Parameter Analysis of CO2 Capture with Anti-Sublimation Process

The anti-sublimation CO2 capture technology has attracted the attention of researchers due to its advantages such as no pollution and high product purity. The anti-sublimation process is the core link of this technology, so the study of this process is of great significance to the low-temperature capture system. At present, there are few research works on the CO2 anti-sublimation process. In order to study the influence of key parameters on the capture performance during CO2 anti-sublimation, a one-dimensional steady-state of CO2 anti-sublimation process in a double pipe heat exchanger was established based on the mixture gas of N2 and CO2. The effects of cooling nitrogen inlet temperature, mixture gas velocity and pressure on the CO2 volume fraction, deposition rate distribution, capture rate and valid capture length are investigated. Optimal operation parameters are obtained, which could be used to provide guidance for parameter setting and design of anti-sublimation heat exchanger.


Introduction
According to statistics from the International Energy Agency, the global energy-related carbon dioxide emissions in 2018 reached the highest level in history of 3.31 billion tons [1]. Currently, there are four ways for the post-combustion method of CO 2 capture: solvent absorption, solid sorbent adsorption, low-temperature separation, and membrane separation [2]. The anti-sublimation CO 2 capture technology has attracted the attention of researchers due to its advantages such as no pollution, high product purity and so on. In the low-temperature separation and capture system, CO 2 change from gaseous state to solid state directly in the anti-sublimation heat exchanger. Due to the significance of the CO 2 antisublimation process in low-temperature CO 2 capture system, it is worth investigating the contributing factors in this process.
Currently, the research on the CO 2 anti-sublimation process mainly focuses on simulation study. Chang et al. [3,4] proposed a heat and mass transfer model for CO 2 anti-sublimation process of landfill gas (CH 4 and CO 2 ), and showed the effects of mixture gas at different CO 2 mole fractions or N 2 to CO 2 mass flow rate ratios on the performance parameters. Yu et al. [5] developed a numerical model of the heat and mass transfer processes in a CO 2 -N 2 gas mixture anti-sublimation cross-flow finned duct heat exchanger system to predict the heat transfer from gas mixture to liquid nitrogen and the anti-sublimation rate of CO 2 in the gas mixture. Naletov et al. [6,7] proposed a quasi-nonstationary mathematical model of the anti-sublimation of carbon dioxide from purified flue gases of heat power systems and obtained the optimal operation estimates and engineering solution. Wang et al. [8] developed a transient model for analyzing the CO 2 anti-sublimating in mixture gas, and drew a conclusion that a low energy consumption will be obtained at high concentration and low flow velocity of CO 2 supply.
From the above, these studies mainly focused on the temperature distribution of the cold and hot fluids and the CO 2 deposition rate when the state parameters of the hot and cold fluid inlets (such as the initial CO 2 mole fraction, the cooling nitrogen inlet temperature, etc.) change during the anti-sublimation capture process. In addition, in the study of the carbon dioxide capture system, some researchers have investigated the effect of the mixture gas inlet pressure on capture system performance. Result show that the change of inlet pressure of the mixture gas could have a great impact on the capture system performance, such as Song et al. [9]. The studies about parameter characteristics are summarized in Tab. 1. In terms of operating parameters, there is a lack of the influence of mixture gas pressure on the anti-sublimation process. Besides, in terms of performance parameters, there is a lack of comprehensive consideration of the valid capture length and capture rate, which could guide the optimal design of the heat exchanger equipment in the anti-sublimation process. Based on this point, future research was completed in this article.
In this paper, a one-dimensional steady-state anti-sublimation process numerical model of CO 2 in N 2 and CO 2 mixture gas was developed. Based on a double-pipe heat exchanger, the model considered the influence of the CO 2 deposition on the heat and mass transfer process, and added the valid capture length to performance parameters to evaluate the capture result comprehensively. Study on the effects of cooling nitrogen inlet temperature, mixture gas flow rate and pressure change on CO 2 volume fraction, deposition rate and distribution, initial anti-sublimation point location, valid capture length and capture rate has been performed. This can not only determine the appropriate boundary conditions of the anti-sublimation process, but also provide guidance for the design of heat exchanger length and position of requiring heat transfer enhancement.

