Heat Transfer Analysis and Operation Optimization of an Intermediate Fluid Vaporizer

Abstract

An intermediate fluid vaporizer (IFV) is a typical vaporizer of liquefied natural gas (LNG), which is used in a large number of LNG terminals. Since it requires a large supply of seawater during its operation, it generates a lot of energy consumption. In this study, to reduce the seawater consumption in the regasification system, the heat transfer process was first numerically calculated, and the heat transfer coefficient of the IFV was determined for different seawater inlet temperatures, seawater flow rates, and LNG flow rates. The calculation results of the heat transfer coefficient were integrated into the numerical model in HYSYS, and the minimum seawater flow of the IFV under different working conditions was obtained. For receiving terminals using multiple IFVs, this study programmed calculations based on optimization software. The operating configuration of the IFVs under different operating conditions was optimized to reduce the consumption of seawater in the regasification system of the LNG terminals.

1. Introduction

Natural gas is considered to be a clean energy source. In recent years, the demand for natural gas in the international market has been continuously increasing. Liquefied natural gas can greatly save space and economic costs for storage and transportation [1,2,3], and China generally relies on LNG for natural gas imports. Therefore, the turnover of LNG terminals is increasing, and the problem of high energy consumption of some equipment in terminals is becoming more and more prominent [4,5,6]. Currently, global environmental problems are becoming more and more prominent, and many countries have introduced policies to control carbon emissions [7,8,9]. Whether in response to the increasingly stringent environmental regulations or to fulfill the corporate social responsibility to protect the environment, reducing the energy consumption of LNG terminals is an urgent task.

Due to its many advantages, the intermediate fluid vaporizer (IFV) has a wide range of applications in LNG terminals [10,11,12,13]. It is the core equipment of the regasification system [14], and therefore, a breakthrough for energy optimization in LNG terminals. From an operational point of view, this vaporizer is very similar to the open rack vaporizer (ORV) in that both use the heat provided by seawater to gasify LNG. The difference is that the ORV uses seawater to heat the LNG directly, while the IFV uses seawater to heat an intermediate fluid with a low boiling point to heat the LNG indirectly, which prevents the seawater from freezing when in direct contact with the LNG. The indirect heating process of an IFV has a combination of multiple heat transfer mechanisms, which makes it necessary to deeply understand the complex internal heat transfer process when analyzing and optimizing it. Many scholars conducted studies on the heat transfer process of IFVs, focusing on aspects such as modeling of the heat transfer process and calculation methods of the heat transfer area, with the goal of enhancing the heat transfer performance for the optimization of IFVs [15]. In order to study the thermal performance of an IFV, Pu et al. [16] developed a lumped model and discussed the effects of LNG pressure, LNG mass flow rate, seawater input temperature, and seawater mass flow rate. Liu Feng et al. [17] studied IFVs in terms of construction, materials, compressive resistance, heat transfer design, and so on. Song Kun et al. [18] analyzed the heat transfer process of an IFV from the viewpoint of heat transfer and thermodynamics and gave the method of heat transfer design of an IFV. Wang Bojie et al. [19] and Chen Zhong [20] both studied supercritical heat transfer in an IFV and analyzed the effect of different operating conditions on the supercritical heat transfer process of LNG. Song Yang et al. [21] studied the heat transfer process of subcooled propane in IFV and analyzed the factors that affect the heat transfer of subcooled fluid.

Many scholars proposed improving IFV performance by changing the type of intermediate fluid. Considering the major requirements for IFVs, the use of some hydrocarbons (e.g., propane, butane, or mixed refrigerants) was suggested [22]. In fact, various hydrocarbons were recently accepted or recommended for refrigeration because of their low cost, availability, and environmental friendliness. These include propylene, propane, isobutane, butane, and dimethyl ether (DME) [23,24,25,26,27,28,29]. However, according to the author’s research on the LNG terminal, the completed IFV will encounter many difficulties when replacing the intermediate fluid. Although changing the intermediate fluid can theoretically bring an improvement to the efficiency of an IFV, the operability of this optimization method is not high.

Making full use of the heat in seawater means gasifying more LNG with less seawater. As a result, the seawater pumps use less electricity, which lowers the overall energy usage. Jesús Betancourt Mena et al. [30] studied the relationship between the capacity of the vaporizer for LNG and the temperature of the seawater. Their research shows that changes in seawater temperature can have an impact on the capacity of the vaporizer and that the increase in seawater temperature is always beneficial for regasification. Shuai Chen and Zhixuan Zhang [31] focused on the energy-efficient operation technology of open-rack vaporizers at low seawater temperatures and pointed out that the key lies in exploring the relationship between the seawater flow rate and the LNG treatment capacity. In other studies, the seawater temperature was generally set above 8 °C. This is because when the seawater temperature is low, the manufacturer of an IFV will recommend disabling the equipment. In this study, however, after investigating the target LNG terminal, it was found that when the seawater inlet temperature was lower than 8 °C, the equipment can also be made to operate by making adjustments to the operating parameters. Meanwhile, the seawater temperature variation at the target LNG receiving terminal ranged from 1.84 °C to 29 °C (the details are shown in Section 3.1), which is beyond the range of others’ studies. Obviously, the operation method of the regasification system in the existing LNG terminal needs to be optimized. Furthermore, the results of previous studies can only be applied to the case of a single IFV scenario, and thus, there is a temporary lack of research on the optimization methods for regasification systems with multiple IFVs.

