CO2 Separation by Using a Three-stage Membrane Process

This work proposed and optimized a three-stage membrane process for CO2 separation. The results of this study revealed that the membrane technology is a suitable process for the CO2 separation in a higher concentration. In addition, the MATLAB was used to simulate and obtain the optimal operational parameters for a three-stage membrane process. This work established a partial cycle and recovered the CO2 from the permeation side of second-stage membrane that enhance a higher purity CO2 gas stream. The results of this study indicated that when the CO2 concentration was higher than 50% and at a flow rate of 100000 Nm3 d–1, the CO2 separation could be achieved at the optimal operation condition. Under the conditions that the membrane areas were 2400, 3800, and 1800 m2 for the first-, second-, and third-stage membrane, respectively and the operational pressure at firstand third stage membrane were 3.0 and 2.5 MPa, respectively, the CO2 separation fraction was higher than 90% and CH4 loss rate was lower than 5%. The results of this study have a high potential for the practical application.


INTRODUCTION
As the pace of oil exploitation was accelerated due to the importance of oil, more and more oilfields became less permeable due to mining and for geological reasons. Generally, the recovery efficiency of low permeability reservoirs is only 20 to 25% in oilfields, and the proportion of low permeability reservoirs in proven oil reserves is increasing annually (Wei et al., 2018). There are many flooding patterns, among which CO 2 -EOR is more available than is the case for water flooding, nitrogen, air and flue gas, and also has the advantages of being low cost and having high natural gas quality (Booran et al., 2016;Bender and Akin, 2017;Wang et al., 2017;Wang et al., 2018). However, CO 2 -EOR flooding leads to a more CO 2 (about 40 to 60% of the injected gas) spilling out of the ground along with the gas produced during oil recovery (hereinafter referred to as the extraction gas). Meanwhile, with continuous exploration, a number of oilfields with higher CO 2 content are being discovered. For example, the CO 2 concentration in extraction gas fields in Malaysia ranges from 28% to 87% (Tan et al., 2012b;Jean et al., 2016;Xie et al., 2017;Yang et al., 2019). Large amounts of CO 2 discharged directly into the atmosphere not only causes serious climate problems, but also can be harmful to human health (Ping et al., 2018;Shiue et al., 2018;Tsai et al., 2018). Therefore, it is a serious issue to find a means by which to capture CO 2 capture from extraction gas.
In recent decades, several CO 2 capture technologies have been developed, including as absorption, adsorption, membranes, and cryogenic technologies (Sreedhar et al., 2017;Vinoba et al., 2017). The chemical absorption method removes CO 2 from the extraction gas through the convection contact between the feed gas and the chemical solvent in the packing column, with the usual solvents being monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA), among others (Tan et al., 2012a;Li et al., 2016). However, a number of drawbacks have been revealed using this method, including a large volume occupancy and some operational problems such as flooding, channeling, entrainment and foaming (Ghasem et al., 2012a). Chemical absorption technology is usually used to process extraction gas within a relatively narrow feed range (Fu et al., 2012). Therefore, in the case of high CO 2 concentrations (approximately 60% or more) at 0.3-0.6 MPa, the chemical method may not be applicable due to excessive circulating amounts and poor absorption effects. Holmes and Ryan (1982) first invented cryogenic distillation for natural gas purification, which also can be used for CO 2 capture. However, due to the high energy consumption of this technology, which accounts for about 50% of the total energy, this technology has not been widely used in CO 2 capture from extraction gas (Ebrahimzadeh et al., 2016).
In recent years, membranes for CO 2 separation are receiving growing attention for application in the field of CO 2 capture and storage (CCS) (Boot-Handford M et al., 2014;Roussanaly S et al., 2016). Compared with chemical absorption, membrane-based separation is more attractive due to its easy installation, a minimal influence of SO x and NO x on membrane materials, and avoidance of regeneration energy consumption (Merkel et al., 2010;Rufford et al., 2012). To achieve good development prospects, the membranebased method must develop "good" membrane modules and membrane materials. Robeson (2008) has identified the upper bound on membrane material selectivity and permeability in many gas separation systems, including CO 2 /N 2 , O 2 /N 2 , CO 2 /CH 4 and H 2 /CH 4 , etc. In the membrane separation process, the membrane material is the first element because the selectivity and permeability of the membrane directly determine the separation efficiency. It is well known that the performance of polymeric membranes is characterized by an 'upper bound' that correlates with permeability and selectivity (Robeson, 2008). However, in recent years, many new materials, such as MOFs and ssz-13, have also been applied in the membrane separation field, with good performance in terms of separation performance and permeability (Rodenas et al., 2015;Chisholm et al., 2018). Gas permeability through a polymer membrane depends on the solution-diffusion mechanism, in which the rate of gas movement correlates with the ratio between the gas molecules and the membrane material and the diffusion rate (Rufford et al., 2012). Polyimide is a very attractive polymer that can be used in membrane technology, due to having high selectivity and high permeability, as well as the fact that it can be used for various applications such as gas and liquid separation (Favvas et al., 2017). In order to obtain high quality product features, a multi-stage membrane separation device was proposed to multi-separate the product gas and in turn improve product purity rather than a single-stage membrane device, which is inexpensive but preforms poorly. Experiments capturing CO 2 from natural gas in a single-stage membrane device were conducted under high pressure conditions or efficient absorbents in order to study the influence of membrane area, membrane pressure, and feed gas flow rate on CO 2 removal rate (Kang et al., 2017). Few studies have been done on multi-stage membrane devices. These studies include separation of O 2 from air, CH 4 from biogases and landfills, CO 2 from coal flue gases, and H 2 from H 2 /CO mixtures (Rautenbach et al., 1987;Bhide et al., 1991;Xu et al., 1996;Zhao et al., 2011). Ohs et al. (2016) recently applied a superstructure method to remove N 2 /CH 4 from natural gas in order to identify the optimal processes and structural parameters. In addition to not fully considering the membrane separation structure and overall operation parameter optimization, they also did not have an overall process design for the CO 2 /CH 4 system. Chong et al. (2017) proposed a polymeric membranes for O 2 /N 2 gas separation through using N,N-dimethylacetamide (DMAc) and tetrahydrofuran (THF) and ethanol as additives, where a polysulfone (PSF) hollow fiber membrane was created. This membrane can be used to achieve a better O 2 /N 2 separation rate.
We proposed a three-stage membrane separation process based on single-stage membranes and the literature on this topic. In this study, the CO 2 capture performance of the membrane separator was investigated using extraction gas with high concentrations of CO 2 (60%) as feed. A mathematical model was established and introduced into MATLAB for numerical simulation of the membrane separation. The effects of the operating pressure and membrane area on the CO 2 recovery fraction and CH 4 loss rate were discussed in regard to the optimal parameters. This investigation will provide guidance for the application of multi-stage membrane separators in the CO 2 capture of extraction gas.

