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Thermodynamics, Transport, and Fluid Mechanics

Thermodynamic modelling and simulation of natural gas dehydration using triethylene glycol with the UMR-PRU model Eirini Georgiou Petropoulou, and Epaminondas Voutsas Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01627 • Publication Date (Web): 04 Jun 2018 Downloaded from http://pubs.acs.org on June 8, 2018

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Industrial & Engineering Chemistry Research

Thermodynamic modelling and simulation of natural gas dehydration using triethylene glycol with the UMR-PRU model Eirini G. Petropoulou, Epaminondas C. Voutsas* Laboratory of Thermodynamics and Transport Phenomena School of Chemical Engineering, National Technical University of Athens 9, Heroon Polytechniou Str., Zografou Campus, 15780 Athens, Greece

Abstract Dehydration of natural gas (NG) by absorption is a common industrial procedure implemented in order to avoid flow blockage and equipment breakdown. Despite the widespread use of dehydration units, few experimental data are available in the literature and most engineering practices are based on empirical correlations for the design and the determination of the optimum operational parameters. In this paper, an accurate thermodynamic model for NG mixtures, the UMR-PRU, is further extended to mixtures containing triethylene glycol (TEG) and is then used to simulate a typical NG dehydration unit using TEG, by incorporating it in commercial simulators through the CAPE-OPEN standard. The results are compared with those obtained by the recommended by Aspen Hysys, TST/NRTL model. The two models calculate similar lean TEG purity, TEG circulation rate and stripping gas rate in order to obtain the same level of dehydration, c.a. 30 ppm water in the dry gas, while some differences are observed in the component distribution in the vapor and liquid phases. In addition, different reboiler duties are calculated by the two models, with those of UMR-PRU to be considered more realistic due to better prediction of the heat capacities of aqueous TEG mixtures. Keywords: TEG dehydration, thermodynamic modelling, UMR-PRU, simulation, TST/NRTL

*

Corresponding author. Tel.: +302107723971; fax: +302107723155 E-mail address: [email protected] (E. Voutsas)

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1. Introduction Natural gas (NG) is saturated with water at reservoir conditions and depending on the field it can also contain various quantities of sour compounds such as carbon dioxide (CO2) and hydrogen sulfide (H2S). Those trace components can be diluted in the free-water phase creating corrosive conditions which could be harmful for equipment as well as product quality. Depending on the application, water is treated either by adding an amount of inhibitor or by its removal by absorption or adsorption. In the majority of natural gas offshore plants, dehydration by absorption using a liquid desiccant, usually some glycol, occurs. Although several glycols, can be successfully used for natural gas dehydration, triethylene glycol (TEG) is the most commonly used one since it combines good absorption properties with low volatility, rendering its application more viable from an economic and environmental point of view1. To comply with the demands for lower water content as well as the environmental legislation regarding e.g. the amount of hydrocarbons lost in the vapor phase or the glycol content in the dry natural gas product, many studies have been suggested in the literature. Most of the proposed works focus on the effect of the operating conditions e.g. reboiler temperature, stripping gas rate, TEG circulation rate and are based on empirical correlations for the TEG and water distributions2-8. Another parameter of interest for the design and operation of dehydration units is the solubility of aromatics in TEG9-11, which is higher compared to those of paraffins, with typical concentrations ranging approximately from 5 - 10% for benzene to 20 – 30% for ethylbenzene and xylenes. Benzene/toluene/ethylbenzene/o-xylene are commonly referred as BTEX components and their distribution in TEG streams is important due to environmental regulations. BTEX remain in the process and they finally end in the regenerator, where they are usually exhausted to the atmosphere. Due to the high temperature and their affinity with TEG, large amounts of BTEX are emitted causing serious environmental concerns even in small plants. Furthermore, BTEX distribution is of interest not only to the dehydration process, but also to the naphtha reforming in oil refineries12. For that reason, adequate thermodynamic modelling of BTEX compounds is necessary for the oil & gas industry in order to comply with the environmental legislation.13 In a series of papers3, 14-16 Bahadori has proposed several numerical correlations for various parameters, such as the solubility of H2S and CO2 in TEG or the water dew point depression, that are of interest during natural gas dehydration with TEG, which can be easily implemented in non-commercial simulating software. Specifically, the light hydrocarbon loss in TEG streams has been estimated with an overall 3.3% absolute average relative deviation (AARD) in a range of conditions close to those which occur in the dehydration process16, yielding more accurate results compared to a cubic equation of state (EoS). Based on their previous work, Bahadori et al.4 have proposed an empirical correlation for sizing the absorbers of a TEG dehydration system. Moreover, they have correlated the water removing efficiency of a contactor as a function of TEG purity and TEG circulation rate for varying operating temperatures and the proposed correlations have been evaluated against the reported Gas Processing Association (GPA) data for the contactor conditions, with satisfactory results. Gandhidasan5 has proposed empirical correlations for the parametric analysis of a TEG dehydration plant. The proposed correlations estimate the lean TEG circulation rate, the column inner diameter and the number of trays required to obtain certain dehydration levels. He concluded that the wet gas temperature 2 ACS Paragon Plus Environment

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has almost no effect on the required number of trays but it severely affects the TEG circulation rate, while when operating at higher temperatures the increase of the number of trays can result in lower TEG circulation rate. Furthermore, the increase of operating pressure results in a decrease of the TEG circulation rate as well as of the inner contactor diameter. A contemporary approach examined by Ghiasi et al.6 and Ahmadi et al.17 is the use of artificial neuron networks for TEG purity predictions and equilibrium water dew temperature of natural gas streams. Their modeling results have confirmed the integrity and have shown the ability of the suggested approach with adequate precision in comparison with the experimental data existing in the open literature. Jacob7 has developed a Hysys simulation to optimize the natural gas dehydration process. His analysis has focused on the number of stages of the contactor, the effect of the reboiler temperature and the stripping gas required for the design of a TEG dehydration plant, although no reference is given to the thermodynamic properties package used. Holoboff and Khoshkbarchi10 have compared the Hysys simulation software and the GRI-GLYCcalc simulation tools to predict benzene emissions from glycol dehydration systems and they showed that Hysys exhibits better performance as a simulator tool. Furthermore, they showed that the Glycol package predicts more accurately the dry gas water content and the TEG circulation rate. Nassar et al.18 have investigated the solubility of hydrocarbons in several physical solvents used as dehydrating agents with the PROSIM software and they concluded that it matches the experimental data very accurately in a range of temperature and pressure similar to the typical absorber conditions. They also concluded that TEG is a good dehydration agent and its use with low circulation rate can reduce the emission of volatile organic compounds (VOCs) into the atmosphere. Hernandez-Valencia et al.19 have also employed PROSIM for the TEG dehydration simulation by using the number of contactor trays, stripping gas rate and reboiler temperature as independent variables. They have concluded that an increase in the number of absorber trays decreases the glycol circulation rate, while the use of a three-stage absorber yields a typical TEG circulation rate as the one encountered in most plants. Darwish et al.9 have exploited the effect of the implemented thermodynamic model for the simulation of a typical TEG dehydration plant in Aspen plus with emphasis given in VOCs emissions in the regenerator. They examined two classic EoS, the Peng – Robinson (PR) and the Soave-Redlich-Kwong (SRK) combined with different mixing rules. They have employed both EoS with the classical van der Waals one fluid mixing rules and the Boston-Mathias expression for the alpha function of the attractive term, with a predictive mixing rule based on the Huron-Vidal (HV), with the modified Huron-Vidal mixing rule (MHV2) and with the Wong – Sandler (WS) mixing rule. They have also examined the predictive SRK model commonly known as PSRK. For all cases, the default interaction parameters existing in Aspen plus database have been utilized. They have concluded that no EoS has an overall advantage, while the use of the same mixing rules yield similar results with both examined EoS. PSRK and MHV2 mixing rules yield the more rational results in terms of VOCs emissions while they predict a quite accurate dehydration rate. Rouzbahani et al.8 have investigated the optimization of a diethylene glycol (DEG) dehydration unit in Aspen plus and they have concluded that the most accurate thermodynamic models to be used for that purpose are cubic EoSs combined with the MHV2 mixing rules. Arya et al.20 have evaluated the performance of the Cubic – Plus – Association (CPA) EoS as incorporated in a process simulator through the CAPE-OPEN protocol. They have satisfactorily correlated various 3 ACS Paragon Plus Environment


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binary mixtures and have predicted multicomponent ones, showing that the CPA EoS can be accurately used for the design of a dehydration system. In the same context, dos Santos et al.21 have validated the CPA EoS by incorporating the model in the PETROX-Petrobras simulator. They investigated the CPA prediction results in binary mixtures of hydrocarbons with alcohols (methanol, ethanol) and glycols (ethylene glycol, TEG) and they have obtained satisfactory results. Finally, they have evaluated the proposed model in an industrial application, in terms of modelling a TEG absorber, as well as a typical dehydration process. They have validated their results through comparison with those obtained with the proposed models for use with the dehydration process in two commercial simulators; that is Twu-SimTassone (TST) for Aspen and SRKM for PRO II, proving that CPA yields similar results with the recommended thermodynamic packages. The scope of this work is to develop a thermodynamic framework able to accurately describe the thermodynamic properties of the mixtures involved in the dehydration process, and to be used for its accurate simulation. To this purpose, the Universal Mixing Rules – Peng Robinson UNIFAC (UMRPRU)22, 23 thermodynamic model, which has been proven to accurately predict the hydrocarbon dew points of natural gas mixtures24, 25 is extended to mixtures involved in TEG dehydration. The model is validated against experimental data and is compared with the predictions of the Twu-Sim-Tassone Non-Random Two Liquid (TST/NRTL)26 EoS/AE model that is recommended by Hysys for the simulation of such process.