In summary, this study simulated the heat transfer of an IFV in a larger range of seawater temperatures using a huge LNG terminal in China as the research object. The heat transfer characteristics of the IFV were analyzed based on numerical calculation methods, and key operating parameters, such as the seawater outlet temperature and NG outlet temperature, were obtained. The minimum seawater flow rate for an IFV operation under each condition was analyzed, and an optimized operating configuration was proposed for the regasification system with multiple IFVs installed. This scheme could minimize the consumption of seawater for a regasification system. To ensure that the results of the study were more operable, numerical calculation models were established based on the real data and operation of an LNG terminal, and the optimization effect was verified by the operation practice of an LNG terminal. The findings of this research can serve as guidelines for the operation of an IFV in an LNG terminal to lower that facility’s energy use and carbon emissions.

2. Basic Theories

2.1. Calculation Method of Heat Transfer Characteristics

The IFV investigated in this study consisted of three sections: the propane vaporizer, the LNG vaporizer, and the NG heater [32]. The propane vaporizer and the LNG vaporizer formed a double tube bundle shell and tube heat exchanger with an intermediate fluid (propane) in the shell. The lower tube bundle was submerged below the intermediate fluid level with seawater in the tube; the upper tube bundle was located above the intermediate fluid level with LNG in the tube. The NG heater was structured as a shell and tube heat exchanger with seawater in the tube and NG in the shell. The heat transfer characteristics of the three segments were calculated as follows.

2.1.1. Propane Vaporizer

The flow of seawater in the heat exchanger tube is turbulent, and the heat exchange between seawater and the heat exchanger tube is forced convection heat exchange, where the heat exchange in the seawater tube is described using the Dittus–Boelter formula [33]:

$$Nu=0.023R{e}^{0.8}P{r}^0{}^{.3}$$

(1)

In Formula (1), Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. The Nusselt number is the ratio of the convective to conductive heat transfer at a boundary in a fluid. The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. The Prandtl number is defined as the ratio of the momentum diffusivity to thermal diffusivity. These three numbers are dimensionless.

Liquid propane is heated and vaporized by seawater heat exchange tubes in the evaporator. The pool boiling heat transfer of propane is described using the Cooper formula [34]:

$$h_{\mathrm{e}\mathrm{v}-\mathrm{o}}=90q^{0.67}M{r}^{-0.5}{\mathrm{P}}_{\mathrm{a}}{}^n{(-\lg Pr)}^{-0.55}$$

(2)

In Formula (2), h_ev-o is the surface heat transfer coefficient of the propane vaporizer outside the tube, W/(m²·K); q is the heat flux density, W/m²; Mr is the molar mass, Mr = 44 kg/kmol; P_a = P/P_c, where P_c is the critical pressure of the fluid and P is the saturation pressure of the fluid; and n is a dimensionless coefficient, where n = 0.12–0.21 lgRp (Rp is the average surface roughness, Rp = 0.35 μm).

2.1.2. LNG Vaporizer

The critical state of LNG has a temperature of −82.5 °C and a pressure of 4.54 MPa. For the pressure of LNG in an IFV, the value is generally kept above 8 MPa, which is much higher than its critical pressure and is always supercritical. Regarding the temperature, the LNG vaporizer will cross the critical point. According to the law of physical change of methane in a supercritical state, it is necessary to calculate the LNG in the tube in segments, and when the LNG temperature is lower than the critical temperature, using the following formula for the calculation [35]:

$$Nu=0.0156R{e}^{{}^{0.82}}P{r}^{{}^{0.5}}{\left(\frac{{\mathsf{\rho }}_{\mathrm{w}}}{{\mathsf{\rho }}_{\mathrm{b}}}\right)}^{0.3}{\left(\frac{\mathrm{C}}{{\mathrm{C}}_{\mathrm{p}\mathrm{b}}}\right)}^n$$

(3)

In this formula, ρ_b is the average density of the fluid, kg/m³; ρ_w is the density when the working fluid is the temperature of the heat exchange tube wall, kg/m³; C_pb is the constant pressure-specific heat capacity, J/(kg·K); and C and n are derived from Formula (4):

$$\begin{gathered} n=\{\begin{array}{c}0.4,for{T}_b<T_w<T_{pc}andfor{T}_{pc}<T_b<1.2T_{pc}\\ 0.4+0.2\left(\frac{T_w}{T_{pc}}-1\right),for{T}_b<T_{pc}<T_w\\ 0.4+0.2\left(\frac{T_w}{T_{pc}}-1\right)\left[1-5\left(\frac{T_b}{T_{pc}}-1\right)\right],for{T}_{pc}<T_b<1.2T_{pc}and{T}_b<T_w\end{array} \\ C={\displaystyle {\int }_{T_{pc}}^{T_w}dT/\left(T_w-T_b\right)}=\left(h_w-h_b\right)/\left(T_w-T_b\right) \end{gathered}$$

(4)

In Formula (4), T denotes the temperature, K; the subscript pc denotes a pseudo-critical value; the subscript b denotes an average value; and the subscript w denotes a value based on the tube wall.

