Simulation-Based Optimization Methodology for Offshore Natural Gas

Article pubs.acs.org/IECR

Simulation-Based Optimization Methodology for Offshore Natural Gas Liquefaction Process Design Kiwook Song, Sangho Lee, Seolin Shin, Ho Jae Lee, and Chonghun Han* School of Chemical and Biological Engineering, Institute of Chemical Processes, Engineering Research Institute, Seoul National University, Gwanak 1, Gwanak-ro, Gwanak-Gu, Seoul 151-742, Korea ABSTRACT: A simulation-based optimization framework is introduced. First, a base case design is conducted using the commercial simulator. Then, design variables are decided. Next, minimum and maximum ranges of the design variable are determined. We will call this the design space. A comprehensive simulation of the design space is executed. Next, empirical modeling of this design space is performed. This is called the process mapping step. After verification of the model using a test data set, the optimization problem is solved using the developed data-driven model. The methodology is applied to the optimal design of a natural gas liquefaction process for an offshore liquefied natural gas (LNG) plant. simulators are basically based on first-principle models but usually do not provide the gradient information needed for deterministic optimization. The conventional optimization technique, when using the process simulator, is to integrate with an external optimizer such as MATLAB. The optimization algorithm in the external optimizer tool runs the simulator to search for the optimal point, but it fails often to converge and is heavily affected by the initial point. Also, models with many recycle loops and design specifications require a large computational effort and are time consuming; they are particularly not appropriate for online applications. The objective of this paper is to discuss a solution to the simulation-based optimization technique. The main concept is to apply process mapping technology to develop an empirical model that predicts the objective function value and constraint function values. The empirical modeling technique has been applied to fitting process models to industrial data,10−12 development of soft sensors (Kadlec et al. provided a comprehensive review on data-driven soft sensors),13 and model reduction for real-time optimization14,15 and monitoring.16,17 Previous studies proved that empirical modeling of chemical processes shows high prediction performance and can be used as an alternative to first-principle models. This paper proposes a simulation-based optimal design framework applied for natural gas liquefaction plants using the double-expander process. Detailed steps of the simulationbased optimization framework are introduced in Section 2. Then, a base case design of the turbo-expander process is described in Section 3. After determining the design space, an empirical model that predicts the objective function value and constraint function values is developed in Section 4. Finally, results are discussed in Section 5.

1. INTRODUCTION Natural gas liquefaction plants utilize various types of liquefaction cycles including cascade, mixed refrigerant, and turbine-based processes.1 Cascade processes with pure refrigerants such as methane, ethylene, and propane have a relatively small market share, while most of the onshore plants are mixed refrigerant process based. Liquefaction plants using a propane-precooled mixed refrigerant process and its variants are well known for their low shaft work requirement and application to high capacity plants. Nitrogen gas and mixtures of nitrogen and methane are used as the working fluid in turbine-based processes. Because liquefied natural gas (LNG) processes with turbines require relatively higher operating costs than mixed refrigerant processes, their applications have been usually limited to peak shaving plants. They have also been suggested for use in reliquefaction of boil-off gas in LNG ships.2 For offshore natural gas production, LNG floating production, storage, and off-loading units (LNG FPSOs) are used. The advantage of offshore LNG production includes a lower investment cost, shorter construction period, and repeated use for small-scale stranded gas resources. For LNG FPSOs, liquefaction cycles using hydrocarbons as refrigerants are not recommended for safety issues.3 However, turboexpander processes offer crucial advantages in floating plants due to inherent safety, easy design, small layout, and low weight.4 The reverse Brayton process is the simplest turbine-based process for natural gas liquefaction. The refrigerant is compressed to high pressure and precooled in the heat exchanger. Then it is expanded to low temperature to be utilized as the cold working fluid in the liquefaction process. Foglietta introduced a dual independent expander cycle with a methane cycle for precooling and a nitrogen cycle for the main cooling.5 Double and triple expander processes that divide the refrigerant stream into two or three portions were suggested by Dubar.6 Commercial process simulators are widely used in both industry and academia for LNG plant modeling.7−9 Significant progress in computer performance and database construction has led to accurate modeling of complex flowsheets. Process © 2014 American Chemical Society

Received: Revised: Accepted: Published: 5539

October 17, 2013 February 21, 2014 March 10, 2014 March 10, 2014 dx.doi.org/10.1021/ie403507p | Ind. Eng. Chem. Res. 2014, 53, 5539−5544

Industrial & Engineering Chemistry Research

Article

Figure 1. Steps of the simulation-based optimization framework.

