MINLP Model for Operational Optimization of LNG Terminals

Round 1

Reviewer 1 Report

“MINLP model for operational optimization of LNG terminals” submitted by Zhencheng Ye, Xiaoyan Mo, and Liang Zhao is well-written manuscript with a clearly defined problem, methodology and application. The paper is, therefore, suitable for publication but after several minor things are addressed:

1) The authors need to stress what is the significance of this paper and to change the conclusion to reflect this. Just presenting an optimization methodology and applying it to an industrial problem is not enough as it has been done many times before. Why is this manuscript different and better than the others?

2) The authors should also address the limitations of their approach.

Author Response

Response to Reviewer 1:

Comment: “MINLP model for operational optimization of LNG terminals” submitted by Zhencheng Ye, Xiaoyan Mo, and Liang Zhao is well-written manuscript with a clearly defined problem, methodology and application. The paper is, therefore, suitable for publication but after several minor things are addressed:

Response: Thank you very much for your positive recommendation. The following is adetailed reply to your comments.

Comment 1: The authors need to stress what is the significance of this paper and to change the conclusion to reflect this. Just presenting an optimization methodology and applying it to an industrial problem is not enough as it has been done many times before. Why is this manuscript different and better than the others?

Response: Many thanks for your valuable comments. We added 11 references to analyze the novelty of our work in the revised version. There are many researches on the LNG clod energy recovery, the design optimization of BOG handling processes and BOG systems. But there are no published literatures considering the scheduling optimization of LP pumps related to the send-out and recirculation flow rates. The send-out flow rate is determined by the requirements of users. And the recirculation flow rate varies with the ambient temperatures since there is a constrain for the temperature differences (∆T) between the inlet and outlet of recirculation pipeline. Besides, we employed a mixed-integer nonlinear programming model to solve the scheduling problems of LNG receiving terminals which was not used in the published literatures. And we proposed a model to estimate the generation rate of BOG which is different from the published literatures [28,33,35]. This content has been added in the revised version. For your easy reference, we list the related revision below.

Action:

In Lines 85-94 of the revised manuscript:

“However, there are no literatures that consider the scheduling optimization of LP pumps related to the send-out and recirculation flow rate, to the best of our knowledge. And a mixed-integer nonlinear programming model was first employed to solve the scheduling optimization problem of LNG receiving terminal. For estimating the generation rate of BOG, a nominal boil-off ratio of 0.05%-1% for the LNG tank capacity per day is used [34,36]. Besides, an empirical equation corrected by the data from the LNG storage tank manufacturers is proposed [28]. In this work, the HYSYS dynamic model of the industrial LNG receiving terminal was developed to generate the data of BOG generation, and the regression model was obtained by the data. Therefore, the model is more suitable for LNG terminal optimization than the methods in the literatures.”

In Lines 99-102 of the revised manuscript, the contributions of the manuscript are re-summarized.

“A MINLP model is developed for the operational optimization of the LNG terminal.

A regression model of BOG generation is proposed considering both model accuracy and computational complexity.

An industrial case study in an actual LNG terminal is employed to indicate the effectiveness of the proposed method.”

Comment 2: The authors should also address the limitations of their approach.

Response: Thanks a lot for your valuable suggestion. We assumed that the LNG receiving terminal is not on the condition of unloading and the recondensation process is used to treat BOG. The unloading condition and handling BOG with high-pressure compressor process are beyond the scope of our research method. Besides, the average temperature in months was used in this work, which is not very realistic since the ambient temperature changes all the time. We have added the limitations of the approach and given some directions to study in the conclusion section. For your easy reference, we list the related revision below.

Action:

In Lines 85-94 of the revised manuscript:

“The proposed optimization method would significantly contribute to the existing LNG terminals. However, the research was on the condition that the LNG was not unloading and the LNG terminal used a recondenser instead of HP compressors to handle BOG. The other working condition will also be studied in the future. Besides, average temperatures of the months were used in this work, which is not very realistic since the ambient temperature changes all the time.”

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and suggestions, in detail, can be found in the attached report.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 2:

Comment: The article investigates an interesting research problem with significant contemporary practical implications. It is well structured. In my opinion, the manuscript is suitable for the journal with a minor revision. One issue the authors should consider is to connect the contribution and advances made in comparison with the state of the art literature. Another general remark is to review the language of the paper in terms of grammar and syntax.