The intermediate medium vapor condenses exothermally outside the LNG vaporizer tube, and the heat transfer coefficient of the membrane condensation heat exchange is calculated using the following formula [36,37]:

$$h_{\mathrm{co}-\mathrm{o}}=0.729{\left[\frac{g{\rho }_l{\lambda }_l^{3}r\left({\rho }_l-{\rho }_g\right)}{\mu d\left(T_{sat}-T_W\right)}\right]}^{0.25}$$

(5)

In Formula (5), h_co-o is the heat transfer coefficient of the LNG vaporizer outside the tube, W/(m²·K); g is the acceleration due to gravity, m/s²; ρ_l is the density of the liquid working medium, kg/m³; ρ_g is the density of the gaseous working medium, kg/m³; λ_l is the thermal conductivity of the liquid working medium, W/(m·K); r is the latent heat of vaporization, J/kg; μ is the dynamic viscosity, Pa·s; d is the diameter of the heat exchange tube, m; T_sat is the saturation temperature of propane, K; and T_w is the wall temperature of the heat exchange tube, K. The dimensions, flow rates, temperatures, etc., involved in the formulas mainly refer to the product specifications provided by the IFV manufacturer and are listed in Section 3.1. The thermal properties involved were calculated using REFPROP and the results are presented in Section 3.3.

2.1.3. NG Heater

In the NG heater, the heat exchange between the NG and seawater is done to temper the NG to above 0 °C and meet the LNG terminal’s transmission demands. The formula for calculating heat transfer in tube-side flow is

$$Nu=0.023R{e}^{0.8}P{r}^0{}^{.3}$$

(6)

The formula for the shell-side flow heat transfer is [38]

$$N{u}_f=\{\begin{array}{l}1.04R{e}_f{}^{0.4}P{r}_f{}^{0.36}{\left(\raisebox{1ex}{$P{r}_f$}\!\left/ \!\raisebox{-1ex}{$P{r}_w$}\right.\right)}^{0.25},1<Re<5\times {10}^2\\ 0.71R{e}_f{}^{0.5}P{r}_{f}0.36{\left(\raisebox{1ex}{$P{r}_f$}\!\left/ \!\raisebox{-1ex}{$P{r}_w$}\right.\right)}^{0.25},5\times {10}^2<Re<{10}^3\\ 0.35{\left(\frac{s_1}{s_2}\right)}^{0.2}R{e}_f{}^{0.6}P{r}_f{}^{0.36}{\left(\raisebox{1ex}{$P{r}_f$}\!\left/ \!\raisebox{-1ex}{$P{r}_w$}\right.\right)}^{0.25},\frac{s_1}{s_2}\le 2,{10}^3<Re<2\times {10}^5\\ 0.4R{e}_f{}^{0.6}P{r}_f{}^{0.36}{\left(\raisebox{1ex}{$P{r}_f$}\!\left/ \!\raisebox{-1ex}{$P{r}_w$}\right.\right)}^{0.25},\frac{s_1}{s_2}>2,{10}^3<Re<2\times {10}^5\\ 0.031{\left(\frac{s_1}{s_2}\right)}^{0.2}R{e}_f{}^{0.8}P{r}_f{}^{0.36}{\left(\raisebox{1ex}{$P{r}_f$}\!\left/ \!\raisebox{-1ex}{$P{r}_w$}\right.\right)}^{0.25},2\times {10}^5<Re<2\times {10}^6\end{array}$$

(7)

In Formula (7), s₁ is the longitudinal tube pitch, m; s₂ is the transversal tube pitch, m. The subscript f denotes that the value is based on a fluid and the subscript w denotes that the value is based on the tube wall. In this study, for an NG heater, the heat exchanger tubes were arranged horizontally, s₁ = 25.00 mm, and s₂ = 21.65 mm.

2.1.4. Heat Transfer Coefficient of Each Segment

For the outer side of the heat exchanger tube of a propane vaporizer, LNG vaporizer, and NG heater, the surface heat transfer coefficient can be obtained according to Formulas (2) and (5). For the inner side of the heat exchanger tube of a propane vaporizer, LNG vaporizer, and NG heater, the surface heat transfer coefficient, i.e., h in this paper, can be obtained from the calculated Nu number according to

$$h=Nu\frac{k_f}{L_c}$$

(8)

In Formula (8), h is the surface heat transfer coefficient, W/(m²·K); L_c is the characteristic length, m; and k_f is the thermal conductivity of the fluid, W/(m·K).

IFV heat transfer through circular tube walls: Assume that the length of the circular tube is L, the inner diameter is d_i, the outer diameter is d_o, the thermal conductivity of the tube wall material is λ_w, the temperature of the fluid in the tube is T_fi, and the surface heat transfer coefficient of the inner wall of the tube is hi. The temperature of the fluid outside the tube is T_fo (T_fi > T_fo), and the surface heat transfer coefficient of the outer wall of the tube is h_o. The surface area of the inner wall of the tube is A_i = πd_iL, and the surface area of the outer wall of the tube is A_o = πd_oL [39]. In the equations below, the subscript i indicates in the tube and the subscript o indicates outside the tube.