2. SIMULATION-BASED OPTIMIZATION FRAMEWORK The simulation-based optimization framework to be introduced here is an optimal design technique using commercial process simulators as a basic process modeling. Figure 1 shows the steps of the proposed technique. The methodology includes process mapping of the design space with empirical modeling. This is to develop a short-cut data-driven model of the target process for the required operation window. Steps in detail are as follows. Step 1. Make a base case design of the target process with initial design points using the commercial simulator. The base structure of the process will remain fixed throughout the optimization procedure. The process simulator calculates all the mass and energy balance of the flowsheet. Step 2. Specify the design variables. Design variables are manipulated process variables that are to be optimized. Parameters, dependent variables, and independent variables should be determined by the user. Parameters are physical quantities that are fixed at a constant value throughout the simulation and optimization. Independent variables are variables that can be varied by the engineer for simulation and optimization, while dependent variables are other variables that are affected by the changes of the independent variables. Step 3. Formulate the optimization problem by specifying the objective function and constraints. The optimization problem can be written as follows minize or maximize z = f (X)

s.t. hI(X) = 0

(2)

hE(X) = 0

(3)

g(X) ≤ 0

(4)

where X is a vector of design variables. Equation 1 is the objective function to be minimized or maximized. Equality constraints may be segregated to implicit and explicit constraints. Equation 2 represents a set of implicit constraints that are met by the simulator, such as material and energy balance. The main advantage of using the simulator in the optimal process design is that the implicit equations are always satisfied. Equation 3 represents the explicit equality constraints that are additionally specified in Step 4. Equation 4 represents the inequality constraints, and main examples of them include bounds on purity, minimum temperature approach, temperature difference, conversion, selectivity, etc. Step 4. Specify explicit equality constraints in the process simulator. Design specifications on stream variables such as temperature, pressure, or flow rate values are main examples. Specifications on units such as pressure drop, heat duty, reflux ratio, conversion, etc. are also useful. This step is incorporating all the equality constraints into the simulator so that we can later map the design space that always meets the equality conditions. Step 5. Specify the appropriate range for each design variable. This is called the “design space”. In a conventional optimization formulation, the design variable range is expressed in an

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dx.doi.org/10.1021/ie403507p | Ind. Eng. Chem. Res. 2014, 53, 5539−5544


Article

Figure 2. Process flow diagram of natural gas liquefaction plant.

heat exchange. ASPEN HYSYS v7.3 is used for steady-state modeling usingthe Peng−Robinson property package.19 Natural gas at 50 bar is cooled to −20 °C in LNG-100 and then liquefied in LNG-101 with a discharge temperature of −90 °C. The LNG-101 module is where the phase change of natural gas to LNG occurrs. LNG is further cooled to −110 °C and −155 °C at LNG-102 and LNG-103, respectively. LNG is expanded in the Joule−Thompson valve (JT1) to 1.2 bar resulting in a temperature decrease to −165.2 °C. There is no phase change in the nitrogen refrigerant, and the cycle is operated only in vapor phase. The nitrogen gas is compressed to 55 bar by compressor modules C1, C2, C3, and C4. Nitrogen after the second stage of compressor (C2) is split in TEE-100 to streams 6 and 8 to be compressed further in C3 and C4, respectively. HX1, HX2, and HX3 are air coolers to cool down the compressor discharge streams to 30 °C. The refrigerant at 10 °C (stream 12) is precooled with the natural gas feed stream (NG2) to −20 °C in LNG-100. Then, the refrigerant is split in the TEE-101 module to streams 14 and 16. Stream 14 is expanded to 9 bar at expander X1 and is mixed with stream 19 to form stream 20, a cold stream that liquefies the natural gas in LNG-102. Nitrogen in stream 16 is further cooled at LNG-101 to −90 °C and later expanded to 9 bar at expander X2. This cold stream at −159.8 °C is used as the coldest stream to ensure that the temperature of LNG falls to −155 °C. Turbo expander X1 is arranged to drive compressor C3, and turbo expander X2 is arranged to drive compressor C4. So, power produced from the expanders is recovered in the compressors. The compressors need not be separate units and can be connected to a common shaft. 3.2. Step 2: Specifying Design Variables. A total of six design variables are to be manipulated in the target process. The design variables include the refrigerant mass flow rate (or refrigerant to natural gas ratio), split ratio of TEE-101 (flow ratio of stream 14), discharge pressure of the refrigerant at expander (streams 15 or 18), and discharge temperature values