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2. Thermodynamic Modelling 2.1. The UMR-PRU model 2.1.1. Brief description of the model The UMR-PRU belongs to the so-called EoS/GE class and combines the PR27, 28 EoS with the UNIFAC29 activity coefficient model, through the Universal Mixing Rules (UMR). The volume translated Peng-Robinson EoS in terms of pressure is described by Eqs. (1) - (7), where Tc and Pc are the compound critical temperature and pressure and ω is the acentric factor. 𝑃=

𝑅𝑇 𝑎 − (𝑣 (𝑣 𝑣+𝑡−𝑏 + 𝑡) ∙ + 𝑡 + 𝑏) + 𝑏 ∙ (𝑣 + 𝑡 − 𝑏)

Eq. (1)

𝑎 = ac a(T)

ac = 0.45724

Eq. (2)

(RTc )2 Pc

Eq. (3)

a(𝑇) = [1 + 𝑚(1 − 𝑇𝑟0.5 )]2

Eq. (4)

𝑚 = 0.37464 + 1.54226𝜔 − 0.26992𝜔2

Eq. (5)

𝑏 = 0.07780

𝑅𝑇𝑐 𝑃𝑐

Eq. (6)

𝑡 = 𝑣𝑐𝑎𝑙𝑐 − 𝑣𝑒𝑥𝑝 , at Tr = 0.7

Eq. (7)

The volume translation (t) proposed by Peneloux et al.30 is adopted in this work to improve the volumetric property predictions. For non-polar components the volume translation of the translated and modified PR EoS is used as it was presented in the original publication of UMR-PRU23 model. In the case of TEG and water a constant translation at the reduced temperature (𝑇𝑟 ) of 0.7 is introduced as described in Section 3.1. The temperature dependent part of the attractive term parameter for pure non-polar compounds is calculated from Eqs. (4) and (5), while for polar compounds by the Mathias-Copeman31 (MC) modification of the PR EoS, as presented in Eq. (8). a(T) = [1 + 𝑐1 (1 − 𝑇𝑟0.5 ) + 𝑐2 (1 − 𝑇𝑟0.5 )2 + 𝑐3 (1 − 𝑇𝑟0.5 )3 ]2

for

𝑇 ≤ 𝑇𝑟

Eq. (8) a(𝑇) = [1 + 𝑐1 (1 − 𝑇𝑟0.5 )]2 for

𝑇 > 𝑇𝑟



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The parameters c1 , c2 and c3 in Eq. (8) are pure-component specific adjustable parameters, which are determined by fitting pure-component vapor pressure data. For the extension to mixtures, the following Universal Mixing Rules (UMR) proposed by Voutsas et al.23 are applied, as per Eqs. (9) and (10). 𝐸,𝑆𝐺 𝐸,𝑟𝑒𝑠 𝑎 1 𝐺𝐴𝐶 + 𝐺𝐴𝐶 ai = + ∑ 𝑥𝑖 𝑏𝑅𝑇 −0.53 𝑅𝑇 𝑏𝑖 𝑅𝑇

Eq. (9)

i

1/2

𝑏 = ∑ ∑ 𝑥𝑖 𝑥𝑗 𝑏𝑖𝑗 𝑖

𝑏𝑖 with 𝑏𝑖𝑗 = (

𝑗

1/2 2

+ 𝑏𝑗

)

2

Eq. (10)

E,SG E,res The Staverman-Guggenheim term of the combinatorial part (GAC ) and the residual part (GAC ) of the E excess Gibbs energy (G ) respectively, are calculated from Eqs. (11) – (14). 𝐸,𝑆𝐺 𝐺𝐴𝐶 𝜃𝑖 = 5 ∑ 𝑥𝑖 𝑞𝑖 𝑙𝑛 , 𝑅𝑇 𝜑𝑖

𝐸,𝑟𝑒𝑠 𝐺𝐴𝐶 = ∑ 𝑥𝑖 𝑣𝑘𝑖 (𝑙𝑛𝛤𝑘 − 𝑙𝑛𝛤𝑘𝑖 ) 𝑅𝑇

𝑖

𝑖

𝑙𝑛𝛤𝑘 = 𝑄𝑘 [1 − 𝑙𝑛 (∑ 𝜃𝑚 𝛹𝑚𝑘 ) − ∑ 𝑚

For compound i:

Eq. (11)

𝑚

𝜑𝑖 = ∑

𝑥𝑖 𝑟 𝑖

𝜃𝑖 = ∑

𝑗 𝑥𝑗 𝑟 𝑗

For group m: 𝜃𝑚 =

𝑋𝑚 𝑄𝑚 , ∑𝑛 𝑋𝑛 𝑄𝑛

𝜃𝑚 𝛹𝑚𝑘 ] ∑𝑛 𝜃𝑛 𝛹𝑛𝑚 𝑥𝑖 𝑞 𝑖

𝑗 𝑥𝑗 𝑞 𝑗

,

Eq. (12)

Eq. (13)

(j)

Xm =

∑j νm xj (j)

∑j ∑n νn xj

,

Eq. (14)

The interaction parameter Ψmk between groups m and k is a function of temperature, and it is calculated by Eq. (15), 𝛹𝑚𝑘 = 𝑒𝑥𝑝 [−

𝐴𝑚𝑘 + 𝐵𝑚𝑘 (𝑇 − 298.15) + 𝐶𝑚𝑘 (𝑇 − 298.15)2 ] 𝑇

Eq. (15)

where Amk, Bmk and Cmk are binary adjustable interaction parameters, which are determined by fitting binary phase equilibrium data. The UNIFAC structural surface area and volume parameters (Ri, Qi) used in UMR-PRU are summarized in Table S.1 in the Supplementary Information.

2.1.2. Implementation to commercial process simulators The UMR-PRU model is not available as a built-in model in commercial process simulators such as Aspen Hysys©. Most commercial simulator tools nowadays are compatible with the CAPE OPEN standard maintained by the co-LAN consortium, which enables the communication between an external property package and a simulator. It gives, thus, the opportunity to implement a user-defined model, in this case the UMR-PRU, instead of the thermodynamic models available as built-in in the process simulators. The 6 ACS Paragon Plus Environment

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CAPE OPEN standard32 defines different properties which can be interfaced from the simulator. The properties currently supported by the UMR-PRU property package are presented in Table S.2. In this work, the UMR-PRU model is implemented through the CAPE OPEN 1.1 protocol to the Aspen Hysys© and Honeywell Unisim© process simulators. 2.2. The TST/NRTL model Twu et al.33, 34 developed a cubic EoS/AE mixing rule by combining the TST35 EoS with the NRTL model through zero-pressure mixing rules26. In this essence, they describe the non-ideal binaries, such as the TEG/water through the advanced mixing rules, while for the traditional components, e.g. hydrocarbons, the model reverts to the TST EoS. Eqs. (16) – (20) present the TST EoS, where Tc and Pc are the compound critical temperature and pressure. The alpha function of the attractive term is the one proposed by Twu et al. 36 as described in Eq. (19), where L, M and N are compound specific pure component parameters determined by fitting vapor pressure data. 𝑃=

𝑅𝑇 𝑎 − 𝑣 − 𝑏 (𝑣 + 3 · 𝑏)(𝑣 − 0.5 ∙ 𝑏) 𝑎 = ac a(T)

ac = 0.470507

Eq. (17)

(𝑅𝑇𝑐 )2 𝑃𝑐

𝑁(𝑀−1) 𝐿(1−𝑇𝑟𝑁𝑀 )

a(𝑇) = 𝑇𝑟

𝑒

𝑏 = 0.0740740

Eq. (16)

𝑅𝑇𝑐 𝑃𝑐

Eq. (18) Eq. (19) Eq. (20)