The heat transfer is given as

$$\varphi =\frac{1}{\frac{1}{A_i{h}_i}+\frac{1}{2\pi L{\lambda }_w}\ln \frac{d_o}{d_i}+\frac{1}{A_o{h}_o}}(T_f{}_i-T_{fo})$$

(9)

Multiplying the numerator and denominator on the right-hand side of the equation by A_o at the same time, we obtain

$$\varphi =\frac{1}{\frac{1}{h_i}\frac{d_o}{d_i}+\frac{d_o}{2{\lambda }_w}\ln \frac{d_o}{d_i}+\frac{1}{h_o}}{A}_o(T_f{}_i-T_{fo})$$

(10)

In engineering, the outer surface area of the tube is generally used as the heat transfer area. Combining the above formulas, we can obtain the formula for the overall heat transfer coefficient K:

$$K={\left(\frac{1}{h_i}\frac{d_o}{d_i}+\frac{d_o}{2{\lambda }_w}\ln \frac{d_o}{d_i}+\frac{1}{h_o}\right)}^{-1}$$

(11)

2.2. Mathematical Model of IFV Operation Optimization Configuration

2.2.1. Model Assumptions

In order to ensure the validity and accuracy of the model and to avoid the influence of uncontrollable factors that an IFV may be subject to during actual operation, the following assumptions were made:

• The seawater temperature will not affect the energy consumption of the seawater pumps;
• The seawater pumps supply seawater to IFVs with fixed energy consumption per unit mass flow of seawater;
• Each IFV performs consistently and operates in ideal conditions;
• The quality of seawater remains unchanged and the physical parameters are the same as those of pure water;
• The flow of seawater and LNG into the IFV can be controlled continuously.

2.2.2. Objective Function

The minimum seawater flow rate of the LNG regasification system was taken as the objective function. Under the premise of satisfying the regasification flow rate, the Q_m of the LNG terminal, and the process parameters of regasification, the optimal IFV start-up scheme and flow distribution scheme were found [40,41]. The optimization objective function was established as follows:

$$\min G\left(x,t,q\right)={\displaystyle \sum _{i=1}^a{x}_{i}H\left(t,q_i\right)}$$

(12)

In Formula (12):

• G—total seawater flow rate of the regasification system, t/h;
• a—total number of IFVs;
• x_i—operating status of the ith IFV, where 1 means on and 0 means off;
• t—seawater inlet temperature of the IFVs, °C;
• q_i—LNG flow rate of the ith IFV, t/h;
• H(t, q_i)—seawater flow required for the ith IFV to operate at the seawater inlet temperature t, °C, and LNG flow q_i, t/h.

2.2.3. Restrictions

(1)

IFV operation flow constraints

The LNG terminal had a stable supply of natural gas to the market, and needs to meet the flow constraints of its flow adjustment range and regasification volume requirements:

$$x_i{q}_{\min }\le x_i{q}_i\le x_i{q}_{\max }$$

(13)

If the LNG flow rate is too low, the heat transfer performance of the IFV will deteriorate. Therefore, q_min was set to 40 t/h. The maximum seawater flow of IFV was related to the seawater temperature.

(2)

Constraints on the output volume of the regasification system

In the LNG terminal, the LNG regasification and transmission system must meet the requirements of the regasification and transmission volume:

$$Q_m={\displaystyle \sum _{i=1}^a{x}_i}{q}_i$$

(14)

In Formula (14), Q_m is the output demand of the LNG regasification system, t/h.

3. Case Study

3.1. Project Overview

The vaporizer setup in the LNG terminal investigated in this study includes eight IFVs. The structure of the IFVs in the terminal is shown in Figure 1, and the key parameters are shown in

Table 1. Key parameters of the IFV.

Parameter	Value	Parameter	Value
LNG inlet temperature (°C)	−160	E2 number of heat exchange tubes	810
LNG inlet pressure (MPa)	9.91	E2 heat exchange tube length (mm)	9000
LNG outlet pressure (MPa)	9.71	E2 heat exchange tube outer diameter (mm)	15.9
NG output temperature (°C)	≥1	E2 heat exchange tube wall thickness (mm)	1.6
Number of vaporizers	8	E2 heat exchange area (m2)	1018.4
E1 number of heat exchange tubes	3152	E3 number of heat exchange tubes	2893
E1 heat exchange tube length (mm)	9008	E3 heat exchange tube length (mm)	3910
E1 heat exchange tube outer diameter (mm)	19.05	E3 heat exchange tube outer diameter (mm)	19.05
E1 heat exchange tube wall thickness (mm)	1.2	E3 heat exchange tube wall thickness (mm)	2
E1 heat exchange area (m2)	1908.2	E3 heat exchange area (m2)	805.94

. In Figure 1, E1 is the propane vaporizer, E2 is the LNG vaporizer, and E3 is the NG heater. The heating medium is seawater, and the flow rate is basically between 6000~7500 t/h before optimization. According to the IFV’s operating theory, the LNG is warmed from −150 °C to −50 °C by seawater heating the intermediate fluid, causing it to evaporate. The intermediate fluid then exceeds the liquid surface and enters the upper gas phase area, where it meets the upper pipe bundle. The heat-absorbed LNG vaporizes and warms up, then enters the NG heater to continue heating and warming it up to more than 1 °C [42].

