Multicomponent Vapor-Liquid Equilibrium Measurements and Modeling of Triethylene Glycol, Water, and Natural Gas Mixtures at 6.0, 9.0 and 12.5 MPa

Triethylene glycol (TEG) is commonly used for natural gas dehydration


Introduction
As the subsea processing facilities are continuously expanding, we have an increasing attention to complex phase behavior of systems containing petroleum fluids and polar chemicals such as water, methanol, or glycols.Among these compounds, called generically as "production chemicals", triethylene glycol (TEG) has been used in vast quantities as the most popular fluid for natural gas dehydration (NGD) facilities, as it provides superior cost-benefit compared to other fluids [1][2][3].The dehydration process needs to achieve very stringent product specifications to ensure asset integrity in downstream transport, since water as impurity in natural gas is associated with several operational problems, such as corrosion and gas hydrate formation [4].On the other hand, this chemical may have a negative effect on the downstream process and might be found in the refined products going to the consumer, which is evidently not desired.The tendency therefore is to balance the use of TEG in considerable process safety margins and its environmental consequences [5].For that, it is important to know the partitioning of the chemical between the gas, crude oil, and water phase.Different methods and software can be used to obtain more or less accurate predictions of the interaction between these chemicals.Mostly of them are dependable on thermodynamic models, which rely on the precision and accuracy of experimental data [6].
In this context, this work has focused on the application of TEG in multicomponent systems of interesting for oil & gas processes, an area where few data are available in open literature.In this paper we present the results of vapor− liquid equilibrium (VLE) experiments for aqueous TEG (above 95 wt.% ) with two different natural gas mixtures, referred as "Synthetic Gas", an artificial gas with high concentration of N 2 , CO 2 and ethane, and "Real Gas", with composition correspondent to that of an actual natural gas with high concentration of CH 4 .The experimental conditions were varied with temperature and pressure within the following ranges: T = (288− 303) K, P = (6.0,12.5) MPa, which are relevant for the aforementioned applications.Additionally, the newly measured data were used in the evaluation of the Cubic-Plus-Association (CPA) EoS in order to assess its applicability for natural gas dehydration facilities modeling.CPA is ideally suited for the description of the interactions between alkanes (for which cubics were developed) with water and glycols (for which the association contribution was developed).Several studies have demonstrated CPA good performance for relevant systems for NGD processes [6][7][8][9].Given that association interactions are specifically accounted for, and the relative simplicity, CPA was chosen for comparison with the experimental data generated in this work.

