG þ C UT Þ ð12Þ X " ! Pk Pn 1 t¼1 UAt i¼1 W i min TAC ¼ 0:1 a1 þ a2 þ a3 þ a4 þ a5 þ a6 X UA0 W0    X TCI0 þ C NG þ C UT ð13Þ  X0

minðC MCHE ; C comp Þ ¼

a1

Pk

t¼1 UAt

UA0

þ a2

Pn

i¼1 W i

W0

!

 X TCI0 X0

ð14Þ

3.4. Optimization variables C3MR and DMR processes have different number of the manipulated variables. DMR has more variables than C3MR since mixed refrigerant used in precooling cycle. The baseline values of variables are stated in Table 3. For subcooling cycle, a mixture of potential hydrocarbons and nitrogen has been used as a candid refrigerant for C3MR and DMR processes. The subcooling mixed refrigerant consists of methane, ethane, propane, i-butane, and nitrogen. The optimal composition of any refrigerant must be non-zero value to ensure feasibility of that specific refrigerant.

953

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

3.5. Optimization constraints

1:5 <

The followings are the optimization constraints for C3MR and DMR processes. (1) The sum of MR mole fraction must be one. For precooling cycle of DMR,

ð15Þ

For subcooling cycle of C3MR and DMR, 5 X xi ¼ 1

ð16Þ

i¼1

where xi are the mole fraction of MR flow. (2) The MR flowing into the compressor must be vapor phase. To prevent any liquid entering compressors, the following constraints are used.

þ F Li

¼1 F Vi

<4

ð18Þ

where Pout is the outlet pressure of compressor i and Pin i i is the inlet pressure of compressor i. (5) The temperature of all outlet streams in MCHEs must be the same [46]. out2 out3 T out1 LNG102 ¼ T LNG102 ¼ T LNG102

i¼1

F Vi

P in i

out2 out3 T out1 LNG101 ¼ T LNG101 ¼ T LNG101

3 X xi ¼ 1

F Vi

Pout i

ð17Þ F Li

where and represent the flowrate of refrigerant in its vapor phase and liquid phase, respectively, entering compressor i. (3) For a feasible heat transfer, the minimum temperature difference between hot and cold composite curves must be above zero. (4) The range of compression ratio is from 1.5 to 4 for technical limitations [45].

Table 3 Optimization variables and their baseline values for precooling and subcooling cycles of C3MR and DMR processes. Variables Precooling cycle Type of refrigerant Refrigerant molar flowrate Refrigerant pressure Refrigerant composition Ethane Propane n-Butane Outlet pressure of C201 Outlet pressure of C202 Outlet pressure of C203 Mass split ratio to T201 Mass split ratio to HX201 Mass split ratio to HX202 Mass split ratio to HX204 Mass split ratio to HX205 Subcooling cycle Type of refrigerant Refrigerant molar flowrate Refrigerant pressure Refrigerant composition Nitrogen Methane Ethane Propane i-Butane Outlet pressure of C301 Outlet pressure of C302 Outlet pressure of C303 Outlet temperature of LNG101 Outlet temperature of LNG102 Outlet temperature of LNG103

Unit

C3MR

DMR

kmol/h kPa

Propane 40,139 1100

Mixed 41,200 1320

0.0 100.0 0.0 268 528 1130 0.127 0.256 0.379 0.213 0.153

45.5 4.9 49.6 850 1350 – – – – – –

kmol/h kPa

Mixed 73,600 2630

Mixed 59,700 3400

mol% mol% mol% mol% mol% kPa kPa kPa °C °C °C

8.5 50.5 33.8 7.1 0.1 454 1212 2690 87.2 124.0 155.9

8.5 50.5 33.8 7.1 0.1 445 1245 3430 36.0 105.0 155.9

mol% mol% mol% kPa kPa kPa

T out1 LNG103

¼

ð19Þ

T out2 LNG103

where Tout is the temperature of outlet stream in MCHEs for LNG. (6) All inlet streams of the mixer must remain in the same pressure. (7) The outlet temperature of the cooler must be lower than its inlet temperature.

T out 6 T in j j

ð20Þ

where T out is the outlet temperature of the cooler j and T in j j is the inlet temperature of the cooler j. (8) For precooling cycle of C3MR, propane flow splitter divides a flow by a split ratio of

0<

F out 1 <1 þ F out 2

ð21Þ

F out 1

out where F out 1 and F 2 represent the propane flow of outlet streams of the splitter.

4. Optimization results The optimization study with 3.0 MTPA C3MR and DMR processes using energy and cost objective functions under numerous decision variables and constraints was carried out. The UA of MCHEs is allowed to be changed at a constant LNG production as design and operation optimization is considered in this task. The simulation of these processes was built in Aspen HYSYSÒ. The Peng–Robinson fluid package is selected for optimization [47]. The optimization and cost estimate methodologies for DMR are the same as that applied for C3MR. Natural gas enters the liquefaction process at a temperature of 25 °C and pressure of 5000 kPa. The flowrate of feed natural gas is 3.99  105 kg/h (equivalent to 2.421  104 kmol/h). The assumption for the case studies of C3MR and DMR processes are made as follow.

