Design and analysis of cryogenic CO2 separation from a CO2‐rich mixture

In this study, we designed and optimized the main process for CO2 cryogenic separation and purification as well as the auxiliary process of refrigeration with ammonia, both these processes are modeled using Aspen HYSYS V11. The energy‐saving potential and greenhouse gas emission reduction potential of the process flow were analyzed using the Aspen Energy Analyzer V11. The effects of the plant inlet pressure, cooling temperature, tower pressure, and number of stages on two key parameters (energy consumption per unit of product and CO2 recovery rate) were studied in detail. Simultaneously, the appropriate design parameters of the plant were obtained, and the reason for the variation law was analyzed. Finally, grey relational analysis was used to explore the correlation between the influence factors and key parameters, indicating that the number of stages has the largest impact on the CO2 recovery rate and the energy consumption per unit of product, whereas tower pressure and cooling temperature have the least impact on the CO2 recovery rate and energy consumption per unit of product, respectively.


| INTRODUCTION
The increasing concentration of CO 2 in the atmosphere has a profound impact on the environment and society. [1][2][3][4][5] Major disasters such as glacier melting, land inundation, climate zone movement, hurricane intensification, ocean current change, frequent occurrence of El Nino, vegetation migration, and species extinction are closely related to it. 6 CO 2 is primarily produced during the combustion of fossil fuels. However, effective control of the use of fossil fuels is difficult in the short term. Carbon capture, utilization, and storage (CCUS) is the main method for reducing CO 2 emissions to the atmosphere without reducing the usage of fossil fuels and is also important technology for reducing greenhouse gas (GHG) emissions, which is a worldwide concern. 7 CO 2 recovery is the source of the CCUS technology; therefore, investigating CO 2 recovery techniques is crucial.
At present, several carbon dioxide recovery technologies that are considered to have the most industrial application prospects mainly include liquid solvent absorption, solid adsorption, membrane separation, and cryogenic separation methods. [8][9][10][11] Particularly, cryogenic separation technology has recently received increasing attention for enhanced oil recovery (EOR) applications because of its low energy consumption and liquid product. 12 Research on cryogenic separation of CO 2 mainly focuses on two types of gases: one is used for CO 2 capture from flue gases produced by power plants. 13 Clodic et al. proposed a CO 2 anti sublimation process that generates liquid CO 2 through condensation, sublimation, and compression. However, this process does not generate CO 2 continuously. 14, 15 Zanganeh et al. developed a cryogenic separation system in which CO 2 is compressed and cooled to a liquid before transit. 16,17 Tuinier et al. separated CO 2 / H 2 O from postcombustion flue gas running periodically in a low hotbed under atmospheric pressure, with liquefied natural gas being used as a cold source. 18,19 Song et al. established a novel application of a free piston Stirling cooler (SC) in the cryogenic CO 2 capture process, in which the CO 2 can be captured as a solid under cryogenic conditions and frosted on the cold head of the SC. 20 Berstad et al. developed a cryogenic process consisting of sections for distillation, flash separation, auxiliary refrigeration, and internal heat recovery. 21 Sipocz et al. developed a new process for obtaining CO 2 solid particles which included continuous compression, cooling, and expansion. The solid CO 2 generated from the cyclone channel was mechanically compressed above its threephase point and transformed from the solid to the liquid phase through heat exchange. Finally, liquid CO 2 was pumped to the required pressure near ambient temperature. 22 Yang et al. proposed a system combining liquefaction and sublimation separation that comprises a compression section, a gas-liquid separation tower, a condensation separation tower, and an expansion section. 23 Xu et al. developed a new integrated CO 2 separation, liquefaction, and purification system for separating CO 2 from flue gas produced from burning fuel in an oxygen atmosphere; the system included two-stage compression, two-stage refrigeration, and two-stage separation. 24 Another aspect is the separation of CO 2 from natural gas mixtures/biogas with high CO 2 content. 25 Ryan and Holmes developed the Ryan-Holmes process, which can separate CH 4 , CO 2 , and mixed hydrocarbon by adding a solid-preventing agent to prevent carbon dioxide from freezing out and improve the volatility of CO 2 -CH 4 and CO 2 -H 2 S. 26,27 Valencia et al. developed a technology controlled freezing zone (CFZ) system, in which a CFZ tower comprises a specifically designed CFZ section and two conventional stripping and rectifying sections. 28,29 Amin et al. proposed the CryoCell cryogenic process, which generates solid CO 2 and requires heating to become liquid. 30,31 Theunissen et al. studied the separation of CO 2 from natural gas and combustion fluent by compression, cooling, and throttling. To reduce the damage to the frost layer, a scrapper was added beside the cold head of the SC to scrap the deposited CO 2 in a timely manner. 32 To recapture CO 2 after carbon dioxide EOR, Peng developed a coupling process of cryogenic distillation and stripping. 33 More recently, a new dualpressure low-temperature distillation process was developed for separating CO 2 from high CO 2 -content natural gas mixtures/biogas. In this process, two distillation towers operating at different pressures are thermally linked, with the condenser of the high-pressure tower being used to reboil the low-pressure tower. [34][35][36][37] In addition to the above two types of feed gas, there are also some other gases such as carbon dioxide well gas, recapture gas after CO 2 EOR, and tail gas from coal-to-gas plants. The CO 2 content of these gases is often extremely high, often exceeding 75 mol% or even 90 mol%. Although the low-temperature fractionation process used to separate carbon dioxide from natural gas can separate the above gases, these processes require low refrigeration temperatures, complex supporting refrigeration cycle processes, and complicated equipment design; therefore, the separation of CO 2 -rich gas is poorly economical.
In this study, the traditional single-tower distillation process and a supporting ammonia refrigeration system were optimized in terms of process and equipment installation. Simulations using Aspen HYSYS V11 were carried out, and the influencing factors of the process were investigated in detail. And the grey relational analysis was first used to explore the correlation between the influence factors and key parameters.