inequality form. In our framework, the optimization space is confined to the design space. Step 6. Split the design space into appropriate discrete points and run a comprehensive simulation of the total range. This is the “data extraction” step. Step 7. Construct a new model of the design space using empirical modeling. This is called the “process mapping” step. The developed empirical model is the short-cut data-driven model of the target process for the design space only. It should not be used for extrapolation. The input variables of the model are the design variables. The model is to predict the objective function value f(X) and inequality constraint function value g(X). Predicting multivariate outputs is an important feature because the values of inequality constraints should be included in addition to the estimation of the objective function value. Step 8. Validate the empirical model using the test data set. If the empirical model shows reasonable prediction performance, then it can be used for optimization. Step 9. Solve the optimization problem of the process using the developed empirical model.

3. BASE CASE DESIGN OF TURBO-EXPANDER PROCESS 3.1. Step 1: Base Case Design. Figure 2 shows the process flow diagram of the natural gas liquefaction process using nitrogen as the refrigerant. The process is based on a United States patent18 and in-house data for 1 MTPA (million ton per annum) LNG production. The natural gas feed stream consists of 5.7 mol % of nitrogen, 94.1 mol % of methane, and 0.2 mol % of ethane. Streams 1 to 22 are nitrogen streams (colored blue in Figure 2) forming a cycle, while NG1 to NG7 are natural gas streams (colored green in Figure 2). Natural gas and nitrogen inlet temperature values are set to 10 °C using coolers HX4 and HX5, respectively. The double expander process is applied to liquefy the natural gas at 50 bar to −155 °C (stream NG6). Four LNG heat exchanger modules (LNG-100, LNG-101, LNG-102, and LNG-103) are used to simulate multistream 5541



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Table 1. Design Variables and Design Space of the Liquefaction Process no.

design variable

initial point

lower bound

upper bound

dimension

1 2 3 4 5 6

N2 refrigerant flow rate split ratio of TEE-101 expander discharge pressure LNG-100 outlet temperature LNG-101 outlet temperature LNG-102 outlet temperature

1300 0.5 9 −20 −90 −110

1000 0.5 9 −20 −90 −120

1300 0.7 12 −10 −80 −110

[ton/h] − [bar] [°C] [°C] [°C]

multiple effects on the process and should be determined by optimization. 4.2. Step 6: Comprehensive Simulation of Design Space. The six design variables have lower and upper bounds. The range for each variable is divided into six intervals. A comprehensive simulation, that is six to the sixth power, is performed for data extraction. An external operator such as MATLAB is used for easy handling of data input and output. The data collected are the objective function value and minimum temperature approach values for each LNG exchanger. Therefore, a data table of six input variables and five output variables is constructed through comprehensive simulation. 4.3. Step 7: Process Mapping of Design Space Using Empirical Modeling. Empirical modeling is used for process mapping. Examples of empirical modeling include multiple linear regressions, partial least-squares regressions,20 and other useful machine learning methods. An artificial neural network is useful when estimating various output variables from various input variables.21 ANN is a well-known technique to model nonlinear characteristics applied to a variety of chemical engineering field.22 In this study, a feed-forward back-propagation network with one input layer−one hidden layer−one output layer configuration is employed. The input layer consists of six nodes, each corresponding to the six design variables. The hidden layer has 20 nodes. The output layer has five nodes, one for the objective function and four for the minimum temperature approach values for LNG exchangers. A tan-sigmoid function in eq 9 is used for the activation function.