Response: Thank you very much for your positive recommendation. We have carefully and thoroughly revised the paper. Following are the responses to your comments.

Abstract

Comment: L. 9-10: “with other fossil fuels”. The emissions comparison should be with other fossil fuels.

Response: Many thanks for your valuable comment. We have fixed it in the revised version. For your easy reference, we list the related revision below.

Action:

In Lines 9-10 of the revised manuscript:

“it has almost no environmental damaging sulfur dioxide compares with other fossil fuels.”

Comment : L.10: “An LNG import terminal”. Clarify this early in the text, as liquefaction plants are also named LNG terminals”

Response: Many thanks for your valuable comments. We have corrected it in the revised version. For your easy reference, we list the related revision below.

Action:

In Lines 10-11 of the revised manuscript:

“An LNG import terminal is a facility that regasifies LNG to natural gas, which is supplied to industrial and residential users.”

 Introduction

Comment: L. 26: “NG liquefaction plants”.

Response: Thank you very much for your valuable comment. We have fixed it in the revised version. For your easy reference, we list the related revision below.

Action:

In Lines 27 of the revised manuscript:

“The traditional LNG supply chain includes NG liquefaction plants”

Comment: L. 27: “LNG import terminals”.

Response: Many thanks for your valuable comment. We have corrected it in the revised version as follows. For your easy reference, we list the related revision below.

Action:

In Lines 28 of the revised manuscript:

“and LNG import terminals”

Comment: L. 37-38: The statement “Research in LNG fields has focused on the operational optimization of the terminal, which 37 is the regasification-to-end-user section of the supply chain [17]” is not valid and is based only on one reference. Please correct.

Response: Many thanks for your valuable comment. We have corrected it in the revised version as follows. We have changed it into “LNG terminals are the regasification-to-end-user section of the supply chain and they can be operated for the whole year.”

Problem Statement

Comment: This section should include a description of the components referenced (L. 68-70) coupled with discussion on Figure 1.

Response: Many thanks for your valuable comments. We have added the description of Figure 1. For your easy reference, we list the related revision below.

Action:

In Lines 104-114 of the revised manuscript:

“The schematic of an actual LNG terminal, which is composed of various devices, such as pumps, tanks, recondenser, and vaporizers, is illustrated in Figure 1. As shown in Figure 1, the BOG produced in the LNG storage tanks is compressed into the recondenser with compressors, and the LNG is pumped into the recondenser by in-tank LNG pumps. When the BOG is completely condensed by a subcooled LNG in the recondenser, the BOG and the subcooled LNG are mixed into one stream. Then, the HP LNG pumps send the stream into an open rack vaporizer (ORV) or submerged vaporizer (SCV), which converts LNG to NG for commercial and household users. In some cases, the NG demands are low, and thus LNG cannot recondense all the BOG. Consequently, the HP compressors are employed to send the BOG to the NG pipes. This BOG handling process is simple, but the operating energy consumption is higher than the recondensation way [32].”

Model Formulation

Comment: It is recommended to include, early in this section, a table with Sets and Parameters of the proposed model.

Response: Thanks a lot for your valuable comments. The tables with Sets and Parameters of the proposed model are listed in Tables1 in Section 4.1.

Action:

In Lines 104-114 of the revised manuscript:

Table 1. Environmental variables and related process parameters of optimization.

Comment: L. 124-126: Why the model formulation does not take into consideration the LNG vaporizer? The vaporization rate is directly connected to the volume of LNG pumped from the tank and affects the BOG generated in the storage tank. If there is a specific reason please state explicitly.

Response: Thanks a lot for raising these insightful questions. We considered the energy optimization of the power system during operation. The vaporization is determined by the requirement of uses, which cannot be optimized as an optimization variable, so the LNG vaporizer is not taken into consideration. The generated rate of BOG is assumed to be the function of the differences between the pressure of the gas phase in the tank and the vapor pressure of the LNG (P-P_v), the temperature of LNG (T_L), and the ambient temperature (T_a). The total volume of LNG tank is 640000m³, which is much larger compared to the volume of LNG pumped from the tank (2521m³/h). So it is reasonable to assume that the volume of LNG pumped from the tank has little impact on the BOG generation.

Comment: L. 158: Explain better ??_? .

Response: Many thanks for your valuable comments. We have changed the explanation of ??_? from ‘the driving force’ to ‘log mean temperature difference’ in the revised version in line 202.