Numerical Model
As shown in Fig. 1, a one-dimensional steady-state model of CO 2 anti-sublimation process is proposed based on a double-pipe heat exchanger. The mixture gas and cooling nitrogen flow reversely in the heat exchanger. The subscript m represents the mixture gas, and the subscript c means the cooling nitrogen, and the temperature of the tube near the mixture gas and cooling nitrogen are T w,m and T w,c respectively. Gas and heat exchanger tube wall temperature, Initial anti-sublimation point location, Tube length, CO 2 deposition rate Yu et al. [5] Cooling nitrogen inlet temperature, Number of heat exchanger fins CO 2 mass flow rate, deposition rate, deposition thickness Naletov et al. [6,7] Time Gas temperature, CO 2 mass flow rate, Deposition rate Wang et al. [8] Time, Initial wall temperature, Inlet CO 2 fraction, Flow velocity of mixture gas Gas temperature, Wall temperature, CO 2 deposition rate, Capture rate, Energy consumption The entire length of heat exchanger is divided into N nodes. When the temperature of the mixture gas drops to the anti-sublimation temperature corresponding to the CO 2 partial pressure at that node, CO 2 antisublimation process occurs. The main assumptions are as follows: (1) The parameters have no radial gradient and it is a one-dimensional steady-state model.
(2) The pressure drop, axial heat conduction and radiant heat leakage are ignored.
(3) The mixture gas and cooling nitrogen are considered to be an ideal gas.

CO 2 Anti-Sublimation Temperature
CO 2 anti-sublimation temperature is calculated by PR equation of state and gas-solid fugacity equation [10].
The solid phase CO 2 product obtained by the CO 2 anti-sublimation capture technology has high purity and it can reach 99% without further purification [7,11]. Therefore, it can be considered that the deposition layer is composed of pure solid CO 2 . In order to calculate the frosting temperature of CO 2 in different components and different pressures in the binary system, the gas-solid fugacity equation is established, as shown in the following equation: where Df V ÀS CO 2 ðT m Þ is the gas-solid phase fugacity difference at T m , x CO 2 is the mole fraction of CO 2 in vapor phase, f V CO 2 is the CO 2 vapor phase fugacity, P m and T m are the mixture gas pressure (kPa) and temperature (K) respectively, P Sat CO 2 Solid is the CO 2 saturation pressure corresponding to the mixture gas temperature, f Sat CO 2 is the mixture gas temperature corresponding to the fugacity coefficient of pure CO 2 , v CO 2 Solid is the molar volume of solid CO 2 .

Anti-Sublimation Process Model
The sum of convective heat from gas mixture and CO 2 latent heat equal to the convective cooling by the cooling nitrogen, and equal to the heat transfer of the wall: Figure 1: Model of double-pipe heat exchanger P 1 and P 2 are the heat transfer perimeters (m) on both sides of the inner tube, i ig is the latent heat of phase transition of CO 2 (J/kg), D _ m CO 2 is CO 2 deposition rate (10 -6 kg·m −1 ·s −1 ), λ d is the equivalent thermal conductivity of the wall and the deposition layer (W·m −1 ·K −1 ), r 1 and r 2 are the inner and outer radius of the inner tube (m), and h is the heat transfer coefficient (W·m −2 ·K −1 ).
According to the equal heat flux, the equivalent thermal conductivity λ d can be obtained by the equation: where th is the thickness of the deposition layer (m). Assuming that the deposition layer is evenly distributed in the radial and circumferential directions, then: where dV CO 2 is the CO 2 deposition volume (m 3 ) on the each node, dV CO 2 ¼ pðR 2 2 À r 2 2 Þdx, R 2 is the equivalent outer radius (m) of the tube wall and the deposition layer.
The density of the solid CO 2 (kg/m 3 ) is [13]: The steady-state flow energy balance equations of mixture gas and cooling nitrogen are as follows: where _ m is the mass flow rate (kg/s), c p is the constant pressure specific heat capacity (J·kg −1 ·K −1 ).
The mass flow rate of N 2 in the mixture gas is unchanged. Before the mixture gas cools down to the CO 2 anti-sublimation temperature, the CO 2 mass flow rate remains unchanged; after reaching the anti-sublimation temperature, the CO 2 mass flow rate decreases.
where h D is the mass transfer coefficient (m/s), q CO 2 is the CO 2 density (kg/m 3 ), q SatðT w;m Þ is the CO 2 saturation density (kg/m 3 ) at the wall temperature.
The mass flow rate and density of N 2 and CO 2 in the mixture gas are expressed as: where u m is the average flow rate of the mixture gas (m/s), A m is the mixture gas flow area (m 2 ), P CO 2 is the partial pressure of CO 2 in the mixture gas (kPa), R N 2 , R CO 2 are the gas constant of N 2 , CO 2 (J·kg −1 ·K −1 ).
The heat and mass transfer coefficient can be calculated by analogy with fully developed flow heat and mass transfer: The friction coefficient f is a function of Reynolds number Re: The Schmidt number Sc is related to the diffusion coefficient D (m 2 /s): where v, μ are the kinematic viscosity coefficient (m 2 /s), the momentum viscosity coefficient (m 2 /s).
The calculation of CO 2 anti-sublimation process is shown in Fig. 2. The main input parameters are the gas inlet pressure, temperature, flow rate, mixture gas inlet CO 2 volume fraction and the initial iteration value of cooling nitrogen outlet temperature. Finally get parameters such as CO 2 deposition rate, volume fraction, and capture rate.

