Thermodynamic study on aqueous polyethylene glycol 200 solution and performance assessment for CO2 separation

Fluid Phase Equilibria 504 (2020) 112336

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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Thermodynamic study on aqueous polyethylene glycol 200 solution and performance assessment for CO2 separation Yifeng Chen a, b, Chunyan Ma b, a, Xiaoyan Ji b, Zhuhong Yang a, Xiaohua Lu a, * a b

Key Laboratory of Material and Chemical Engineering, Nanjing Tech University, Nanjing, 210009, China Energy Engineering, Division of Energy Science, Lulea University of Technology, 97187, Lulea, Sweden

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 May 2019 Received in revised form 17 September 2019 Accepted 23 September 2019 Available online 23 September 2019

To develop polyethylene glycol 200 (PEG200) and aqueous PEG200 solutions (PEG200/H2O) as solvents for CO2 separation, in this study, the available thermo-physical properties of PEG200 and PEG200/H2O measured experimentally were surveyed, evaluated, and correlated with empirical equations. The solubility of CO2 in PEG200 was also surveyed, evaluated and described with the Henry's law with the Poynting correction, while the solubilities of CH4 and N2 in PEG200 were determined experimentally and then described with the Henry's law. The CO2, CH4 and N2 solubilities in PEG200/H2O were measured and described with the RedlicheKwong Nonrandom-Two-Liquid (RK-NRTL) model. In addition, the performances of PEG200, PEG200/H2O and other commercialized physical solvents for CO2 separation were discussed based on the properties, and the biogas upgrading was chosen as the example to quantitatively evaluate the performances of PEG200 and PEG200/H2O with process simulation and compared with the high pressure water scrubbing (HPWS). It shows that the total energy usage and the amount of recirculated solvent for biogas upgrading can decrease by 9.1% and 26.5%, respectively, when H2O is replaced by PEG200 completely. © 2019 Elsevier B.V. All rights reserved.

Keywords: CO2 PEG200 Solubility Modelling Process simulation

1. Introduction Global warming is now widely recognized as being the biggest global issue facing human beings, and the excessive CO2 emissions in the atmosphere are believed to be the main cause [1,2]. CO2 separation is of importance to mitigate CO2 emissions from fossilfuel plants with the option of CO2 capture and storage [3]. Meanwhile, CO2 separation is also needed for gas purification in order to produce renewable fuels from biomass or biowaste [4,5]. Technologies have been developed for CO2 separation, and absorption is the state-of-the-art technology with the advantages of high efficiency and continuous operation [6]. For the absorption technologies, the physical solvents are preferred for the gaseous streams with high CO2 partial pressure [7]. Dimethyl ether of polyethylene glycol (DEPG) is a typical organic physical solvent that is known as Selexol and Genosorb [8,9], Rectisol with methanol is considered as the most economic process for acid gas removal from the partial oxidation of oil or coal [10], and propylene carbonate (PC) is often used to remove CO2 and

* Corresponding author. E-mail address: [email protected] (X. Lu). https://doi.org/10.1016/j.fluid.2019.112336 0378-3812/© 2019 Elsevier B.V. All rights reserved.

H2S from the pressurized natural gas [11]. In addition, high pressure water scrubbing (HPWS) is one of the widely-used processes for biogas upgrading in the European countries [12,13]. Previous work also indicated that PEG can be used as a physical solvent for CO2 separation even at high temperatures [14,15] due to its low vapor pressure [16], high CO2 absorption, and the reasonable viscosity and price. In fact, PEG has been used for gas upgrading [17,18]. Meanwhile, water extensively exists in the gas streams (i.e. biogas and flue gas), and it is often viewed as a promising and benign cosolvent. The selectivity of CO2/CH4 in water is also competitive to the other physical solvents [19]. This makes it important to study the effect of water on the performance of PEG as well as the direct use of the aqueous PEG solutions for CO2 separation. However, the relevant research work has not been conducted sufficiently. To evaluate the performance of PEG and its aqueous solution for CO2 separation, thermo-physical properties and gas solubility are the prerequisites. The thermo-physical properties of PEG and aqueous PEG solution, as well as the CO2 solubility in PEG have been measured experimentally, however, the available experimental data has not been systematically surveyed and evaluated. Meanwhile, the CH4 and N2 solubilities are still not studied extensively, and only N2 solubility in PEG200 at 298.15 K [20] and CH4 solubility

2

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

in PEG200/H2O at atmospheric pressure have been reported [21]. Based on the thermo-physical properties and gas solubility, other thermodynamic properties can be estimated. For example, Henry's constant [22], gas selectivity [23] and absorption enthalpy [24] can be calculated based on the gas solubility. The performance of solvents can be compared with one another according to the properties for the first hand. However, to obtain a quantitative performance evaluation of the solvents, process simulation needs to be conducted, and the commercial software Aspen Plus can be used as an effective tool. The techno-economic analysis of CO2 separation from flue gas with the aqueous monoethanolamine (MEA) solution has been extensively studied in Aspen Plus [25,26]. In our previous work, the performance of several physical solvents and aqueous deep eutectic solvents have been evaluated based on the results from Aspen Plus [27e29], however, PEG was excluded due to the lack of sufficient information from Aspen Databank. For a specific system, a proper model needs to be chosen and the model parameters can be obtained from the fitting of the experimental data. Empirical equations such as Rackett [30], IK-CAPE [31], DIPPR [32] and Andrade [33] can be used to correlate thermophysical properties of pure and mixed solvents. Equations of state (RK [34] and PengeRobinson [35]) can be used to describe the nonideal behavior of the gaseous components, while NRTL [36], electrolyte NRTL model [37] and Universal QuasieChemical model [38] can be used to describe the non-ideal behavior for the components in the liquid phase. However, for PEG and its aqueous solutions, the parameters for describing the properties and gas solubility are still unavailable in Aspen Plus. The objective of this study was to perform a systematical study on PEG and PEG/H2O as the solvents for CO2 separation. To achieve this, the thermo-physical properties of PEG200 and PEG200/H2O were surveyed, evaluated, and correlated with the empirical equations. The solubility of CO2 in PEG200 was surveyed, evaluated and described by the Henry's law with the Poynting correction, while the solubilities of CH4 and N2 in PEG200 were measured and described with the Henry's law. In addition, the CO2, CH4 and N2 solubilities in PEG200/H2O were measured and correlated with RKNRTL model. The fitted parameters were embedded into Aspen Plus, and the performance of PEG200 and PEG200/H2O for biogas upgrading was further evaluated and compared with H2O. 2. Experiment 2.1. Material PEG200 (average molecular weights of 200 g mol
1, analytical grade) was supplied by Guandong Guanghua Sci-Tech Corporation. Phosphorus pentoxide (analytical grade) was purchased from Shanghai Lingfeng Chemical Reagent Corporation Ltd. CO2 and N2 were purchased from Nanjing Tianhong gas factory, and CH4 was supplied by AGA factory in Sweden. H2O was purified in our laboratory through a reverse osmosis membrane. The details of the materials used in this study are summarized in Table 1.