Comment: L. 167: From the objective function it seems the goal is to minimize the total energy consumption and no monetary terms is included to justify “min Cost”. The authors should settle upon the goal of the optimization and follow up on this throughout the article.

Response: Many thanks for your valuable comments. We have changed the objective function from ‘min Cost’ to ‘min Energy Consumption’ in the revised version. It is the energy consumption of BOG compressors and LP pumps.

Comment: L. 211-213: Please check and correct the MINLP model. Regarding the objective function (which is equation n.10 not 11) the above comment applies. Furthermore, please note and include explicitly in the objective function the decision variables, which are used to optimize it and establish the non-linear nature of the proposed model.

Response: Many thanks for your valuable comments. We have corrected the objective function (equation 10) in line 212. The decision variables are recirculation flow rate and the operation strategy of BOG compressors and pumps, which have an impact on the objective function.

Action:

In Lines 209-218 of the revised manuscript:

This work aims to obtain the optimal operation condition by minimizing the total energy consumption of the BOG compressors and LP pumps. Based on the developed basic component models, the objective function is defined as follows:

,    (10)

where the item  and   are the electricity consumptions of compressors and LP pumps, respectively. The third one is the penalty item for the complicated operations of compressors, where σ is a small positive penalty coefficient.  is the binary integer variable that indicates whether the operation mode of compressor i at level z is used. For example, using a small number of compressors is better than using several compressors. The index i and j represent the compressor and pump number respectively, and z is the compressor load level.

 Conclusions

Comment: Except for the verification results of the model, the authors should elaborate on the advancements towards current state of the art and possible extension of the research.

Response: Many thanks for your valuable comments. In this work, only one working condition was considered, the LNG receiving terminal could be on unloading condition and HP compressors could be on operation when LNG was not enough to liquefy all BOG. The average temperature of the months was selected to study which was not very suitable since the ambient temperature varies all the time. We have added the advancements towards current state of the art and possible extension of the research in the revised version. For your easy reference, we list the related revision below.

Action:

In Lines 401-406 of the revised manuscript:

The proposed optimization method would significantly contribute to the existing LNG terminals. However, the research was on the condition that the LNG was not unloading and the LNG terminal used a recondenser instead of HP compressors to handle BOG. The other working condition will also be studied in the future. Besides, average temperatures of the months were used in this work, which is not very realistic since the ambient temperature changes all the time.

Author Response File: Author Response.docx

Reviewer 3 Report

This is a technical paper conducting a modelling and simulation based study proposing an optimization method based on mixed-integer nonlinear programming to reduce the energy consumption of a LNG terminal, in particular operating on the boil-off gases compressors.

In my opinion, due to the following comments, the paper is not eligible for publication in the current form:

• Although the topic is good and worth to analyze, the manuscript is ambiguous and hard to catch the original academic contribution for a journal publication. Indeed, as a reader and as energy engineer, I could not catch what is the difference and original idea of this paper comparing to the existing literature. This is a known topic, and the finding itself does not have a big academic contribution. To show the worth of the academic idea, the novelty must be clearly specified thorough analysis and comparison of existing literature is required.
• The authors should describe more extensively the literature presented and, above of all, add more literature works related to the optimization of LNG terminal.
• The authors should further clarify what is the software involved in the thermodynamic calculation and in the optimization algorithm (Hysys, Matlab, GAMS, etc. etc.) and whether a fully dynamic or a modified steady state approach has been applied.
• It is not clear what is the unit system for the energy consumption (kW or kW/h).
• The conclusions section should be further elaborated providing more numerical results.

Author Response

Response to Reviewer 3:

Comment: This is a technical paper conducting a modelling and simulation based study proposing an optimization method based on mixed-integer nonlinear programming to reduce the energy consumption of a LNG terminal, in particular operating on the boil-off gases compressors.

Response: Many thanks for your valuable comments. We will answer your questions one by one.

Comment 1: Although the topic is good and worth to analyze, the manuscript is ambiguous and hard to catch the original academic contribution for a journal publication. Indeed, as a reader and as energy engineer, I could not catch what is the difference and original idea of this paper comparing to the existing literature. This is a known topic, and the finding itself does not have a big academic contribution. To show the worth of the academic idea, the novelty must be clearly specified thorough analysis and comparison of existing literature is required.