The zero pressure mixing rules are expressed by Eqs. (21) - (26). The TST zero-pressure mixing rules assume that the excess Helmholtz energy of the van der Waals fluid at zero pressure, 𝐴𝐸0,𝑣𝑑𝑤 , can be approximated by the excess Helmholtz energy of the van der Waals fluid at infinite pressure, 𝐴𝐸∞,𝑣𝑑𝑤 , as per Eq. (24). ∗ 𝑎𝑣𝑑𝑤 1 𝐴𝐸0 𝐴𝐸0,𝑣𝑑𝑤 𝑎∗ = 𝑏 ∗ [ ∗ + ( − )] 𝑏𝑣𝑑𝑤 −0.518850 𝑅𝑇 𝑅𝑇

𝑎∗ =

Eq. (21)

𝑃𝑎 (𝑅𝑇)2

Eq. (22)

𝑃𝑏 𝑅𝑇

Eq. (23)

𝑏∗ =



∗ 𝐴𝐸0,𝑣𝑑𝑤 𝐴𝐸∞,𝑣𝑑𝑤 𝑎𝑣𝑑𝑤 𝑎𝑖∗ = = −0.59413 ∙ [ ∗ + ∑ 𝑥𝑖 ∗ ] 𝑅𝑇 𝑅𝑇 𝑏𝑣𝑑𝑤 𝑏𝑖

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Eq. (24)

𝑖

𝑏 = 𝑏𝑣𝑑𝑤 = ∑ ∑ 𝑥𝑖 𝑥𝑗 𝑏𝑖𝑗 with 𝑏𝑖𝑗 = 𝑖

𝑗

𝑏𝑖 + 𝑏𝑗 2

𝑎𝑣𝑑𝑤 = ∑ ∑ 𝑥𝑖 𝑥𝑗 𝑎𝑖𝑗 𝑤𝑖𝑡ℎ 𝑎𝑖𝑗 = √𝑎𝑖 𝑎𝑗 (1 − 𝑘𝑖𝑗 ) 𝑖

Eq. (25)

Eq. (26)

𝑗

Since A0E in Eq. (21) is at zero-pressure, its value is identical to the excess Gibbs free energy GE at zeropressure. Twu et al.26 proposed a multicomponent equation for GE that has the same structural form with the NRTL activity coefficient model, as shown in Eqs. (27) - (29), 𝑛

∑𝑛𝑗 𝑥𝑗 𝜏𝑗𝑖 𝐺𝑗𝑖 𝐺𝐸 = ∑ 𝑥𝑗 𝑛 ∑𝑘 𝑥𝑘 𝐺𝑘𝑖 𝑅𝑇

Eq. (27)

𝑖

𝜏𝑗𝑖 =

𝐴𝑗𝑖 + 𝐵𝑗𝑖 𝑇

𝐺𝑗𝑖 = exp(−𝛼𝑗𝑖 𝜏𝑗𝑖 )

Eq. (28) Eq. (29)

where 𝐴𝑗𝑖 , 𝐵𝑗𝑖 and 𝛼𝑗𝑖 are the NRTL interaction parameters. The pure component and binary interaction parameters for the TEG/water binary mixture are taken from Twu et al.26, while for the rest from the Hysys vs 8.8 database. 3. Extension of the UMR-PRU model to mixtures involved in TEG dehydration 3.1. Pure component parameters The critical properties (Tc and Pc) and the acentric factors (ω) required for the UMR-PRU model are taken from the DIPPR37, 38 data compilation. The Mathias-Copeman (MC) parameters, c1 , c2 and c3 , for water are taken by Boukouvalas et al.39, while a constant translation has been calculated by the experimental liquid molar volume at 𝑇𝑟 = 0.7. For TEG, the MC parameters have been determined in this work by fitting pure TEG vapor pressure data in order to get comparable results with the TST/NRTL model, for which the same procedure has been followed. Due to the very low volatility of TEG significant differences are encountered among the available vapor pressure experimental data. Furthermore, the DIPPR correlations differ throughout the years, depending on which dataset has been included in the correlation as well as the temperature range of interest. Derawi et al.40 in order to obtain pure TEG parameters for the CPA EoS, evaluated DIPPR1989 and DIPPR-2001, and concluded that the latter is in better agreement with the raw experimental data. Figure 1 presents a comparison of three versions of DIPPR correlations (1981, 1987 and 2001) along with raw experimental data, while the critical properties related to each correlation are tabulated in Table S.3.


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Figure 1: Vapor pressure of pure TEG. (a). Comparison of three DIPPR correlations against raw experimental data and model predictions: Experimental data (□) by Wise et al.41, (○) by Steele et al.42 and (∆) by Stull et al.43. DIPPR1981 with black dotted line, DIPPR-1987 with black dashed line, DIPPR-2001 with black long dash, dotted line, UMR-PRU with black solid line and TST/NRTL with grey dashed line; (b) focus at low temperatures.

DIPPR-1981 is closer to the raw experimental vapor pressures than the other DIPPR correlations at low temperatures as shown in Figure 1(b), which are of utmost importance for the design of the absorber in a TEG dehydration unit. On the other hand, similar vapor pressures with DIPPR-2001 are calculated for the higher temperatures, as shown in Figure 1(a). DIPPR-1987 correlation although performs well at the low temperature area, deviates from the majority of the experimental data and from DIPPR-2001 at the higher temperatures. Additionally, the critical properties provided by DIPPR-1987 differ from those of DIPPR1981 and DIPPR-2001, which are in good agreement with the experimental data40. For these reasons, in this work, the PR MC parameters have been fitted to the vapor pressure data generated by the DIPPR1981 correlation. It is noted that the temperature range for the fitting of the MC parameters is 323.15 – 692.15 K, in order to avoid the high uncertainty encountered due to the very low vapor pressure at the lower temperatures. Thus, Figure 1(b) presents extrapolation results for the UMR-PRU, which are very satisfactory. Moreover, a constant value of volume translation has been estimated by the experimental molar volume at 𝑇𝑟 = 0.7 taken from DIPPR-1981. The pure component parameters of UMR-PRU for water and TEG are presented in Table S.4 along with the results obtained by TST/NRTL. UMR-PRU yields better results than TST/NRTL at the lower T-range, Figure 1(b), while similar ones are obtained by the two models at the higher temperatures. Apart from the vapor pressure and liquid density, another significant property for simulation purposes is the heat capacity, since it determines the required heat duty in equipment where heat exchange takes place, such as the reboiler or heat exchangers. The isobaric heat capacity is calculated from Eq. (30), 𝑐𝑝 = (

𝜕𝐻 ) 𝜕𝑇 𝑃,𝑛

Eq. (30)

where H stands for the molar enthalpy, T for the temperature, P for the pressure and n for the number of moles. The isobaric heat capacity of TEG and water has been predicted with UMR-PRU and TST/NRTL 9 ACS Paragon Plus Environment


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and has been compared to experimental data available in the literature42, 44-46. UMR-PRU yields an overall AARD in TEG heat capacity equal to 9.4%, while TST/NRTL 23.1%. A graphical comparison between experimental and predicted heat capacities is shown in Figure 2. TST/NRTL systematically overestimates the 𝑐𝑝 of TEG, erroneously predicting a minimum at 353 K, while UMR-PRU predicts satisfactorily the experimental data both qualitatively and quantitatively, although it gives a relatively higher effect of temperature on 𝑐𝑝 . Especially for the temperature range of 373.15K – 473.15K where the reboiler of a still column of a dehydration unit works, and determines more than 25% of the overall energy requirement of the dehydration unit, the AARD is 5% for the UMR-PRU while it is over 14% for the TST/NRTL model. In order to improve the performance of the model in this property, the MC parameters can be simultaneously fitted to vapor pressure, enthalpies of vaporization and heat capacity data, following the procedure suggested by Le Guennec et al.47. For water, both models yield good results with TST/NRTL to be superior to UMR-PRU. Specifically, the corresponding errors are 3.5% for UMR-PRU and 1.7% for TST/NRTL.