| Basic data
The feed gas originates from the upstream CO 2 dehydration station in which the gas from the CO 2 gas well is dehydrated and subjected to hydrocarbon removal treatment. The incoming gas pressure is 5.0 MPa, and the temperature is 20°C. The gas composition is listed in Table 1. The CO 2 content of the liquid products must not be less than 99 mol%.
T A B L E 1 Basic composition of the feed gas. We designed a CO 2 cryogenic separation and purification process as shown in Figure 1. The feed gas from the upstream first enters the feed gas pre-cooler to exchange heat with the noncondensable gas from the overhead condenser and then enters the liquefier for deep cooling to condense approximately 80 mol% into a liquid. The deeply cooled CO 2 mixture enters the flash separator for the preliminary flash separation. The liquid phase obtained from the flash separator enters the fractionation tower, where a liquid product with more than 99 mol% CO 2 is obtained. The noncondensable gas from the tower enters an overhead condenser for condensation and then enters an overhead separator for gas-liquid separation. The throttled noncondensable gas from the overhead separator is mixed with the throttled flash vapor from the flash separator to provide a refrigeration output for the overhead condenser. The mixed noncondensable gas subsequently enters the precooler for further cold recovery and finally enters the vent system for combustion and venting. The liquid from the overhead separator is returned to the top of the tower for refluxing. The heat of the bottom reboiler is provided by the high-temperature gas ammonia generated in an ammonia compression refrigeration system.

| Design of the refrigeration process with ammonia
Refrigeration systems with ammonia are essential utility systems for the cryogenic separation and purification processes of CO 2 . The flow of this process is illustrated in Figure 2. The refrigerant liquid from the condenser is divided into two parts: a small part is evaporated in the economizer after passing through the auxiliary throttle valve, to cool the other part of the liquid that is not throttled, and thus supercool the high-pressure liquid. The supercooled liquid is supplied to the evaporator via the main throttle valve and vaporizes after absorbing the heat of the heating medium in the evaporator. The gaseous refrigerant from the economizer and evaporator enters the suction port of the compressor. The resulting stream is then divided into two parts: one part is transmitted to the bottom reboiler to provide heat for CO 2 purification and become a saturated liquid, while the other part is condensed by the condenser and becomes a saturated liquid. The two parts of the liquid are then mixed for subsequent circulation.

