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Strategies for Process and Size Selection of Natural Gas Liquefaction Processes: Specific Profit Portfolio Approach by Economic Based Optimization Inkyu Lee, and Il Moon Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03327 • Publication Date (Web): 03 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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Industrial & Engineering Chemistry Research

Strategies for Process and Size Selection of Natural Gas Liquefaction Processes: Specific Profit Portfolio Approach by Economic Based Optimization

Inkyu Lee and Il Moon*

Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea

Special Issue on “PSE Advances in Natural Gas Value Chain” in Industrial Engineering Chemistry Research. August 07, 2017 KEYWORDS: LNG Plant, Process Selection Strategy, Size Selection Strategy, Economic Optimization, Specific Profit Portfolio Approach

ACS Paragon Plus Environment

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ABSTRACT This study focuses on the strategies for process and size selection of various natural gas liquefaction processes by economic based optimization. As various types of liquefaction processes can be differentiated by their energy efficiency and equipment requirements, the energy requirement and cost of a liquefaction process have to be considered simultaneously to find the optimal process for a given plant size. Herein, we developed two mathematical models, i.e., the thermodynamic model and cost model, based on the unit equipment that were integrated into a profit optimization model that could be applied to various natural gas liquefaction processes and plant sizes. In this study, the profit optimization model was applied to three representative natural gas liquefaction processes: single mixed refrigerant (SMR), dual mixed refrigerant (DMR), and propane pre-cooled mixed refrigerant (C3MR) processes. The capacity of the plants ranged from 1 to 7 million tons per annum (MTPA). As a result of profit optimization, specific profit portfolios were obtained and the economical plant size ranges were figured out: 1 to 2.2 MTPA for the SMR process, 2.2 to 4 MTPA for the DMR process, and 4 to 7 MTPA for the C3MR process.


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1. INTRODUCTION According to the Outlook for Energy (2016), natural gas demand is forecasted to increase by 40 % from 2014 to 2040, and liquefied natural gas (LNG) exports are expected to almost triple in the same period.1 A mass of LNG occupies about 600 times a smaller volume than the same mass of vapor phase natural gas.2 Generally, LNG is produced by cooling natural gas to below −160 °C at atmospheric pressure.3 Thus, the natural gas liquefaction process is energy intensive owing to its cryogenic characteristics, and most of the energy is required by the compression unit.4 Therefore, minimizing the compression energy requirement is the major concern in design and optimization of the natural gas liquefaction processes.

1.1. Characteristics of Natural Gas Liquefaction Processes The natural gas liquefaction process is operated under a wide range of temperatures using one or more refrigerants.5 Therefore, understanding the characteristics of various natural gas liquefaction processes is important to optimize these processes. Various natural gas liquefaction processes have been developed over the last few decades. The natural gas liquefaction processes can be classified by the types of refrigerants used and the number of refrigeration cycles.6 The types of refrigerants can be divided into two categories: pure refrigerants, which mainly use latent heat generated through phase changes, and mixed refrigerants. A SMR process that uses only one mixed refrigerant cycle has a simple configuration.7 Generally, the mixed refrigerant consists of nitrogen and hydrocarbons, and is compressed by multi-stage compression. A DMR process is one of the favored natural gas liquefaction technologies for on-shore locations because it is one of the highest-efficiency processes.8 The DMR process uses two different mixed refrigeration cycles; one cycle utilizes a warm mixed


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refrigerant and the other one utilizes a cold mixed refrigerant.9 The natural gas is pre-cooled by the warm mixed refrigerant and then liquefied by the cold mixed refrigerant. Generally, the cold mixed refrigerant consists of nitrogen, methane, ethane, and propane, while the warm mixed refrigerant contains the components methane, ethane, propane, n-butane, and i-butane.10 Therefore, the warm mixed refrigerant has a higher boiling point compared to the cold mixed refrigerant. Because the concentrations of mixed refrigerants can be adjusted easily, the DMR process has the advantage of high flexibility to adjust intermediate temperatures.11 Moreover, refrigerants with a wide range of temperatures can be utilized, from the low boiling to the high boiling refrigerant in mixed refrigerants.12 Both the cold and warm mixed refrigerants are compressed by multi-stage compressions. A C3MR process, one of the most dominant liquefaction processes, uses both pure and mixed refrigeration cycles.13 The C3MR process was introduced by Air Product and Chemicals, Inc. (APCI) to combine the advantages of mixed and pure refrigeration cycles.14 The propane is used in this process as a pure refrigerant to pre-cool the natural gas to about −33 °C; then, the natural gas is sub-cooled by the mixed refrigerant.15 The pure refrigeration cycle is compressed by multi stage compression. Each pressure level of the pure refrigerant cools down the natural gas and the mixed refrigerant by multi stage heat exchange. The cold mixed refrigerant is compressed by successive multi stage compressors, and it liquefies the natural gas.16 Generally the mixed refrigerant in the C3MR process contains nitrogen, methane, ethane, and propane as its component.

1.2. Natural Gas Liquefaction Process Optimization In the last few decades, many researchers have focused on minimizing compression energy requirements in LNG refrigeration cycles. The majority of these studies have focused on


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minimizing shaft work requirements with different target processes and different optimization techniques. The natural gas liquefaction process optimization field can be classified in two categories: energy minimization and cost minimization.