Performance Indicator
In this paper, there are four indicators to evaluate the performance of the anti-sublimation capture process: (1) Capture rate: the ratio of CO 2 anti-sublimation amount on the total amount of CO 2 in the inlet gas mixture.
(2) Initial anti-sublimation point position x 1 : the point where CO 2 begins changing from the gas phase to the solid phase, as shown in Fig. 3a. The earlier the initial anti-sublimation point is, the more uniform heat transfer between two fluids.
(3) Valid capture length L 1 : as shown in Fig. 3a, it is derived from the CO 2 separation target proposed by the US Department of Energy (95% purity and above 90% separation rate) [14]. Considering that the purity of the CO 2 product obtained by the low-temperature capture technology can generally reach 99%, the distance from the mixture gas inlet to the position of 90% capture rate can be defined as the valid capture x (m) Figure 3: Initial anti-sublimation point, valid capture length and CO 2 anti-sublimation rate length. The longer the valid capture length, the more uniform the anti-sublimation distribution of solid CO 2 , and the smaller the impact on the heat transfer heterogeneity during the anti-sublimation process.
(4) CO 2 anti-sublimation rate distribution: as shown in Fig. 3b, the physical meaning of the antisublimation rate is the mass of CO 2 anti-sublimation per unit time and tube length, and its distribution trend represents the distribution of sloid CO 2 deposition. The lower CO 2 peak deposition rate and uniform distribution can increase the capture operation time, and reduce the excessive local thermal resistance.

Simulation Results
In this model, tube length L = 1 m, the number of nodes N = 200, the inner and outer radius of the inner tube are r 1 = 2 mm, r 2 = 3 mm, and the inner radius of outer tube is r 3 = 4 mm. At the inlet of gas mixture, T mix (0) is fixed at 298.15 K, the inlet CO 2 volume fraction is given at 12%, the cooling nitrogen inlet pressure is 200 kPa, and its flow rate is 3.5 m/s.

Influence of Cooling Nitrogen Inlet Temperature
In order to analyze the individual effect of cooling nitrogen inlet temperature on the capture performance, only this parameter is changed while other parameters are kept constant. The inlet pressure of the mixture gas is 200 kPa and its flow velocity is 0.3 m/s. The inlet temperature of cooling nitrogen varies between 130 K and 160 K, and its influence on the anti-sublimation process is shown in Figs. 4 and 5. Capture rate (%) Figure 5: Effects of coolant inlet temperature on valid capture length and capture rate As shown in Fig. 4a, when the inlet temperature of the cooling nitrogen increases from 130 K to 160 K, the initial anti-sublimation point position moves from 0.03 m to 0.12 m, meanwhile, the volume fraction of CO 2 changes smoothly, and the mixture gas outlet CO 2 volume fraction increases from 0.02% to 1.76%.
In Fig. 4b, The CO 2 deposition rate decreases significantly, and its peak value decreases from 25.73 10 -6 kg·m −1 ·s −1 to 7.45 10 -6 kg·m −1 ·s −1 when the inlet temperature of cooling nitrogen increases. Meanwhile, the deposition rate distribution becomes smooth. When the cooling nitrogen inlet temperature is 130 K, the deposition rate distribution is concentrated between 0.03 and 0.34 m. While the deposition rate distribution corresponding to 160 K is concentrated between 0.11 m and 0.73 m. The uniform distribution of solid CO 2 deposition is good for heat and mass transfer process and effectively utilize the entire length of heat transfer.
As shown in Fig. 5, when the inlet temperature of cooling nitrogen rises from 130 K to 160 K, the valid capture length increases from 0.18 m to 0.99 m, so the problem of excessive local deposition was reduced. When the inlet temperature of the cooling nitrogen rises to 153 K, the valid capture length changes significantly. However, the capture rate decreases rapidly, from 99.85% to 86.92%. When the minimum capture requirement is 90%, the corresponding cooling nitrogen inlet temperature is about 157.5 K. It can be seen that the inlet temperature of cooling nitrogen has a great influence on the valid capture length and capture rate. In the experimental operation, the cooling nitrogen inlet temperature should be set by comprehensively considering the anti-sublimation performance parameters.