Extraction Gas
We have been injecting CO 2 into the underground oil layer since 2012. In the subsequent six years, the changes in CO 2 concentrations over time in the Shengli oilfield and the CO 2 concentrations were continuously monitored in the extraction gas, as shown in Fig. 1. As shown in Fig. 1, in the entire oil recovery process after the CO 2 injection, the CO 2 content in the extracted gas increased from the original 1.5% to above 90%. The CO 2 content in Well89 1-7 increased sharply in the initial phase and quickly rose in the second phase, while Well89 S1 remained stable at a low content for a long time in the initial phase. However, after a period of time, the CO 2 concentration in both wells rose rapidly in the third phase, where the concentration range was stable at 60%-90%. After a few years, the total gas volume may increase tenfold compared to the gas injection, causing significant fluctuations in CO 2 gas, which will result in technical difficulties related to separation and further treatment.
Results related to heavy hydrocarbon components are demonstrated in Fig. 2, where it can been seen that heavy hydrocarbon content of C 5+ is relatively stable, at about 2%-3%, but the content of C 3+ is volatile, as high as 15%. Therefore, it is necessary to design a special pretreatment module to remove these compounds. The C 5+ content may contaminate membrane devices and in turn cause membrane material poisoning. Therefore, a special pretreatment module should be designed to remove heavy hydrocarbons, which will be carried out in the future work.
According to the CO 2 content shown in Fig. 1, we divided the produced gas into area Ⅰ (CO 2 concentration< 30 mol%), area Ⅱ (30 mol% < CO 2 concentration < 60 mol%), and area Ⅲ (CO 2 concentration > 60 mol%). In conclusion, the extraction gas in area III has the following characteristics: large gas flow, high CO 2 partial pressure, high CO 2 concentrations (60% or greater), and the main components are CO 2 and CH 4 . For CO 2 concentrations above 60%, our primary work and that of Kang et al. (2017) recommend membrane separation, which is also a key part of this work.