Table 4 Baseline values of energy consumption and cost for C3MR and DMR processes. Variables

Unit

C3MR

DMR

Energy consumption Total shaft work required Specific shaft work Total cooling duty Specific cooling duty LMTD Precooling UA Subcooling UA

MW MJ/tonne-LNG MW MJ/tonne-LNG °C MW/°C MW/°C

245.1 2319.1 336.2 3181.2 18.82 – 16.39

231.5 2190.2 322.6 3052.4 19.06 27.39 12.83

Cost OPEX Specific OPEX CAPEX Specific CAPEX Annual cost Specific annual cost

$million/year $/tonne-LNG $million $/MTPA $million/year $/tonne-LNG

453.0 135.8 294.4 98.1 747.0 224.2

448.0 134.4 300.5 100.2 748.0 224.5

954

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

(1) The plant produces 3.0 MTPA of LNG at a temperature of 161.3 °C and pressure of 101.3 kPa. (2) The ambient temperature is 25 °C at 101.3 kPa. (3) The adiabatic efficiency of all compressors is assumed as 75%. (4) The temperature of MR after the water cooler is 30 °C. (5) The capital investment (TCI) of a C3MR plant are expected to be around $3 billion for a capacity of 3 MTPA. The specific cost index of a DMR plant to a C3MR plant is 1.05 [48]. (6) For LNG plants, the typical operating capacity factor (CF) is in a range of 0.85 and 0.9. The annual operation hours are 8760  CF h/year. (7) The price of pre-treated feed natural gas is $2/MMBtu. (8) The price of electricity is $10.99/GJ [49]. (9) The price of cooling water is $0.40/GJ [49].

Table 6 Optimal results for the cost of C3MR process using four objective functions. Variables

Unit

OF1

OF2

OF3

OF4

OPEX Specific OPEX CAPEX Specific CAPEX Annual cost Specific annual cost

$million/year $/tonne-LNG $million/year $/tonne-LNG $million/year $/tonne-LNG

414 124.1 324.0 972.0 736 220.7

430 128.9 290.4 871.2 720 216.0

423 127.0 292.9 878.8 716 214.9

440 132.0 291.4 874.4 731 219.4

The process performance can be represented in the composite curves shown in Fig. 5. In Fig. 5(a), the base C3MR process has a temperature difference of more than 10 °C between hot and cold composite curves. It has more room for energy improvement. Obviously, the average temperature difference of composite curves in Fig. 5(b) is approaching more closely to 3 °C in the temperature range of 30 °C and 163 °C while having the largest UA value of MCHEs. In Fig. 5(d), it is found that the optimized composite curves have the LMTD of 11.56 °C. It is the second smallest temperature difference among these optimal results. In Fig. 5(c) and (e), the gap of optimized composite curves obtained through optimization with objective function 2 slightly increases to 21.77 °C and decreases to 18.15 °C with objective function 4. However, they have relatively the least UA value of 12.8 MW/°C for C3MR process.

Table 4 presents the baseline values of energy consumption and cost for C3MR and DMR processes. The optimal operating conditions of C3MR and DMR processes obtained from four objective functions are summarized in Tables 5 and 7. The optimal cost of both processes is shown in Tables 6 and 8. The hot and cold composite curves are presented in Figs. 5 and 6.

4.1. C3MR process The optimal results of C3MR process are compared with its baseline values (see Fig. 7). The specific shaft work of C3MR process from OF1 is found to be the lowest energy consumption. Total shaft work decreases from its baseline value of 2319.1 MW/tonneLNG to 1288.2 MJ/tonne-LNG with the highest exergy efficiency of 35.8% while increasing the UA value of MCHEs from its baseline value of 16.4 MW/°C to 113.5 MW/°C. This high UA value of MCHEs leads to the significant increase in specific CAPEX up to $966.6/ tonne-LNG which exceeds its baseline value of $883.4/tonneLNG. From economic point of view, the specific annual cost of $214.9/tonne-LNG is the lowest value obtained through OF3 among four objective functions. The specific shaft work of 1547.3 MJ/tonne-LNG and the exergy efficiency of 29.8% are the second best results. The optimal results for C3MR process are illustrated in Table 5.

4.2. DMR process The optimal results of DMR process in Fig. 8 illustrate the similarity of C3MR process. For OF1, they have the most significant improvement of energy. The specific shaft work decreases from its baseline value of 2190.2 MJ/tonne-LNG to 1125.8 MJ/tonneLNG. The large shaft work reduction results from an increase in UA value of MCHEs. The UA value of MCHEs in subcooling cycle increases from its baseline value of 12.83 MW/°C to 113.5 MW/°C. The optimized specific CAPEX of $1238.2/tonne-LNG is higher than its baseline value of $901.5/tonne-LNG. From economic point of view, the lowest specific annual cost of $213.4/tonne LNG obtained through OF3 with the compression energy of 1356.5 MJ/tonne-LNG and exergy efficiency of 31.9%. It enables to reduce the specific CAPEX to $885.7/tonne-LNG.