The conductivity of H2O is 0.25 ms/cm (308.15 K), which was determined with conductivity meter (METTLER TOLEDO, FiveEasy Plus). Before the experiment, PEG200 was dried in the vacuum oven at 353.15 K, and P2O5 was used to remove the trace amount H2O in the oven. The water content of PEG200 is less than 200 ppm after drying. The amounts of PEG200 and H2O were weighted with the mass balance (Sartorius, BSA224S) and then mixed in the beaker. The precision of the mass balance is 0.0001 g. The water content in PEG200/H2O was further determined by the Karl Fischer titration (Shanghai Peiou, V100) before and after experiments. 2.2. Property measurement The density and viscosity of PEG200 and PEG200/H2O were measured with the density and viscosity meter (Anton Paar, DMA 5000 and Lovis 2000 ME), and the precisions for density and viscosity are 0.1 kg m
3 and 0.1 mPa s, respectively. Before the measurement, the density and viscosity meter were calibrated with the deionized water and standard oil (S3, Anton Paar). The refractive indices of PEG200 was measured with the Refractometer (Anton Paar, Abbemat 300), and the precision is 0.0001 nD. Calibration of Refractometer was also made by measuring the refractive indices of deionized water. The accuracy of temperature for the measurements of the density, viscosity and refractive indices is 0.01 K. 2.3. Gas solubility measurement and calculation The schematic diagram of the set-up for gas solubility measurement is illustrated in Fig. 1. It involves an equilibrium cell, a gas reservoir, a magnetic stirrer, two pressure sensors (Rosemount 3051) and a water bath featuring a temperature control system. The temperature of water bath was measured with a thermocouple (ZCT-01, Wuxi Zhongce Sensor Technology Corporation) with an uncertainty of 0.1 K. Before the experiment, the accuracy of the thermocouple was calibrated using the grade 1 standard mercuryin-glass thermometer with a precision of 0.05 K (Wuqiang Zhongxing Glass Gage Factory). The volumes of the gas reservoir (487.60 ml) and equilibrium cell (53.01 ml) were measured by filling with water. For each experiment, around 10.00 ml PEG200 or PEG200/H2O was put into the equilibrium cell. In order to reduce the evaporation of water, the cell was degassed by a vacuum pump at the desired temperature (not absolute vacuum) in a short time, and the water concentration after the absorption was further determined using Karl Fischer titration method, confirming a negligible loss of water during degasing. Then, the gas was introduced into the equilibrium cell, and the stirring system was switched on. When the pressure of the system maintained as a constant for 1 h, it was assumed that equilibrium was reached. The

Table 1 Details of the materials used in this study. Chemicals name

Symbol

CAS

Puritya

Carbon dioxide Nitrogen Methane Phosphorus pentoxide Polyethylene glycol 200 Water

CO2 N2 CH4 P2O5 PEG200 H2O

124-38-9 7727-37-9 74-82-8 1314-56-3 25322-68-3 7732-18-5

99.99 vol% 99.99 vol% 99.99 vol% 98.5 wt% 99.9 wt% Deionized

a

As stated by the supplier.

Fig. 1. Schematic diagram of gas solubility measurement set-up.

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

amount of gas in the absorbent was calculated according to the pressure changes of the equilibrium cell before and after the gas absorption. All the measurements were repeated for three times, and the average values were reported. The gas solubility in the studied solutions was calculated using the following equations:


ngas ¼

xgas ¼

 P 0
P v ðVA
VL Þ Z1 RT




 e  P
P v ðVA
VL Þ Z2 RT

ngas ngas þ nPEG200 þ nH2 O

(1)

(2)

where P0 and Pe are the initial and equilibrium pressures of the equilibrium cell, respectively. Pv is the vapor pressure of the solution before the gas injection. Z1 and Z2 are the compressibility factors corresponding to the initial and equilibrium states, respectively. The values of Z were calculated from the second virial coefficients [39], in which the gas phase was assumed as the pure component. VA and VL represent volumes of the equilibrium cell (53.01 ml) and absorbent, respectively. R is the universal gas constant. The uncertainties of gas solubility consist of system errors for pressure, temperature, volume and mass. The measurement errors of temperature, pressure, volume and mass are u(T) ¼ 0.1 K, u(P) ¼ 0.001 MPa, u(V) ¼ 0.01 ml, and u(m) ¼ 0.0001 g, respectively. The uncertainty for the measured gas solubility can be calculated from following equations:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP P uc ðxÞ u ðuðni ÞÞ2 ðuðni ÞÞ2 þ uðnl Þ2 ¼t þ  2 2 x ng ng þ nl

n uðni Þ ¼ i R

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi       uðPi Þ 2 uðVi Þ 2 uðTi Þ 2 þ þ Pi Vi Ti

(3)

3.2. Phase equilibria In this study, three gases (i.e. CO2, CH4 and N2) and three solvents (PEG200, H2O and PEG200/H2O) are involved in describing the gas-liquid equilibrium. The gas solubility (i.e. CO2, CH4, or N2) in H2O has been extensively studied, and no further study was conducted. In this part, the solubilities of CH4 and N2 in PEG200 were measured experimentally. Meanwhile, new CO2 solubility in PEG200 was also determined to verify the accuracy of the available experimental results. In addition, the CO2, CH4 and N2 solubilities in PEG200/H2O was measured. The experimental results of the gas solubility in the solvents were further represented with models. After the model parameters were obtained from the fitting of experimental data, they were implemented into Aspen Plus to conduct process simulation. 3.2.1. Theory The solubility of CO2, CH4 and N2 in PEG200 and PEG200/H2O can be expressed as