Figure 2: Prediction of heat capacity at constant pressure for pure components. Black solid line indicates the UMR-PRU prediction and grey dashed line the TST/NRTL one. (a). TEG heat capacity at 1 bar. Circles indicate experimental points by Stephens et al.46, diamonds by Steele et al.42 and triangles by Li et al.48. (b). Saturated water heat capacity. Circles indicate experimental data by NIST44. 3.2. Binary Mixtures The UNIFAC interaction parameters (IPs) for the light gases with water and TEG and for the HC groups with TEG which are required for the UMR-PRU model, have been fitted to experimental binary vapor – liquid equilibrium (VLE) data taken from the literature. The detailed list of the references of the experimental data is given in Table S.5. The objective function (S) that has been minimized is given by Eq. (31), 1

𝑛

𝑝 S = 𝑛 ∑𝑖=1 100 · 𝑝

𝑒𝑥𝑝

𝑎𝑏𝑠(𝑋𝑖

−𝑋𝑖𝑐𝑎𝑙𝑐 )

𝑒𝑥𝑝 𝑋𝑖


Eq. (31)

Page 11 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where np is the number of experimental data points used for parameter fitting, and 𝑋 stands for the bubble point pressure or temperature of the datapoint i. Superscript 𝑒𝑥𝑝 refers to the experimental value and 𝑐𝑎𝑙𝑐 to the calculated one. The IPs between water with HCs groups, have been fitted to liquid – liquid equilibrium (LLE) data of water/hydrocarbon binary mixtures (Table S.6) using the same objective function as in Eq. (31), but in this case 𝑋 stands for the solubility of water in the hydrocarbon-rich phase or for the solubility of hydrocarbon in the water-rich phase. The UMR-PRU IPs for the mixtures involved in this work are presented in Table S.7. 3.2.1. Vapor – Liquid Equilibrium Results The detailed binary VLE results with the UMR-PRU and TST/NRTL models are presented in Table 1.


Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 12 of 46

Table 1: Binary VLE results with the UMR-PRU and TST/NRTL model.

System

Ref

Correlation results Water (2) with 49 TEG 50 N2 51-56 CO2 57-63 CH4 50, 59, 64 C2H6 TEG (2) with 65 CO2 65 CH4 65 C2H6 66 C3 67 cyC6 68 Benzene 68 Toluene Prediction results Water (2) with 69-72 CH4 64, 69, 72-76 C2H6 TEG (2) with 77 CO2 66, 67

CH4

78

np

Calcul ation type

%AARD1 T range (K)

P range (bar)

x1 range

y1 range

UMRPRU

TST/NRTL

1000*AAD2 UMRTST/NRTL PRU

18 34 160 116 65

BPT BPP BPP BPP BPP

371.6 - 421.3 298.2 - 513.2 278.2 - 598.2 274.2 - 588.7 274.3 - 444.3

0.85 25.00 - 1013.00 3.25 - 1500.00 5.67 - 980.70 3.73 - 137.89

0.0454 - 0.8830 0.0002 - 0.0051 0.0005 - 0.2500 0.0002 - 0.0151 0.0001 - 0.0017

0.0001 - 0.0220 0.0800 - 0.9993 0.1678 - 0.9998 -

2.2 4.7 22.4 10.3 10.9

2.2 14.6 31.7 12.1 52.2

2.3 54.4 21.0 -

1.3 31.9 13.8 -

40 67 59 40 19 11 10

BPP BPP BPP BPP BPP BPT BPT

298.2 - 398.2 273.2 - 398.2 298.2 - 398.2 298.2 - 398.2 343.0 - 473.0 354.7 - 428.8 385.2 - 442.5

0.00 - 202.50 1.09 - 202.00 1.10 - 204.80 0.16 - 64.50 0.07 - 13.65 1.01 1.01

0.0046 - 0.4848 0.0006 - 0.0840 0.0016 - 0.1482 0.0007 - 0.1043 0.0000 - 1.0000 0.0680 - 0.8849 0.0815 - 0.9353

0.0000 - 1.0000 0.0000 - 0.9999 0.0000 - 0.9995

5.7 4.5 10.6 13.5 10.4 0.2 0.1

3.5 6.6 3.4 11.3 5.4 0.2 0.1

23.1 0.5 0.5

21.5 0.4 0.4

192 248

Flash Flash

253.2 - 510.9 278.1 - 510.9

13.00 – 1103.00 3.00 – 1103.00

-

0.1900 - 1.0000 0.2000 - 0.9998

-

-

9.2 7.9

3.8 8.2

29 48 12

Flash Flash Flash

273.2 - 343.2 313.2 - 333.2 298.2 - 316.8

4.20 - 374.00 27.58 – 154.30 16.06 - 86.97

0.0260 - 0.5060 -

0.9990 - 1.0000 0.9999 - 1.0

6.9 -

5.5 -

0.0500 0.0001

0.2500 0.0004

𝑒𝑥𝑝

1

%AARD is defined as: %AARD = 100 ∙

𝑎𝑏𝑠(𝑋𝑖 −𝑋𝑐𝑎𝑙𝑐 ) 𝑖 , 𝑒𝑥𝑝 𝑋𝑖

where X stands for bubble point pressure (BPP) or bubble point temperature

(BPT). In case of flash prediction, X stands for liquid phase solubility of component 1, 𝑥1 . 𝑒𝑥𝑝 2 1000*AAD is defined as: 1000*AAD = 1000 ∙ 𝑎𝑏𝑠(𝑦1 − 𝑦𝑐𝑎𝑙𝑐 1 ), where 𝑦1 stands for the vapor phase solubility of component 1.


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Α mixture of utmost importance in the dehydration process is the TEG/water binary. The TEG/H2O binary interaction parameters for the UMR-PRU have been fitted to bubble point temperature (BPT) experimental data49. The correlation is very satisfactory, with an AARD in BPT equal to 2.2% and an AAD in vapor phase composition equal to 2.3. The deviations with TST/NRTL are similar to those obtained with UMRPRU as shown in Table 1 and graphically in Figure 3(a). Furthermore, as illustrated in Figure 3(b) both models perform similarly also in the prediction of the bubble point temperature against the experimental data of Piemonte et al.79, which have not been included in the database used for the fitting of the UMRPRU IPs. For these data, UMR-PRU yields an AARD equal to 5.4% and TST/NRTL 7.4%. Both models are able to capture well the effect of the pressure in the bubble point temperature, while they predict better the richer in water compositions. Ιn Figure 3(c), it is shown that UMR-PRU describes better than TST/NRTL the activity coefficients of water, where UMR-PRU gives an AARD in water activity coefficient equal to 1.5% while TST/NRTL 7.4%. Due to their importance in the dehydration process, especially in the simulation of the regenerator, the infinite dilution activity coefficients of water in its mixture with TEG have been examined. The results presented in Figure 3(d) indicate that UMR-PRU predicts infinite dilution coefficient values that agree fairly well with the data of Bestani and Shing80. On the other hand, TST/NRTL describes very accurately the data of Parrish et al.81, which have been included in the correlation of the TST/NRTL model parameters26. According to Bestani and Shing80, the difference of their experimental data with those of Parrish et al.81 are approximately 15% which is higher than the experimental uncertainty, but an application of a correction factor to the data of Parrish et al.81 leads to a difference of 2-3%, which is in the limits of the experimental uncertainty. This difference is reflected on the absorbing ability of TEG and as it is shown in Section 4, the TST/NRTL model requires lower amount of TEG than UMR-PRU to obtain the required dehydration level. Moreover, the performance of the models has been evaluated in the prediction of the excess enthalpies of the TEG/water mixture. As it is apparent from Figure 3(e), UMR-PRU predicts very well the experimental data (AARD equal to 2.7%), while TST/NRTL systematically overestimates them (AARD equal to 44.1%). This result indicates that the temperature dependency of the UMR-PRU IPs is better as compared to the one of TST/NRTL, although both models use linear dependency for the specific mixture. Finally, Figure 3(f) compares the predicted heat capacities with the experimental ones for the TEG/water mixture. Fairly good predictions are obtained with the UMR-PRU model for the mixtures especially at the lower TEG concentrations, while TST/NRTL model systematically overestimates the experimental values predicting also an opposite temperature dependency than the experimentally observed. Overall, UMR-PRU yields an overall AARD equal to 7.3% and TST/NRTL 19.8%, while detailed results for various TEG/water compositions are presented in Table S.8.




Page 14 of 46

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Figure 3: TEG/water mixture results with the UMR-PRU (black solid line) and the TST/NRTL model (grey dashed line). (a). VLE of TEG/water at 0.85 bar. () Experimental VLE data by Mostafazadeh et al.49, (b). VLE of the TEG/water mixture at constant pressure. Experimental data by Piemonte et al.79, (○) at 0.07 bar, (∆) at 0.13 bar, (□) at 0.27 bar and () at 0.54 bar. (c). Water activity coefficients. Experimental data by Herskowitz et al.82 (○) at 297.6 K and () at 332.6 K. (d). Water infinite dilution activity coefficients. Experimental data (○) by Parrish et al.81 and () by Bestani et al.80, (e). Excess Enthalpies of the TEG/water mixture. () Experimental data by Hamam et al.83 and (f). Heat capacity at constant pressure. Experimental data by Li et al. 45. (○) 𝑥𝑇𝐸𝐺 = 0.2, () 𝑥𝑇𝐸𝐺 = 0.4, () 𝑥𝑇𝐸𝐺 = 0.5, (□) 𝑥𝑇𝐸𝐺 = 0.6 and (∆) 𝑥𝑇𝐸𝐺 = 0.8. For the mixtures of light gases with water, UMR-PRU describes very well the bubble point pressure yielding better results than TST/NRTL especially for the ethane/water binary. As shown in Figure 4(a) UMR-PRU predicts satisfactorily the water vapor phase compositions, while TST/NRTL systematically underestimates them especially at the lower temperatures. As a result, since methane is the major NG component, the TST/NRTL model predicts lower water content in the saturated gas. UMR-PRU and TST/NRTL perform well in the case of ethane/water mixture as presented in Figure 4(b).