Table 5 Optimal results for C3MR process using four objective functions. Variables

Unit

OF1

OF2

OF3

OF4

Precooling refrigerant Refrigerant flow Refrigerant pressure

kmol/h kPa

Propane 40,791 1086

Propane 40,019 1110

Propane 41,741 1085

Propane 39,630 1125

Subcooling refrigerant Refrigerant flow Refrigerant pressure Refrigerant composition Nitrogen Methane Ethane Propane i-Butane

kmol/h kPa

Mixed 63,773 2547

Mixed 65,323 2877

Mixed 66,149 2352

Mixed 74,319 3194

mol% mol% mol% mol% mol%

7.42 47.98 35.64 8.65 0.32

5.66 51.55 35.82 6.80 0.18

4.33 49.47 37.44 8.37 0.39

6.40 55.04 32.95 5.17 0.44

MCHE Outlet temperature of LNG101 Outlet temperature of LNG102

°C °C

98.6 144.3

92.9 117.9

90.5 114.8

94.2 124.6

Energy consumption Total shaft work required Specific shaftwork Total cooling duty Specific cooling duty Exergy efficiency LMTD UA

MW MJ/tonne-LNG MW MJ/tonne-LNG % °C MW/°C

136.1 1288.2 227.3 2150.4 35.8 3.19 113.5

180.9 1711.3 272.0 2573.5 27.0 14.76 16.7

163.5 1547.3 254.6 2409.4 29.8 9.54 26.9

209.5 1982.0 300.6 2844.2 23.3 18.40 14.4

955

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961 Table 7 Optimal results for DMR process using four objective functions. Variables

Unit

OF1

OF2

OF3

OF4

Precooling refrigerant Refrigerant flow Refrigerant pressure Nitrogen Methane Ethane Propane i-Butane n-Butane

kmol/h kPa mol% mol% mol% mol% mol% mol%

Mixed 39,955 1283 0.40 2.07 33.85 24.08 1.61 37.99

Mixed 32,364 2073 1.97 0.30 30.74 32.18 5.07 29.74

Mixed 36,062 1366 0.75 0.26 33.70 25.16 3.15 36.98

Mixed 28.224 1990 0.18 0.21 36.82 39.03 3.91 19.86

Subcooling refrigerant Refrigerant flow Refrigerant pressure Refrigerant composition Nitrogen Methane Ethane Propane i-Butane

kmol/h kPa

Mixed 47,936 3386

Mixed 38,256 3944

Mixed 40,050 3793

Mixed 31,041 3598

mol% mol% mol% mol% mol%

7.29 42.44 44.35 0.10 5.81

8.11 37.12 46.58 7.24 0.94

7.05 40.39 45.55 5.87 1.14

2.73 39.62 43.36 7.30 6.99

MCHE Outlet temperature of LNG101 Outlet temperature of LNG102

°C °C

33.0 115.9

35.0 109.9

34.6 104.2

35.2 115.8

Energy consumption Total shaft work required Specific shaft work Total cooling duty Specific cooling duty Exergy efficiency LMTD UA

MW MJ/tonne-LNG MW MJ/tonne-LNG % °C MW/°C

119.0 1125.8 210.1 1988 41.0 1.00 215.5

175.1 1656.6 266.2 2519 27.9 13.27 12.0

143.4 1356.5 234.5 2219 31.9 6.66 25.9

169.7 1605.9 260.9 2468 28.7 11.91 11.6

Table 8 Optimal results for the cost of DMR process using four objective functions. Variables

Unit

OF1

OF2

OF3

OF4

OPEX Specific OPEX CAPEX Specific CAPEX Annual cost Specific annual cost

$million/year $/tonne-LNG $million/year $/tonne-LNG $million/year $/tonne-LNG

407 122.2 412.7 1238.2 820 246.1

428 128.3 289.8 869.4 717 215.2

416 124.9 295.2 885.7 711 213.4

426 127.7 288.0 864.0 714 214.1

The composite curves of DMR process are shown in Fig. 6. In Fig. 6(a), the composite curves of the base DMR process have a similar gap to the base C3MR process. The smaller temperature difference of composite curves in Fig. 6(b) has reached to be less than 3 °C in the temperature range of 60 °C and 70 °C resulting in high thermodynamic efficiency. In Fig. 6(c)–(e), they can reach the same conclusion of C3MR process. It is noticed that the optimized composite curves of DMR process are bringing the gap closer and getting higher efficiency of heat transfer. 5. Sensitivity analysis and discussion In general, problems formulated using different techniques, such as energy minimization and cost minimization, impact on the optimal results. Two types of optimization formulations are proposed which provide the different control effort of optimization. The formulation of OF1 represents an optimization problem of energy consumption. It is the greatest improvement with energy consumption. However, the size of MCHEs turns out to be finitely large. The formulation of cost functions (OF2, OF3 and OF4) denotes an optimization problem of energy consumption and size of MCHEs. We achieved our predictive objectives through the preliminary cost functions which comprise the conflicts of the total

energy consumption (W) and the size of MCHEs (UA). This formulation has restrictions on the size of MCHEs. OF4 turns out to be the most efficient to optimize shaft work and UA. It can reduce the size of MCHEs and power consumption. Next, sensitivity analysis was performed to identify the effect of varying the objective-function coefficient of variables on optimal results. There are two scenarios explored through the simplified objective function of OF4 as an example.

