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Total Cost Optimization of Single Mixed Refrigerant Process based on the Equipment Cost and Life Expectancy Inkyu Lee, and Il Moon Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b01864 • Publication Date (Web): 13 Sep 2016 Downloaded from http://pubs.acs.org on September 19, 2016

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Industrial & Engineering Chemistry Research

Total Cost Optimization of Single Mixed Refrigerant Process based on the Equipment Cost and Life Expectancy Inkyu Lee and Il Moon*

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

Submitted to Industrial & Engineering Chemistry Research May 15, 2016 KEYWORDS: LNG Plant, Liquefied Natural Gas, Natural Gas Liquefaction Ratio, Energy Optimization, Cost Optimization

ACS Paragon Plus Environment

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ABSTRACT This study mainly focuses on minimizing the total cost of the single mixed refrigerant (SMR) process based on the equipment cost equations considering equipment life expectancy. Moreover, the energy and cost analyses are performed by comparing optimization results with two different objectives. The objective functions to be minimized include the total compression energy and the total annual cost, which is the sum of the annual capital cost and annual operating cost. By the compression energy minimization, the operating cost is significantly reduced by 16.2% because the largest part of this cost is taken by electricity for the compression energy requirement. In addition, an 14.0% capital cost saving is realized by the energy minimization. The results of total cost minimization shows a 16.0% operating cost reduction from the base case, which is a little lower compared to energy minimization, but the capital cost saving is dramatically higher at 28.3%. Through the cost analyses, it is found that the compressors greatly affect not only the operating cost but also the capital cost. Two major variables that determine the energy requirement and cost of compressor are the compression ratio and flow rate. The compression ratio affects the operating cost more than the flow rate but for the capital cost, it is the other way around. Therefore, finding the optimal design for the compressor is the key consideration in minimizing the cost. This study found the optimal design and operating conditions to obtain the minimum total cost. As a result of cost minimization, the total cost can be reduced by 19.2% with a 15.61 total compression ratio and 520.7 t/h refrigerant flow rate.


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1. INTRODUCTION According to the Outlook for Energy (2016), the growth of natural gas demand is projected to increase by 40% from 2014 to 2040 because it is the cleanest burning fossil fuel.1 When natural gas is liquefied, its volume is reduced by more than 600 times.2 For this reason, natural gas is transported by liquid state over long distances. The temperature of natural gas has to be lower than −161°C to liquefy it at atmospheric pressure.3 Therefore, the natural gas liquefaction process is operated under cryogenic condition, which has a high energy demand.4 For this energy intensive operation characteristics, many researches on liquefied natural gas (LNG) plants have been studied to improve energy efficiency of the process.5 Majority of previous studies have focused on compression energy saving. However, the compression energy minimization will not always guarantee the maximum profit. Even though the compression energy supply takes a large portion of the operating cost, the capital and other operating costs cannot be ignored. Despite an increase of energy requirement, the process can still be economical when the savings in equipment cost exceed the rise in energy cost. Therefore, total cost optimization is required in an economic point of view. Natural gas liquefaction processes are classified by the type of refrigerants and the number of refrigeration cycles.6 Among these various liquefaction processes, single mixed refrigerant (SMR) process is mainly targeted in LNG plant optimization because it is the simplest process, which uses only one mixed refrigerant cycle.7 Lee et al.8 performed the SMR process optimization based on the decision variables of mixed refrigerant composition, flow rate, compressor inlet and outlet pressures, and separator temperatures. The objective functions of their study were minimization of the crossover, minimization of the sum of the crossovers, and minimization of the shaft work requirement. They applied the pinch technology and nonlinear programming