Figure 4: Binary VLE results for mixtures of light gases with water with the UMR-PRU (black solid line) and the TST/NRTL (grey dashed line) model. (a) Vapor phase composition predictions for the methane/water mixture. Experimental data by Sage et Lacey69. (○) at 310.93 K, (+) at 344.26 K, (∆) at 377.59 K, () at 410.93 K, (□) at 444.26 K and () at 477.59 K. (b). Vapor phase composition predictions for the ethane/water mixture. Experimental data by Yarrison et al.72. (○) at 314.8 K, (∆) at 366.5 K, (□) at 422 K and () at 466.5 K. Very good VLE results are obtained from UMR-PRU and TST/NRTL for the binary mixtures with TEG (Table 1 and Figure 5). Both models are able to capture the crossing of the solubility lines of light gases with increasing temperature both for the vapor phase, Figure 5(c), and for the liquid phase, Figures 5(e) and 5(f). UMR-PRU and TST/NRTL describe also very well the VLE of heavier hydrocarbons with TEG,



Page 16 of 46

Figures 5(g) and 5(h). Overall, the results in the VLE of binary mixtures with TEG are comparable with those calculated with the CPA EoS20 that explicitely accounts for the association effects.


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Page 18 of 46

Figure 5: VLE of light gases and hydrocarbons with TEG with the UMR-PRU (black solid line) model and the TST/NRTL (grey dashed line) model. (a). CO2/TEG mixture. Experimental points by Jou et al.65. (∆) at 298.15 K, (○) at 323.15 K and () at 373.15 K. (b). Methane/TEG mixture. (∆) Experimental points by Wilson et al.66 at 298.15 K, (○) by Jou et al.65 at 323.15 K and () by Jou et al.65 at 373.15 K. (c). Vapor phase of the CO2/TEG mixture. Experimental data (○) at 313.15 K by Kaminishi et al.84 and Yonemoto et al.85, (∆) at 323.15 K by Yonemoto et al.85 and () at 333.15 K Kaminishi et al.84 and Yonemoto et al.85. (d). Vapor phase of the methane/TEG mixture. Experimental data by Jerinic et al.78. (○) at 298.15 K and () at 316.75 K. (e). Ethane/TEG mixture. Experimental points by Jou et al.65. (∆) at 298.15 K, (○) at 323.15 K and () at 373.15 K. (f). Propane/TEG mixture. Experimental points by Jou et al.65. (∆) at 298.15 K, (○) at 323.15 K, () at 373.15 K and (□) at 398.15 K. (g). Benzene/TEG mixture at 1.01325 bar. () Experimental points by Gupta et al.68 and (h). Toluene/TEG mixture at 1.01325 bar. () Experimental points by Gupta et al.68. 3.2.2. Liquid – Liquid Equilibrium (LLE) Results (a). Water/hydrocarbon mixtures Table 2 presents the detailed LLE results, while Figure 6 presents a comparison between the predicted and the experimental mutual solubilities for six binary water/hydrocarbon mixtures. In the case of water/propane mixture, water vapor phase compositions are also included. The UMR-PRU model gives very good description of the LLE behavior of the water/hydrocarbon mixtures, with the higher errors encountered for propane and n-butane. Taking into consideration the well-known challenge of the modelling of water/HCs LLE due to their high immiscibility, the results presented here, using the groupcontribution approach to describe a range of HCs from propane to n-decane, are considered very good. Additionally, using the same IPs obtained from normal alkanes, the UMR-PRU model is able to predict accurately the LLE of naphthenic HCs and branched alkanes with water. Furthermore, it captures well the minimum of the HC solubility with the temperature in the aqueous phase. On the other hand, TST/NRLT gives good results only for the relatively light hydrocarbons, propane and n-butane, while it yields poor ones for the higher molecular weight HCs, especially for the solubility of the HC in the water-rich phase. Apart from the quantitatively results, TST/NRTL predicts an ascending behavior with the temperature for the HCs solubility in aqueous phase, which is rational given that it uses only linear temperature dependency in its IPs. (b). TEG/hydrocarbon mixtures As mentioned in Section 3.2, the IPs of the UMR-PRU model between the HC groups and TEG have been fitted only to VLE data. As shown in Table 2 and Figure 7, UMR-PRU is able to predict quite satisfactorily the LLE of TEG/hydrocarbon mixtures using the IPs fitted only to VLE data. For the n-heptane/TEG mixture, Figure 7(a), UMR-PRU gives satisfactory predictions in both phases while TST/NRTL fails. For the benzene/TEG mixture, Figure 7(b), UMR-PRU yields slightly better results than TST/NRTL, while for the toluene/TEG, Figure 7(c), both models yield satisfactory results.


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Table 2: LLE results with UMR-PRU and TST/NRTL System

Ref.

np T range (K)

Water (2) with Propane n-butane

86

n-pentane

70, 73, 74

n-hexane

90

n-heptane

91-93

n-octane

94

n-nonane

95-98

n-decane

99-101

Isobutane

70, 72

Isopentane

54, 69, 70

Cyclohexane

90, 92, 102-106

Benzene

90

Toluene

92, 100, 107

Ethylbenzene

94

o-xylene

94, 108

m-xylene

93, 97

p-xylene

92, 98

TEG (2) n-heptane

87-89

12, 109

Benzene

68

toluene

68

P range (bar)

x1(I) range

x1(II) range

10

278.9 - 360.9

5.7 - 37.1

0.0001990 - 0.0003660

0.000105 - 0.005580

12

278.7 - 377.6

0.2 - 6.5

0.0000553 - 0.0001400

0.000098 - 0.008500

10

273.2 - 423.3

0.1 - 5.8

0.0000101 - 0.0000145

0.000104 - 0.032200

9

298.2 - 473.2

0.2 - 35.2

0.0000024 - 0.0001930

0.000441 - 0.109000

15

293.2 - 443.8

0.1 – 7.0

0.0000004 - 0.0000180

0.000534 - 0.002660

9

298.2 - 498.2

0.1 - 36.7

0.0000001 - 0.0000780

0.000520 - 0.193690

7

288.2 - 409.7

1.0

3E-8 – 7.1E-7

0.000081 - 0.000320

7

296.2 - 573.0

1.0 – 150.0

12

280.2 - 363.2

8

273.1 - 333.1

1.2E-8 - 0.0000023

0.000280 - 0.511000

0.1 - 4.0

0.0000960 - 0.0001050

0.000090 - 0.000270

1.0

0.0000117 - 0.0000198

0.000110 - 0.002340

15

278.3 - 450.8

0.2 - 17.3

0.0000125 - 0.0003100

0.000160 - 0.083000

21 19

279.2 - 490.8 283.2 - 473.5

0.1 - 41.9 0.0 – 138.0

0.0004000 - 0.0086000 0.0001110 - 0.0025900

0.001667 - 0.257797 0.001690 - 0.159200

4

310.9 - 479.5

0.0 - 4.9

0.0000000 - 0.6860000

0.004300 - 0.163000

6

273.1 - 479.5

1.0

0.0000241 - 0.9800000

0.000130 - 0.163000

21

278.2 - 473.3

1.0 - 20.1

0.0000173 - 0.5230000

0.006450 - 0.248000

17

288.2 - 448.2

0.0 - 11.7

0.0000286 - 0.9941000

0.000220 - 0.102000

12

309.4 - 409.6

1.0 - 1.0

0.01117 - 0.01952

0.00040 - 0.0135

5

279.6 - 287.6

0.1 - 0.08

0.63422 - 0.67324

0.07062 - 0.10952

17

279.0 - 345.4

-

0.30839 - 0.48498

0.01074 - 0.08661

%Δx1(I)1

%Δx2(II) 1

%Δy21

UMRPRU

TST/NRTL

UMRPRU

TST/NRTL

UMRPRU

TST/NRTL

133.6 72.9 103.9 49.6 67.7 24.3 46.3 83.9 10.9 48.4 48.7 5.1 11.7 32.8 20.2 28.9 19.4

10.6 13.7 31.7 100.0 100.0 100.0 100.0 100.0 62.6 10.6 165.1 28.1 99.1 14.4 25.9 18.5 20.2

85.7 100.5 42.5 25.8 32.2 6.5 279.3 18.2 106.5 11.7 16.8 2.7 5.4 10.7 15.8 39.9 17.3

18.1 17.1 46.8 8.3 41.8 14.8 259.2 22.3 6.1 15.5 99.9 45.2 79.1 21.9 5.3 58.5 55.1

13.1

5.0

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

23.1 17.6 5.1

91.4 25.8 7.9

63.9 16.6 62.7

728.4 44.6 19.4

-

-

-

-

-

-

exp

1

%ΔX = 100 ∙

abs(Xi −Xcalc i ) , exp Xi

where X stands for the liquid phase composition, xi , or the vapor phase composition, y2 . (I) stands for the polar

phase and (II) the HC-rich phase.