1.2.1. Energy minimization In early studies of optimization of the natural gas liquefaction process, nonlinear programming (NLP) was usually applied. Vaidyaraman and Maranas17 focused on the synthesis of refrigeration systems with mixed refrigerants as working fluids, and developed an objective function that minimized the total work input to the system. They set the problem as a nonconvex NLP to optimize the cascade mixed refrigerant process. Kim et al.18 proposed a strategy of selecting the mixed refrigerant composition by using a combined NLP based on the thermodynamics. The target process was the PRICO process, a type of the single mixed refrigerant (SMR) process, and the objective was to minimize the shaft work requirement. Lee et al.19 performed SMR process optimization with the decision variables of mixed refrigerant composition, flow rate, compressor inlet and outlet pressures, and separator temperatures. They applied the pinch technology and NLP techniques to solve the problem. Aspelund et al.20 focused on minimizing the total shaft work requirement of the expander process. They developed extended pinch analysis and design (ExPAnD), which is a methodology for process synthesis that extends pinch analysis and exergy analysis. Shah and Hoadley21 used the targeting method, which demonstrates the relationship between the expansion–compression pressure ratio and the minimum temperature difference of the heat exchanger. The optimization objective was shaft work minimization of the cascade N2 expander process. Wang et al.22 applied a simulation-based optimization conducted in Aspen Plus, in which the sequential quadratic programming (SQP) solver was employed for the


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optimization. The objective of their work was to minimize the total shaft work requirement of the propane pre-cooled mixed refrigerant (C3MR) process. Wang et al.23 employed the LINDOGlobal solver in GAMS software in their successive study, in which the mixed integer nonlinear programming (MINLP) model was developed for the energy minimization of the C3MR process. Wahl et al.24 applied the SQP solver to minimize the energy requirement of the SMR process, and concluded most of the optimization results were better and the execution times are much lower than in most studies of similar optimization cases with stochastic optimization methods. Lee et al.15 focused on the energy minimization of the pure refrigeration cycle in the C3MR process. They applied the successive reduced quadratic programming (SRQPD) solver with gPROMS, which is an equation-oriented commercial software, and proposed a new design of the pure refrigerant process for the sub-cooling in their study. Tak et al.25 compared four different configurations of the SMR process with three natural gas compositions in their study. Thus, twelve different cases were optimized with the SRQPD solver. Lee et al.16 applied the SRQPD solver to minimize the compression energy requirement of the C3MR process. They attempted to determine the optimal liquefaction ratio of the natural gas liquefaction. The objective functions were the total energy consumption and specific energy consumption. Na et al.26 suggested dividing a hyper rectangle (DIRECT) algorithm to optimize the mixed refrigerant cycle in the natural gas liquefaction process. They compared DIRECT algorithm to other deterministic and stochastic optimization techniques. One of the major stochastic optimization techniques applied in the natural gas liquefaction process research is the genetic algorithm. Nogal et al.27 applied the genetic algorithm to overcome local optima. The target process of their work was cascade mixed refrigerant process. Shirazi and Mowla7 also applied the genetic algorithm to minimize the shaft work requirement of


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the PRICO process. Taleshbahrami and Saffari28 focused on minimizing the compression energy requirement in the C3MR process by using the genetic algorithm. The commercial software MATLAB was used for the modeling and simulation of the C3MR process in their work. Alabdulkarem et al.29 minimized energy consumption in the C3MR process by using the genetic algorithm. They used the commercial process simulation software Aspen HYSYS to calculate the thermodynamic properties with the genetic algorithm optimizer in MATLAB. They performed and compared four different optimizations with different pinch temperatures, and they concluded that decreasing pinch temperature makes power consumption savings possible. Xu et al.30 coupled the genetic algorithm with the process simulation software Aspen Plus. They focused on determination of the composition of the mixed refrigerant of the PRICO process. They found that the concentrations of methane, ethylene, and propane have to be decreased, and i-pentane has to be increased when the ambient temperature increases. Xu et al.31 also applied the genetic algorithm with Aspen Plus in their successive work, where they minimized the specific energy consumption of the PRICO process. Ding et al.32 applied genetic algorithm in MATLAB combined with Aspen HYSYS to optimize the mixed fluid cascade process. The objective function was minimizing specific work. Some researchers have tried to apply other stochastic optimization techniques besides the genetic algorithm. Aspelund et al.33 developed a gradient free optimization-simulation method. They applied the Tabu Search (TS) combined with the Nelder–Mead Downhill Simplex (NMDS) method. The objective of their work was to minimize the total required compression energy of the PRICO process. Morin et al.34 applied an evolutionary search method to minimize the energy requirement of the SMR, PRICO, and TEALARC processes. Khan and Lee35 employed the


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particle swarm paradigm to optimize the SMR process. Minimization of the compression energy requirement was selected as the optimization objective function.

1.2.2. Cost minimization Although the majority of natural gas liquefaction process optimization is energy minimization, some studies have considered the cost of the LNG plants. One of the earliest studies of cost minimization was adapted to the pure refrigeration system by Barnés and King.36 In addition, Cheng and Mah37 developed an interactive synthesis of cascade refrigeration systems, while Vaidyaraman and Maranas38 used mixed-integer linear programming to minimize investment and the operating costs for refrigerant selections. Furthermore, Jensen and Skogestad39 developed a total annual cost (TAC) equation to minimize capital and operating costs. However, only the capital cost of the heat exchanger and operating costs for the compression energy were considered in their work. Castillo and Dorao40 focused on cost minimization by considering the market cost, power consumption, and heat transfer area. Jensen and Skogestad41 introduced the cost factor as an adjustable parameter in a study whose objective was to maximize the LNG flow rate and minimize the heat exchanger and natural gas costs. In other studies, Jensen and Skogestad42,43 focused on minimizing the total annualized cost, which is the sum of fuel, feed, and operating costs. Wang et al.44 performed optimizations with four different objective functions: total shaft work, total cost investment, total annualized cost, and total capital cost of compressors and main cryogenic heat exchangers. In their work, they used a percentage of the equipment cost in total capital cost instead of the specific equipment cost. In most of the previous studies, the energy requirement has been regarded as part of the operating cost, and the electricity has been adapted to supply the required energy. However, most of industrial sites