Pyi fi ¼ Hi ðT; PÞxi g*i

(6)

ln g*i ¼ lngi
ln g∞ i

(7)

when P represents the system pressure, Hi ðT; PÞ is the Henry's constant of component i (i ¼ CO2, CH4 or N2) in the absorbent at temperature T and P, fi is the fugacity coefficient of i in the vapor phase, gi is the asymmetric activity coefficient of i in the liquid phase, gi is the activity coefficient of i in the liquid phase, g∞ is the i infinitely dilute activity coefficient of i in the liquid phase, and yi and xi are the mole fractions of component i in the vapor and liquid phases, respectively. For the gas solubility in the pure solvent, the expression of Hi ðT; PÞ is depicted in Eqs. (8e11), and the pressure effect was considered with Poynting correction:

(4) Hi ðTÞ ¼ lim

x/0

uðnl Þ ¼

uðmÞ M

3

(5)

where uc(x) is the combined standard uncertainty of gas solubility in the absorbent, ni is the amount of gas in the gas phase before and after absorption, ng is amount of gas absorbed in the liquid phase, nl is the amount of the solvents in the equilibrium cell, and M is molecular weight of the absorbent.

3. Results and discussion 3.1. Thermo-physical properties of solvents In this study, the solvents can be PEG200, H2O and PEG200/H2O. For the pure H2O, its properties have been studied extensively, and no further study was conducted in this work. Meanwhile, as the evaluation of the solvents was also based on the process simulation, the properties needed are mainly on the critical properties, density, viscosity, surface tension and heat capacity. The properties of PEG200 in this study were measured at 308.15 K to guarantee its quality, then the thermo-physical properties of PEG200 and PEG200/H2O were surveyed, evaluated, and correlated with the empirical equations. All these were depicted in Supporting Information.

Pf x

lnHi ðTÞ ¼ c1 þ c2 =T

(8) (9)

∞

PV i Hi ðT; PÞ ¼ Hi ðTÞexp RT

(10)

V∞ i ¼ d1 þ d2 T

(11)

where Hi ðTÞ is the Henry's constant of gas i at system temperature T and zero pressure, and V ∞ i is the infinitely dilute partial volume of gas i in the absorbent. The value of V ∞ i can be obtained from the fitting of the gas solubility in the absorbent or calculated using the Brelvi-O’Connell model [40,41] with the characteristic volumes for BO the gas i (V BO i ) and solvent j (V j ). Actually, Aspen Plus can also be used for the gas solubility modelling, but the V ∞ i can't be used as the input value for the process simulation. The general relationship between V ∞ i and Brelvi-O’Connell model [28,42] is:


BO BO l V∞ i ¼ fcn V i ; V j ; V j

(12)

V BO ¼ V0 þ eT

(13)

where V lj is the mole volume of solvent j, and the V lj value of PEG200 was calculated from density. The VBO values of gases and PEG200 are listed in Table 2 in which the VBO value of PEG200 was

4

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

Table 2 VBO values of gases and PEG200. VBO(m3$kmol
1)

CO2

CH4

N2

PEG200

V0 e

0.177
0.000342

0.0992 -

0.0896 -

0.574 -

represented with the Vc value. For the gas solubility in the mixed solvent, the Henry's constant of gas i in the mixed solvent (Hi;mix ) was calculated from those of pure solvents

1

0 ln@

Hi;mix

g∞ i;mix

A¼




Hij T; P X wj ln ∞ j

!

gij

 2=3 xj Vc;j wj ¼ P  2=3 xk Vc;k

(14)

(15)

lngi ¼

tji Gji xj

j¼1 m P

Gli xl

3 x t G r rj rj 7 m X Gij xj 6 6 7 r¼1 þ 6tij
m 7 m P P 4 5 j¼1 Glj xl Glj xl

l¼1

2

l¼1

m P

(18)

l¼1

whereGij ¼ expð
atij Þ and Gji ¼ expð
atji Þ a was assumed to be 0.2 in this study, Gij, Gji, tij and tji are binary NRTL interaction parameters, and



tij ¼ mij þ nij T tji ¼ mji þ nji T

(19)

In Eq. (19), m and n are the coefficients to describe the temperature-dependent binary NRTL interaction parameters.

where Vc;j is the critical volume of the solvent j, g∞ is the infii;mix nitely dilute activity coefficient i in the mixed solvent, g∞ ij is the infinitely dilute activity coefficient of i in the pure solvent j, and wj is the weighting factor. The Vc values of H2O [43] and PEG200 were set to be 0.056 and 0.574 m3 kmol
1, respectively. As depicted in the introduction section, the vapor pressure of PEG200 is negligible, and for PEG200/H2O, it was assumed that H2O content in the vapor phase is very low and can be neglected. Therefore, in modelling, it was reasonable to assume that only the gaseous component i is in the vapor phase. In this study, RK equation of state was used to describe the non-ideal behavior of the gaseous component, and the NRTL model was chosen for the liquid phase. These models have been embedded in Aspen Plus, and the reliabilities of these two models for describing the solubilities of gas (e.g. CO2, CH4 and N2) in H2O, ionic liquids (ILs) and other organic solvents have been verified in our previous work [27,28]. The expression of f calculation using RK equation of state is depicted in Eq. (16):

. ! a R2 T 2:5 lnð1 þ bP = ZRTÞ b=RT (16)

where

RT a 8
P¼ > > ðVm
bÞ T 0:5 Vm ðVm þ bÞ > > > > > > > > R2 T 1:5 > ci > > ¼ 0:42748023 a > i > Pci > > > > > > > > RT < bi ¼ 0:08664035 ci Pci > > > > > > Z ¼ PVm =RT > > > > > p ffiffiffi X pffiffiffiffi > > yi ai a¼ > > > > > i > > > > X > : y i bi b¼

m P



k

ln f ¼ Z
1
lnðZ
bP = RTÞ


gas mixture, and b is the constant that corrects for volume in the gas mixture. The critical pressures (Pc) and temperatures (Tc) of CO2, CH4 and N2 are (304.2 K, 7.38 MPa), (190.6 K, 4.61 MPa), and (126.2 K, 3.39 MPa), respectively [43]. The expression for NRTL model is depicted in the following equations:

(17)

3.2.2. Model parameterizing In this study, to calculate gas solubility, the Henry's constants (H(T)) in PEG200, the infinitely dilute partial volumes (V ∞ CO2 ) in PEG200, and the binary interaction parameters of H2O/PEG200 in NRTL (tij and tji) need to be obtained. The procedure to obtain these parameters was described as the following steps: (1) the H(T) value of a gas was obtained from the fitting of the gas solubility in the whole pressure range if the gas solubilities (i.e. for CH4 and N2 in this work) in PEG200 increase linearly with increasing pressure within the detected range, while the H(T) value was obtained from the fitting of the gas solubility up to 2 MPa (i.e. for CO2 in this work) if the gas solubilities in PEG200 increase non-linearly with increasing pressure at high pressures. This was done at each temperature, and then the temperature-dependent Hi(T) values were obtained, i.e. c1 and c2 in Eq. (9); (2) V ∞ CO2 in PEG200 at each temperature was obtained from the fitting of the CO2 solubility in PEG200 within the whole compositional or pressure range, and then the temperaturedependent V ∞ CO2 values were calculated, i.e. d1 and d2 in Eq. (11); principally, using NRTL with binary interaction parameters of CO2/PEG200 can further improve the model performance for the CO2 solubility in PEG200. While in this work, it was found that the consideration of Poynting correction with the parameter V ∞ CO2 is enough to represent the CO2 solubilities in PEG200 in the whole pressure range. Thus, the binary interaction parameters of CO2/PEG200 in NRTL were set to be zero, i.e. the values of mCO2 ;PEG200 , nCO2 ;PEG200 , mPEG200;CO2 and nPEG200;CO2 in Eq (19) are zero; (3) the binary interaction parameters of H2O/PEG200 in NRTL were obtaining from the fitting of the CO2 solubility in PEG200/H2O in the whole compositional or pressure range at each temperature, in which the Henry's constants of CO2 in PEG200/H2O were estimated with the mixing rule (i.e. Eqs (14) and (15)). The temperature-dependent binary NRTL interaction parameters were further obtained based on the parameters at different temperatures, i.e. mH2 O;PEG200 , nH2 O;PEG200 , mPEG200;H2 O and nPEG200;H2 O in Eq. (19).

i

In Eqs. (16) and (17), Vm is the molar volume of gas, a is the constant that corrects for attractive potential of molecules in the

3.2.3. Solubility of CO2 in PEG200 Before determining the gas solubility in the absorbent, the CO2

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

solubilities in H2O and PEG200 were also measured to make the comparison with the literature for further verifying the accuracy of the apparatus, which was also depicted in Supporting Information. The CO2 solubility in PEG200 has been measured experimentally with the sources listed in Table 3. The CO2 solubility in PEG200 was measured by Hou et al. [44] (T ¼ 303.2e323.2 K, P ¼ 1.0e8.0 MPa), Li et al. [45] (T ¼ 303.2e333.2 K, P ¼ 0.072e1.18 MPa), Gourgouillon et al. [46] (T ¼ 313.2e348.2 K, P ¼ 5.63e26.50 MPa), and Aschenbrenner at al [20] (T ¼ 298.2 K, P ¼ 0.10 MPa). In this study, the CO2 solubility in PEG200 was also measured at the temperature of 293.2 and 313.2 K and the pressure ranging from 0.51 to 2.50 MPa. The comparison of the available experimental results is depicted in Fig. 2. As shown in Fig. 2 (b), (c) and (d), the CO2 solubility measured by Hou et al. [44] can be questionable as the CO2 solubility cannot approach zero when the pressure approaches zero. After checking the original work, it was found that the CO2 solubility was determined by measuring the loss of weight for the sample in the sample bomb. This method may result in a large deviation because it is hard to keep the pressure of sample bomb being the same as the equilibrium cell. Therefore, the results from Hou et al. [44] were excluded for the further study. The Henry's constant of CO2 in PEG200 (HCO2 ðTÞ) was obtained with Eq. (8) based on the available experimental data of CO2 solubility at the pressures lower than 2 MPa at each temperature. After that, the temperature-dependent HCO2 ðTÞ was obtained as listed in Table 4. With the obtained Henry's constant, Eq. (6) was used to describe the CO2 solubility in PEG200 within the whole compositional range. In this study, the infinitely dilute partial volume of CO2 in PEG200 (V ∞ CO2 ) was set to be an adjustable parameter. The preliminary study shows that the inclusion of NRTL cannot improve the model performance significantly, and thus g∞ i was assumed to be one for this system. Following this assumption and the temperature-dependent V ∞ CO2 was obtained from the fitting of the experimental CO2 solubility in the whole compositional range. The fitted constants for calculating V ∞ CO2 are listed in Table 4. The modelling results are illustrated in Fig. 2, and the individual average relative deviations (ARDs) are 2.81%, 7.20%, 13.47%, 11.33% and 9.85%, respectively, at 293.2, 303.2, 313.2, 323.2 and 333.2 K. In this study, the experimental data points from different sources were used for parameters fitting, and the discrepancies of the model from experimental results are mainly due to the inconsistency of the experimental results from different sources, instead of the model itself. For example, the CO2 mole fractions in PEG200 at 313.2 K and 1.1 MPa (Hou et al. [44], Li et al. [45], and this work) showed an mean relative deviation (MRD) of 18.4%, while the reported experimental uncertainties are 0.3%, and 0.2%, respectively, for the work of Li et al. [45] and this work. All these imply that the modelling results agree with the experimental data and the RKNRTL model is reasonable for the gas solubility modelling. Meanwhile, the value of V ∞ CO2 can also be calculated by the Brelvi-O’Connell model. The results obtained with this model are 41.42, 40.78, 39.90, 39.20 and 38.30 cm3 mol
1, respectively, at 293.2, 303.2, 313.2, 323.2 and 333.2 K. The values of V ∞ CO2 fitted in this work are 41.40, 40.73, 39.94, 39.14 and 38.35 cm3 mol
1, respectively, at 293.2, 303.2, 313.2, 323.2 and 333.2 K. The two sets of V ∞ CO2 are also the same. In addition, others also reported that the