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techniques to solve the problem. Nogal et al.9 applied one of the stochastic optimization techniques— genetic algorithm (GA). They explained that their approach overcome local optima using the GA technique. The shaft work requirement minimization and capital cost minimization were performed in their work; however, the operating cost was not considered. Shirazi and Mowla10 also employed the GA using MATLAB software to minimize energy consumption of the SMR process. Aspelund et al.11 applied a different stochastic optimization technique—tabu search (TS), combined with the Nelder–Mead downhill simplex (NMDS) method. They mainly focused on the effect of the combined optimization method, thus simplifying the liquefaction process. Marmolejo-Correa and Gunderson12 focused on the comparison of different exergy efficiencies, especially for the SMR process. They analyzed specific exergy, which is exergy per unit mass of LNG product. Kahn and Lee13 employed the particle swarm optimization, a nontraditional stochastic technique, to optimize the SMR process. They selected the optimization objective as minimizing the compression energy requirement. Wahl et al.14 used sequential quadratic programming (SQP), a deterministic optimization method, to shorten the execution time. The objective function of their work was the power consumption of the compressor. Xu et al.15,16 analyzed the effect of the mixed refrigerant composition on the SMR process. To determine optimal composition of mixed refrigerant, they performed linear regression. Tak et al.17 compared multistage compression configurations of SMR processes. They performed mathematical optimization to compare different configurations under optimal design and operating conditions. The purposes of previous researches for SMR process were mainly minimizing compression energy requirement. The objective function of the work of Kim et al.18 was minimizing shaft work of compressor. Lee et al.8 compared three different objective functions, minimizing shaft


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work requirement, crossover, and sum of crossover. Nogal et al.9 performed the minimization of the shaft work and capital cost. Shirazi and Mowla10 focused on the minimizing shaft work requirement. Aspelund et al.11, Morin et al.19, and Tak et al.17 also performed minimization of the shaft work requirement. Few researches have focused on the cost optimization. Jenson and Skogestad20 tried to perform the economic optimization for SMR process. They considered heat exchanging areas, compressor size, temperature, and pressure as the design parameters. They introduces cost factor which represents the trade-off between the operation cost and the capital cost. However, the objective of their work was maximize LNG flow rate with given compressor design and the results were only analyzed by the cost factor not the equipment cost. The main purpose of the study is minimizing the total cost of the SMR process by optimizing the capital and operating cost simultaneously. To compare the compression energy requirement and total cost, optimization is performed with two different objective functions. The first objective function, which is the main purpose of this study, is minimizing the capital and operating cost. The energy requirement is converted to the electricity cost, and forms part of the operating cost. The plant life and equipment life expectancy are also considered. The second is minimizing total compression energy, which is the most general objective function for the LNG plant. The optimizations are mathematically modeled and performed based on deterministic optimization approach. The optimization found optimal operating conditions as well as the equipment capacity.

2. SMR PROCESS DESCRIPTION The target plant studied in this work is the SMR process, which uses one mixed refrigerant cycle to liquefy natural gas. Considering industrial capacity, the size of target SMR process is set


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as 1 million tons per annum (MTPA). The process flow diagram of the SMR process is shown in Figure 1. The lowest pressure of the mixed refrigerant is compressed through successive multistage compression. The compressed mixed refrigerant in each compression stage is cooled down by the cooler. The highest pressure of mixed refrigerant is further cooled through the multistream heat exchanger (MSHE) and expanded by passing through the valve. The cold refrigerant is used to liquefy the natural gas. The pressure drop at the MSHE is assumed as 100 kPa and the minimum temperature difference (MTD) is 3°C. The cold stream outlet of the MSHE goes to the first stage compressor, and this cycle is continuously repeated. The natural gas feed temperature and pressure is at 37°C and 5,000 kPa while the flow rate is 114,155 kg/h to meet the 1 MTPA design capacity. The natural gas is assumed to be 100% liquefied through the process. The natural gas composition is shown in Table 1 and the process design basis is shown in Table 2.