Page 20 of 46

Figure 6: LLE prediction results of hydrocarbons with water with the UMR-PRU model (solid black line) and the TST/NRTL model (grey dashed line). Experimental points (○) in the aqueous phase (I), () in


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the HC-rich phase (II), and (∆) in the vapor phase. (a). Propane/water. Experimental data by Kobayashi et al.86. (b). n-hexane/water. Experimental data by Tsonopoulos et al.90. (c). n-decane/water. Experimental data by Revellame et al.99, Ng et al.100 and Economou et al.101. (d). cyclohexane/water. Experimental data by Burd et al.102, Guseva et al.103, Pereda et al.104, Marche et al.92, Pierotti et al.105, Goldman et al.106 and Tsonopoulos et al.90. (e). Benzene/water. Experimental data by Tsonopoulos et al.90. (f). p-xylene/water. Experimental data by Chen et al.110 and Jou et al.107.

Figure 7: LLE prediction results of hydrocarbons with TEG with the UMR-PRU model (solid black line) and the TST/NRTL model (grey dashed line). Experimental points (○) in the polar phase (I), () and (∆) in the HC-rich phase (II). (a). n-heptane/TEG. Experimental points by Derawi et al.109 and Rawat et al.12. (b). Benzene/TEG. Experimental data by Folas et al.111. (c). Toluene/TEG. Experimental data by Folas et al.111 and Hughes et al.112.



Page 22 of 46

3.3. Prediction in multicomponent mixtures 3.3.1. Ternary Mixtures VLE prediction results for ternary mixtures with UMR-PRU and TST/NRTL are tabulated in Table 3. Overall, the results from the two models are comparable. For the CO2/TEG/water mixture, Figure 8, UMRPRU underpredicts the effect of water on the VLE behavior of the mixture while TST/NRTL overpredicts it. For the TEG/water/toluene mixture, Figure 9, both models predict accurately the BPT as well as the TEG composition in the vapor phase, while UMR-PRU yields better prediction of the water solubility in the vapor phase. Figure 10 compares the predicted partition coefficients in ternary mixtures containing methane, an aromatic hydrocarbon and TEG with the corresponding experimental data. Excellent predictions are obtained by both models for the distribution of methane and the aromatic compounds.

Figure 8: VLE prediction results for the CO2/TEG/water mixture with the UMR-PRU (black solid line) and the TST/NRTL model (grey dashed line). () 0% wt. water, (□) 3.5% wt. water, (+) 7% wt. water, 22 ACS Paragon Plus Environment

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(○) 10% wt. water, (∆) 40% wt. water and () 60% wt. water. (a). Experimental data at 297.04 K by Kaminishi et al.113, at 298.15 K by Wise et al.77 and Jou et al.65. (b). Experimental data by Kaminishi et al.113 at 322.04 K. (c). Experimental data by Wise et al.77 at 343.15 K.

Figure 9: VLE bubble point temperature prediction results for the TEG/water/toluene mixture with the UMR-PRU (black solid line) and the TST/NRTL model (grey dashed line). Experimental data by Mostafazadeh et al.49. (○) Experimental solubility data of toluene in liquid phase, () Experimental solubility data of TEG in vapor phase and (∆) Experimental solubility data of water in vapor phase; (a), (b) indicate different tielines.



Page 24 of 46

Figure 10: VLE prediction results for ternary mixtures containing methane, an aromatic hydrocarbon and TEG with the UMR-PRU (black solid line) and the TST/NRTL model (grey dashed line). (○) Experimental partition coefficients of methane and () Experimental partition coefficients of the respective aromatic hydrocarbon. Experimental data by Ng et al.114; (a). methane/benzene/TEG at 348.15 K, (b). methane/ethylbenzene/TEG at 348.15 K, (c). methane/toluene/TEG at 348.15 K and (d). methane/toluene/TEG at 398.15 K.


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Table 3: LLE ternary mixtures prediction results with the UMR-PRU and the TST/NRTL model. System

Ref.

np T range (K)

l

2

CO2/TEG/water CH4/benzene/TEG CH4/toluene/TEG CH4/ethylbenzene/TEG

115

TEG/water/toluene4

49

100 100 100

30 5 4 2

297.1 - 322.1 348.1 - 398.2 348.2 - 398.2 348.2 - 348.2

17

368.8 - 412.6

1000·Δx11,2 P range (bar) UMRPRU TST/NRTL Vapor – Liquid -Equilibrium 25.2 - 80.3 28.6 28.6 6.9 - 107.5 1.1 0.9 6.9 - 22.5 0.2 0.8 6.5 - 17.4 0.2 0.3 %ΔT3 0.85 0.2 1.6

1000·Δx2 1000·Δy2 UMRUMRPRU TST/NRTL PRU TST/NRTL 0.3 1.6 0.03 %Δy1 0.03

0.3 1.6 0.03

0.1 0.6 0.06 %Δy2

0.1 0.4 0.02

0.03

6.1

10.7

The indexes (1), (2) and (3) correspond to the order of the compound in the specific mixture. 𝑒𝑥𝑝 1000 · 𝛥𝑋 = 1000 ∙ 𝑎𝑏𝑠(𝑋𝑖 − 𝑋𝑖𝑐𝑎𝑙𝑐 ), where X stands for the liquid phase composition of component i, 𝑥𝑖 , or the vapor phase solubility of component i, 𝑦𝑖 . 𝑒𝑥𝑝

𝑎𝑏𝑠(𝑇𝑖

−𝑇𝑖𝑐𝑎𝑙𝑐 )

3

%𝛥𝑇 = 100 ∙

4

For the specific mixture, bubble point temperature prediction has been performed.

𝑒𝑥𝑝 𝑇𝑖

, where T stands for the bubble point temperature.



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3.3.2. Multicomponent Mixtures Containing BTEX components The UMR-PRU model has been evaluated in the prediction of multicomponent aqueous mixtures of methane and TEG with BTEX compounds. The available experimental data of Ng et al.116 are close to the conditions encountered in the flash drum, the contactor and the regenerator of a typical TEG dehydration process. Representative prediction results with UMR-PRU and TST/NRTL are presented in Figure 11. Both models predict very accurately the distributions of the BTEX components, as it is proved by the proximity of the points to the diagonal line. As for the methane and TEG distribution, both models yield accurate results with the UMR-PRU to be slightly superior than TST/NRTL.


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Figure 11: VLE prediction results for mixtures containing methane, BTEX, water and TEG at different conditions relative to dehydration process. Experimental data by Ng et al. 116. Modelling results (○) with



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the UMR-PRU model and (∆) with the TST/NRTL model; (a). Flash drum conditions on dry basis, at 348.1 K and 6.89 bar, (b). Flash drum conditions with 1% wt. water, at 348.1 K and 6.89 bar, (c). Regenerator conditions on dry basis, at 477.59 K and 1.38 bar, (d). Regenerator conditions with 1% wt. water, at 477.59 K and 1.62 bar, (e). Contactor conditions on dry basis, at 298.1 K and 68.95 bar and (f). Contactor conditions with 1% wt. water, at 298.1 K and 68.95 bar.


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4. Simulation of TEG dehydration The aforementioned results verify that the UMR-PRU model can adequately describe the phase equilibrium and other properties of mixtures containing compounds relevant to the TEG dehydration process. Thus, the model has been applied for the simulation of the TEG dehydration process. To this purpose the UMR-PRU model has been implemented through the CAPE OPEN 1.1 protocol to the Aspen Hysys© and the Honeywell Unisim© process simulators. Two cases have been considered: Case I is a simple absorber, and Case II simulates a simplified offshore dehydration unit. For comparison purposes the results obtained by Aspen Hysys with the built-in TST/NRTL model are also presented. 4.1. Case I: the simple absorber A dehydration unit has a number of variables that affect its efficiency, such as the lean TEG purity, TEG circulation rate, number of trays in the absorber and the regenerator, as well as the operating conditions. As a first step, a simple absorber has been considered, where the feed and operating conditions are fixed, approximately at 40 bar and 305 K (Table 4). The schematic diagram of the absorber, consisting of three ideal trays, is presented in Figure 12. The wet gas feed enters at the bottom of the absorber (contactor) and the solvent that is lean (in water) TEG, enters at the top and flows countercurrent to the gas. The dry gas product exits at the top of the contactor, while the rich (in water) TEG leaves at the bottom of the column. The composition of the wet gas used as feed to the absorber and of the lean TEG used as solvent is taken from the work of dos Santos et al.21 and contain hydrocarbons up to n-hexane.