of natural gas at LNG exchangers LNG-100, LNG-101, and LNG-102 (streams NG3, NG4, and NG5). 3.3. Step 3: Optimization Formulation. The optimization formulation is as follows min Z (total shaft work)

(5)

s.t. hI(XD) = 0

(6)

hE(XD) = 0

(7)

MTA k ≥ 3 (for k = LNG‐100, LNG‐101, LNG‐102, and LNG‐103) (8)

where XD is a vector of design variables specified in Section 3.2. The objective function for optimal design of the liquefaction process in eq 5 is to minimize the total shaft work, which means compression work of C1 and C2. The equality constraints in eq 6 include all the thermodynamic equations together with unit operation equations. Additional equality constraints to be expressed explicitly in eq 7 will be explained in Section 3.4. The inequality constraints in eq 8 represent the minimum temperature approach (MTA) of each LNG exchanger. Here, the lower limit is 3 K. 3.4. Step 4: Providing Additional Constraints in the Simulator. The temperature value of stream 13 is set to be equal to the temperature of stream NG3. In addition, the temperature values of stream 17 and NG4 are set to be equal. The pressure values of streams 15 and 18 are also set to be equal. Pressure values of streams 7 and 9 are also set to be equal and are fixed at 55 bar. The split ratio of TEE-100 is not a design variable and is rather a variable that is adjusted depending on split ratio of TEE-101 and expander discharge pressure value. Discharge pressure of C2 (stream 4) is also a variable that is adjusted depending on the power recovered in C3 and C4. These design specifications are easily modeled in process simulators.

y=

exp(x) − exp( −x) exp(x) + exp( −x)

(9)

5. RESULTS AND DISCUSSION 5.1. Step 8: Empirical Modeling Validation. A test data set of 5000 randomly sampled observations is utilized for

4. SIMULATION-BASED OPTIMIZATION 4.1. Step 5: Determining Design Space. Table 1 shows the design variables, their initial points, and variable range. The design space is the operating window that we are interested in. To minimize the shaft work of compressor, nitrogen flow rate (or refrigerant to natural gas ratio) should be decreased from the initial point. Split ratio of TEE-101 (flow ratio of stream 14 to stream 16) should be increased from the initial point to minimize the heat duty of LNG-101, which makes it possible to further decrease the refrigerant requirement. The expander discharge pressure value should be increased from the initial point because the compressor discharge pressure is fixed in this case, and the lower expander discharge pressure results in higher compression ratio and higher power consumption. The outlet temperature value of each LNG exchanger has

Table 2. Prediction Performance of the Neural Network Model output variable

average error

RMSE

dimension of RMSE

total shaft work MTA of LNG-100 MTA of LNG-101 MTA of LNG-102 MTA of LNG-103

0.029% 0.017% 0.014% 0.042% 0.127%

3.611 0.006 0.043 0.011 0.049

[kW] [K] [K] [K] [K]

empirical model validation. The model predicts five output variables, total shaft work, and minimum temperature approach values for each LNG exchanger. Validation of the model means comparing the predicted values with the original simulator data. The results show excellent agreement between the simulator 5542



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Table 3. Optimization Results of the Liquefaction Process Using Proposed Methodology category design variable

objective function constraints

variable

before optimization

N2 refrigerant flow rate split ratio of TEE-101 expander discharge pressure LNG-100 outlet temperature LNG-101 outlet temperature LNG-102 outlet temperature total shaft work LNG-100 MTA LNG-101 MTA LNG-102 MTA LNG-103 MTA

after optimization

1300 0.5000 9.0000 −20.00 −90.00 −110.00 57954 14.17 15.53 15.87 8.06

dimension

1078 0.5900 9.6483 −20.00 −85.96 −110.00 45938 3.00 3.00 4.71 3.00

[ton/h] − [bar] [°C] [°C] [°C] [kW] [K] [K] [K] [K]