Process Description
The process of membrane-based separation was displayed in Fig. 3. The extraction gas is first processed through the pretreatment module, in which the liquid water, heavy hydrocarbons, and solid particles carried in the EOR extraction gas are removed. Otherwise, the membrane components will be blocked, and the membrane materials will be contaminated,  which will affect the normal operation of the membrane system. Since the research on the pretreatment process is not mature, the design was not discussed in this paper. After processing through thee pretreatment module, the gas (material 1) that is passed through the pretreatment system was then compressed into the first-stage membrane device for gas separation. Furthermore, the gas was split into two streams, one of which was permeate gas loaded with CO 2 (material 2), and the other of which was entrapped gas loaded with CH 4 (material 3). The former entered the thirdstage membrane separator after being pressurized in compressor for further purification, and the latter directly entered the second-stage membrane for purification of CH 4 gas. The permeate gas stream treated by the third-stage M Ⅰ : First-stage membrane unit, M Ⅱ : Second-stage membrane unit, M Ⅲ : Third-stage membrane unit membrane separator was the CO 2 product gas (material 4) while the stream generated by the second-stage membrane was the CH 4 product gas (material 5). However, the permeate gas from the second-stage membrane contained in the CO 2 (material 6) was designed to mix with the inlet gas to carry out a partial circulation because the concentration of CO 2 was similar to that of the feed gas. The entrapment side of the third-stage membrane was discharged as exhaust gas (material 7). The module used in the design was a hollow fiber which is equivalent to the mass transfer of a shell and tube heat exchanger (Mat et al., 2014). This type of assembly can significantly improve the performance of the membrane by increasing the chemical potential difference across the membrane. A polyimide membrane was selected as the membrane material, and the separator parameters followed Robeson (2008). The design parameters were selected as shown in Table 1.
In the case of the membrane-based capture, there are two main factors that affect the CO 2 recovery fraction and CH 4 loss rate in the entire process. One is the membrane area, and Polyimide PI-5 α (CO 2 /CH 4 ) 33.9 Target (vol%) CO 2 recovery fraction > 0.9 CH 4 loss rate < 0.05 the other is the membrane pressure, which are also the two objects we discussed herein. The membrane areas comprised the first-second-and third-stage membrane areas. The CO 2 concentration in the purified gas was mainly affected by the second-stage membrane area, while that in the captured gas was mainly affected by the third-stage membrane area. There was no required connection between the second-stage membrane and the third-stage membrane. Therefore, the second-and third-stage membrane areas were tentatively determined to optimize the first-stage membrane area. After analyzing the influence of first-stage membrane area on the CO 2 concentration in purified gas and the concentration of the CO 2 product gas, the first-stage membrane area was obtained, and then the second-stage membrane area and the third-stage membrane area were optimized. The operating pressure was the outlet pressure of the compressor, which directly affected the pressure of the feed gas, where if the pressure of the feed gas was increased, the gas passed more quickly through the membrane, which increased the CO 2 recovery fraction and decreased the membrane area.

Process Simulation Membrane Unit Model
As shown in Fig. 4, a counter-current flow pattern was developed in this study utilizing the tank-in-series concept Lee et al., 2018). This ideal model did not take into account the pressure drop, concentration polarization, or scaling on the residual side. Simulation optimization conditions were achieved using the Simulink component optimization in MATLAB, which is a reliable calculation method.
Mass differential equation: Differential equation of flow: Differential equation for change in CO 2 concentration: Differential equation for change in CH 4 concentration: where U is the flow of feed gas, Nm 3 h -1 ; V is flow of permeate gas, Nm 3 h -1 ; X is the concentration of CO 2 in the feed gas; Y is the concentration of CO 2 in the permeate gas; P h is the pressure of the feed gas, MPa; P l is the permeate pressure, MPa; and A is membrane area, m 2 . With boundary conditions: l = 0; U = U 0 ; x = x 0 ; l = L; V = 0; x L = y L .
The following is the integral from the entry (l = 0) of the separator to any section of Eq. (3): Using Eq. (3), the permeate gas concentration of each cross section in fiber bundles (l ≠ L) can be obtained. Because when L = l, V = 0, the permeation gas concentration of y L cannot be directly obtained from Eq. (3). Therefore, y L is now defined as: When l → L, y L , is defined as: The simulation results can be obtained by means of differential equations and boundary conditions using MATLAB.