Figure 12: Flowchart of Case I, as constructed in the Hysys environment. Table S.9 summarizes the simulation results obtained with UMR-PRU implemented in Hysys and Unisim and those obtained by TST/NRTL with Hysys. Also, Figure 13 presents a graphical comparison of the predicted molar compositions of the components in dry gas and rich TEG streams. The first observation is that identical results are obtained with the UMR-PRU model in Hysys and Unisim.



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Figure 13: Simulation results for Case I with the UMR-PRU implemented in Hysys and Unisim and the TST/NRTL model. UMR-PRU in Hysys is given with solid black fill, TST/NRTL is given in solid grey fill and UMR-PRU in Unisim is given with stripped patterned black color in grey background; (a). TEG and water composition in the dry gas, (b). Natural gas components composition in the dry gas, (c). TEG and water composition in the Rich TEG stream and (d). Natural gas components composition in the Rich TEG stream. For the same purity and lean TEG circulation rate, UMR-PRU yields about 9 ppm (molar) of water in the dry gas, while TST/NRTL yields 8 ppm. TST/NRTL yields also lower concentration of TEG in the dry gas than UMR-PRU. This behavior is attributed to the fact that TST/NRTL underpredicts the vapor phase solubility of water, Figure 4(a), and TEG, Figure 5(d), in their mixtures with methane, which is the major natural gas component, while UMR-PRU gives results that are in better agreement with the experimental data. UMR-PRU and TST/NRTL predict similarly the natural gas components distribution in the dry gas and rich TEG streams. In the rich TEG stream, instead, TST/NRTL predicts lower solubility of the HCs compared to UMR-PRU. This difference is higher in the case of n-hexane, which is the heavier component of the specific gas. This behavior is attributed to the difference in the HCs distribution in the polar phase 30 ACS Paragon Plus Environment

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of the binary mixtures. As presented in Figure 6, TST/NRTL systematically underpredicts the HC solubility in the aqueous phase with the exception of cyclohexane, while the opposite is valid for the distribution of n-heptane in TEG (Figure 7). It seems that despite of the higher TEG content of the rich TEG stream examined here, the dominating factor is the solubility of HCs in water. Finally, both models calculate similar energy values for the gaseous streams, while this is not the case for the TEG-rich ones. This difference is attributed to the different heat capacities (cp ) of the TEG/water mixture predicted with the two models. As it has been shown in Section 3.2.1, at the specific operating conditions of the absorber, UMR-PRU predicts this property better than TST/NRTL, which systematically overpredicts the experimental data. The simulation results for the absorber are in good agreement with the simulations of dos Santos et al.21, where the CPA EoS has been evaluated.

4.2. Case II: A simplified offshore dehydration unit The process flowsheet, as simulated in Hysys, is presented in Figure 14. Of course, many variables affect the dehydration operation, such as the number of stages in the columns, the lean TEG circulation rate and its purity, the selected operating conditions, the sort of the configuration used to increase the lean TEG purity such as stripping gas or vacuum etc. The optimization of the whole process is outside the scope of this work and, thus, typical values of the operating variables are used, which are kept constant during the simulations.


Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Figure 14: Flowchart of Case II, as constructed in the Hysys environment.


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The input composition of the saturated wet gas feed (Table S.10) is taken by the work of dos Santos et al.21 and is typical for units operating in Brazil. The contactor is simulated by an absorber unit subflowsheet, consisting of three ideal trays. The contactor operates essentially isothermally at high pressure and low temperature conditions, about 56 bar and 303 K. Since the mass of water and TEG is small as compared to the gas flow, the inlet gas controls the absorber temperature1. The specified parameters for the contactor are presented in Table 4. The dry gas exits at the top of the contactor, with a concentration in water approximately 30 ppm molar. At the bottom of the contactor exits the rich TEG. Table 4: Specifications for the columns for the simulation of Case II. Contactor Regenerator Column type Absorber Distillation Column Ideal trays 3 3 Reboiler 1 Condenser 1 Efficiency 1 1 Degrees of freedom 0 2 Condenser temperature (K) 373.15 Reboiler temperature (K) 477.15 1 Feed Lean TEG (1) SG2 (3)2 Wet gas (3) S4 (3) 1 2

numbers in parenthesis indicate the stage (counting from the top) where the feed is inserted to the column. The labeling of the inlet streams refers to the names indicated in Figure 14.

The regenerator is usually a stripper, but for simulation purposes a distillation column is used. It operates at atmospheric or close to atmospheric pressure and high temperature, due to the high TEG boiling point, c.a. 540 K44. The rich TEG stream from the contactor is decompressed to 5.1 bar, before it enters the glycol/glycol Heat Exchangers (HE-1, HE-2). In the real process, the Rich TEG stream passes through the top of the regenerator, condensing the vapor stream, while it is preheated. For simulation purposes, a heater is added after the decompression valve and before the HE-1, where its energy duty is set equal to the condenser duty at the top of the regenerator. Furthermore, the glycol filters are omitted and their effect has been added as a pressure drop equal to 100 kPa in the Glycol/Glycol Heat Exchangers. The preheated rich TEG (S3) exiting HE-1 is routed to an isothermal flash to exhaust the diluted hydrocarbons, which can be either mixed with other streams for HC recovery or it is sent to the flair. The liquid outlet stream (S4) enters the HE-2, and then, after its pre-heat from the lean TEG stream (S8), it enters at the bottom of the Regenerator. Stripping gas (SG) is used to increase the TEG purity, which for simplicity reasons, is considered to enter the regenerator directly, at the bottom tray, along with the rich TEG inlet. The operating conditions of the regenerator are determined by the glycol decomposition temperature, which for TEG is approximately 479.15 K. In industrial practice, in the regenerator unit where no air is present, no noticeable decomposition is observed for temperatures close to the decomposition one. The lean glycol composition is determined by the bubble point composition at the regenerator pressure. In order to increase the purity of the lean TEG, a decrease of the partial pressure of the glycol solution is required which is achieved in practice either by operating at lower pressure or by the introduction of a stripping gas. Since in NG industry fuel is readily available while the operation in vacuum conditions requires high energy 33 ACS Paragon Plus Environment


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consumption, usually the latter solution is preferred. A make-up stream is added to account for the TEG loss in the process. Finally, the pressure increase is achieved by using glycol pumps P-1 and P-2, in order to reach the contactor conditions. The specification to be met in the simulations is the water content of the dry gas, which is set to approximately 30 ppm molar. The independent variable that is used to control the lean TEG purity and thus the required level of dehydration is the stripping gas flow, while all the other parameters are kept constant. The simulation results regarding some important variables are summarized in Table 5, while the detailed results are given in Tables S.10 - S.12. Table 5: Simulation results in Hysys for Case II, with the UMR-PRU and TST/NRTL models.

dry gas water content (ppm) purity lean TEG (%wt.) lean TEG (kmol/h) TEG circulation rate (kg TEG/kg absorbed water) total TEG loss (kmol/h) % TEG loss of the total in the regenerator1 Stripping gas rate (kmol/h) 1

%TEG loss in Regenerator = 100 ∙ abs (

UMR-PRU

TST/NRTL

29.1 99.4 34.3 1.2

29.1 99.4 34.8 1.2

0.006 86.4 9.0

0.004 90.6 9.7

moles TEG in vapor moles TEG in dry gas+moles TEG in flash gas+moles TEG in vapor

)

Figure 15: Simulation results for the Contactor of Case IΙ with the UMR-PRU (solid black fill) and the TST/NRTL (solid grey fill). (a). NG Component distribution in the dry gas stream and (b). TEG and water distribution in the Rich and Lean TEG streams. UMR-PRU and TST/NRTL models calculate similar TEG circulating rate and purity of lean TEG. TST/NRTL requires slightly higher stripping gas rate as compared to UMR-PRU, which leads to a slightly higher lean TEG flow. On the other hand, the calculated TEG circulation rate per kg of absorbed water is 34 ACS Paragon Plus Environment

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almost the same for both models. As it is illustrated in Figure 15, the composition of the obtained dry gas is also similar for all components except for TEG where TST/NRTL yields lower concentration than UMR-PRU, which is attributed to the difference of the models in the description of the methane/TEG binary.