Thermodynamic modeling with CPA-EoS
The Cubic-Plus-Association (CPA) EoS is based on the Soave-Redlich-Kwong (SRK) [10] model, which accounts for the inter-molecular attraction from physical forces and repulsion, while the association term (taken from the Statistical Associating Fluid Theory [11,12]) accounts for specific site-site interactions such as hydrogen bonding.The 1999 version of CPA [13], which includes a simplified expression for the radial distribution function, has been used in this work.The pressure-explicit form of the model is described using three terms in Eq. 1.The model has been discussed in our previous works [14,15], and therefore only a brief description is provided here.
Five The first three parameters are used directly in the calculation of the SRK contributions in Eq. 1, where a 0 and c 1 are implemented inside the α-function (Eq.2).The reduced temperature (T R ) is the system temperature divided by the component critical temperature (T c ): Table 1 CPA pure component parameters for the compounds used in this work.
The ε and β parameters are required to describe the association contribution, being directly used for the association strength (Δ Ai Bj ) between site A on molecule i (A i ) and site B on molecule j (B j ) calculation: Here, the chosen association scheme determines which interactions are possible in the calculation of the association strength (Eq.3).In this study, two associating molecules were considered: TEG and H 2 O.Both molecules have parameter sets readily available in the literature using the 4C association scheme (see Tables 1-2) adopted in this study.In addition to the well-stablished 4C scheme, with pure component parameters by Derawi et al. [16], TEG was also modelled with the newly proposed 4F, 5F, 6F and 5C association schemes, with parameters by Qvistgaard et al. [15].A visual representation of each scheme can be seen in Fig. 1.
The association strength carries forward into the calculation of the fraction of non-bonded sites: X Ai refers exactly to those association sites A on molecule i which are not involved in any site-site interactions.To picture the effect of the association scheme, consider the simplified case of a mixture of two molecules i and j, each with association sites A and B. If A and B cannot interact, the exponential term in Eq. 3 will become 1 and therefore the association strength will become 0. Therefore in Eq. 4, X A i will be equal to 1 i.e., all sites A on i will be unbonded.Conversely, if A-B interactions are allowed then Eq. 3 resolves to a positive number meaning that the denominator in Eq. 4 is greater than 1.Therefore, X A i will be equal to a positive number smaller than 1 i.e., some molecules i are now bonded via site A. If the decreased X Ai is carried through to Eq. 1, it is following the logical result: increased hydrogen bonding results in lower pressure.Although X Ai is a function of X Bi , the set of equations evolving from Eq. 4 can be resolved relatively simply into analytical functions as shown by Huang and co-workers [26,27].Michelsen [28] has proposed a minimization/maximization approach for solving this problem.
For mixtures, these pure component association parameters are subject to combining rules.In this work the CR-1 rule has been applied, where the association energy is obtained by the arithmetic average, and a geometric average is used for the association volume: Solvation in TEG-CO 2 was accounted by applying a modified CR-1 rule (mCR-1), where the cross-association volume is fitted to experimental data, mathematically formulated as in Eq. 8: ε Ai Bj = ε associating 2 (Eq.7) β AiBj = β cross (fitted to exp.data) (Eq.8) For the CO 2 -H 2 O mixture, solvation was accounted by fitting the cross-association volume to experimental data, and cross-association energy was obtained from experimental data as shown by Tsivintzelis et al. [18].This is considered a custom combining rule, denoted as cCR-1 in Table 2.
For the SRK-terms, the standard van der Waals one-fluid mixing rules have been applied for α(T) and b: Where: A temperature-dependent binary interaction parameter (k ij ) is used in Eq. 11, which has the general form: Fig. 1.Association schemes proposed in literature for TEG.The 6D association scheme (as proposed by Breil et al. [25]) is not used in this study.Image borrowed with permission from Qvistgaard et al. [15].
In this work, each k ij was implemented by using either k ij,2 or k ij,3 , but not both.The pure component parameters of CPA are shown in Table 1 and the interaction parameters for the involved mixtures are presented in Table 2.
Binary interaction parameters between TEG and the alkanes ethane, propane, i-butane, n-butane, n-hexane and n-pentane are only available for the TEG 4C association scheme in literature.Therefore, the 4F, 5F, 6F and 5C association schemes will be modelled with the 4C binary interaction parameters for beforementioned binaries in this study, which likely will reduce model performance.
All thermodynamic calculations were performed with the "Pythermo" Python package, using Python version 3.8.Pythermo is a wrapper package, containing functions capable of modelling thermodynamic properties of fluid phase equilibria, and core functionality developed by the Center for Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering at Technical University of Denmark (DTU).

Materials
The compounds used in this work were classified as a liquid or gas depending on how they were loaded into the equilibrium cell.The specifications of the liquid compounds are given in Table 3.No additional purification was performed.
The other compounds were loaded into the cell from two different natural gas mixtures cylinders.These mixtures will be referred as "Synthetic Gas", an artificial gas with high concentration of N 2 , CO 2 and ethane, and "Real Gas", with composition corresponding to that of an actual natural gas.The gas mixture composition was determined by GC with the molar composition given in Table 4 and Table 5.
The gas phase content for components heavier than C 6 were in the low ppm level.For practical purposes, these trace components were too near the limit of detection of the μGC to allow for accurate quantification, especially for the "flash gas" analysis.For this reason, C 6+ is modelled as n-Hexane in this study.