| Comparison with traditional processes
In the conventional CO 2 cryogenic separation and purification processes, the overhead condenser and bottom reboiler are independent of the purification tower. The overhead condenser uses an external refrigerant to provide cooling capacity, whereas the bottom boiler uses a heat source to provide heat.
In our design, tower-top condensation is achieved by the cooling capacity generated by self-evaporating gas throttling, while the heat of the bottom reboiler is provided by the high-temperature gas ammonia generated in an ammonia compression refrigeration system. This design not only reduces the energy consumption required for external cooling capacity but also saves fuel gas for heating loads and reduces operational costs. From the equipment installation perspective, the F I G U R E 1 Flow diagram of CO 2 cryogenic separation and purification.
F I G U R E 2 Flow diagram of refrigeration with ammonia.
condenser at the top of the tower is turned into a coiled tube and installed inside the top of the purification tower. The condensate obtained after condensation can flow automatically back to the purification tower, thus saving the overhead reflux tanks and pumps while conserving the supporting heating system by optimizing the bottom reboiler process, thus simplifying the process and reducing equipment investment.

| Establishment of the simulation model
In this study, we used Aspen HYSYS V11 to establish the process flow sheets, 38 and we selected the Peng-Robinson equation of state. 39 The simulation models are shown in Figures 3 and 4, respectively. The variable settings for each device used in the simulation are shown in Table 2.

| Energy saving potential and emission reduction potential of process flow
Energy analysis was completed by Aspen Energy Analyzer V11, and the carbon emissions were also obtained simultaneously. The energy savings potential and GHG emission reduction potential of the process are shown in Figure 5. Evidently, the consumption of thermal utilities is consistent with the target value, both of which are 0, and the consumption of cold utilities is consistent with the target value, both of which are 695.4 kJ/s. Simultaneously, the GHG emissions are the same as that of the target emissions. The above analysis shows that energy utilization and GHG emission reduction of the processing unit are optimized. The reason for the "actual" value is exactly equal to the "target" value for all variables is as follows: In the process design, the heat required by the processing system is provided by the high-temperature gas ammonia of the ammonia refrigeration system, and there is no need to set up a separate heating system to provide the heat, so the actual heating utilities is 0; at the same time, the cooling capacity of the system has reached the maximum utilization value that can be reached by theoretical calculations after several cycles of recycling. And for the same reason, GHG emissions are exactly equal to the target value.

| Calculation of key parameters
We used the CO 2 recovery rate and energy consumption per unit of product, that is, the power consumption per F I G U R E 3 Process flow sheet of CO 2 cryogenic separation and purification. kilogram of CO 2 produced, as the key parameters for plant parameter optimization.
The CO 2 recovery rate and energy consumption per unit of product can be obtained separately from Equations (1) and (2): where η is the CO 2 recovery rate; M p is the molar flow of CO 2 in vent air, mol/s; M a is the molar flow of CO 2 in the feed gas, mol/s; Q is energy consumption per unit product, kJ/kg; W is the total power consumption of the unit, kJ/s; and c is the quantity of CO 2 products per second, kg/s.