5.1. Sensitivity of component cost (k) and equipment cost (bf) to optimization The effects of alternative alpha values on optimal results were conducted. Alpha value (af) corresponds to the percentage of capital cost of a LNG plant in LNG value chain (k) and the percentage of component cost of a LNG plant (bf). However, accurate data on plant costs and equipment costs is not available. The cost variation depends on a number of uncertainties such as manufacturing location and equipment types (see Table 9) as well as whether it is a greenfield or brownfield plant. If either k value or bf value change, the af value will change. It results in a proportional change among the cost items of cost functions. There are two scenarios with regards to the adjustment of af values using OF4. For each scenario, we estimate k value and bf value under a set of values in Tables 10 and 11. Scenario 1: the effects of varying the percentage of the liquefaction plant cost to the total cost of entire LNG value chain (k) on optimal results. To determine the effects of alternative af values on the optimal results, the sensitivity analysis was carried out by varying the percentage cost of a LNG plant in LNG value chain (k) in a range of 25% and 50%. In base case, the liquefaction plant accounts for 25% of total capital cost of the LNG value chain. Another two cases run under cost assumption of 35% and 45% respectively.

956

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

-30

Temperature (°C)

(a) -60 -90 -120 -150 -180

Cold composite curve Hot composite curve 0

2

4

6

8

10

12 x 108

Heat Flow (kJ/h) -30

-30

(c)

-60

Temperature (°C)

Temperature (°C)

(b) -90 -120 -150 -180

Cold composite curve Hot composite curve 0

2

4

6

8

10

-60 -90 -120 -150 -180

12

Cold composite curve Hot composite curve 0

Heat Flow (kJ/h)

6

8

10

12 x 108

-30

(d)

(e)

-60

Temperature (°C)

Temperature (°C)

4

Heat Flow (kJ/h)

-30

-90 -120 -150 -180

2

x 108

Cold composite curve Hot composite curve 0

2

4

6

8

Heat Flow (kJ/h)

10

12 x 108

-60 -90 -120 -150 -180

Cold composite curve Hot composite curve 0

2

4

6

8

Heat Flow (kJ/h)

10

12 x 108

Fig. 5. Composite curves for C3MR process (a) Base (b) OF1 (c) OF2 (d) OF3 (e) OF4.

Based on the optimal results of sensitivity in Fig. 9, it is found that the percentage of the liquefaction plant cost (k) increases linearly with a consistent increase of all alpha values through all cost objective functions. As expected, OF2 and OF4 associating with the capital cost of major equipment enable to reduce shaft work and UA of MCHEs for C3MR process. The optimal results from OF4 remain constant under changes in k value. Total annualized cost (OF3) as objective function indicate the more energy saving than OF2 and OF4, while their optimal UA values increase more than double of their baseline values. As the percentage of a LNG plant cost increases, this objective function can limit the UA value of MHCEs to be infinitely large. Scenario 2: the effects of varying percentage of equipment cost of the liquefaction plant (bf) on optimal results. Scenario 2 attempts to discover the effect of varying equipment cost of the liquefaction plant (bf) on optimal results. Along with the capital cost of a liquefaction plant, the equipment cost of a liquefaction plant is another important factor to influence on plant cost. The key pieces of equipment in liquefaction system are refrigerant compressors and main cryogenic exchangers. As an example, the variation of compressor cost for C3MR process is considered. It ranges from 50% decrease of the original cost

estimate to 50% increase. It is assumed to be 10% proportional change in compressor costs for each attempt as shown in Table 11. Fig. 10 illustrates the cost and sizing optimization results using b values in Table 11. As evident in Fig. 10, the specific cost of compressors is $40.6/tonne-LNG for the base case with b2 value of 0.227. At lower extreme condition of b2 = 0.128, the specific cost of compressors declines to $26.5/tonne-LNG while it becomes $57.3/tonne-LNG at the upper extreme of b2 = 0.306. Interestingly, although specific cost of compressors increases as the compressor prices rise (b2), specific size of compressors declines to reach a minimum point at b2 value around 0.244 after which it increases. As the size of compressors approaches its minimum value, the sizes of other unit operations, such as cold box, tend to increase (See UA line in Fig. 11). However, because the size of compressors is limited to a minimum (1988.3 MW/tonne-LNG), an increase in cost of other equipment that outweighs the benefits of savings in cost of compressors is limited. This implies that there is a limit in the level of benefits in savings in cost of compressors. This is clearly evident from Fig. 11 which shows the optimal operation results with the variation of b2 value; the increase of b2 value, results in the increase in UA value of MCHEs and decline in LMTD until reaching optima respectively.