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produce energy from natural gas fuel. Therefore, the environment of the actual industrial site have to be considered. Moreover, comparisons of various natural gas liquefaction processes and various sizes by optimization has not been studied comprehensively yet. The main purpose of the study is to propose strategies for process and size selection by finding the optimal natural gas liquefaction processes for various plant sizes. To determine the optimal design and size of the plant, the operating cost and capital cost have to be considered simultaneously. A cost-based model can consider the plant size, which cannot be considered in thermodynamic model. Moreover, the price and flow rate of the natural gas feed and LNG also affect the profit. Therefore, the profit optimization model has to be developed because it can consider the cost of the raw materials and final product. In our previous study, we developed a profit optimization model to maximize the annual profit of a plant with a capacity of 1 million tons per annum (MTPA) that utilized the dual mixed refrigerant (DMR) natural gas liquefaction process.10 In this successive study, we adopt the profit optimization model, which is an integrated model of the thermodynamic model and cost model, to find the most economic optimal design and operating condition. The profit optimization model is applied to three representative natural gas liquefaction processes: the SMR, DMR, and C3MR process. The capacity range of the plant is set from 1 to 7 MTPA . The specific profit concept, which is the profit per unit mass of liquefied natural gas, is introduced to compare different liquefaction processes by size.

2. PROBLEM STATEMENT The main objective of this study is to compare various natural gas liquefaction processes by size, and the comparisons have to be performed under the same conditions. In our previous work,


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our objective was to find the optimal liquefaction ratio of the liquefaction process in an energy self-sufficient system.10 Our results showed that, for an economically optimal liquefaction ratio, the quantity of the produced boil-off gas (BOG) needed to be as much as the fuel consumed, and the produced BOG needed to be used for energy generation. Therefore, the energy self-sufficient system in this work is stated as illustrated in Figure 1. The energy requirement increases to achieve a higher liquefaction ratio, and it decreases when the liquefaction ratio decreases. The stated energy self-sufficient system can consider the tradeoff relationship between the energy requirement and the liquefaction ratio by balancing the amount of the BOG and LNG product. This system is applied to three different natural gas liquefaction processes: the SMR, DMR, and C3MR processes. The design basis is shown in Table 1, and same design basis is applied to all process.

2.1. SMR process description The SMR process uses one mixed refrigerant cycle to liquefy natural gas. The process flow diagram of the SMR process is shown in Figure 2.45 The lowest pressure of the mixed refrigerant is compressed through successive multistage compressions. The compressed mixed refrigerant in each compression stage is cooled down by the cooler. The mixed refrigerant with the highest pressure is further cooled through the multistream heat exchanger (MSHE) and then expanded when it passes through the valve. The cold refrigerant is used to liquefy the natural gas as well as cool the refrigerant. The cold stream outlet of the MSHE goes to the first stage compressor, and this cycle is continuously repeated.

2.2. DMR process description


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Figure 3 illustrates the process flow diagram of the DMR process.10 The DMR process uses two mixed refrigerant cycles: the warm mixed refrigerant (WMR) cycle which is used to precool the natural gas and the mixed refrigerants, and the cold mixed refrigerant (CMR) cycle which is used to liquefy the natural gas and to cool the CMR itself. Generally, the WMR contains methane, ethane, propane, and butane, and the CMR contains nitrogen, methane, ethane, and propane.12 Both mixed refrigerant cycles are compressed and cooled through successive multistage compressors and coolers.

2.3. C3MR process description In the C3MR process, pure and mixed refrigerants are used to liquefy the natural gas. Figure 416 describes a process flow diagram of the C3MR process. Propane (C3) is used as the pure refrigerant to pre-cool the natural gas and to cool the mixed refrigerant by means of a multistage refrigeration cycle. The pure refrigerant with the lowest pressure is compressed through successive pressure stages. The compressed pure refrigerant is liquefied by the cooler. The liquid pure refrigerant is expanded by the valve and then cools down the natural gas and the mixed refrigerant at each pressure level. The mixed refrigerant is compressed by four compressors; it is cooled by the cooler and then cooled further by means of the pure refrigerant. The cooled mixed refrigerant is separated into liquid and vapor. The liquid mixed refrigerant is expanded through a valve after the main cryogenic heat exchanger. The mixed refrigerant vapor is cooled further by the main cryogenic heat exchanger, and expanded by another valve. The expanded mixed refrigerants are used as the cold stream in the MSHE. The mixed refrigerant is returned to the mixed refrigerant compressor and the successive steps are repeated. The process flow diagram of the C3MR process is illustrated in Figure 4.16 Different liquefaction process have different


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process efficiencies and different complexities. Comparisons of the complexities of the three liquefaction processes indicate that the SMR process is the simplest and the C3MR process is the most complex because of the multi-stage pre-cooling system of the pure refrigerant: the main devices used in the natural gas liquefaction process are MSHEs, compressors, pumps, and coolers, and the SMR process contains eight main devices, the DMR process contains twelve main devices, and the C3MR process consists of sixteen major devices. The number of major devices for the SMR, DMR, and C3MR process is shown in Table 2.