5

infinitely dilute partial volume of CO2 in H2O increases from 32.66 to 40.77 cm3 mol
1 with increasing temperature from 293.2 to 393.2 K [47]. All these illustrate that the values of V ∞ CO2 obtained in this work are reliable and conforms that it is reasonable to assume g∞ i to be one for this system. 3.2.4. Solubility of CH4 and N2 in PEG200 CH4 is one more important component in biogas, and N2 is the main component in the flue gas. However, the solubilities of CH4 and N2 in PEG200 have not been determined extensively, only the N2 solubility in PEG200 has been reported by Aschenbrenner at al [20] (T ¼ 298.2 K, P ¼ 0.1 MPa). In this study, the solubilities of CH4 and N2 in PEG200 were measured at temperatures from 293.2 to 353.2 K with the pressure up to 2.5 MPa. The measured results in this work are listed in Table 5 and depicted in Fig. 3, where x1 represents the mole fraction of the gas (CH4 or N2) in PEG200. Similarly, the Henry's constants of CH4 and N2 in PEG200 (HCH4 ðTÞ and HN2 ðTÞ) were also obtained with Eq. (8) but based on all measured solubility data points due to the almost linearly increase of the gas solubility with increasing pressure. The temperature-dependent HCO2 ðTÞ and HN2 ðTÞ were obtained as listed in Table 4. With the obtained Henry's constants, Eq. (6) without the Poynting correction was used to describe the CH4 and N2 solubilities in PEG200. The modelling results are depicted in Fig. 3, and the corresponding ARDs for CH4 and N2 are 5.05% and 5.06%, respectively. All these also illustrate that the modelling results agree with the experimental data. 3.2.5. Solubility of CO2 in PEG200/H2O In this study, the CO2 solubility in PEG200/H2O was also measured at different temperatures, pressures and H2O contents for the first time. Due to the molecular weight of PEG200 is much larger than that for H2O, the mole fraction of H2O in the solvent of (PEG200/H2O) (before absorption) only changes from 0.7585 to 0.9783 when the mass fraction increases from 0.20 to 0.80. The experimental results are listed in Tables 6 and 7, where x3’ represents the mole fraction of H2O in PEG200/H2O (before absorption) and x1 represents the mole fraction of CO2 in PEG200/H2O. With the Henry's constants of CO2 in PEG200 and H2O [48], Eq. (6) was also used to describe the CO2 solubility in PEG200/H2O. In modelling, the Henry's constant of CO2 in PEG200/H2O was calculated according to Eqs. (14) and (15), and the binary NRTL parameters between PEG200 and H2O were set as adjustable parameters and obtained based on the measured CO2 solubility in PEG200/H2O. The fitted parameters are listed in Table 8. The modelling results are illustrated in Figs. 4 and 5, showing the model can describe the experimental results well. As shown in Fig. 4(b), the deviation of the CO2 solubility at 308.2 K from the experimental measurement is slightly high, while it is still acceptable. The ARDs at 293.2 K with different H2O contents are 8.94% (x3' ¼ 0.9783), 8.49% (x3' ¼ 0.9437), 8.43% (x3' ¼ 0.8814) and 5.25% (x3' ¼ 0.7585), the ARDs at 308.2 K with different H2O contents are 7.94% (x3' ¼ 0.9783), 11.05% (x3' ¼ 0.9437), 10.54% (x3' ¼ 0.8814) and 4.50% (x3' ¼ 0.7585), and the ARDs at x3' ¼ 0.9437 and different temperatures are 8.49% (T ¼ 293.2 K), 11.05% (T ¼ 308.2 K), 6.28% (T ¼ 323.2 K), 3.11% (T ¼ 338.2 K) and 5.84% (T ¼ 353.2 K), respectively.

Table 3 Sources of gas solubility in PEG200 and PEG200/H2O. Solubility

CO2

CH4

N2

PEG200 PEG200/H2O

[20,44e46] and this study This study

This study [21] and this study

[20] and this study This study

6

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

Fig. 2. CO2 solubility in PEG200 at different temperatures. Symbols, experimental data; Curves, model correlation.

Table 4 lnH(T) and V ∞ i parameters of gases in PEG200. Gas

Solvent

c1

c2

d1

d2

CO2 CH4 N2

PEG200

7.16 9.58 12.44


1524.49
1582.94
2064.20

64.87 -


0.08 -

3.2.6. Solubility of CH4 and N2 in PEG200/H2O Gas selectivity based on the measured accurate solubility data is very important in the design of gas separation processes. However, the solubilities of CH4 and N2 in PEG200/H2O have not been measured extensively, only the CH4 solubility in PEG200/H2O at 298.2 K and 0.1 MPa has been reported [21]. In this study, the CH4 and N2 solubilities in PEG200/H2O were also measured at 293.2 K

and different H2O contents for the first time (Table 9). Additionally, the CH4 and N2 solubilities in PEG200/H2O were also predicted using RK-NRTL model. As depicted in Fig. 6, the measured solubility results of CH4 and N2 in PEG200/H2O agree with the predicted CH4 and N2 solubilities. The corresponding ARDs for CH4 (N2) are 9.67% (5.03%), 6.52% (8.09%), 6.86% (10.04%), and 9.99% (9.44%) for the H2O mole fractions (x3’) of 0.9783, 0.9437, 0.8814 and 0.7585, respectively. Therefore, the theoretical prediction in this study is reliable. To further investigate this assumption, the composition in the vapor phase was predicted with the model. It was found that only the CO2 solubility in PEG200/H2O at 353.2 K and at the pressures of 0.466 and 1.011 MPa might be questionable due to the relatively high H2O mole fractions in the vapor phase. The further investigation shows that the assumption of negligible vapor pressure of

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

7

Table 5 Solubility of CH4 or N2 (1) in PEG200 (2).a T(K)