| RESULTS AND DISCUSSION
3.1 | Analysis of the influence factors on the key parameters

| Influence of the plant inlet pressure
We fixed the cooling temperature of the G6 stream in Figure 3 at −20°C and the number of stages to 12. The relationship between CO 2 recovery rate and energy consumption per unit of product with the plant inlet pressure under different tower pressures was investigated and shown in Figure 6A,B. As seen in Figure 6A, the energy consumption per unit of product changes slowly with the change in plant inlet pressure at a fixed tower pressure, however, at a fixed plant inlet pressure, the energy consumption per unit of the product decreases with the decrease in tower pressure. Based on Figure 6B, the CO 2 recovery rate exhibits no obvious change with the change in the plant inlet pressure when the tower pressure exceeds 3.0 MPa; contrastingly, the recovery rate increases with the increase in plant inlet pressure when the tower pressure is less than 3.0 MPa. The increasing trend is more pronounced when the plant inlet pressure is increased from 3.0 to 3.5 MPa, while the increasing trend of the CO 2 recovery rate becomes significantly slower when the plant inlet pressure exceeds 3.5 MPa. Generally, the larger the difference between the inlet and tower pressures, the smaller the CO 2 recovery rate (Table 3). To explain the above phenomena, we fixed the tower pressure at 2.5 MPa and studied the latent heat of the phase transition, dew point, bubble point, and other relevant parameters of the CO 2 mixture in stream G5 at different plant inlet pressures, as listed in Table 2. The table shows that the plant inlet temperature, liquefier inlet temperature, dew point, and bubble point all decrease with decreasing plant inlet pressure. With a decrease in pressure, both cooling capacity 1 and cooling capacity 3 decreases, while cooling capacity 2 increases. Consequently, the total cooling capacity remains essentially constant over the range of studied pressures, and thus the energy consumption per unit of product. However, the CO 2 recovery rate depends on the degree of liquefaction of the mixed gas. When the pressure is lower than 3.5 MPa, the feed gas cannot be completely liquefied when cooled to −20°C, and the lower the pressure, the lower the liquefaction rate. Consequently, the CO 2 recovery rate varies significantly within this pressure range. When the pressure exceeds 3.5 MPa, the feed gas is completely liquefied when cooled to −20°C. Thus, at pressures higher than 3.5 MPa, the upward trend of the CO 2 recovery rate slows significantly and remains essentially unchanged. Therefore, the appropriate plant inlet pressure for the feed gas is 3.5 MPa.
T A B L E 2 Variable settings for each device in the simulation.

Device
Variable settings Note Pre-cooler The pressure of Stream 1 varies from 3.0 to 5.0 MPa In Figure 3 The pressure of Stream G16 is 0.5 MPa The temperature of stream vent gas is 10°C The equipment pressure drop is 30 kPa

Liquefier
The temperature of Stream G6 varies from −25°C to 0°C In Figure 3 The equipment pressure drop is 30 kPa

Flash tank
The temperature of Stream G6 varies from −25°C to 0°C In Figure 3 The equipment pressure drop is 30 kPa The feed tray location is the first layer from the top

Overhead condenser
The temperature of Stream 28 varies from −13°C to −28°C In Figure 3 The pressure of stream G14 is 1.

MPa
The equipment pressure drop is 30 kPa

Reflux tank
The temperature of Stream 28 varies from −13°C to −28°C In Figure 3 Subcooler The temperature of stream product is −20°C In Figure 3 The equipment pressure drop is 30 kPa

Compressor 1
The pressure of Stream 3 is 0.65 MPa In Figure 4 The temperatures for Streams G21 and 15 are both −25°C The vapor/phase fraction for both Streams G21 and 15 are 1

Air cooler 1
The temperature of stream 20 is 50°C In Figure 4 The equipment pressure drop is 30 kPa

Compressor 2
The pressure of Stream 5 is 1.4 MPa In Figure 4 Air cooler 2 The temperature of Stream 23 is 85°C In Figure 4 The equipment pressure drop is 30 kPa

Bottom reboiler
The temperature of Stream G23 is 30°C In Figure 4 The equipment pressure drop is 30 kPa

Evaporative condenser
The temperature of Stream 44 is 40°C In Figure 4 The equipment pressure drop is 30 kPa

Flash economizer
The temperatures for Streams 6 and 45 are both −25°C In Figure 4 Liquefier The temperature of Stream G21 is −25°C In Figure 4 The equipment pressure drop is 30 kPa