3. PROFIT OPTIMIZATION MODEL The mathematical simulation–optimization model for the natural gas liquefaction processes is developed by using gPROMS, an equation oriented optimization software, and the Peng– Robinson equation of state, which is used for the thermodynamic property calculations.46 The mathematical optimization is performed with a successive reduced quadratic programming (SRQPD) solver to find the optimal solutions. The profit optimization model consists of the thermodynamic model and the cost model, which contains capital and operating cost equations. The development of the mathematical model is schematically illustrated in Figure 5.

3.1.Thermodynamic Model 3.1.1. Compression unit The compression units, compressor, and pump, are modeled in isentropic compression as follows:


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W = ∙ , − , /

(1)

, = ,

(2)

, = , − , / + ,

(3)

where W is work, is mass flow rate, H is specific enthalpy, S is specific entropy, and η is efficiency. The subscripts out, in, isen, and act, represent the outlet stream, the inlet stream, isentropic condition, and actual value, respectively. The isentropic efficiency, ηisen, is assumed to be 0.75 on the basis of industrial experience.16

3.1.2. Multi-stream heat exchanger The MSHE contains multiple hot streams, and the model is developed based on heat balance as follows:

= ∙ , − , = ∑ { , ∙ , , − , , }

(4)

where is heat flow; the subscripts i is the ith hot stream, hot is the hot stream, and cold is the cold stream in the MSHE. The temperature range inside the MSHE is divided into a number of intervals to produce composite curves and to check the feasibility of heat transfer. The temperature difference between the hot and cold streams must be larger than or equal to the minimum temperature difference inside the heat exchanger. In this model, the intervals are evenly divided in temperature into 40 nodes, from the lowest to the highest temperature, among all

the

hot

streams.


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,!

= min {

, %

(

,2

= =

, , }

= &' {

(5)

, , }

(6)

)*+,,*-.* /)*+,,0+1

(7)

2/3 ,!

+ (5 − 1) ∙ (

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(8)

where min is minimum value, max is maximum value, dT is temperature range between the successive two nodes, and z is zth node; the subscript low is the lowest temperature, high is the highest temperature, and z is zth node. The hot composite curve which is heat flow to temperature can be obtained by integrating all hot streams.

,2 = ∑ { , ∙ , ,2 }

(9)

The enthalpy for each node of the cold stream is calculated by the enthalpy for each node of the hot stream. The model can be described as follows:

, = ∙ ,2

(10)

,2 = ,2 + ,

(11)

The temperature of the cold stream can be easily calculated by the enthalpy because the enthalpy is function of the temperature, pressure, and composition.

3.1.3. Gas Turbine The gas turbine model is described as follows:


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89) = :;; ∙ H, + (1 − >;) ∙ ,

(14)

where VF is the vapor fraction; the subscripts v and l represent vapor and liquid, respectively.

3.1.5. Other Equipment


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The expansion valve is modeled based on isenthalpic expansion; thus the outlet temperature of the expansion valve is calculated by its outlet pressure. The cooler is modeled based on the heat balance. The mixer and splitter are modeled by mass and heat balance.

3.2. Cost Model 3.2.1. Capital Cost The annual capital cost is defined as the summation of major equipment investment costs:

:I, = ∑{J ∙ :?K,L + :KK + M ∙ :9) + :NO@P + :?Q,< }/RSK) (15)

where C is the cost, M is the number of compression units, N is the number of gas turbines during the plant’s life, and Lf is life expectancy; the subscripts CP represents the compressor, PP the pump, MSHE the multi-stream heat exchanger, CL the cooler, j the jth compressor, k the kth cooler, and PT the plant. The total plant life, LfPT, is assumed as 20 years because the life cycle of a natural gas liquefaction plant is known to be around 20 to 25 years.48 The life expectancy of the compression units is approximately 5 years; thus, the compressors are needed four times during the plant’s life.49 The life expectancy of the gas turbine is approximately 11 to 18 years.50 Therefore, the gas turbines are replaced two times. The equipment investment cost is modeled mainly based on the six-tenths-factor rule51: the cost of an equipment can be approximately calculated by using capacity ratio and exponent factor. The six-tenth-factor rule is described as follows:


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: = :T ∙ (U /UT )VI (16)

where X is equipment capacity and exp is the exponent factor; the subscripts a and b refer to equipment a and b, respectively. The exponent factors for the compressor, pump, and cooler are 0.69, 0.33, and 0.60, respectively.51 The reference sizes and costs of the equipment are obtained by pilot plant experience and by using the commercial software Aspen Process Economic Analyzer. To calculate the capacity and the cost of the MSHE, the B-value method is applied.52 The MSHE model is described as follows:

> = 1.15 ∙ ∑2 >2 >2 =

(17)

YZ /QN)[Z

(18)

BZ )

*+,,-] RJ \ = abc ()

/ )^+0_,+`, / )*+,,+`, /)^+0_,-]

*+,,-] / )^+0_,+`, )⁄)*+,,+`, /)^+0_,-] e

(19)

where V is volume, LMTD is log mean temperature difference, B is B-value, and T is temperature. The actual volume of the MSHE is calculated by the LMTD, heat flow, and the B-value. The Bvalue and the cost of the MSHE can be obtained from published data.53 The capital cost of the gas turbine is modeled by the amount of the energy supply, which is 230 USD/kW.47

:9) = 230 ∙ :; /i ∙ 8

(20)


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where the subscript s-hr refers to hr/s. The comparisons must be performed in same standard. Therefore, the interest rate is considered for every piece of equipment, and is obtained from the equation as follows.