293.2

308.2

323.2

338.2

353.2

P(MPa)

x1$103

P(MPa)

x1$103

P(MPa)

x1$103

P(MPa)

x1$103

P(MPa)

x1$103

CH4

0.301 0.551 0.78 0.891 1.003

4 ± 0.07 8.6 ± 0.07 11 ± 0.07 13 ± 0.07 15 ± 0.07

0.298 0.547 0.709 0.881 1.007

3.4 ± 0.07 6.2 ± 0.07 8.1 ± 0.07 10.1 ± 0.07 11.6 ± 0.07

0.290 0.514 0.691 0.878 1.008

2.5 ± 0.07 4.9 ± 0.07 6.8 ± 0.07 8.3 ± 0.07 9.5 ± 0.08

0.344 0.576 0.744 0.870 0.997

2.3 ± 0.06 4.3 ± 0.06 5.4 ± 0.06 6.7 ± 0.06 8.1 ± 0.06

0.341 0.56 0.736 0.905 0.998

1.8 ± 0.06 3 ± 0.06 4.3 ± 0.07 5.6 ± 0.07 6.3 ± 0.07

N2

0.653 1.150 1.665 2.111

3.7 ± 0.07 5.4 ± 0.08 7.5 ± 0.08 10 ± 0.09

1.105 1.538 2.013 2.518

3.2 ± 0.07 4.4 ± 0.07 5.9 ± 0.08 7.2 ± 0.09

1.133 1.842 2.442 2.575

2.7 ± 0.06 4.8 ± 0.07 6 ± 0.07 6.5 ± 0.08

1.100 1.587 2.078 2.592

1.9 ± 0.06 2.9 ± 0.06 4.2 ± 0.07 5.2 ± 0.08

1.157 1.651 2.110 2.696

1.2 ± 0.06 2.1 ± 0.06 2.6 ± 0.07 3.6 ± 0.07

a

Standard uncertainties u are u(P) ¼ 0.001 MPa and u(T) ¼ 0.1 K. The values of uc(x1) are listed in the table.

Fig. 3. CH4 (a) or N2 (b)(1) solubility in PEG200(2) at different temperatures: model correlation.

:, 293.2 K; -, 308.2 K; B, 323.2 K; C, 338.2 K; ,, 353.2 K. Symbols, experimental data; Curves,

Table 6 Solubility of CO2 (1) in PEG200 (2) þ H2O (3) with different H2O mole fraction (x3’) (T ¼ 293.2 and 308.2 K).a x3' T(K)

0.9783

0.9437

0.7585

0.7585

P(MPa)

x1$103

P(MPa)

x1$103

P(MPa)

x1$103

P(MPa)

x1$103

293.2

0.412 0.920 1.613 1.862 2.521

2.91 ± 0.008 6.59 ± 0.009 11.1 ± 0.009 12.7 ± 0.011 17 ± 0.011

0.432 0.930 1.591 1.846 2.531

3.65 ± 0.02 9 ± 0.02 13.9 ± 0.02 16.1 ± 0.02 21 ± 0.02

0.432 0.983 1.628 1.830 2.531

5.53 ± 0.03 12.4 ± 0.03 21.2 ± 0.03 25 ± 0.03 32 ± 0.03

0.446 0.928 1.657 1.849 2.531

11.2 ± 0.04 23 ± 0.04 42.6 ± 0.05 48.3 ± 0.05 61 ± 0.05

308.2

0.466 1.010 1.594 2.110 2.670

2.6 ± 0.008 5 ± 0.009 8.4 ± 0.009 12.1 ± 0.01 15.1 ± 0.011

0.466 0.953 1.545 2.164 2.673

2.9 ± 0.02 5.4 ± 0.02 9.4 ± 0.02 13.8 ± 0.02 17.6 ± 0.02

0.474 1.024 1.588 2.042 2.565

4.3 ± 0.03 9.3 ± 0.03 14.2 ± 0.03 18 ± 0.03 23.3 ± 0.03

0.578 0.999 1.507 1.996 2.623

10.2 ± 0.04 17.9 ± 0.04 27.6 ± 0.05 36.7 ± 0.05 47.5 ± 0.06

a x3’ is the mole fraction of H2O in the mixture of PEG200/H2O before CO2 injection. Standard uncertainties (u) are u(P) ¼ 0.001 MPa, u(T) ¼ 0.1 K and u(x3’) ¼ 0.0001. The values of uc(x1) are listed in the table.

Table 7 Solubility of CO2 (1) in PEG200 (2) þ H2O (3) at different temperatures (x3’ ¼ 0.9437).a T(K)

293.2

308.2
3

x3'

P(MPa)

x1$10

0.9437

0.432 0.930 1.591 1.846 2.531

3.65 ± 0.02 9 ± 0.02 13.9 ± 0.02 16.1 ± 0.02 21 ± 0.02

323.2
3

P(MPa)

x1$10

0.466 0.953 1.545 2.164 2.673

2.9 ± 0.02 5.4 ± 0.02 9.4 ± 0.02 13.8 ± 0.02 17.6 ± 0.02

338.2
3

P(MPa)

x1$10

0.535 1.017 1.499 2.023 2.622

2.8 ± 0.02 4.9 ± 0.02 7.2 ± 0.02 10 ± 0.02 13 ± 0.02

353.2
3

P(MPa)

x1$10

0.506 1.014 1.536 2.037 2.563

2.1 ± 0.02 4.4 ± 0.02 6.5 ± 0.02 8.8 ± 0.02 11.1 ± 0.02

P(MPa)

x1$10
3

0.466 1.011 1.492 1.962 2.506

1.5 ± 0.02 3.1 ± 0.02 4.8 ± 0.02 6.2 ± 0.02 8.2 ± 0.02

a x3’ is the mole fraction of H2O in the mixture of PEG200/H2O before CO2 injection. Standard uncertainties (u) are u(P) ¼ 0.001 MPa, u(T) ¼ 0.1 K and u(x3’) ¼ 0.0001. The values of uc(x1) are listed in the table.

8

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

Table 8 The binary NRTL parameters of CO2-PEG200, CO2eH2O [49], H2O-PEG200. NRTL CO2 CO2 H2O

PEG200 H2O PEG200

mij

nij

mji

nji

10.06 11.82


3268.10
3092.62

10.06 0.97


3268.10
1616.61

Fig. 4. CO2(1) solubility in PEG200(2)/H2O(3) at different H2O mole fraction (x3’) ((a), T ¼ 293.2 K; (b), T ¼ 308.2 K): experimental data; Curves, model correlation.