For the seawater temperature, the seawater temperature around the receiving station was counted from 2021, using noon as the daily recording point. The highest seawater temperature of 29 °C was recorded on 9 August 2021. The lowest temperature of 1.94 °C was recorded on 28 January 2022. While the temperature of the seawater varied the most between winter and spring, the seawater temperature was around 20 °C for most of the time. In this study, the range of seawater temperature considered was 2–30 °C.

3.2. Numerical Simulation

Combining the results of numerical simulations with heat transfer calculations, the effects of different seawater temperatures, seawater flow rates, and LNG flow rates on the heat transfer efficiency of the IFV could be obtained. The variations in the seawater inlet temperature, seawater mass flow rate, and LNG mass flow rate all had significant effects on the heat transfer performance of the IFV. Since the heat transfer area of the IFV was fixed, after obtaining the heat transfer efficiency under various operating conditions, the KA value could be calculated and then input into the HYSYS model (in the software, the overall heat transfer coefficient K is denoted by the symbol U). In this way, data such as the seawater outlet temperature and NG outlet temperature could be obtained, and the variation pattern of the IFV operation parameters under various conditions could be simulated. The HYSYS-based IFV process simulation is shown in Figure 2.

In Figure 2, flow 1 refers to the LNG input; flow 8 refers to the NG output; flows 2, 3, and 6 refer to seawater flow; flows 4 and 5 refer to intermediate fluid flow; E-100 refers to the LNG vaporizer; E-101 refers to the propane vaporizer; and E-102 refers to the NG heater.

The simulation was performed in HYSYS using the model. The model in this study was simplified. For example, this study ignored the heat loss indicated in papers such as reference [43]. The reason for performing this series of simplifications was that we found the studies that focused mainly on the heat transfer process of IFV, such as reference [29], did not take into account the heat loss and other factors, making the calculation process easier. To demonstrate the feasibility of this simplification, we compared the calculated results with the measured data. Taking the seawater inlet temperature of 25.5 °C and the LNG inlet flow rate of 168.4 t/h as an example, the calculated value of the NG outlet temperature was 21.67 °C and the measured value on site was 21.90 °C, with an error of −1.05%. The calculation results were very close to the field data, and although there were some errors, in general, the results matched well with reality.

3.3. Thermal Properties of the Working Fluid

In this calculation, propane was selected as the intermediate fluid, while LNG and seawater were simplified to be considered pure methane and pure water, respectively. This simplification was proposed by reference [29]. In this study, the thermal properties are obtained from REFPROP and the thermal properties of methane are shown in Figure 3.

4. Results

In this section, calculations for the surface heat transfer coefficient and the overall heat transfer coefficient of the propane vaporizer, the LNG vaporizer, and the NG heater are presented. The surface heat transfer coefficient is h in Section 2.1 and the overall heat transfer coefficient is K in Section 2.1.

4.1. Calculation Results of Propane Vaporizer

In the propane vaporizer, the tube-side fluid of the heat exchanger was seawater, and the shell-side fluid was propane. The seawater temperature was controlled at 288 K, and the surface heat transfer coefficient of E1 was studied when the mass flow rate of seawater was 5500 t/h~7500 t/h. The variation in the surface heat transfer coefficient of E1 with the mass flow rate of seawater is shown in Figure 4.

As can be seen from Figure 4, with the increase in seawater mass flow rate, the surface heat transfer coefficient showed an increasing trend, which was due to the increase in seawater turbulence in the seawater tube with the increase in seawater mass flow rate. With the increase in Reynolds number, the heat transfer resistance between the seawater and the tube wall decreased, thus increasing the surface heat transfer coefficient.

The variation interval of seawater temperature in the area where the target LNG terminal was located was 274 K~305 K. The mass flow rate of seawater was controlled to be 7000 t/h during the study, and the influence of seawater temperature on the heat transfer coefficient was studied by changing the seawater inlet temperature. The variation in the shell-side heat transfer coefficient with seawater temperature is shown in Figure 5.

Analysis of the variation curve of the shell-side heat transfer coefficient with seawater temperature showed that with the increase in seawater temperature, the shell-side heat transfer coefficient also increased. As the seawater temperature increased, the boiling heat transfer outside the tube was enhanced, and thus, the shell-side surface heat transfer coefficient increased.

The pressure of the intermediate fluid was mainly influenced by the seawater temperature, which, in turn, significantly affected the surface heat transfer coefficient of the shell side of the propane vaporizer. By varying the working pressure of the intermediate medium, the variation curve of the surface heat transfer coefficient on the shell side with the seawater temperature was found, with the results shown in Figure 6.