957

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

-30

Temperature (°C)

(a) -60 -90 -120 -150 -180

Cold composite curve Hot composite curve 0

2

4

6

8

10

12 x 108

Heat Flow (kJ/h) -30

-30

(c)

-60

Temperature (°C)

Temperature (°C)

(b) -90 -120 -150

Cold composite curve Hot composite curve

-180 0

2

4

6

8

10

Heat Flow (kJ/h)

-60 -90 -120 -150 -180

12 x 108

Cold composite curve Hot composite curve 0

6

8

10

12 x 108

-30

(d)

(e)

-60

Temperature (°C)

Temperature (°C)

4

Heat Flow (kJ/h)

-30

-90 -120 -150 -180

2

Cold composite curve Hot composite curve 0

2

4

6

8

10

Heat Flow (kJ/h)

12

-60 -90 -120 -150 -180

Cold composite curve Hot composite curve 0

2

x 108

4

6

8

10

12 x 108

Heat Flow (kJ/h)

2000

200

1500

150

1000

100

500

50

0

0 Base Case OF1

OF2

OF3

Specific shaftwork

OF4 UA

Fig. 7. Baseline values and optimal results of C3MR process.

5.2. Comparison of C3MR and DMR processes The comparison of C3MR and DMR processes can be identified in terms of process configuration, performance, and capital cost. To make a fair comparison, they were simulated and optimized

2500

250

2000

200

1500

150

1000

100

500

UA (MW/°C)

250

Specific shaftwork (MW/tonneLNG)

2500

UA (MW/°C)

Specific shaftwork (MW/tonneLNG)

Fig. 6. Composite curves for DMR process (a) Base (b) OF1 (c) OF2 (d) OF3 (e) OF4.

50

0

0 Base Case OF1

OF2

Specific shaftwork

OF3

OF4 UA

Fig. 8. Baseline values and optimal results of DMR process.

using the same feed gas condition, refrigerant mixture for subcooling, and LNG production. For the process configuration comparison, the main differences between C3MR and DMR processes are the types of precooling equipment. C3MR process is more complex than DMR process. Although propane precooled mixed refrigerant cycle has

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

Equipment

C3MR

Precooling cycle MR/C3 compressor Precooler

Number 3 1

Type Centrifugal Kettle

Number 2 1

Type Centrifugal CWHE

Subcooling cycle MR compressor LNG exchanger

3 3

Centrifugal CWHE

3 2

Centrifugal CWHE

Specific equipment cost ($/tonneLNG)

Table 9 Key equipment count. DMR

Table 10 Various sets of a and k values for Scenario 1 at constant bf values. k (%)

b1

b2

a1

a2

25 35 45

0.227 0.227 0.227

0.349 0.349 0.349

0.0871 0.122 0.157

0.0568 0.0796 0.102

60

2400

50

2300

40

2200

30

2100

20

2000

10

1900

0 0.10

0.15

0.20

0.25

0.30

Specific size of compressor (MW/tonneLNG)

958

1800 0.35

β2 Specific cost of MCHE Specific size of compressor

Specific cost of compressor

Fig. 10. The effect of varying b value on specific equipment cost and specific size of compressor. Table 11 Various sets of a and bf values for Scenario 2 at a constant k value of 25%. b1

b2

a1

a2

25

50% 40% 30% 20% 10%

0.393 0.383 0.374 0.365 0.357

0.128 0.150 0.171 0.191 0.209

0.0983 0.0958 0.0935 0.0913 0.0892

0.0321 0.0375 0.0427 0.0476 0.0523

25

Baseline value

0.349

0.227

0.0871

0.0568

25

10% 20% 30% 40% 50%

0.341 0.333 0.326 0.319 0.313

0.244 0.261 0.277 0.292 0.306

0.0852 0.0833 0.0816 0.0799 0.0782

0.0611 0.0652 0.0692 0.0729 0.0765

decrease decrease decrease decrease decrease

Objective Function 2 2000

30

1500 20 1000 10

500

0

0 25%

35%

45%

λ Non-optimum shaftwork Non-optimum UA

Optimum shaftwork Optimum UA

Specific Shaftwork (MJ/tonneLNG)a

UA (MW/C)

40

2500

Objective Function 3 2500

40

2000

30

1500 20 1000 10

500 0

0 25%

35%

45%

λ Optimum Shaftwork Optimum UA

Non-optimimum Shaftwork Non-optimum UA

Objective Function 4 40

2500 2000

30

1500 20 1000 10

500

UA (MW/C)

Specific Shaftwork (MJ/tonneLNG)

increase increase increase increase increase

considerably a large number of equipment, a precooling step using a single large coil wound heat exchanger (CWHE) for DMR process is considerably more cost-prohibitive than the multiple kettle type exchangers for propane precooling cycle of C3MR process. For the performance comparison, C3MR and DMR processes require a large amount of energy. The optimal results of OF1 show that the specific power consumption required by DMR is lower than C3MR while they have almost the same UA value of MCHEs. As displayed in Figs. 5 and 6, the option of using MR in precooling narrows the temperature difference between natural gas curve and refrigerant curve of a typical natural gas liquefaction to achieve

0

0 25%

35%

45%

λ Optimum Shaftwork Optimum UA

Non-optimum Shaftwork Non-optimum UA

Fig. 9. The effect of varying k value on the optimal results of C3MR process.