: i = :I T ∙ (1 + r)

(21)

where r is price escalation factor and t is number of years between the published year of the reference data and the 2016; subscripts cur is current year (2016) and pub is published year of the reference data. The capital costs for minor equipment such as the separator, valve, mixer, and splitter are considered negligible because the costs of those units are relatively low.10

3.2.2. Operating Cost Because the system is considered to be an energy self-sufficient system, the operating cost can be classified into two categories: the maintenance cost and cooling water cost. The annual operating cost is modeled as

:I, = :k , + :! ,

(22)

where the subscripts op, mt, and wt refer to operating, maintenance, and cooling water, respectively. The annual maintenance cost is assumed to be 3% of the total capital cost.51 The maintenance cost model is described as follows:


18

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:k , = 0.03 ∙ ∑{:?K,L + :KK + :9) + :NO@P + :?Q,< }

(23)

The cooler discharge temperature is set at 30°C, and the unit cost of cooling water is 0.354 USD/GJ.54 The cooling water cost is modeled as follows:

:! , = 0.354 ∙ :;9=/ ≤ 380,000 (w /ℎy)

(28)

where > is the volumetric flow rate of a single centrifugal compressor, and it cannot be larger than 380,000 m3/hr.41


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4. SMR PROCESS OPTIMIZATION For commercial natural gas plants, the available capacity sizes are known to range from 1 to 7 MTPA, and different processes have different available portfolios of single-train capacity.6 To find the most economical process, the profit optimizations of various processes are performed for natural gas plants with a capacity of 1 to 7 MTPA with a 1 MTPA step size. The first targeted liquefaction process is the SMR process, which uses one mixed refrigerant cycle to liquefy natural gas. To make a base case, profit optimization of the SMR process in a plant with a 1 MTPA capacity is performed first. Then, based on the design and operating conditions of the optimization result, simulations for the SMR process in plants with 2 to 7 MTPA sizes are performed. For each simulation, every design and operating condition is the same with the 1 MTPA optimal conditions except for the flow rates. The natural gas and mixed refrigerant flow rates are proportionally multiplied to meet each plant size, i.e., for the 2 MTPA base case simulation, the natural gas and mixed refrigerant flow rates are double those of the 1 MTPA optimization result, and other operating conditions are the same with the 1 MTPA optimal conditions. Then, the profit optimizations of the other 6 sizes are performed individually. To compare the results for various sizes, the indicators are converted to a specific value. The base case and the optimal cases are compared in terms of specific profit, specific cost, liquefaction ratio, specific energy, and volumetric flow rate of the largest compressor. The specific cost is the cost per unit mass of LNG (USD/ton-LNG), the specific energy is the energy requirement per unit mass of LNG (kW/kg-LNG), and the specific profit is the profit per unit mass of LNG (USD/ton-LNG). The volumetric flow rate of the largest compressor is analyzed to check the feasibility of the process.


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4.1. Base Case: Sizing-up Simulation Results The profit optimization result for SMR process in a plant with a 1 MTPA capacity and the sizing-up simulation results for SMR process are shown in Table S2. The table shows that, as the flow rate increases, the total required compression energy also linearly increases. The sizing-up effect cannot be considered in the thermodynamics-based energy optimization model. The specific work, operating temperature, operating pressure, total compression ratio, and the liquefaction ratio are the same in the simulation results of all sizes in the base case. However, the decrease in the specific plant cost is not linear with the increase in the plant size because the equipment cost model basically follows the six-tenths rule, which is nonlinear. Moreover, the specific profit is not same in all cases because the specific cost affects the specific profit. The specific profit increases with an increase in the plant size, but the growth rate decreases gradually. Another important factor that has to be analyzed in the plant size-up simulation and optimization is the volumetric flow rate of the compressor. The maximum limit of the volumetric flow rate for a single flow centrifugal compressor is known to be 380,000 m3/hr.41 Therefore, to check the feasibility of a plant of a certain size, the volumetric flow rate of the compressor has to be checked. As shown in Table S2, Comp1 has the largest volumetric flow rate because it is operated at the lowest pressure level. The volumetric flow rates of the compressors increase linearly with plant size because the mixed refrigerant flow rate increases linearly under the same operating conditions: temperature, pressure, and composition. The size-up simulation results also show that plants with 6 MTPA and 7 MTPA capacities are infeasible because the volumetric flow rate of the largest compressor exceeds the maximum limitation, which is 380,000 m3/hr.


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Therefore, the profit optimizations have to be performed in each size of the SMR process to find the feasible solutions of economically optimal design and operating conditions. 4.2. Profit Optimization Results Additional profit optimizations are performed with 2 to 7 MTPA of SMR processes to find the optimal solutions for these sizes. Table S3 shows the profit optimization results for plants with 1–7 MTPA sizes for the SMR process. As shown in the Table S2, the equipment cost is reduced but the specific energy is not reduced when the process size is increased under the same operating conditions. The optimization for the larger size is performed to the direction of the increasing capital cost and the decreasing energy cost than the smaller size of the plant. Because the compression energy requirement can be saved when operating under lower pressure levels, the suction pressure and discharge pressure steadily decrease as the plant size increases from 1 to 5 MTPA. After 5 MTPA, the suction and discharge pressures rapidly increase owing to the compressor volume limitation. Increasing of the suction pressure causes decreasing of the process efficiency, the flow rate have to be increased to absorb required amount of the heat. Therefore, the flow rate of the mixed refrigerant also sharply increases as the size increases from 5 to 7 MTPA for the SMR process. Therefore, to reduce the volume due to the increased amount of refrigerant, the operating pressure has to be increased. As the size of the plant increases from 5 MTPA to 7 MTPA, the specific cost and specific profit decrease, which is due to a decrease in the energy efficiency of the SMR process in plants with 6 and 7 MTPA sizes compared with those with a 5 MTPA size. The volumetric flow rate of Comp1 meets the maximum limitation for the SMR process in plants with 6 and 7 MTPA sizes. The base case and the profit optimal cases are compared on five terms: specific energy, liquefaction ratio, volumetric flow rate for the largest compressor, specific cost, and specific