During the operation of an IFV, the change in seawater temperature will cause a large fluctuation in the propane working pressure, which may lead to a reduction in heat transfer. As can be seen from Figure 6, when the seawater temperature varied from 5 °C to 25 °C, the higher surface heat transfer coefficient was located in the range of 300 kPa to 400 kPa, and keeping the pressure of propane in this range could effectively improve the IFV’s performance. Therefore, in this study, by default, the IFV was operated with the optimal propane pressure at each seawater temperature, and the calculations were based on this.

The seasonal influence on seawater temperature was considered by adjusting the seawater outlet temperature and NG outlet temperature. The temperature and flow rate of seawater are the main variables during IFV operation. Therefore, the effect of seawater temperature and mass flow rate on the overall heat transfer coefficient was investigated, and the trend of the overall heat transfer coefficient is shown in Figure 7.

As can be seen from Figure 7, the overall heat transfer coefficient increased with the increase in seawater mass flow rate and seawater temperature in E1. As the seawater temperature increased, the increasing rate of the overall heat transfer coefficient increased. Furthermore, the larger the seawater mass flow rate was, the greater the effect of the seawater temperature on the overall heat transfer coefficient. Compared with the influence of the seawater temperature on the overall heat transfer coefficient, the influence of the seawater mass flow rate on the overall heat transfer coefficient was relatively small.

4.2. Calculation Results for the LNG Vaporizer

In the LNG vaporizer, the tube-side fluid of the heat exchanger was LNG and the shell-side fluid was propane vapor. Combined with the adjustment range of the LNG regasification volume by the IFV in the target LNG terminal, the surface heat transfer coefficient of the LNG vaporizer at different LNG mass flow rates was studied and the results are shown in Figure 8.

With the increase in the LNG inlet mass flow rate, the tube-side surface heat transfer coefficient of E2 increased. This was because the increase in the LNG flow rate led to a slight change in the laminar sublayer by increasing Re. As a result, the surface heat transfer resistance between the LNG and the tube wall was reduced and the surface heat transfer coefficient on the tube side of E2 was increased. A higher LNG flow rate required a higher heat duty, which inherently led to higher propane condensation rates and a larger film thickness. The increase in condensate thickness caused an increase in the shell-side thermal resistance of E2, resulting in a decreasing trend for the shell-side surface heat transfer coefficient.

By setting the variation range of the LNG inlet temperature from 108 K to 123 K, the subsequent variation in the heat transfer coefficient of E2 was investigated. By keeping the mass flow rate of LNG at 160 t/h during the calculation, the variation curve of the heat transfer coefficient is shown in Figure 9.

The thermal conductivity of LNG decreased with increasing temperature, and at the same time, as the temperature of the LNG inlet increased, the temperature difference between inside and outside the heat exchanger tube was reduced, and the heat flow rate decreased at the same LNG flow rate, making the propane condensation rate decrease. As a result, the shell-side propane condensate film thickness decreased, resulting in a tendency for the shell-side surface heat transfer coefficient to increase.

According to the operating data of the target LNG terminal of this study, the LNG inlet flow rate and temperature were adjusted to obtain the overall heat transfer coefficient variation as shown in Figure 10.

With the increase in the LNG inlet temperature, the overall heat transfer coefficient gradually increased, while the effect of the LNG inlet temperature on the overall heat transfer coefficient was small. As the LNG mass flow rate increased, the surface heat transfer coefficient of E2 increased on the tube side and decreased on the shell side, and the overall heat transfer coefficient showed a decreasing trend. The overall heat transfer coefficient was inversely related to the LNG mass flow rate. In the range of the LNG flow rate specified by the IFV, the smaller the LNG mass flow rate, the larger the overall heat transfer coefficient. Therefore, when the seawater temperature was low, reducing the LNG mass flow rate could effectively increase the NG outlet temperature.

4.3. Calculation Results for the NG Heater

In the NG heater, the tube side fluid was seawater, and the shell side fluid was NG. Combined with the adjustment range of the seawater flow rate of the seawater pump in the target LNG terminal, the surface heat transfer coefficient of the NG heater at different seawater mass flow rates was studied.

As shown in Figure 11. With the increase in the seawater mass flow rate and the seawater temperature, the surface heat transfer coefficient on the tube side gradually increased. The increase in seawater mass flow rate at the same seawater temperature increased the degree of turbulence in the seawater tube, influenced the turbulence and mixing on the inner wall of the tube, and strengthened the forced convection heat transfer process. As the seawater temperature increased, the dynamic viscosity of the fluid decreased, which also increased the degree of turbulence in the seawater tube and strengthened the heat transfer on the tube side.

It can be seen from Figure 12 that when the seawater mass flow rate ranged from 5000 t/h to 7500 t/h and the seawater temperature ranged from 5 °C to 30 °C, the extreme value of the variation in the surface heat transfer coefficient of the shell side was only 9 W/m²⸱K. This shows that the change in operating parameters of seawater in the NG heater had little effect on the surface heat transfer coefficient of the shell side.