UA (MW/C)

Compressor cost

Specific Shaftwork (MJ/tonneLNG)

k (%)

2400

16

2300

15

2200

14

2100

13

2000

12

1900

11

1800

10

30 28

24 22

LMTD (°C)

26

UA (MW/°C)

Specific shaftwork (MW/tonneLNG)

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

20 18 16

0.10

0.15

0.20

0.25

0.30

0.35

β2 Specific power

UA

LMTD

Fig. 11. The effect of varying b value on the optimal results of C3MR process.

high refrigeration efficiency and reduce energy consumption. This option provides additional flexibility in the optimization. For the cost comparison, the size and count of equipment are the main factors influencing the capital cost. The equipment cost of a LNG plant inflates as each plant has its own unique characteristics including manufacturing locations, construction years, and

959

project’s specific requirements. In addition, only a limited data is available regarding the facility costs of liquefaction process. Using the cost consideration aforementioned, the cost evaluation is to compare a relative cost of the two processes rather than the accurate estimates. DMR process is assumed to be more costly due to the use of MHCEs in precooling. The optimal results reveal that capital costs are similar in both processes through the cost function, while the capital cost of DMR is slightly higher than C3MR through the energy function. For the energy function (OF1), there is no restriction on the UA of MCHEs. It leads to a significant increase in UA value, especially DMR process. This additional cost is compensated partially by saving more energy. In contrast, precooling UA of DMR is included in the cost functions. Cost functions can be sensitive to the overall UA value of DMR while the subcooling UA of C3MR is only available. It is noticeable from cost functions of OF2 and OF4 that DMR process has more potential on minimization of equipment size and energy consumption. Figs. 12 and 13 show the distribution patterns of exergy loss for C3MR and DMR processes. It is noticeable that the exergy distribution of two processes is similar. For OF1, the compression system is the major exergy loss for using OF1. It accounts for 35% for C3MR and 38% for DMR in total respectively. The second largest exergy

Fig. 12. Distribution of exergy loss in C3MR process (a) OF1 (b) OF4.

Fig. 13. Distribution of exergy loss in DMR process (a) OF1 (b) OF4.

960

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961

loss is contributed by MCHE which is 20% of overall for C3MR and 25% for DMR. In contrast, the MCHE is the largest exergy loss for using OF4 which are 37% for C3MR and DMR. The optimization objective for OF4 is to reduce both shaft work and UA. The smaller the size of heat exchangers, the larger the temperature difference between hot and cold composite curves. It results in more exergy loss of heat exchangers. Additionally, the compression system had a higher exergy loss at 29% for C3MR and DMR. 5.3. MR composition The effect of MR components on process performance is investigated. The subcooling MR in literature is typically comprised of methane, ethane, propane, i-butane and nitrogen as reviewed. Table 5 shows the optimum refrigerant composition obtained from different objective functions for C3MR process. Mixed refrigerant compositions have slight variation in the subcooling cycle. The optimal results obtained from OF4 present the relatively worse optimum performance with the best UA value of MCHEs. MR components are favorable to have more methane but less propane. The initial composition of methane and i-butane in MR stream before optimization was 50.5% by mole fraction. After optimization, the composition of methane was increased to 55.04% by mole fraction. Also, there was a decrease in the percentage composition of propane from 7.1% by mole fraction to 5.17% by mole fraction. Three components of refrigerant are used in the precooling of DMR which consists of ethane, propane and n-butane. We allow more refrigerant components as variables to show the effect of nitrogen, methane, ethane, propane, i-butane and n-butane on process performance. As shown in Table 7, the optimal refrigerant mixtures in subcooling obtained from OF1 are compared with those of baseline values. There is the absence of propane which is in agreement with Hatcher et al. [14] and Wang et al. [1]. 6. Conclusions The optimization of the C3MR and DMR processes is performed. Power consumption is taken as objective function for energy reduction, and a new formulation of economic objective function is developed for minimizing energy consumption and equipment size. The cost estimates for DMR used the same methodology as that applied for C3MR. The cost optimization considers not only power consumption but also equipment size as they all contribute to the most expenditure of LNG processes. The cost components considered include capital costs (compressors, main heat exchangers and others) and utility costs (water, electricity, and natural gas costs). We compared the optimal results of C3MR and DMR processes through four objective functions to their base cases at the same LNG production. The optimal results show the similar conclusions for C3MR and DMR. The results of OF1 appear to be the most thermodynamic efficiency from energy point of view. We implement the proposed cost function as objective function to minimize cost, shaft work and UA. The optimal results of cost function revealed that a trade-off between shaft work and UA. The finding in the optimal results of OF4 shows the simultaneous improvement needed for energy consumption and equipment size. Compared with the optimal results of OF4, the formulations of OF2 and OF3 were of acceptable to reduce certain amount of shaft work and UA. They appear lower specific power, while they have relatively higher UA than their baseline values. There are two scenarios for sensitivity study to identify the effects of two variable costs (k and bf) on the optimal results through cost objective functions. In scenario 1, varying the per-