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profit (Figure 6). The specific costs of plants with 6 and 7 MTPA sizes for the optimal case are lower than those for the base case. As shown in Figure 6 (a) and (b), the liquefaction ratio is directly affected by the energy efficiency. The energy requirements of the plants with 6 and 7 MTPA sizes for the optimal case are larger than those for the base case, and the liquefaction ratios are lower than those of the base case. The lower liquefaction ratio means that a higher amount of BOG is produced, and it also means the fuel requirement is higher than in the base case. For the volumetric flow rates, for the base case, plants with 6 and 7 MTPA sizes are infeasible because they exceed the compressor volume limitation. However, when the compressor volume constraint is added to the profit optimizations, a feasible solution can be obtained for the SMR process. The volumetric flow rates for plants with 6 and 7 MTPA sizes meet the maximum limitation of volumetric flow rate. It means, the lowest pressure level of operating condition have to be increased to decrease the volume for the increased amount flow rate. It causes energy efficiency decrease, thus the energy requirement is increased to absorb the enough amount of heat from the natural gas with limited refrigerant flow rate. With a limited refrigerant flow rate, the energy requirement is therefore increased to absorb a sufficient amount of heat from the natural gas. Figure 6 (e) presents the specific profit, which is profit per unit mass, of the LNG product. The specific profit of the base case result steadily increases as the plant size increases, but the optimal case shows maximum specific profit is achieved with a plant size of 6 MTPA owing to the compressor limitation. The volumetric flow rate limitation causes a decrease in the energy efficiency of the SMR process in the plants with a large size. Despite the decrease in efficiency, the specific profit of the plant with a 6 MTPA is higher than that of the 5 MTPA because the increase in plant size causes a decrease in the specific investment cost. However, the amount of increased profit cannot


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exceed the amount of decreased efficiency in 7 MTPA size SMR process. As the result of the profit optimizations of 1 through 7 MTPA size SMR processes, the 6 MTPA plant size shows the highest specific profit. Plant size ranges without the compressor volume limitation, the size-up characteristics of the natural gas liquefaction process can be determined by comparing optimal results and base case simulation results for the plants with 1 to 5 MTPA sizes. Compared with the base case, the optimal case shows a higher specific profit. However, the specific cost for the optimal case is higher than that for the base case, which means the specific profit increase is achieved by a decrease in energy.

5. STRATEGIES FOR PROCESS AND SIZE SELECTION The main objective of this study is to propose strategies for process and size selection by finding economically optimal natural gas liquefaction processes for various plant sizes. To find the optimal process, additional profit optimizations of the DMR and C3MR processes are performed for plants with 1 to 7 MTPA sizes with a 1 MTPA step size.

5.1. Profit Optimization Results for Various Liquefaction Processes Table S4 shows the profit optimization results of specific cost for the SMR, DMR, and C3MR processes. The optimization results of specific cost show that the C3MR process has the highest cost and the SMR process has the lowest cost for all sizes due to the number of major pieces of equipment. The specific cost for the C3MR process is the highest among the natural gas liquefaction processes, and the specific cost difference between the smallest and the largest sizes is also the highest. On the other hand, the specific cost is the lowest for SMR process, as is the decreasing range with the sizing-up is the lowest, i.e., the decreasing rate of the specific cost for


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the C3MR process from 1 MTPA to 2 MTPA is 1.77 USD per ton-LNG and for the SMR process from 1 MTPA to 2 MTPA is 0.84 USD per ton-LNG. However, the decreasing range decreases as the size increases for all processes. Note that, the volumetric flow rates of the largest compressor for the DMR and C3MR processes do not exceed 380,000 m3/h for all sizes. The profit optimization results for the SMR, DMR, and C3MR processes are illustrated in Figure 7. The specific energies of the optimization results for the three different natural gas liquefaction processes are shown in Table S5. The specific energy for the SMR process deceases gradually from 1 to 5 MTPA and then increases sharply from 5 to 7 MTPA, owing to the compressor volume limitation. However, the DMR and C3MR processes use two refrigeration cycles; thus, these two processes do not exceed the maximum compressor volume limitation under the 1 to 7 MTPA plant size range. Therefore, the specific energy steadily decreases as plant size increases for both of DMR and C3MR processes. The optimal operating conditions for the SMR processes require around 1,200 kW/kg of LNG production for all plant sizes. Within the same plant size range for the SMR process, the specific work requirements for DMR processes are around 1,140 and specific work requirements for C3MR processes are around 990 kW/kg of LNG with the optimal operating conditions. The specific energies of the optimal designs and operating conditions for these three natural gas liquefaction processes show that the C3MR process requires the lowest energy and SMR process requires the highest energy, which indicates that the C3MR process is the most efficient of the liquefaction processes, with economically optimal operating conditions. The liquefaction ratio shows an opposite tendency. A higher energy efficiency requires a lower amount of fuel, and a lower amount of fuel makes the lower amount of natural gas feed flow rate