Mass Balance Equations for the Three-stage Membrane Process
Binary variables are used in this study to represent the presence or absence of any structural options in this optimization. Additionally, a genetic algorithm (GA) is applied in the simulation, which can easily obtain the variable calculation results in the MATLAB simulation environment (Lee et al., 2018). The mass equilibrium and composition equilibrium based on binary variables are defined as follows: The flow rate mass balance for the first membrane stage is: where F 1 is the flow rate, Nm 3 h -1 ; F feed is the flow rate of feed gas, Nm 3 h -1 ; F e is the flow rate on the entrapped side, Nm 3 h -1 ; F p is the flow rate on the permeate side, Nm 3 h -1 ; s is splitter numbers; n is the stage number of the membranes; S p is the binary variable for flow connections on the permeate side; S e is the binary variable for flow connections on the entrapped side, and N is the overall number of membrane stages. The composition balance for the first membrane stage is: N N e s n e n i e n p s n p n i p n s n n i n where f i is the mole fraction of the component; f feed is the mole fraction of each component at the overall feed flow rate; f e is the mole fraction of the entrapped side component, and f p is the mole fraction of the permeate side component.

Power Consumption
Power consumption is an important parameter for evaluating CO 2 capture performance. However, the power requirement of the three-stage membrane process is due to the compressor, so the calculation of power consumption is shown as follows (Song et al., 2017):

Effects of Membrane Area First-stage Membrane Area
The optimal first-stage membrane area was obtained by changing the membrane area from 2300 to 2700 m 2 , obtaining the CO 2 concentration in the outlet gas stream, and measuring the CO 2 recovery fraction and the CH 4 loss rate. Based on previous studies, the second-and third-stage membrane areas were 3500 and 2000 m 2 , respectively.
In Figs. 5 and 6, it can be seen that an increase in the firststage membrane area affected the separation efficiency of CO 2 /CH 4 . It was negatively correlated with the CO 2 recovery fraction and CO 2 concentration and was positively correlated with the CH 4 loss rate. The above results indicated that an increase in the membrane area hindered the separation of CO 2 and CH 4 .
When the first-stage membrane area was greater than 2500 m 2 , the CH 4 loss rate was as high as 5%. In order to lower the of CH 4 loss rate, the first-stage membrane area needed to be less than 2500 m 2 . However, if considering both the CO 2 recovery fraction and CH 4 loss rate, the firststage membrane area was selected to be 2400 m 2 , which resulted in a 98.6% CO 2 recovery efficiency and a 4.2% CH 4 loss rate.

Second-stage Membrane Area
After the first-stage membrane, the CO 2 concentration had to be further purified. If the first-and third-stage membrane areas were selected to be 2400 and 3000 m 2 , respectively, the second-stage membrane area was varied from 2000 to 4000 m 2 for the purpose of obtaining an optimal secondstage membrane area.
The main purpose of the second-stage membrane was to  obtain a higher concentration of CH 4 gas. Therefore, a lower CO 2 permeate concentration was better. In Fig. 7 shows that a higher second-stage membrane area did decrease the permeate CO 2 concentration from 3% to less than 0.5%. In order to ensure that permeate CO 2 concentration be less than 2%, the second-stage membrane area was set to be 3800 m 2 .

Third-stage Membrane Area
When the first-and second-stage membrane area were selected to be 2400 and 3800 m 2 , respectively, the optimal membrane area of the third-stage was determined by looking at the CO 2 recovery fraction and CH 4 loss rate data. Fig. 8 shows that an increase in the third-stage membrane area resulted in an increase in the CO 2 recovery fraction, which rose from 50% to higher than 95% and finally became stable.
When the third-stage membrane area was higher than 2000 m 2 , the CO 2 recovery fraction and CH 4 loss rate were both stable and at around 97% and 4.5%, respectively. However, when the membrane area was greater than 2000 m 2 , the CH 4 loss rate declined both linearly and rapidly. Under conditions where the third-stage membrane area was 1800 m 2 , the CO 2 recovery fraction and CH 4 loss rate reached 90.5% and 4.45%, respectively.