The variation in the overall heat transfer coefficient in the NG heater is shown in Figure 13. With the increase in seawater mass flow rate and the seawater temperature, the overall heat transfer coefficient increased. In this process, the change in the shell-side surface heat transfer coefficient was small, and the change in the overall heat transfer coefficient was mainly influenced by the tube-side surface heat transfer coefficient.

5. Discussion

In this study, several factors that influenced the operation of the IFV were analyzed: seawater flow rate, seawater temperature, and LNG flow rate. In the following, the analysis results of the minimum seawater flow of the IFV are presented, and the optimal configuration method of the IFV in the regasification system is proposed.

5.1. Minimum Seawater Flow Rate Analysis of the IFV

For IFVs, handling larger LNG flows with smaller seawater flows is the main goal of optimization, which means that the heat carried by the seawater needs to be fully utilized, i.e., the temperature difference between the seawater inlet and outlet needs to be as large as possible within the allowed range. The seawater flow rate has an impact on the seawater inlet and outlet temperature difference. For the same seawater temperature and LNG flow rate, the higher the seawater flow rate, the lower the difference between the seawater inlet and outlet temperature, as shown in Figure 14.

By law, the temperature difference between the seawater inlet and outlet needs to be controlled to 5 °C or lower. A lower limit of seawater flow exists to ensure that the equipment operates within the limits allowed by the regulations. The lower limit of seawater flow is also influenced by the LNG flow rate. All other things being equal, the LNG flow rate significantly affects the seawater outlet temperature, and the higher the LNG flow rate, the greater the temperature difference between the seawater inlet and outlet, as shown in Figure 15. Therefore, the LNG treatment capacity needs to be strictly limited for each IFV operating at the lower limit of the seawater flow, and the maximum treatment capacity at each seawater flow rate and seawater temperature is shown in Figure 16.

When the IFV is operating, it is also necessary to ensure that the NG outlet temperature is higher than specified. The NG outlet temperature is also affected by seawater flow rate, seawater temperature, and LNG flow rate, but the LNG flow rate is the main influencing factor. The option of increasing the seawater flow to increase the NG outlet temperature was not considered as the effect of the seawater flow on the NG outlet temperature was minimal. If the NG outlet temperature does not meet the outgoing demand when the equipment is operating at the lower limit of seawater flow, only the LNG flow rate reduction needs to be considered. When the LNG terminal operates in IFVs, the NG outlet temperature is also generally controlled by controlling the LNG flow rate. In the LNG terminal investigated in this study, for example, the NG outlet temperature needed to reach above 1 °C. In this way, the minimum seawater flow rate was calculated for each LNG flow rate and seawater temperature, as shown in Figure 17.

5.2. Fitting of the Minimum Seawater Flow Rate

In the following, the relationship among the seawater flow, seawater temperature, and LNG flow was fitted to facilitate the subsequent optimization solution. To avoid the situation of seawater freezing, the IFV will stop operation when the seawater temperature is lower than 1 °C. The change law between the three will change greatly around 6 °C, and thus, two functions were calculated in the fitting, with 6 °C as the boundary to ensure the accuracy of the fitting.

The fitting results are shown in Figure 18. When the seawater temperature was higher than 6 °C, the relationship between seawater flow, seawater temperature, and LNG flow could be expressed using Formula (15); when the seawater temperature was lower than 6 °C, the relationship among the three could be expressed using Formula (16).

$$\begin{array}{l}{y}_1=587400+9972x+3312t+254.7x^2+171.9xt-313.2t^2\\ -1.064x^3+1.187x^{2}t-4.583x{t}^2+10.92t^3\end{array}$$

(15)

$$\begin{array}{l}{y}_2=7091000+763300x-11880000t-7808x^2-108300xt+2978000t^2\\ +36.09x^3+360.7x^{2}t+5698x{t}^2-221000t^3\end{array}$$

(16)

where x is the LNG flow rate of IFV, t/h; t is the seawater inlet temperature of the IFV, °C; y₁ is the minimum seawater flow rate under the specified state when the seawater temperature is higher than 6 °C, t/h; and y₂ is the minimum seawater flow rate under the specified state when the seawater temperature is lower than 6 °C, t/h.

5.3. Optimization Results

The mathematical model for the optimal configuration of the IFV operation was solved using optimization software. The fitting results of the minimum seawater flow above were input into the objective function, and then the boundary conditions were determined by combining the field conditions and the results obtained from the previous numerical calculations [44,45]. Based on the objective function and boundary conditions, the software was programmed to finally calculate the optimal seawater flow and LNG flow allocation that satisfied the constraints. In this study, a mixed-integer nonlinear programming (MINLP) model was used. The variable x_i in Formula (11) was a discrete variable and the rest of the variables were continuous. For this model, the problem was solved using the optimization software LINGO. The calculation results interface is shown in Figure 19.

Running the IFVs based on this calculation result could minimize the total seawater flow rate of the regasification system while ensuring that the total output volume met the requirements. After the optimization, the corresponding seawater flow and LNG flow for each IFV were matched according to the seawater temperature and a new operation scheme was obtained. The optimization results under some typical working conditions are shown below. The LNG outputs included 782.6 t/h and 462.3 t/h; the corresponding seawater temperatures were 8 °C and 20 °C. In

Table 2. IFV operation configuration scheme with a total processing capacity of 782.6 t/h and seawater temperature of 8 °C.