3. OPTIMIZATION MODEL DEVELOPMENT A mathematical model for simulation and optimization of the SMR process is developed by using the commercial software gPROMS. For the thermodynamic calculation, the PengRobinson equation of state is selected by recommendation for gas refinery and petrochemical applications.21 The Multiflash module is used to provide thermodynamic properties to gPROMS. Additionally, equation-oriented mathematical model has the strength for including optimization algorithms. Whal et al.14 announced that the execution time for the SQP solver was 2-6 minutes in their work which is dramatically faster than the stochastic optimization for a similar problem. In the work of Aspelund et al.11, the execution time was 4-12 hours using tabu-search and the execution time of the work of Morin et al.19 using evolutionary search technique was around 22


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hours. Whal et al.14 concluded that the SQP is better than other stochastic optimization methods because its routine is very robust and the calculation time is very fast. For this reason, a successive reduced quadratic programming (SRQPD) solver, which is an advanced sequential quadratic programming (SQP) solver is used in this work. The major thermodynamic equipment models, capital cost models, operating cost models, objective functions, optimization variables, and optimization constraints are described in this chapter.

3.1. Equipment Model 3.1.1. Compression unit The compression units such as compressors and pump are modeled as isentropic compression. The energy demands for these units are calculated by following Eqs 1–3.

W = , − /

(1)

, =

(2)

= , − / +

(3)

where W is energy demand, H is enthalpy, S is entropy, and η is isentropic efficiency. The subscripts out, in, and isentropic respectively represent the outlet stream, the inlet stream, and isentropic compression conditions. The enthalpy and entropy are functions of temperature, pressure, and composition. Eq 2 is used to calculate the isentropic temperature, which is then used to calculate the isentropic enthalpy. The isentropic efficiency (ηisentropic) is assumed to be 0.75 on the basis of industrial experience.


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3.1.2. Cooler The cooler model is developed based on the following heat balance:

, − , = , − ,

(4)

where is the flow rate, and the subscripts cw and hot represent the cooling water and hot streams of the heat exchanger respectively.

3.1.3. Multistream heat exchanger The multistream heat exchanger (MSHE) contains multiple hot streams especially the two hot streams for the SMR process. The MSHE is modeled based on heat balance as follows:

= , − , = ∑ {, ,, − , , }

(5)

where is heat flow and the subscript i refers to the ith hot stream. The hot stream temperature range is divided into 30 points to check the feasibility of the MSHE. As for the constraints, the temperature difference between the hot and cold streams must be larger than the MTD at each point.

3.1.4. Expansion valve The expansion valve is modeled based on isenthalpic expansion, which means that the inlet enthalpy of the valve is equal to the outlet enthalpy. Because the enthalpy is a function of the


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temperature, pressure, and composition, the outlet temperature can be calculated by the outlet pressure.

3.1.5. Mixer and splitter The mixer and splitter are modeled by mass and heat balance.

3.2. Capital Cost Model For the cost optimization, the model has to include cost equations. The capital cost is set as the summation of the major equipment; MSHE, compressor, pump, and cooler. The equipment costs for the capital cost calculation is mainly based on the six-tenths-factor rule22: If the cost of a given unit at one capacity is known, the cost of a similar unit can be approximated by an exponent of 0.6 times the cost of the initial unit. The six-tenth-factor rule can be described as follows:

!" = !# $%" /%# &'.)

(6)

where C is equipment cost and X is equipment capacity; the subscripts a and b respectively represent the equipment a and b, which have different capacities. Different types of equipment have different exponential values for cost calculation. The exponents for compressor, pump, and cooler are 0.69, 0.33, and 0.60, respectively.22 The reference size and cost of equipment are obtained by using the commercial software, Aspen Economic Evaluation and pilot plant experience.


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Majority of equipment costs can be approximately calculated by the six-tenths-factor rule. However, the cost for the MSHE cannot is difficult to calculate because of its complexity. Therefore, the B-value cost calculation method, which is based on the MSHE volume calculation is applied.23 The B-value can be read by published data and the active volume can be calculated from the B-value.24 The volume, B-value, and log mean temperature difference models are described as follows in Eqs 7–9.

* = 1.15 ∑- **- =

(7)

./ /0123/

(8)

4/

5678 =

29:;, 2?:@A,:B; > 29:;,:B; >2?:@A,

Total Cost Optimization of a Single Mixed ... - ACS Publications

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