centage of capital cost of a LNG plant in LNG value chain (k) influences insignificantly on the optimal results of cost functions. Total equipment costs (OF2 and OF4) as objective function indicate the performance improvement and the UA value reduction. The optimal results from scenario 2 show a trade-off between power consumption and UA value. OF4 could reduce certain amount of energy demand and size of MCHEs which provides the feasible solution of optimization. It is recommended to optimize the long-term expenditures to ensure the profit from liquefaction plant.

References [1] Wang M, Khalilpour R, Abbas A. Operation optimization of propane precooled mixed refrigerant processes. J Nat Gas Sci Eng 2013;15:93–105. [2] Shukri T. LNG Technology Selection. Hydrocarbon Engineering; 2004. [3] Venkatarathnam G, Timmerhaus KD, Rizzuto C. Cryogenic mixed refrigerant processes. Springer Science+Business Media; LLC2008. [4] Usama MN, Sherine A, Shuhaimi M. Technology review of natural gas liquefaction processes. J Appl Sci 2011;11:3541–6. [5] Lim W, Choi K, Moon I. Current status and perspectives of liquefied natural gas (LNG) plant design. Ind Eng Chem Res 2012;52:3065–88. [6] Lee GC, Smith R, Zhu XX. Optimal synthesis of mixed-refrigerant systems for low-temperature processes. Ind Eng Chem Res 2002;41:5016–28. [7] Vaidyaraman S, Maranas CD. Synthesis of mixed refrigerant cascade cycles. Chem Eng Commun 2002;189:1057–78. [8] Aspelund A, Gundersen T, Myklebust J, Nowak MP, Tomasgard A. An optimization-simulation model for a simple LNG process. Comput Chem Eng 2010;34:1606–17. [9] Wahl PE, Løvseth SW, Mølnvik MJ. Optimization of a simple LNG process using sequential quadratic programming. Comput Chem Eng 2013;56:27–36. [10] Shirazi MMH, Mowla D. Energy optimization for liquefaction process of natural gas in peak shaving plant. Energy 2010;35:2878–85. [11] Alabdulkarem A, Mortazavi A, Hwang Y, Radermacher R, Rogers P. Optimization of propane pre-cooled mixed refrigerant LNG plant. Appl Therm Eng 2011;31:1091–8. [12] Wang M, Zhang J, Xu Q. Optimal design and operation of a C3MR refrigeration system for natural gas liquefaction. Comput Chem Eng 2012;39:84–95. [13] Hasan MMF, Karimi IA, Alfadala HE, Grootjans H. Operational modeling of multistream heat exchangers with phase changes. AIChE J 2009;55:150–71. [14] Hatcher P, Khalilpour R, Abbas A. Optimisation of LNG mixed-refrigerant processes considering operation and design objectives. Comput Chem Eng 2012;41:123–33. [15] Khan MS, Lee S, Lee M. Optimization of single mixed refrigerant natural gas liquefaction plant with nonlinear programming. Asia-Pac J Chem Eng 2012;7:S62–70. [16] Khan MS, Lee M. Design optimization of single mixed refrigerant natural gas liquefaction process using the particle swarm paradigm with nonlinear constraints. Energy 2013;49:146–55. [17] Khan MS, Lee S, Rangaiah GP, Lee M. Knowledge based decision making method for the selection of mixed refrigerant systems for energy efficient LNG processes. Appl Energy 2013;111:1018–31. [18] Hwang J-H, Roh M-I, Lee K-Y. Determination of the optimal operating conditions of the dual mixed refrigerant cycle for the LNG FPSO topside liquefaction process. Comput Chem Eng 2013;49:25–36. [19] Paradowski H, Bamba M, Bladanet C. Propane pecooling cycles for increased LNG train capacity. In: 14th International conference and exhibition on liquefied natural gas; 2004. p. 107–24. [20] Remeljej CW, Hoadley AFA. An exergy analysis of small-scale liquefied natural gas (LNG) liquefaction processes. Energy 2006;31:2005–19. [21] Hasan MMF, Karimi IA, Alfadala HE. Optimizing compressor operations in an LNG plant. In: Hassan EA, Reklaitis GVR, Mahmoud M. El-HalwagiA2 – Hassan E Alfadala GVRR, Mahmoud ME-H, editors. Proceedings of the 1st annual gas processing symposium. Elsevier, Amsterdam; 2009. p. 179–84. [22] Jensen JB, Skogestad S. Optimal operation of simple refrigeration cycles: Part II: Selection of controlled variables. Comput Chem Eng 2007;31:1590–601. [23] Jensen JB, Skogestad S. Optimal operation of simple refrigeration cycles: Part I: Degrees of freedom and optimality of sub-cooling. Comput Chem Eng 2007;31:712–21. [24] Jacobsen MG, Skogestad S. Active constraint regions for a natural gas liquefaction process. J Nat Gas Sci Eng 2013;10:8–13. [25] Avidan AA, Gardner RE, Nelson D, Borreli EN. LNG links remote supplies and markets. Houston: Oil & Gas Journal; 1997. [26] Jensen James T. The development of a global LNG market. Is It likely? If so, When? Oxford Institute for Energy Studies; 2004. [27] Hirschhausen Cv, Neumann A, Ruester D-W-IS, Auerswald D. Advice on the Opportunity to Set up an Action Plan for the Promotion of LNG Chain Investments Dresden University of Technology Dresden; 2008. [28] Humphrey G. Current state & outlook for the LNG industry. Rice Global Engineering & Construction Forum; 2011.