		IFV (A)	IFV (B)	IFV (C)	IFV (D)	IFV (E)	IFV (F)	IFV (G)	IFV (H)	Total
Before	QLNG	103.7	101.8	104.6	123.7	120.5	0	104.6	123.7	782.6
	QSW	6776.2	6596.7	7365.3	6223.1	6723.8	0	6288.7	6254.7	46228
After	QLNG	109.4	109.4	109.4	109.4	109.4	109.4	65.3	65.3	787
	QSW	4786.3	4786.3	4786.3	4786.3	4786.3	4786.3	2866.6	2866.6	34,451

and

Table 3. IFV operation configuration scheme with a total treatment capacity of 462.3 t/h at a seawater temperature of 20 °C.

		IFV (A)	IFV (B)	IFV (C)	IFV (D)	IFV (E)	IFV (F)	IFV (G)	IFV (H)	Total
Before	QLNG	136.1	139.9	0	29.6	154.6	0	0	25.6	485.8
	QSW	6929.4	7088.9	0	6662.1	7164.6	0	0	5725.5	33,570
After	QLNG	147.6	169.1	169.1	0	0	0	0	0	485.8
	QSW	6202.2	5667.9	5667.9	0	0	0	0	0	15,943

, Q_LNG means the mass flow rate of LNG, t/h; Q_SW means the mass flow rate of seawater.

According to the results of the on-site investigation at the LNG terminal, before optimization, the flow rate of seawater was generally controlled between 6000–7500 t/h, and major adjustments were not made according to changes in external transportation conditions and environmental conditions. There was no obvious law in the control of the LNG flow rate, and only the number of IFVs to be opened was limited. These two points caused large amounts of seawater waste. According to Table 2 and Table 3, it was found that the seawater flow rates of the IFV could be greatly reduced by using software for operation optimization, which were reduced by 11.8 t/h and 13.8 t/h, respectively. This was because the optimized LNG flow of each IFV was intentionally controlled according to the calculation results, and the heat in the seawater was applied as much as possible by adjusting the LNG flow and seawater flow rate.

6. Conclusions

In this study, the heat transfer process of the IFV was numerically calculated and the heat transfer coefficients of the IFV were determined for different seawater inlet temperatures, seawater flow rates, and LNG flow rates. Based on the numerical model in HYSYS, the minimum seawater flow rate of the IFV under different operating conditions was determined. In addition, for the LNG terminal using multiple IFVs, this study optimized the operating configuration of the IFVs under different operating conditions based on software programming calculations to reduce the consumption of seawater in the regasification system of the LNG terminal. The following conclusions were obtained:

• A heat transfer calculation model was established based on the IFV used in the target LNG terminal investigated in this study, and the IFV was divided into three sections: the LNG vaporizer, the propane vaporizer, and the NG heater. The heat transfer coefficients of each section were calculated according to the corresponding equations. The results showed that with the increase in seawater mass flow rate, the overall heat transfer coefficient increased significantly in E1, increased slowly in E3, and remained almost unchanged in E2; with the increase in seawater temperature and the decrease in seawater viscosity, the overall heat transfer coefficient increased significantly in E1 but remained unchanged in the other two sections; with the increase in the LNG mass flow rate, the overall heat transfer coefficient increased slightly in each section.
• The KA value of IFV under different conditions was obtained through the results of numerical calculations and then calculated for different operating conditions through HYSYS. The calculation results showed that the decrease in seawater flow rate or the increase in LNG flow rate increased the temperature difference between the inlet and outlet of seawater, and thus, the maximum processing capacity and minimum seawater flow rate of the IFV under various working conditions were calculated. The NG outlet temperature increased with the increase in the seawater inlet temperature and decreased with the decrease in the LNG flow rate. However, the seawater flow had little effect on the NG outlet temperature. Therefore, when the equipment was operating at the lower limit of seawater flow, if the NG outlet temperature did not meet the demand for external transportation, reducing the LNG flow was the best method.
• Based on the results of the minimum seawater flow analysis, the relationship between the minimum seawater flow rate, seawater temperature, and the LNG flow rate was fitted using MATLAB. Due to the physical characteristics of seawater and IFV operation requirements, two cases of seawater inlet temperatures higher than 6 °C and lower than 6 °C were fitted separately, and finally, the two binary cubic polynomials listed in the study were obtained.
• When operating an LNG terminal, the seawater flow rate and LNG flow rate of the IFV should be flexibly adjusted according to different seawater temperatures and transmission demands. The optimal IFV operation configuration method for different conditions was found using the programming calculations of the software used in this study. After inputting the seawater temperature and the total transmission volume, the LNG flow rate and seawater flow rate allocation of each IFV in the regasification system were calculated so that the consumption of seawater in the regasification system was minimized. It ensures that the heat in seawater was fully utilized, effectively reduced the consumption of seawater, and provided a reference for the operation of the LNG terminal.