Subcooler
The temperature of Stream 15 is −25°C In Figure 4 The equipment pressure drop is 30 kPa

| Influence of tower pressure
We fixed the cooling temperature of the G6 stream in Figure 3 at −20°C and the number of stages to 12. The relationship between CO 2 recovery rate and energy consumption per unit of product with tower pressure under different plant inlet pressures was studied, as shown in in Figure 7A,B. The energy consumption per unit of product increases linearly with an increase in tower pressure. When the tower pressure increases from 2.5 to 3.5 MPa, the CO 2 recovery rate increases with tower pressure however, the recovery rate decreases when the pressure continues to increase beyond 3.5 MPa because as the tower pressure increases, the temperature of the CO 2 mixture entering the tower also increases. The pressure factor plays a major role when the tower pressure increases from 2.5 to 3.5 MPa. Thus, the CO 2 recovery rate increases within this pressure range. When the pressure increases from 3.5 to 4.5 MPa, the temperature factor plays a major role. Consequently, the CO 2 recovery within this pressure range is reduced. The temperature of the product at the bottom of the tower increases with the pressure, and the cooling capacity required to cool the product in the sub-cooler increases. Thus, the energy consumption per unit of the product increases. Therefore, the appropriate tower pressure is 3.4 MPa.

| Influence of cooling temperature
We fixed the tower pressure at 2.5 MPa and the number of stages to 12. The influence of cooling temperature on the CO 2 recovery rate and energy consumption per unit of product under different plant inlet pressures was studied as shown in Figure 8A,B. With an increase in cooling temperature, both the CO 2 recovery rate and energy consumption per unit of product decrease. At the same pressure, the lower the cooling temperature, the higher the liquefaction rate of the feed gas, and the more CO 2 enters the liquid phase; thus, the CO 2 recovery rate increases. Meanwhile, the lower the cooling temperature, the larger the cooling capacity absorbed by the feed gas, and the higher the energy consumption per unit of product.
In addition, when the cooling temperature was lower than −20°C, the energy consumption per unit product and the CO 2 recovery rate are basically the same under different plant inlet pressures. When the temperature is higher than −20°C, the greater the plant inlet pressure, the higher the energy consumption per unit product and CO 2 recovery rate. However, as the cooling temperature increases, the effects of the plant inlet pressure on the CO 2 recovery rate and energy consumption per unit product becomes more notable because the cooling temperature becomes progressively higher than the bubble point as it increases. Therefore, the fraction of the energy consumed by the phase-transition latent heat in the system gradually decreases, while the fraction of the energy consumed due to the temperature  difference gradually increases. Meanwhile, the cooling temperature is higher than the bubble point, and the liquefaction rate is affected more by the plant inlet pressure. Therefore, the appropriate cooling temperature is −20°C.

| Influence of the number of stages
We fixed the cooling temperature of the G6 stream in Figure 3 at −20°C and the plant inlet pressure at 5.0 MPa. The relationship between the CO 2 recovery rate and energy consumption per unit of product with the number of stages under different tower pressures was studied, as shown in Figure 9A,B. Evidently, with an increase in the number of stages, the energy consumption per unit of the product gradually decreases, while the CO 2 recovery rate gradually increases. When the number of stages exceeds 12, the CO 2 recovery rate and energy consumption per unit of product remain essentially unchanged. This is because the heat and mass exchange of the fluid becomes more sufficient as the number of stages increases. However, the resistance of the phases increases, leading to a reduction in the separation effect. Therefore, the appropriate number of stages is 12. 3.2 | Checking the absence of solid CO 2 within the tower When dealing with CO 2 separation from a hydrocarboncontaining mixture using cryogenic distillation, the possibility of CO 2 freeze-out should be investigated. 12 Research shows that the "CO 2 freeze-out" tool in Aspen HYSYS is a reliable approach for checking the CO 2 freezing conditions in different simulations. 40 Therefore, a freezing check was performed using the "CO 2 freezeout" tool in Aspen HYSYS V11. Because the tower temperature profile illustrated in Figure 10 is always above the calculated vapor and liquid freezing temperature, there is no risk of solid CO 2 formation within the tower.