Experimental procedure
The experiments were conducted using a high-pressure equilibrium cell manufactured by Sanchez Technology (now Core Laboratories), which has been previously described [8,29,30].Fig. 2 shows the two cylindrical nickel-alloy compartments connected through a sapphire window.A magnetic stirrer (S-1) was fitted inside the lower piston to ensure mixing of phases.The apparatus was placed inside an air bath within ± 0.5 K maximum temperature variation in the range (223, 473) K and three inlet/outlet valves were connected to the cell.
The loading and equilibration procedures are those used by Kruger et al. [8], with the exception that natural gas mixtures have replaced pure methane.The cell was first set to its minimum volume (~30 ml) and washed with water and acetone before placed under vacuum (P < 0.0002 MPa) for about 12 h to secure a complete cleaning.The temperature, measured using a PT100 element and P-655-Ex digital thermometer (Dostman Eletronic) (TT) with an accuracy of ± 0.05 K, was stabilized on the desired experimental condition.Thereafter, the cell was pressurized (6.0, 9.0, or 12.5 MPa), with approximately 250 ml of the gas mixture via valve V-2 A. The pressure, measured with a Keller Pax 33X digital high-pressure transmitter (PT) with < 0.2% of accuracy in the full scale (up to 100 MPa), was controlled during the experiments by hydraulic pumps (P-1 and P-2) that adjusted the cell volume, changing the pressure in the hydraulic oil on the behind of each piston.Instantaneous pressure fluctuations (resulting from the opening of a sampling valve) of greater than 0.8% of the experimental pressure would result in automatic exclusion of the results, but typically values better than 0.33% were observed.Then, the prepared TEG/water liquid solution (50 ml ± 2) was loaded into the cell by using a Quizix pump    (P-1) via valve V-3 A. Once loading was completed, the magnetic stirrer was turned on and set to a constant speed.Equilibrium conditions were reached typically within 12 h.Once equilibrium was achieved, sampling commenced.Therefore, typically 10 gas samples (~500 ml each) were routed, via valve V-1 A, through ATD tubes and analyzed by GC− MS-2 to calculate TEG vapor composition (y 1 ).Duplicate three-point calibration (versus standard solutions) was performed for each batch of samples.The water content of the gas phase (y 2 ) was measured by routing 5-8 vapor samples (~500 ml each), via valve V-1 B, to the KF analyser (Metrohm 831, u = ± 0.03).Depending on the volume of gas available and the stability of the measurement, between 5 and 15 parallel samples (around 300 ml of gas each) were taken.The gas sample volume was estimated using the gas meter (GM-2) operating at atmospheric pressure.
For the liquid phase, firstly, the entire sampling pathway, including the gas meter, was evacuated by using a vacuum pump (P-2).The sample space was then pressurized to 0.115 MPa with helium to minimize atmospheric ingress.The tubing between the cell and the separator was then flushed with approximately 5 ml of liquid from the cell before a single 25 ml sample was taken via valve V-3 B. The gas meter (GM-1) volume change, in addition to the liquid sample mass (Ohaus Explorer Pro, m ± 0.001 g), water content (Metrohm 915 Ti-Touch, u = ± 0.02), and density (Anton Paar DMA 4500 M, ρ ± 0.00007 g.mol − 1 ) were used to determine the dissolved gas content in the liquid phase.The Agilent 3000 μGC with four channels (details in Table 6), in its turn, was used for the quantification of each component dissolved in the "flash gas" (x NG ) and in the vapor composition (y NG ).For that, it were taken, respectively, 5-8 samples from the GM-1 via valve V-4 A, and 46 samples directly from the vapor phase of the equilibrium cell through V-2 B and V-4 B (green pathway in Fig. 3).
The μGC was calibrated using four calibration gasses, allowing for the quantification of up to 15 components.Periodic verification and recalibration were performed in order to ensure accurate measurements.Also, the first few samples were used to flush the sampling system until a predefined threshold (i.e., GC peak area) for O 2 content was met, as air ingress into the sampling pathways could not be completely negated.Thereafter it was still necessary to reprocess the N 2 composition, by subtracting the amount of air contamination.It was assumed that the N 2 contamination from air was related to the O 2 content according to a 79:21 ratio.Leakage was typically negligible for the y NG measurements (due to the high pressure in the system after a single sample flush), while for the contamination of the "flash gas" it was typically around 1.5 mol %.