Effects of Operating Pressure Operating Pressure for the First-stage Membrane
When the CO 2 concentrations in the inlet gas stream were 0.5, 0.6, 0.7, and 0.8 and the operating pressure at first-stage membrane was set at 1.5, 2.0, 2.5, 3.0, and 3.5 MPa, respectively, the variations in the CO 2 recovery fraction and CH 4 loss rate for the first-stage membrane were calculated and analyzed.  In Fig. 9 shows that as the operating pressure for the firststage membrane continued to rise, both the CO 2 recovery fraction and CH 4 loss rate were increased. When the operating pressure for the first-stage membrane pressure was 3 MPa, the CO 2 recovery fraction was over 90%, and CH 4 loss rate was less than 5%. Obviously, a high pressure did increase the flux of CO 2 gas through the membrane. According to the curve in Fig. 10, it can be seen that excessive pressure lead to a reduction in the CO 2 recovery fraction.
(a) The CO 2 concentration in the inlet gas stream is 50% (b) The CO 2 concentration in the inlet gas stream is 60% (c) The CO 2 concentration in the inlet gas stream is 70% (d) The CO 2 concentration in the inlet gas stream is 80% Fig. 9. CO 2 recovery fraction and CH 4 loss along with changes in the operating pressure. A proper membrane operating pressure lead to a good gas separation effect and also improved CO 2 recovery efficiency. Therefore, the operating pressure was setting to range from 2 to 4 MPa. According to Fig. 10, when the optimal pressure was 3 MPa, the power consumption was 115.4 kW.

Operating Pressure for the Third-stage Membrane
The operating pressure for the first-stage membrane was fixed at 3 MPa, and those for the third-stage membrane were set at 1.0, 1.5, 2.0, and 3.0 MPa, respectively. This made it possible to obtain the optimal pressure for the third-stage membrane can be obtained.
As shown in Fig. 11, both the CO 2 recovery fraction and CH 4 loss rate increased with increases in the operating pressure. When the CO 2 concentration in the input gas stream was either 0.5 or 0.6, the operating pressure for the third-stage membrane was 2.0 MPa; the CO 2 recovery fraction was higher than 90%, and the CH 4 loss rate was less than 5%. When the CO 2 concentration in the input gas stream was either 0.7 or 0.8, the operating pressure for the third-stage membrane was 2.5 MPa, and both a high CO 2 recovery fraction and a low CH 4 loss rate can also be obtained. The driving force required for a low CO 2 concentration was lower than that for a high one. Therefore, from the perspective of saving energy, a different operating pressure could be adopted for CO 2 separation for different CO 2 input concentrations. A data analysis indicated that the operating pressure for the third-stage membrane should be set at 2.5 MPa.
Under conditions where the first-, second-and third-stage membrane areas were 2400, 3800 and 1800 m 2 , respectively, and the operating pressure for the first-and third stage membrane was 3.0 and 2.5 MPa respectively, the simulation results are shown in Table. 2, which indicates that the CO 2 recovery fraction was over 90%; the CH 4 loss rate was less than 5%, and the power required was 203.4 kW (Fig. 12). By contrast, Song et al. (2017) obtained a CO 2 recovery fraction of 84.6%, and the power required was 2.8 MJ kg -1 . The three-stage membrane process used in the current study can thus improve power consumption by 4% power consumption and can achieve a higher CO 2 recovery fraction.

CONCLUSIONS
1. Membrane technology is more suitable for the CO 2 separation at higher concentrations. 2. In this study, MATLAB was used to simulate and obtain the optimal operational parameters for the three-stage membrane process. This work established a partial cycle (a) The CO 2 concentration in the inlet gas stream is 50% (b) The CO 2 concentration in the inlet gas stream is 50% (c) The CO 2 concentration in the inlet gas stream is 60% (d) The CO 2 concentration in the inlet gas stream is 80% Fig. 11. CO 2 recovery fraction and CH 4 loss along with changes in the operating pressure. and recovered the CO 2 from the permeation side of a second-stage membrane, thus improving the purity CO 2 of the gas stream. 3. The results of this study indicated that when the CO 2 concentration is higher than 50% and at a flow rate of 100000 Nm 3 d -1 , CO 2 separation can be achieved under optimal operating conditions. Under conditions where the membrane areas were 2400, 3800, and 1800 m 2 for the first-, second-, and third-stage membrane, respectively, and the operating pressure for the first-and third stage membranes was 3.0 and 2.5 MPa, respectively, the CO 2 separation fraction was higher than 90%, and the CH 4 loss rate was less than 5%. 4. The results of this study can be applied in practical engineering applications.