| Grey relational analysis of influential factors
The grey relational analysis is a type of grey system analysis method that measures the degree of correlation between factors according to the degree of similarity or difference in the development trend between factors. 41 Here, we used the grey relational analysis method to analyze the correlation between the influencing factors and key parameters. Four influence factors were extracted, thus the sequence length of the data was four: the plant inlet pressure is X1, the cooling temperature is X2, tower pressure is X3, and the number of stages is X4. These four factors constitute the comparison order factor in the proposed method. Then, we set the reference time series {YN} (N = 1, 2) and select CO 2 recovery rate and energy consumption per unit product as the reference sequence factors. The raw data are listed in Table 4. The specific calculation procedure is as follows: 1. Processing transformed and dimensionless data The raw data are transformed and the mean value transformation is used for dimensionless data. The formula is as follows: 2. Calculating the correlation coefficient Dimensionless data are substituted in each comparison time series {X i } and reference time series {Y i }. The correlation coefficient between each comparison sequence and the reference sequence can be calculated according to Equation (4).
where, the two-stage maximum difference is Meanwhile, the two-stage minimum difference is ρ (0 < ρ < 1) is the resolution coefficient, 0.5. 3. Solving the correlation degree.
The grey correlation between the reference sequence and each of the comparison sequences was solved and calculated as follows: The results are shown in Table 5, which indicates that the number of stages has the largest impact on the CO 2 recovery rate and energy consumption per unit of product, while tower pressure and cooling temperature have the smallest effect on the CO 2 recovery rate and energy consumption per unit of product, respectively.

| Engineering construction and operation of the plant
We designed and built a CO 2 cryogenic separation and purification plant in the Shengli Oilfield based on the above research, calculations, and design (shown in Figure 11A,B). The construction of the plant comprised the design of several major activities, including system engineering, fabrication, installation, commissioning, and checkup for the acceptance of a completed project. The designed flow rate of the CO 2 gas mixture treated by the demo plant was 80,000 Nm 3 /day, and stainless steel gauze structured packing was selected. Assembly welding was primarily used during construction. All of the equipment was hoisted onto the equipment foundation after the equipment foundation was fully poured and had the corresponding bearing capacity. After the equipment level and positioning were completed, secondary grouting was conducted, followed by the installation of indoor and outdoor pipes, valves, and instruments. The plant has been in good operation for 16,000 h after being put into operation; All process parameters are normal, and the operation results are in good agreement with the simulation data (as shown in Table 6). The product purity and production meet the requirements.

| CONCLUSION
The main process of CO 2 cryogenic separation and purification and the auxiliary process of refrigeration with ammonia were designed and optimized. Towertop condensation is achieved by the cooling capacity generated by self-evaporating gas throttling, while the heat of the bottom reboiler is provided by the hightemperature gas ammonia generated in an ammonia compression refrigeration system.
The simulation model was constructed using Aspen HYSYS V11, and the energy-saving potential and GHG emission reduction potential of the process flow were analyzed using Aspen Energy Analyzer V11. The analysis shows that the process is optimized in terms of energy use and reduction of GHG emissions.
We considered the energy consumption per unit product and the CO 2 recovery rate as the key parameters, and studied the effects of the plant inlet pressure, cooling temperature, tower pressure, and number of stages on the two key parameters in detail. The appropriate design parameters of the plant are as follows: plant inlet pressure, 3.5 MPa; tower pressure, 3.4 MPa; cooling temperature, −20°C; and the number of stages, 12. The simulation results agree well with the actual operating parameters.
The correlation between the influencing factors and key parameters was analyzed using the grey relational analysis method, and the results show that the number of stages has the largest impact on the CO 2 recovery rate and energy consumption per unit of product, while tower pressure and cooling temperature have the smallest effect on the CO 2 recovery rate and energy consumption per unit of product, respectively.
T A B L E 6 Comparison between simulation data and actual operation data.

Process parameters
Simulation data Actual operation data