Results and discussion
A total of 42 and 27 vapor-liquid equilibria (VLE) measurements combining different temperature, pressure, and water content in the liquid solution filled into the equilibrium cell were evaluated for the Real and the Synthetic Gas mixtures, respectively.Table 7 shows all the VLE data for both gasses.All experiments were repeated 2-4 times to obtain stable experimental conditions and a saturated sampling system.The reported experimental result will in general be the last experiment at a given condition.Unless stated otherwise, the uncertainty was calculated in the relative form presented in Eq. 14, where σ refers to the standard deviation and μ to the average of the parallel experimental figures, respectively: The experimental effort needed to precisely measure the composition of the vapor phase in these systems can be seen in Table 7, as even though each experiment was repeated until stable conditions it was not possible to obtain the glycol and water content for some points.In addition, it is notable how slight changes of experimental conditions cause a great variation in the experimental data reported.Experiments number 5 and 6 with Real Gas, for example, differ only in 0.1 K, 0.02 bar and 0.06 in water content, but their final glycol concentration in the gas phase differ in 0.0021 ppm of TEG and 5.63 ppm of water, which means 59% and 93%, respectively, in this very low scale.
The CPA performance using the different TEG parameter sets provided in Tables 1 and 2 was also compared with the experimental data according to average absolute relative deviation (AARD) expressed as percentage.
Where N is the number of data points, and n refers to the index for a particular data point.
Here, the model values were obtained through VLE flash calculations, in which the feed composition was obtained by combining the proportion TEG/water of the aqueous solution weighted and the composition from Table 4 or 5 for the vapor phase at each experimental condition (T, P, V gas ).The compressibility factor was calculated using the CPA equation of state.
The parameters obtained by Derawi et al. [16] for the 4C association

Table 7
Experimental conditions (temperature (T), pressure (P), and water content (mass basis) in liquid loaded into the equilibrium cell (w 2 )) and VLE data as mole fractions of triethylene glycol (y 1 ) and water (y 2 ) in the vapor phase, and gas solubility in the liquid phase (x NG ) given as the sum of mole fractions of compounds listed in Table 4    scheme presents overall best results for the systems in study.The deviations obtained for gas solubility and water in the gas phase agree with values reported by previous studies of glycols with natural gas [8,30], while the TEG content in the vapor phase stood out with high values.This might not necessarily be a problem, as the high measurement uncertainty for such low concentrations (<1 ppm) may negatively affect model performance.
The results are shown in Table 8 for Synthetic Gas and Table 9 for Real Gas, respectively:

TEG in gas phase
Fig. 4 shows TEG in gas phase (y 1 ) measurements along with CPA modeling as a function of temperature.It is possible to observe that higher pressure results in higher TEG content in the vapor phase, with the values at 125 bar being usually two orders of magnitude higher than at 60 bar for the same temperature and TEG purity.In relation to temperature, an exponential relation of y 1 is seen and, although small, a direct proportional dependence of y 1 on the TEG purity is also noted.This last observation combined with the significant higher TEG content for the Synthetic Gas in comparison to the Real Gas at same experimental conditions, suggest a strong interaction effect between TEG and molecules such as CO 2 , where a solvation effect is exhibited.
The average standard deviation is determined as ± 0.01 for the parallel measurements, yielding an overall uncertainty of ± 28%.Furthermore, it is observed that the CPA model generally overpredicts the glycol content in the gas phase, especially for higher TEG/water ratio.This might be explained by the measurement uncertainty from contamination of moisture from the atmosphere.According to this explanation, it would be expected to see higher uncertainty for the 99 wt.%TEG/water solution than for the 95 wt.% TEG/water solution, since the atmospheric moisture content is more significant when the weight fraction of water in TEG is low.
Besides the high values for the AARD in this case, CPA captures the data trends.It is also noted the distribution of ARD values has a long tail in the high end, meaning the mean is artificially pulled up.Therefore, a more reasonable metric might be the median absolute relative deviation (MARD); the MARD of TEG in gas phase measurements for the 4C association scheme is 111%.
From a practical point of view, in which glycol in the vapor phase should be minimized, a low pressure and higher water content in the loaded liquid mixture are preferable.Therefore, the design of a natural gas dehydration unit at high pressure would necessarily have to consider the trade-off between the water and glycol specifications in terms of finding the optimal operating pressure and glycol purity.In both cases, lowering the temperature is a mechanism for improved dehydration.