:,

0.9783; -, 0.9437; +, 0.8814; C, 0.7585. Symbols,

detecting the gas composition (i.e. the gas chromatography) needs to be used when the vapor pressure of H2O is relatively high. While it should be pointed out that the model results with the consideration of these two points or not are almost the same.

3.3. Solvents comparison based on properties

Fig. 5. CO2(1) solubility in PEG200(2)/H2O(3) (x3' ¼ 0.9437) at different temperatures: △, 293.2 K; -, 308.2 K; :, 323.2 K; C, 338.2 K; +, 353.2 K. Symbols, experimental data; Curves, model correlation.

H2O results in around 8% and 4% higher CO2 solubilities than the actual values. Therefore, it should be careful to use the assumption of negligible vapor pressure of H2O, and an effective tool for

The performance of solvents for CO2 separation strongly depends on the properties, such as absorption capacity, selectivity, viscosity, etc. The comparison of the properties can provide preliminary evaluation, which can be very useful for preliminary screening of solvents. In this part, the commercialized physical solvents of DEPG, methanol and PC were chosen for comparing with PEG200 and PEG200/H2O. Meanwhile, based on our previous work [27], the IL of 1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl)-imide ([bmim][Tf2N])) can be a promising physical solvent for CO2 separation, and it was also included in comparison. Considering the comparison is based on physical solvents, in comparison, besides the density, viscosity, CO2 absorption capacity and gas selectivity, the CO2 absorption enthalpy can be one more important factor for performance evaluation.

Table 9 Solubility of CH4 or N2 (1) in PEG200 (2) þ H2O (3) with different H2O mole fraction (x3’) at 293.2 K.a x3'

0.9783

0.9437

0.8814

0.7585

P(MPa)

x1$10
3

P(MPa)

x1$10
3

P(MPa)

x1$10
3

P(MPa)

x1$10
3

CH4

0.340 0.465 0.655 0.846 1.039

0.11 ± 0.005 0.22 ± 0.006 0.25 ± 0.006 0.34 ± 0.006 0.4 ± 0.007

0.299 0.46 0.664 0.869 1.034

0.25 ± 0.006 0.35 ± 0.006 0.4 ± 0.007 0.5 ± 0.008 0.6 ± 0.009

0.293 0.428 0.608 0.79 1.02

0.28 ± 0.009 0.5 ± 0.01 0.65 ± 0.01 0.75 ± 0.01 1 ± 0.01

0.281 0.485 0.691 0.898 0.988

0.8 ± 0.02 1.4 ± 0.02 2 ± 0.02 2.4 ± 0.02 2.7 ± 0.02

N2

0.711 1.334 1.691 2.146 2.512

0.09 ± 0.006 0.23 ± 0.006 0.3 ± 0.007 0.33 ± 0.007 0.4 ± 0.007

0.65 1.107 1.643 2.122 2.551

0.15 ± 0.008 0.19 ± 0.008 0.31 ± 0.009 0.44 ± 0.009 0.46 ± 0.01

0.572 1.093 1.645 2.125 2.552

0.22 ± 0.01 0.35 ± 0.01 0.51 ± 0.01 0.61 ± 0.01 0.75 ± 0.01

0.599 1.268 1.772 2.12 2.511

0.42 ± 0.02 0.82 ± 0.02 1.14 ± 0.02 1.32 ± 0.02 1.5 ± 0.02

a x3’ is the mole fraction of H2O in the mixture of PEG200/H2O before gas injection. Standard uncertainties (u) are u(P) ¼ 0.001 MPa, u(T) ¼ 0.1 K and u(x3’) ¼ 0.0001. The values of uc(x1) are listed in the table.

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

9

Fig. 6. CH4 (a) or N2 (b)(1) solubility in PEG200(2)/H2O(3) at different H2O mole fraction (x3’) (T ¼ 293.2 K): C, 0.9783; B, 0.9437; -, 0.8814; ,, 0.7585. Symbols, experimental data; Curves, model prediction.

In this study, the CO2 absorption enthalpy in the solvent was estimated with the following well-known equations [50,51] by neglecting the excess enthalpy:

DHabs ¼ DHdis ¼
RT 2



vlnHCO2 ðT; PÞ vT

(20)

There are three approaches to calculate the gas selectivity: the ratio of mole fractions of the gases in the liquid at the certain temperature and pressure, the ratio of the bubble-point pressures of the gases at the certain temperature and composition, and the ratio of the Henry's constants of the gases in the liquid. In this study, the ideal gas selectivity of CH4 over CO2 (SCH4 =CO2 ) or N2 over CO2 (SN2 =CO2 ) was calculated as the ratio of their Henry's constants (H(T)) [23].

 SCH4 =CO2 ¼

   HCH4 ðTÞ HN2 ðTÞ and SN2 =CO2 ¼ HCO2 ðTÞ HCO2 ðTÞ

(21)

All the properties are listed in Table 10 for comparison, in which 293.2 K and 0.8 MPa were set to be the temperature and pressure because these are the typical operational conditions for the biogas upgrading with physical solvents. It can be seen that [Bmim][Tf2N] has the largest molecular weights (Mw) together with the highest density. The values of Mw for PEG200, DEPG and PC are also exceeded 100, and the viscosity is closely related to Mw except DEPG and PC, i.e. the higher the Mw, the higher the viscosity. Both DEPG and PC show advantages on the aspects of viscosity and CO2 absorption capacity. For all the solvents, the CO2 absorption enthalpy (DHabs) is always lower than
20 kJ mol
1. The methanol has the optimal CO2 absorption capacity and viscosity while

SCH4 =CO2 is the lowest, which means that it might not be appropriate for biogas upgrading. Meanwhile, SCH4 =CO2 and SN2 =CO2 of PEG200 are also lower among these physical solvents. With the addition of H2O, the CO2 absorption capacity and viscosity of PEG200 decrease while SCH4 =CO2 increases. This implies that PEG200/H2O might have an advantage for biogas upgrading with the consideration of higher CO2 absorption capacity compared to H2O. 3.4. Performance evaluation on biogas upgrading In our previous work [29], the performance of DEPG and PC has been evaluated and compared with H2O as a benchmark, showing that DEPG is inferior to H2O while the PC is better than H2O. In this study, the performance of PEG200 and PEG200/H2O for CO2 separation was also compared with H2O. To further evaluate the performance of PEG200 and PEG200/H2O for CO2 separation, biogas upgrading was chosen as an example because the performance of other physical solvents for biogas upgrading has been evaluated in our previous work [27,28]. There are seven components (i.e. H2O, PEG200, CO2, CH4, N2, O2 and H2S) involved in the biogas upgrading with PEG200/H2O. The content of H2S can be ignored because there is an H2S pretreatment in the real upgrading process. At the same time, the trace percentages of N2 and O2 can also be neglected in the process simulation. A conceptual process for biogas upgrading with physical solvents has been constructed in our previous work [27,28], and it was used directly in this work. The simulation was performed with the equilibrium approach. The operational parameters of the biogas upgrading process are listed in Table 11, which are similar as in our previous work [27,28].