Response: Thank you very much for your valuable suggestion. We have added the analysis and comparison of the existing literature. There are many researches on the LNG clod energy recovery, the design optimization of BOG handling process and BOG systems. But there are no published literatures considering the scheduling optimization of LP pumps related to the send-out and recirculation flow rate. The send-out flow rate is determined by the requirements of users. And the recirculation flow rate varies with the ambient temperature since there is a constrain for the temperature difference (∆T) between the inlet and outlet of recirculation pipeline. Besides, we employed a mixed-integer nonlinear programming model to solve the scheduling problems of LNG receiving terminals. We also proposed a model to estimate the generation rate of BOG which is different from the published literatures [28,33,35]. This content has been added in the revised version. For your easy reference, we list the related revision below.

Action:

In Lines 89-94 of the revised manuscript:

“For estimating the generation rate of BOG, a nominal boil-off ratio of 0.05%-1% for the LNG tank capacity per day is used [34,36]. Besides, an empirical equation corrected by the data from the LNG storage tank manufacturers is proposed [28]. In this work, the HYSYS dynamic model of the industrial LNG terminal was developed to generate the data of BOG generation, and the regression model was obtained by the data. Therefore, the model is more suitable for LNG terminal optimization than the methods in the literatures.”

Comment 2: The authors should describe more extensively the literature presented and, above of all, add more literature works related to the optimization of LNG terminal.

Response: Thanks for this comment. We have added more literature works to the paper. For your easy reference, we list the related revision below.

Action:

In Lines 41-94 of the revised manuscript:

The cryogenic operations in an LNG import terminal consume considerable power for driving devices, such as compressors and pumps [13,17]. Energy consumption in LNG import terminals can be reduced in two ways. The first one refers to the LNG cold energy recovery. In the past decades, the recovery of cold energy from the regasification process has became a research hotspot. Around 830 kJ/kg of cold energy are generally stored in per kilogram LNG [18]. Thus, the larger the system, the more cold energy is wasted [19]. Re-searches introduced different LNG cold energy utilization systems and discussed other potential directions beyond electric power generation [11,20,21].

The second way refers to the modeling and optimization of the boil-off gas (BOG) handling process. Due to the low bubble point of LNG, the BOG always arises at terminals and can cause damages [22]. Specifically, the heat will leak to LNG through the tank and the shell of the circling pipeline. Thus, the timely removal of the BOG is important to en-sure the safe operation of the storage tank under the absolute pressure. Excessive amount of the BOG in a tank can result in safety issues, whereas scant amount of the BOG causes an unnecessary waste of energy [23]. Accordingly, these two issues are important to ad-dress in the design and optimization of an LNG terminal.

BOG compressors are used to remove extra gas and ensure the safety of tanks. They have intensive and high-energy properties. Thus, they are the first target for energy saving. The minimization of the total compression energy is the general objective function of the LNG terminals, although many mathematical models of the compressors have been de-veloped and applied in the simulation and optimization of LNG terminals [24-26]. Ter-minals normally used several multi-stage compressors in parallel to keep the BOG flow rate in a specific range. Several investigators have studied BOG compressor systems. Shin et al. proposed a mixed-integer linear programming (MILP) model for optimizing the BOG compressor [27]. A simplified tank model was then proposed to predict the pressure when failure occurred [28]. To improve the accuracy of the model, they lately used the rigorous model developed by Aspen Dynamic simulation [29].

Some researchers focused on the issues of multi-stage compression, multi-stage con-densation, and cooling before or after a compressor in an LNG terminal. For example, Rao et al. used the Nonlinear Optimization by Mesh Adaptive Direct Search (NOMAD) algo-rithm to prove that the two-stage recondensation is superior to other structures[30]. Tak et al. investigated the influences of multi-stage compression on single-mixed refrigerant pro-cesses [31]. Yuan et al. analyzed the parameters in four types of BOG recondensation sys-tems. They compared the power consumptions between the integrated and the non-integrated systems considering the conditions of different BOG components [18].