Water in gas phase
Measurements of H 2 O content in the gas phase and predictions by CPA with all five association schemes are shown in Fig. 5.
Naturally, the amount of water in gas decreases as the water in the Combining this result with those discussed in the previous section, a low temperature, high pressure, and high purity glycol would be ideal for natural gas dehydration, which highlight the effects of the temperature and pressure as thermodynamic mechanisms for natural gas dehydration: higher pressure forces larger quantities of water into the liquid, and lower temperatures allow more water to condense into the liquid.
The CPA model provides a good description of the data, but generally under-predicts the experimental values, with an overall AARD of 47.8%.

Gas in liquid phase
Measurements and CPA modeling for gas content in the liquid phase are shown in Fig. 6.The data present almost a constant behavior, showing a low dependence in relation to temperature.The parallel measurements exhibit an average standard deviation of ± 0.0003, yielding an experimental uncertainty of ± 0.8% for both sets.
The dissolved gas content is directly proportional to the pressure and TEG purity.This indicates that both gas mixtures preferentially dissolve in glycol at high pressures.CPA over-predicts the experimental data, with an AARD calculated as 27%.It can be seen that the 4C scheme performs best for the Real Gas, at all water concentrations.However, for the Synthetic Gas there is no significant difference in the performance between 4C and the remaining association schemes.

Additional modelling
In this section, modeling of the Real Gas and Synthetic Gas is made for non-measured properties or ranges outside the measured conditions.For this part of the study, only the 4C association scheme is considered for TEG, due to its superior performance, as shown in the previous section.The motivation for this part of the study, is to utilize the advantage a predictive model gives us to improve our understanding of this system.
One of the measured properties is gas content in liquid phase, however the composition of the "gas" in liquid phase is not measured.Therefore, four molecules are selected from the gas mixture for further modeling: N 2 , CO 2 , CH 4 and Ethane.These molecules are chosen due to their high content in both the Synthetic and Real Gas.The presence of these four molecules in the liquid phase is modelled in three scenarios: at varying temperature with constant pressure and water content and at varying pressure with constant temperature and water content.Results can be seen in Fig. 7-8 respectively.
From the temperature dependency curves, it is seen an increase in temperature has only a slight effect on the gas content in the liquid phase with the CH 4 exception, liquid phase content decreases.From the pressure dependency curves in Fig. 7, the opposite trend is notice as an increase in pressure leads to an increase in gas content in the liquid phase, which is true for all four tested molecules and for both Synthetic and Real Gas mixtures.     1 and CR-1 for cross-association.The y-axis represents the sum of mole fractions of compounds listed in Table 4 and Table 5. .[16] parameter set (Table 1) and CR-1 for cross-association were used.