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possible. Moreover, a decrease in the natural gas feed flow rate causes a decrease in the raw material cost. The liquefaction ratios of the optimization results for three liquefaction processes are shown in Table S6. The profitable liquefaction ratios for the C3MR, DMR, SMR processes for 1 to 7 MTPA plant sizes are around 93.8%, 92.9%, and 92.6%, respectively. The most economical process for a certain size of plant can be determined by drawing specific profit portfolios for various plant sizes of various liquefaction processes. Table S7 shows the specific profits of the profit optimization results for the SMR, DMR, and C3MR processes for 1 MTPA to 7 MTPA plant sizes. Based on the optimization result, the specific profit portfolios for these processes are illustrated in Figure 8. The SMR process, which has the simplest configuration, has an economic strength in plants with small sizes. Even though its energy efficiency is the lowest among the three liquefaction processes, its low plant cost can make up for this disadvantage in plants with a small size. However, as the plant size increases, the DMR process catches up with the SMR process in terms of the specific profit. The configuration of the DMR process is more complex, and it requires much more equipment than SMR process. For the medium-size plant, the higher energy efficiency makes the DMR process economical compared with the SMR process. For the large plant size, the C3MR process is the most economical because it has the highest efficiency although it requires much more equipment compared with the SMR and DMR processes. The specific profit portfolios for the SMR, DMR, and C3MR processes present the economical range for each process as follows:

The SMR process is economical for plants whose sizes range from 1 to 2.2 MTPA.

The DMR process is economical for plants whose sizes range from 2.2 to 4 MTPA.

The C3MR process is economical for plants whose sizes range from 4 to 7 MTPA.


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5.2. Discussion Through the profit optimizations, the specific profit portfolios are determined and the most economical processes and ranges are found. Although the specific profit differences between different processes look small, less than 2 USD per ton-LNG, they cause large differences in overall profit, i.e., a specific profit difference of 0.5 USD per ton-LNG causes an overall profit difference of 3.5 million USD per year in a plant size with a 7 MTPA. The actual plants do not draw smooth cost curve by plant size increasing because most of the equipment sizes and costs are fixed by the vendor. The fixed capacity and cost of the equipment make another optimization that is concerned with the equipment selection necessary. In particular, the driver selection for power generation is one of the major issues in the equipment selection field.56,57 Furthermore, the utility system of the plant can affect the cost and profit; thus the availability and reliability of the utility system can be considered in its optimization.58 In addition, there are many uncertainties in real industry practice. For example, the natural gas and LNG prices can be changed according to many reasons, such as oil price changes, energy source changes, fossil fuel regulations, or other political issues. This study considers equipment costs to be a non-linear equation, basically following six-tenth factor rule. Therefore, the fixed sizes and fixed costs of the equipment are neglected. However, it is believed that the trends of the cost and the profit by plant size will be maintained. Moreover, the profit optimization model and specific profit portfolio approach can be adopted in different situations, as well. This study is performed with 2.5 USD/Mcf for the natural gas price and 4.5 USD/Mcf for the LNG price. By applying those prices, the economical ranges of each process are figured out. In addition, the natural gas liquefaction process selection strategies are suggested. There is a possibility that different prices


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of the natural gas and the LNG could show different economical ranges of various liquefaction processes. However, the optimizations with the profit optimization model that is developed in this work can be applied and be used to suggest the process selection strategies for different situations. Moreover, the specific profit portfolio approach can be applied to other natural gas liquefaction processes. It can be an excellent standard to prove the economic strength range of a plant size for the natural gas liquefaction processes.

6. CONCLUSION This study focuses on strategies for process and size selection of various natural gas liquefaction processes by cost-based optimization. The natural gas processes can be classified by the number of refrigeration cycles and the refrigerant types. Different processes for liquefying natural gas have different energy requirements and require a different number of equipment. Therefore, the energy requirement and the cost have to be considered simultaneously to find the optimal design and operating conditions. By performing profit optimizations for the various natural gas liquefaction processes by plant size, several portfolios are determined for each liquefaction process. These include specific cost portfolios, specific energy portfolios, liquefaction ratio portfolios, and specific profit portfolios. The specific cost portfolios show that the C3MR process has the highest cost and the SMR process has the lowest cost for all sizes because of the required number of major equipment. The specific energy portfolios indicate that the C3MR process requires the lowest energy and the SMR process requires the highest energy. Furthermore, they show that the C3MR process is the most efficient among the three natural gas liquefaction processes. However, the liquefaction ratio portfolios show an opposite tendency. A higher energy efficiency requires less fuel, which makes


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a lower amount of natural gas feed flow rate possible. In addition, a decrease in the natural gas feed flow rate results in a decrease in the raw material costs. The specific profit portfolios indicate that the natural gas liquefaction process with a simple configuration that requires less equipment has economic advantages for small-size LNG plants. On the other hand, the energy efficient process is more profitable for the large plant size. In conclusion, this study suggests strategies for selecting the natural gas liquefaction process and plant size by using specific profit portfolios. The specific profit portfolios are undertaken by performing profit optimizations with various liquefaction processes and plant sizes based on the cost optimization model. Through the specific profit portfolios, the optimal design and operating conditions for various LNG plant sizes are determined. This work will provide innovative solutions that will aid the decision making process for profitable liquefaction of LNG plants. Moreover, adapting the specific profit portfolio can be an excellent way to show the economic strength range of plant sizes for the natural gas liquefaction processes.