Various researches recover the LNG cold energy for utilization [11,12,19-21]. Many studies investigate the design optimization of BOG handling process to improve the ener-gy efficiency while ensuring the system safety [32-35]. Studies on BOG compressor sys-tems have also been done [24-29]. But there is only a little focused on the recirculation op-erations. Park et al. determined the optimal recirculation flow rate to reduce operating costs in LNG terminal [15]. Wu et al. built a dynamic simulation model to optimize the re-circulation and branch flow rate [34]. However, there are no literatures that consider the scheduling optimization of LP pumps related to the send-out and recirculation flow rate, to the best of our knowledge. And a mixed-integer nonlinear programming model was first employed to solve the scheduling optimization problem of LNG terminal. For esti-mating the generation rate of BOG, a nominal boil-off ratio of 0.05%-1% for the LNG tank capacity per day is used [34,36]. Besides, an empirical equation corrected by the data from the LNG storage tank manufacturers is proposed [28]. In this work, the HYSYS dynamic model of the industrial LNG terminal was developed to generate the data of BOG genera-tion, and the regression model was obtained by the data. Therefore, the model is more suitable for LNG terminal optimization than the methods in the literatures.

Comment 3: The authors should further clarify what is the software involved in the thermodynamic calculation and in the optimization algorithm (Hysys, Matlab, GAMS, etc. etc.) and whether a fully dynamic or a modified steady state approach has been applied.

Response: Thank you very much for raising this comment. We have further explained the software in the revised version. In this work, the HYSYS dynamic model of the LNG tank was used to produce the data of BOG generation rate varying with the operation. The main program is written by MATLAB. MATLAB provided the initial values to GAMS. Then GAMS solved the model (LNG-OOM) by using DICOPT solver and results was sent back to MATLAB to calculate the tank pressures and judge if a standby compressor should be operated. The dynamic simulation was used to produce the data of BOG generation rate, so there was no need to establish a full dynamic simulation model for the whole LNG receiving terminal.

Action:

In Lines 158-159 of the revised manuscript:

“In this work, the HYSYS dynamic model of the LNG tank was used to generate the data of BOG generation rate varying with the operations.”

In Lines 333-344 of the revised manuscript:

“In the proposed operational optimization framework, the steady-state pressure is first presented to determine whether the results are optimal or not. Meanwhile, the SRK equation of state is selected for the physical property calculation. First, MATLAB provides the initial variables based on the actual operating condition and minimum compressor load. And then the variables are input to GAMS to obtain the optimal recirculation flow rate, number of LP pumps in operation by solving the model (LNGT-OOM). The obtained operation strategy will be sent back to MATLAB and steady-state pressure of the tank can be calculated. If the steady-state pressure is higher than the flare pressure, then the compressor load must be increased, and then a new steady-state pressure is calculated. After the termination condition is achieved, whether a standby compressor needs to be turned on or not must be decided. Finally, the total power consumption of the LP pumps and BOG compressors is obtained.”

Comment 4: It is not clear what is the unit system for the energy consumption (kW or kW/h).

Response: Thanks a lot for this comment. The unit system for the energy consumption is kw. We have corrected the unit in this the revised manuscript.

Comment 5: The conclusions section should be further elaborated providing more numerical results.

Response: Thanks a lot for your valuable suggestion. The conclusion section has been rewritten in the revised version. We provided more numerical results to further elaborated the conclusion. For your easy reference, we list the related revision below.

Action:

In Lines 391-400 of the revised manuscript:

“One BOG compressor and two pumps can be turned off after optimization. The energy consumption can be reduced from 4727.70kw to 3128.30kw and 33.83% energy saving was obtained for the given operating condition. Furthermore, the scenarios of different months were analyzed. From April to October, when the compressor load changed from 19t/h to 14.77t/h and the recirculation flow rate increased from 120t/h to 139.21t/h, the energy consumption can be reduced by 9.15%. From November to March, the optimal operating pressure rose to 124.49kPa due to the decrease of ambient temperatures. The optimized compressor load and recirculation flow rate were 8.44t/h and 122.58t/h, respectively. Compared with the previous period, 26.1% of energy can be saved after optimization. About 16.21% of energy consumption can be saved annually.”

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

The authors effectively improved the quality of the paper that can be accepted for publication. As a minor recommendation, I suggest adding to Figure 4 the block related to the generation of the BOG data through a dynamic model of Aspen HYSYS.

Author Response

Response to Reviewer 3:
Comment: The authors effectively improved the quality of the paper that can be accepted for publication. As a minor recommendation, I suggest adding to Figure 4 the block related to the generation of the BOG data through a dynamic model of Aspen HYSYS.

Response: Thank you very much for your valuable comment. We have further added the block related to the generation of the BOG data to Figure 4. 

Author Response File: Author Response.docx