Table 10 Properties of physical solvents at 293.2 K and 0.8 MPa. Solvent

Mw

ra (kg$m
3)

ha (mPa$s)

cb (g CO2$g
1 solvent)


DHabs (kJ$mol
1)

SCH4 = CO

H2O [24],c PEG200 PEG200(1)/H2O(2) x2¼0.9437d PEG200(1)/H2O(2) x2¼0.7585d DEPG [29,52,53],c PC [29,53],c Methanol [54],c [Bmim][Tf2N] [27]

18.01 200.00 28.81 61.95 280.00 102.00 32.04 419.36

997.8 1124.0d 1060.1 1115.2 1055.4 1188.4 792.0 1441.0

1.0 66.0 4.4 34.6 7.6 2.8 0.6 60.0

0.0045 0.0087d 0.0046 0.0054 0.0150 0.0158 0.0292 0.0106

17.34 12.67 17.08 16.21 11.49 13.75 13.64 14.09

25.30 9.26 17.24 11.38 15.55 25.46 8.62 15.89

Standard uncertainties u are u(r) ¼ 0.1 kg m
3, u(h) ¼ 0.1 mPa s, u(x2) ¼ 0.0001 and u(c) ¼ 0.0001 g CO2$g
1 solvent. a At 293.2 K and 0.1 MPa. b At 293.2 K and PCO2 ¼ 0.28 MPa. c Aspen Databank. d Measured in this study.

2

SN2 =CO2 55.32 31.30 53.24 48.23 57.94 93.61 28.17 -

10

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336 Table 11 The parameters of process simulation. Parameter

Units

Values

CH4/CO2 Praw biogas Traw biogas Pabsorber/Pflash/Pdesorber Tabsobenr/Tdesorber Plant capacity CO2 removal CH4 loss

mol% MPa K MPa K Nm3$h
1 % %

50/50 0.1 293.15 0.8/0.3/0.1 293.2/293.2 250 96.15 <1

Fig. 7. The recirculated solvent (m) and the energy usage (E) of biogas upgrading using PEG200(1)/H2O(2).

The biogas upgrading using PEG200 and PEG200/H2O as solvents was simulated. After upgrading, the CH4 contents in the biogas are all increased to 96.2 mol% that can be used as the fuel for the public vehicles. The results of the total energy usage (Etotal) and the amount of recirculated solvent (m) are depicted in Fig. 7. With increasing the PEG200 content, both Etotal and m decrease, which indicates that adding PEG200 can improve the performance for biogas upgrading. It is worth noting that the energy used for the raw biogas compression occupies more than 50% in Etotal. When H2O is replaced by PEG200 completely, the values of Etotal and m can decrease by 9.1% and 26.5%, respectively. Therefore, even there is the negative effect on SCH4 =CO2 and viscosity of solvents with PEG200 adding, PEG200/H2O are still promising solvents for biogas upgrading.

PEG200, the CO2 absorption capacity and viscosity of PEG200/H2O increase while SCH4 =CO2 decreases. When H2O is replaced by PEG200 completely, the total energy usage and the amount of recirculated solvent can decrease by 9.1% and 26.5%, respectively. PEG200 and PEG200/H2O are promising solvents for biogas upgrading.

4. Conclusions

Supplementary data to this article can be found online at https://doi.org/10.1016/j.fluid.2019.112336.

A systematical study on PEG200 and PEG200/H2O was conducted in order to use them as solvents for CO2 separation. The available experimental thermo-chemical properties of PEG200 and PEG200/H2O were surveyed, evaluated and correlated with empirical equations. The solubility of CO2 in PEG200 was surveyed, evaluated and described with the Henry's law with Poynting correction, while the solubilities of CH4 and N2 in PEG200 was determined experimentally and then described with the Henry's law. The CO2 solubility in the PEG200/H2O was also measured and correlated with RK-NRTL model. All the modelling results agree well with the experimental results from literature or measured in this work. In addition, the performances of PEG200, PEG200/H2O and other commercialized physical solvents for CO2 separation were compared based on the properties, and biogas upgrading was chosen as the example to quantitatively evaluate the performances of PEG200 and PEG200/H2O. PEG200 has a relatively high CO2 absorption capacity, but SCH4 =CO2 is relatively low. With the addition of

Acknowledgments We would like to thank the National Natural Science Foundation of China (21729601, 21776123, 21136004, 21476106, 21428601, 21490584). C. Ma and X. Ji thank Swedish Energy Agency and Y. Chen thanks Kempe foundation in Sweden for financial support. Appendix A. Supplementary data

Nomenclature

Abbreviations P pressure, MPa T temperature, K H Henry's constant, MPa xi mole fraction of component i in the liquid phase Z compression factor R gas constant, 8.314 J mol
1 K
1 yi mole fraction of component i in the gas phase V∞ infinitely dilute partial volume of gas i in solvent, i m3$kmol
1 V lj mole volume of the solvent j, m3$kmol
1 V BO characteristic volume for i, m3$kmol
1 i Tb normal boiling temperature, K Tc critical temperature, K

Y. Chen et al. / Fluid Phase Equilibria 504 (2020) 112336

Pc Zc Vc P0 Pe Pv VA VL DH S Mw m

critical pressure, MPa critical compression factor critical volume, m3$kmol
1 initial pressure of the cell, MPa equilibrium pressure of the cell, MPa pressure of the vapor, MPa volume of the cell, m3 volume of the absorbent, m3 enthalpy, kJ$mol
1 gas selectivity molecular weight, g$mol
1 recirculated solvent amount, ton/h

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