Influence of Mixture Gas Flow Velocity
Calculation data in Figs. 6 and 7 are obtained under following conditions: the inlet temperature of cooling nitrogen is 150 K, the inlet pressure of mixture gas is 200 kPa, and its flow velocity varies from 0.2 m/s to 0.5 m/s. As shown in Fig. 6a, when the flow rate of mixture gas rises from 0.2 m/s to 0.6 m/s, the position of the initial sublimation point moves from 0.04 m to 0.365 m, and the change of CO 2 volume fraction becomes gentle. In Fig. 6b, when the mixture gas flow rate is 0.5 m/s, the peak deposition rate is the lowest, and the distribution of the deposition rate is smooth. When the mixture gas flow rate is 0.2 m/s, the deposition rate distribution is concentrated between 0.03 and 0.34 m, and the corresponding distribution is concentrated between 0.21 and 0.99 m when the flow rate ascends to 0.5 m/s, which will extend the capture operating time. As illustrated in Fig. 7, with the mixture gas flow rate increases from 0.2 m/s to 0.6 m/s, the valid capture length increases significantly, from 0.21 m to 0.96 m, and the capture rate drop from 96.13% to 87.9%. When the mixture gas flow rate exceeds 0.5 m/s, as the flow rate of the mixture gas increases, the capture rate drops significantly. When the mixture gas flow rate further increases to 0.58 m/s, the capture rate falls to 90%. It can be concluded that the mixture gas velocity has a great impact on valid capture length and capture rate, and get a better performance in both sides when the velocity is 0.5 m/s.

Influence of Mixture Gas Pressure
Figs. 8 and 9 show the influence of mixture gas pressure on the capture performance when the mixture gas pressure varies between 100 kPa and 400 kPa and its velocity is 0.3 m/s. The inlet temperature of cooling nitrogen is 150 K and its pressure is 200 kPa.
As depicted in Fig. 8a, with the mixture gas pressure increases from 100 kPa to 400 kPa, the initial antisublimation point moves from 0.04 m to 0.24 m, and the change of CO 2 volume fraction tended to be gentle. It can be seen that the mixture gas pressure has a great impact on the position of the initial anti-sublimation point and the volume fraction of CO 2 . In Fig. 8b, as the mixture gas pressure increases, the peak value of CO 2 deposition rate of each curve was similar, but the deposition rate distribution from 0.03 m~0.31 m to 0.23 m~1 m, the problem of excessive local deposition is significantly reduced.
In Fig. 9, the mixture gas pressure increases from 100 kPa to 400 kPa, and the valid capture length increases from 0.23 m to 0.83 m, indicating that the larger mixture gas pressure is conducive to make better use of the entire section of heat transfer length. Meanwhile, the capture rate increases slightly from 92.27% to 97.5% and then decreased to 96.4%, indicating that the increment of mixture gas pressure can improve the capture performance, but excessive increment of the mixture gas pressure will lead to the problem of CO 2 capture rate decrease.

Optimal Parameter Setting Results
With the aim that valid capture length ratio higher than 70% and capture rate higher than 90%, the optimized operating parameters range are shown in Tab. 2:

Conclusions
In this work, a one-dimensional steady-state model of the CO 2 anti-sublimation process of N 2 -CO 2 binary mixture gas was established. Study on the effects of cooling nitrogen inlet temperature, mixture gas flow rate and pressure change on CO 2 volume fraction, deposition rate and distribution, initial antisublimation point location, and valid capture length and capture rate has been performed. The conclusions are drawn as follows: (1) Increasing cooling nitrogen inlet temperature, mixture gas flow rate and pressure can make the position of the initial anti-sublimation point move backward. Meanwhile, the change of CO 2 volume fraction tends becomes smooth, the distribution of anti-sublimation rate tends to be uniform, and the valid capture length increases. But the CO 2 capture rate drops significantly when the inlet temperature of cooling nitrogen increases. There exists an optimal mixture gas flow rate and pressure for achieving the maximum CO 2 capture rate.
(2) With the aim that valid capture length ratio higher than 70% and 90% capture rate, the suggested operating parameters are as follows: the inlet temperature of the cooling nitrogen is between 155.5 and 157.5 K, the flow rate of the mixture gas varies between 0.45 m/s and 0.58 m/s, the pressure of the mixture gas is a variable in range of 200 kPa~400 kPa, and the suggested position of heat transfer Capture rate (%) Figure 9: Effects of mixture gas pressure on valid capture length and capture rate enhancement is between 0.5 m and 0.7 m. Considering that the adjustment of pressure in actual operation often brings additional energy consumption, the cooling nitrogen inlet temperature and mixture gas flow rate should be adjusted first to obtain a better valid capture length.
Funding Statement: The authors would like to acknowledge the National Natural Science Foundation of China (No. 51636005 and No. 51906237) and the National Postdoctoral Program for Innovative Talents (No. BX20190311) for grants and supports.
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.