Conclusions
The phase behavior of natural gas dehydration systems is of great interest for the development of novel subsea facilities.In this context, new vapor-liquid equilibria data points were measured for the system triethylene glycol (1) + water (2) + gas mixtures (3) at 6.0, 9.0 and 12.5 MPa, temperature range between 15 • C to 40 • C, and glycol content above 95 wt.%.Two types of natural gas, a Synthetic Gas (x CH4 = 0.62) and a Real Gas (x CH4 = 0.92), were evaluated.The phase distributions have been quantified using a combination of Karl Fischer titration, gas chromatography, and density measurements.The relative experimental uncertainty range observed was u = (0.2-32)%, with the highest uncertainties for glycol (y 1 ) and water (y 2 ) in the vapor, measured in order of ppm.
Measurements and modeling show that the TEG content in the gas phase is directly proportional to pressure and temperature, while the presence of water in TEG has a minor but inverse effect on this parameter.Water in the gas phase was shown to be inversely proportional to TEG purity and pressure, and presented a direct relation to temperature.In relation to the gas content in the liquid phase, an increase in pressure and TEG purity leads to an increase of x NG .Temperature, however, showed a very minor influence on gas solubility.These observations are true for both Synthetic Gas and Real Gas.Modeling work shows that the well-established 4C association scheme for TEG provides better results that the remaining ones (4F, 5F, 6F and 5C).However, since these schemes also used binary interaction parameters for TEG-alkane fitted with TEG modelled as 4C, improvements may likely be found in future work by fitting new interaction parameters for each association scheme.The quantity of measurement for the model's performance used was the AARD, which shows high model to data errors for gas phase measurements (AARD > 100%), while model performance in liquid phase composition is higher (AARD < 30%) for the 4C association scheme.Poor performance in H 2 O content in the gas phase modeling is probably due to contamination from atmosphere, as discussed.Despite high AARD for TEG content in the gas phase, visual inspection reveals that the model can predict the trend of the experimental data.
The newly measured data support the application of subsea natural gas dehydration at high pressure, with lower temperatures also being advantageous.High glycol purity has been shown to be necessary to sufficiently dehydrate the gas, which makes this part of the process an optimization problem to find the ideal operating pressure and glycol purity relation that maximizes efficiency while reduces the TEG vapor content within process specifications.From a process design perspective, the CPA can be used for feasibility studies related to the product quality of natural gas dehydration units, but the over-prediction of gas solubility should be taken into account for the design of glycol regeneration units and predictions of the volume of sales gas.[16] parameter set (Table 1) and CR-1 for cross-association were used.

Fig. 2 .
Fig. 2. Schematic representation of the high-pressure cell used in this work for vapor-liquid equilibrium measurements.

Fig. 3 .
Fig. 3. Schematic representation of the experimental setup used for in this work to measure the vapor-liquid equilibrium of systems containing glycol, water, and gas mixtures.Green line represents the pathway to quantification of natural gas mix vapor (y NG ) and liquid (x NG ) compositions.

Fig. 4 .
Fig.4.TEG in gas phase (y 1 ) experimental data at 60 (◊) and 125 (x) bar in relation to temperature for the three loaded TEG purities (wt.%).CPA modeling (lines) used the different parameter sets presented in Table1and CR-1 for cross-association.

Fig. 5 .
Fig. 5. H 2 O in gas phase (y 2 ) experimental data at 60 (◊) and 125 (x) bar in relation to temperature for the three loaded TEG purities (wt.%).CPA modeling (lines) used the different parameter sets presented in Table1and CR-1 for cross-association.

Fig. 6 .
Fig.6.Gas solubility (x) experimental data at 60 (◊) and 125 (x) bar in relation to temperature for the three loaded TEG purities (wt.%).CPA modeling (lines) used the different parameter sets presented in Table1and CR-1 for cross-association.The y-axis represents the sum of mole fractions of compounds listed in Table4and Table5. .

Fig. 7 .
Fig. 7. CPA modelling of N 2 , CO 2 CH 4 and ethane content in liquid phase at constant pressure (90 bar) and water content (5 wt.% in TEG solution) in relation to temperature.Derawi et al.[16] parameter set (Table1) and CR-1 for cross-association were used.

Fig. 8 .
Fig. 8. CPA modelling of N 2 , CO 2 CH 4 and ethane content in liquid phase at constant temperature (25 C) and water content (5 wt.% in TEG solution) in relation to pressure.Derawi et al.[16] parameter set (Table1) and CR-1 for cross-association were used.

Table 2
Binary interaction parameters and combining rules for the binary mixtures considered in this work.The k ij is formulated in Eq. 13.Combining rules are formulated in Eq. 5, 6, 7 & 8.

Table 3
List of liquid components used in this work.*Resistivity at 298.15 K: 10-15 μS/ cm.

Table 4
Synthetic Gas Composition, where x refers to the mole fraction.

Table 5 Real
Gas Composition, where x refers to the mole fraction.C 6+ is modelled as n-Hexane in this study.

Table 7
Standard uncertainties are u(T) = 0.05K and u(P) = 0.2MPa.The expanded uncertainties for compositions are reported in the supported information. a

Table 8
Average absolute relative deviations between model predictions and Synthetic Gas data.Underlined values indicate the best performing association scheme in each category.

Table 9
Average absolute relative deviations between model predictions and Real Gas data.Underlined values indicate the best performing association scheme in each category.