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AUTHOR INFORMATION Corresponding Author *To whom correspondence should be addressed. Tel.: +82 2 2123 2761. Fax: +82 2 312 6401. E-mail: [email protected].

ACKNOWLEDGMENTS This study 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.

NOMENCLATURE Variables B

coefficient for B-value method

C

cost (USD)

CF

unit conversion factor

CR

compression ratio

cur

current year

CV

calorific value (kcal/kg)

dT

temperature range between the successive two nodes (°C)

exp

exponent factor

H

mass enthalpy (kJ/kg)

Lf

life expectancy (yr)

LMTD

log mean temperature difference (°C)

mass flow rate (kg/h)


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M

number of compression units

max

maximum value

min

minimum value

N

number of turbines

nBOG

component mass fraction of BOG

Pf

profit (USD)

pub

published year of the reference data

heat flow (kJ/h)

Rv

revenue (USD)

S

mass entropy (kJ/kg·K)

T

temperature (K)

t

number of years (yr)

V

volume (m3)

>

volumetric flow rate (m3/h)

VF

vapor phase fraction

W

power (kJ/h)

X

equipment capacity

η

efficiency

Subscripts a

equipment a

act

actual value

ann

annual

b

equipment b

BOG

boil off gas

CH4

methane

CL

cooler


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cold

cold stream

CP

compressor

GJ-kJ

GJ/kJ

GT

gas turbine

high

the highest temperature

hot

hot stream

hr-yr

hour/year

i

ith hot stream in MSHE

in

inlet stream

isen

isentropic condition

j

jth compressor

k

kth cooler

kJ-kcal

kJ/kcal

l

liquid

LNG

liquefied natural gas

low

the lowest temperature

MSHE

multi-stream heat exchanger

net

net value

NG

natural gas

mt

maintenance

MTD

minimum temperature difference (°C)

op

operation

out

outlet stream

PP

pump

PT

plant

r

price escalation factor

s-hr

hr/s conversion

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tt

total

v

vapor

wt

cooling water

z

zth node in the multi-stream heat exchanger


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(50) Slottner, P. Life Extension of SIEMENS Industrial-sized Gas Turbines. 18th Symposium of the Industrial Application of Gas Turbines Committee, Banff, Alberta, Canada, October 19-21, 2009. (51) Peters, M. S.; Timmerhaus K. D.; West R. E. Plant Design and Economics for Chemical Engineers, 5th ed.; McGRAW-HILL: Boston, MA, 2011. (52) Guo, K.; Zhang, N.; Smith, R. Optimisation of Fin Selection and Thermal Design of Plate-Fin Heat Exchangers. Chem. Eng. Trans. 2014, 39, 325-330 (53) Selection and Costing of Heat Exchangers, Plate-Fin Type, ESDU data item No.97006; EDSU: London, UK, 1997. (54) Turtion, R.; Bailie, R.C.; Whiting, W. B.; Shaeiwitz, J. A.; Bhattacharyya, D. Analysis, Synthesis, and Design of Chemical Processes, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2012. (55) Natural Gas Prices. https://www.eia.gov/dnav/ng/ng_pri_sum_dcu_nus_m.htm (accessed August 5, 2017) (56) Del N.; Frank. L.; Kim, J. K.; Perry, S.; Smith, R. Synthesis of mechanical driver and power generation configurations, Part 1: Optimization framework. AIChE J. 2010, 56 (9), 2356-2376. (57) Del N.; Frank. L.; Kim, J. K.; Perry, S.; Smith, R. Synthesis of mechanical driver and power generation configurations, Part 2: LNG applications. AIChE J. 2010, 56 (9), 23772389. (58) Aguilar, O., Kim, J. K., Perry, S., & Smith, R. (2008). Availability and reliability considerations in the design and optimisation of flexible utility systems. Chem. Eng. Sci. 2008, 63 (14), 3569-3584.


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FIGURE LIST Table of Contents (TOC)


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Figure 1. Energy self-sufficient system for natural gas liquefaction


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Figure 2. Process flow diagram of the SMR process45


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Figure 3. Process flow diagram of the DMR process10


45


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Figure 4. Process flow diagram of the C3MR process16


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Figure 5. Mathematical optimization model development


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Figure 6. Base case and profit optimization results for the SMR process: (a) specific energy, (b) liquefaction ratio, (c) volumetric flow rate for the largest compressor, (d) specific cost, and (e) specific profit


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Figure 7. Profit optimization results for various liquefaction processes: (a) specific energy, (b) liquefaction ratio, and (c) specific cost


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Figure 8. Specific profit portfolio for various natural gas liquefaction processes by plant size


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TABLE LIST Table 1. Process design basis10 parameters

values

natural gas feed temperature

37 °C

natural gas feed pressure

5,000 kPa

Natural gas feed composition (mole fraction) nitrogen (N2)

0.0020

methane (C1)

0.9130

ethane (C2)

0.0540

propane (C3)

0.0210

i-butane (i-C4)

0.0050

n-butane (n-C4)

0.0050

LNG product pressure

100 kPa

MTD in MSHE

3 °C

cooler discharge temperature

30 °C

pressure drops in MSHE

100 kPa

pressure drops in coolers

0 kPa

isentropic efficiency of compression units

75 %

gas turbine calorific power efficiency

38 %


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Table 2. Number of major pieces of equipment for SMR, DMR, and C3MR processes Equipment

SMR process

DMR process

C3MR process

Compressor

3

5

6

Pump

1

1

-

Heat exchanger

-

-

6

MSHE

1

1

1

Cooler

3

5

3

Total

8

12

16


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