M. Wang et al. / Energy Conversion and Management 88 (2014) 947–961 [29] Barnés FJ, King CJ. Synthesis of cascade refrigeration and liquefaction systems. Ind Eng Chem: Process Des Dev 1974;13:421–33. [30] Cheng WB, Mah RSH. Interactive synthesis of cascade refrigeration systems. Ind Eng Chem Process Des Dev 1980;19:410–20. [31] Vaidyaraman S, Maranas CD. Optimal synthesis of refrigeration cycles and selection of refrigerants. AIChE J 1999;45:997–1017. [32] Nogal FD, Kim J-K, Perry S, Smith R. Optimal design of mixed refrigerant cycles. Ind Eng Chem Res 2008;47:8724–40. [33] Jensen JB, Skogestad S. Problems with specifying DTmin in the design of processes with heat exchangers. Ind Eng Chem Res 2008;47:3071–5. [34] Castillo L, Dorao CA. Consensual decision-making model based on game theory for LNG processes. Energy Convers Manage 2012;64:387–96. [35] Shah NM, Rangaiah GP. Multi-objective optimization of the dual independent expander gas-phase refrigeration process for LNG. Salt Lake City, UT, USA: AIChE annual meeting; 2007. [36] Shah N, Rangaiah GP, Hoadley A. Multi-objective optimization: techniques and applications in chemical engineering. In: Rangaiah GP, editor. World Scientific Publishing Company, Incorporated; 2009. [37] Jensen JB, Skogestad S. Single-cycle mixed-fluid LNG process Part I: Optimal design. 1st Annual Gas Processing Symposium; 2009. p. 10–2. [38] Jensen JB, Skogestad S. Optimal operation of a simple LNG process. In: Proceedings Adchem; 2006. p. 241–7. [39] Jensen JB, Skogestad S. Single-cycle mixed-fluid LNG process Part II: Optimal operation. In: 1st Annual Gas Processing Symposium; 2009. p. 10–2.

961

[40] Castillo L, Dorao CA. On the conceptual design of pre-cooling stage of LNG plants using propane or an ethane/propane mixture. Energy Convers Manage 2013;65:140–6. [41] Bichsel M. Floating LNG – a natural gas innovation. SHELL GLOBAL; 2012. [42] Roberts MJ, Ott CM. Alternative pre-cooling arrangement. Air Products and Chemicals, Inc. (Allentown, PA, US), United States; 2010. [43] Yin QS, Li HY, Fan QH, Jia LX. Economic analysis of mixed-refrigerant cycle and nitrogen expander cycle in small scale natural gas liquefier. In: AIP conference proceedings, vol. 985; 2008.p. 1159–65. [44] Jager MD, Kaart S. Method and apparatus for cooling a hydrocarbon stream. Google Patents; 2009. [45] Finlayson BA. Introduction to chemical engineering computing. Hoboken, N.J.: Wiley-Interscience; 2006. [46] Hasan MMF, Karimi IA, Alfadala H, Grootjans H. Modeling and simulation of main cryogenic heat exchanger in a base-load liquefied natural gas plant. In: Plesu V, Agachi PS, editors. 17th European symposium on computer aided process engineering. Elsevier; 2007. [47] Baek S, Hwang G, Lee C, Jeong S, Choi D. Novel design of LNG (liquefied natural gas) reliquefaction process. Energy Convers Manage 2011;52:2807–14. [48] Vink KJ, Nagelvoort RK. Comparison of Baseload Liquefaction Processes. LNG12; 1998. [49] Turton R, Bailie RC, Whiting WB. Analysis, synthesis, and design of chemical processes. Prentice Hall; 2009.