Table 4. Empirical Model and Simulator Values Using Optimized Design Variables category design variable

objective function constraints

variable

empirical model

N2 refrigerant flow rate split ratio of TEE-101 expander discharge pressure LNG-100 outlet temperature LNG-101 outlet temperature LNG-102 outlet temperature total shaft work LNG-100 MTA LNG-101 MTA LNG-102 MTA LNG-103 MTA

simulator

1078 0.5900 9.6483 −20.00 −85.96 −110.00 45938 3.00 3.00 4.71 3.00

and data-driven model. Average error percent and root mean squared error (RMSE) of the values are tabulated in Table 2. The average error is less than 0.2%, and the difference between simulator and neural network model is negligible. Therefore, the developed empirical model can be utilized as a representative model for the target design space instead of the commercial simulator itself. It has been shown that empirical modeling of the design space shows great performance of process mapping. However, the prediction performance may vary with the dimension of design space, broadness of each input variable range, structure of the empirical model, etc. Process engineers should predefine a tolerance for the prediction error and only use the proposed methodology when the performance of the developed datadriven model is acceptable. 5.2. Step 9: Optimization. For the initial design point, optimization using MATLAB linked with HYSYS does not converge to a value and fails to solve the problem. Case studies with different initial points were also performed, and the results of conventional optimization showed a high dependence on initial value. However, when the process design space is mapped using the suggested technique, the optimization problem is solved regardless of the starting point. The optimization results are tabulated in Table 3. To finally check the reliability of the empirical model, the optimized values need to be compared with the simulator values. Table 4 shows the results, and the difference between the empirical model and simulator is in the acceptable range. The advantage of the proposed optimization framework is that process designers can take full advantage of the process simulators. Process simulators are easy to handle and inherently calculate unit operation equations with a vast and accurate thermodynamic database. Also, process designers can readily

dimension

1078 0.5900 9.6483 −20.00 −85.96 −110.00 45941 3.01 2.98 4.71 3.00

[ton/h] − [bar] [°C] [°C] [°C] [kW] [K] [K] [K] [K]

apply many design specifications into the simulator that need some iteration steps to solve. The main disadvantage of the suggested methodology is that the data-extraction step can be time consuming, especially with many design variables. Development of the empirical model with the least data set available will be discussed in future work.

6. CONCLUSION Commercial process simulators are effective when modeling complex processes such as a liquefaction process with multistream heat exchangers and recycle streams. For the optimal design of such a process using the simulator environment, this paper introduced a simulation-based optimization framework using a systematic process mapping technology. The main concept is to develop a short-cut datadriven model. The method includes a comprehensive data extraction phase of the process in a prespecified operating range. The design space of the process is modeled using an empirical modeling technique such as an artificial neural network. The performance of the proposed method was shown by use of a case study of a natural gas liquefaction plant for floating production, storage, and off-loading. The proposed optimization framework can be applied to any process design and real-time optimization.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +82-2-880-1887. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 5543



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Article

(22) Himmelblau, D. Applications of artificial neural networks in chemical engineering. Korean J. Chem. Eng. 2000, 17, 373−392.

ACKNOWLEDGMENTS This research was supported by the second phase of the Brain Korea 21 Program in 2014, the Institute of Chemical Processes in Seoul National University, the MKE, a grant from the LNG Plant R&D Center funded by the Ministry of Land, Transportation and Maritime Affairs (MLTM) of the Korean government, and by the Energy Efficiency & Resources Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) who granted financial resources from the Ministry of Trade, Industry & Energy, Republic of Korea (2010201020006D, 20132010201760, and 20132010500050).

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REFERENCES

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Simulation-Based Optimization Methodology for Offshore Natural Gas

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