Figure 16: Simulation results for the Regenerator of Case IΙ with the UMR-PRU (solid black fill) and TST/NRTL (solid grey fill). (a). Vapor stream and (b). Reflux stream. The composition of the vapor and reflux streams of the regenerator are presented in Figure 16. It is shown that both models yield similar results concerning the compounds of interest, which are the light gases, TEG and water. Additionally, they give similar vapor rate, with the one of TST/NRTL to be a little higher. This corresponds in slightly higher HCs loss in the case of TST/NRTL, which consists mostly of the lighter compounds. The models differ, also, in the calculated composition of hydrocarbons heavier than butane in the vapor phase, as well as in n-hexane in the reflux polar phase. The latter is due to the significantly low solubility of n-hexane in water predicted by the TST/NRTL, as shown in Section 3.2.2. It is interesting to note that the low solubility of the heavier HCs with the TST/NRTL in the gaseous streams examined here is an outcome of the low solubility predicted by the model in the rich TEG stream, which is essentially the input to the column. Moreover, similar reflux rate is required to achieve the TEG regeneration, which is 0.021 kmol/h for the UMR-PRU and 0.018 kmol/h for TST/NRTL. Finally, in Table 6, the energy requirements of the dehydration process are compared. It is shown that TST/NRTL systematically yields higher duties compared to UMR-PRU, which is due to the high overestimation of the heat capacity values for the TEG/water (Section 3.2.1). Although this is systematic for all equipment, the difference is more apparent in the reboiler. Of course, part of the increased duty is also due to the slightly higher stripping gas rate calculated with TST/NRTL model. In the temperature range of the regenerator, i.e. 373 – 477 K, UMR-PRU predicts fairly well the 𝑐𝑝 , so it is expected that the UMR-PRU results should better meet the actual process data.



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Table 6: Simulation Results in Hysys concerning the Energy Requirements for Case II, with the UMR-PRU and the TST/NRTL model. UMR-PRU Duties (kW)

HE 1 HE 2 Glycol Cooler Reboiler Condenser

127.0 174.0 201.9 283.8 3.4

TST/NRTL

194.6 228.9 209.1 332.5 3.7

Another aspect of interest from the engineering point of view is the TEG loss encountered in the process. UMR-PRU predicts a higher TEG loss compared to TST/NRTL. This is rational considering that UMRPRU yields higher TEG solubility in the vapor phase compared to TST/NRTL, as it has been shown in Figures 5(c) and 5(d). It should be noted that UMR-PRU predictions are in better agreement with the available experimental data, indicating that the TEG loss calculated with the UMR-PRU model is more accurate than the one calculated with TST/NRTL. 4.3. Temperature change from isenthalpic expansion In natural gas processing the Joule –Thomson (JT) valves are usually used to enhance natural gas liquids (NGL) recovery, since hydrocarbons exhibit a positive Joule – Thomson coefficient. According to Satyro et al.117, liquid TEG and water show a reverse behavior, i.e. negative JT coefficients, which results in temperature increase during expansion. Satyro et al.117 experimentally measured the temperature in the outlet of a Joule-Thomson valve, after the rich TEG stream exiting the contactor. They studied pure water and TEG as well as their mixture and they showed that a temperature increase occurs in all cases. In this work, the predictions of TST/NRTL and UMR-PRU model in the conditions tested by Satyro et al.117 have been compared with the experimental data and the respective results are tabulated in Table 7. Table 7: Temperature effect of decompression valve with the UMR-PRU and TST/NRTL models. Experimental data by Satyro et al.117 ΔT* (K) Mixture P (bar) UMRInlet T (K) Exp. TST/NRTL PRU Pure water 292.7 4.4 1.4 1.43 1.42 TEG 99% pure 291.9 4.4 2.4 3.43 1.93 Aqueous TEG (1% wt.) 292.8 4.4 2.1 3.41 1.92 *ΔT=Τout-Tin, where in stands for the rich TEG stream exiting the contactor which is routed to the isenthalpic valve and out stands for the stream exiting the valve.

It is observed that both UMR-PRU and TST/NRTL predict positive JT coefficient in all cases, in accordance with the experimental data. Both models give almost the same ΔΤ for pure water, while for pure TEG and aqueous TEG TST/NRTL underestimates the temperature increase while UMR-PRU overestimates it.


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5. Conclusions The UMR-PRU model has been successfully extended to the thermodynamic modelling of natural gas mixtures with water and TEG, encountered during the NG dehydration process. After evaluation of the TEG pure component properties, temperature dependent group interaction parameters have been fitted to a database consisting of binary phase equilibrium data. Satisfactory results have been obtained in all cases, especially for TEG solubility in methane vapor phase, which is of special interest for the accurate calculation of TEG loss during the dehydration process. Also, for the LLE in binary mixtures of hydrocarbons with water, UMR-PRU is able to accurately describe the mutual solubilities. UMR-PRU has been also successfully applied in the prediction of multicomponent systems involving natural gas components, TEG and water. Moreover, the UMR-PRU has been implemented into Aspen Hysys and Honeywell Unisim simulators through the CAPE OPEN protocol. The model is then evaluated in the simulation of the dehydration process and has been compared with the TST/NRTL model proposed by Hysys. In Case I that represents a simple absorber, UMR-PRU yields the same level of dehydration as the TST/NRTL model. In Case II that represents a simplified offshore dehydration process, it is shown that UMR-PRU and TST/NRTL calculate similar stripping gas rate, TEG purity and circulation rate for achieving the same dehydration level in the dry gas. The two models differ in the calculated TEG loss, where UMR-PRU is considered to be closer to the real case than TST/NRTL. UMR-PRU also predicts lower duties in the reboiler, condenser and heat exchangers compared to TST/NRTL, which is considered more realistic due to the better prediction of the TEG/water heat capacities. Finally, calculation of the temperature change after the decompression of the rich TEG stream in an isenthalpic JT valve has been performed and it is shown that both UMR-PRU and TST/NRTL predict positive JT coefficient in agreement with the experimental data. Based on the abovementioned results, it is concluded that the UMRPRU model can be used to accurately simulate natural gas TEG dehydration units. Supporting Information UNIFAC R and Q parameters; CAPE OPEN exchange properties; TEG pure component properties; vapor pressure and liquid density pure component results for TEG and water; database of experimental data used for fitting of model parameters; UNIFAC group interaction parameters; aqueous TEG heat capacity prediction results; detailed simulation results for Case I; detailed simulation results for Case II.

List of symbols a attractive term parameter of a cubic EoS (bar∙cm6∙mol-2) ac

constant term of the attractive parameter of a cubic EoS

a(T)

term that express the temperature dependency of the attractive parameter of a cubic EoS

A

Helmholtz energy

Aji

NRTL binary interaction parameters between components i and j (K)

Anm, Bnm, Cnm UNIFAC binary interaction parameter between groups n and m



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b

co-volume parameter of a cubic EoS (cm3∙mol-1)

Bji

NRTL binary interaction parameters between components i and j (-)

c1, c2, c3

Mathias – Copeman parameters

cp

specific heat capacity of a component (kJ∙kmol-1∙K-1)

H

molar enthalpy (J∙kmol-1)

G

molar Gibbs free energy (J∙mol-1)

Gij

NRTL energy parameter between the components i and j (-)

Ki

partition coefficient of a component i between the two phases in equilibrium (-)

L, M, N

Twu alpha function pure component parameters (Eq. 19)

m

Soave parameter for the expression of the temperature dependency of the attractive term of an EoS (-)

np

number of data points used for the fitting of model parameters used in Eq. (31) (-)

P

pressure (bar)

Ps

vapor pressure (bar)

Qi

relative van der Waals surface area of group i (-)

R

universal ideal gas constant (83.14 bar∙cm3∙mol-1∙K-1)

Ri

relative van der Waals volume of group i (-)

S

model fitting objective function to be minimized (Eq. 31).

t

Peneloux translation to improve the volumetric properties for TEG and water with the PR EoS (cm3∙mol-1)

T

absolute temperature (K)

v

molar volume (cm3∙mol-1)

vl

saturated liquid volume (cm3∙mol-1)

xi

liquid mol fraction of component i

yi

vapor mol fraction of component i


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Abbreviations

AAD

1

n

p Absolute Average Deviation, AAD = 100 ∙ n ∑i=1 | x exp − x calc |, where np is the number p

of points, exponent exp indicates the experimental value of the size x and exponent calc indicates the calculated value of the size x by the respective thermodynamic model AARD

1

n

p Absolute Average Relative Deviation, %AARD = 100 ∙ n ∑i=1 p

| xexp − xcalc | xexp

, where np is

the number of points, exponent exp indicates the experimental value of the size x and exponent calc indicates the calculated value of the size x by the respective thermodynamic model BTEX

Benzene, toluene, ethyl-benzene, and xylene compounds

BPP

Bubble point pressure (bar)

BPT

Bubble point temperature (K)

Cond.

Condenser of the TEG Regenerator

CPA

Cubic Plus Association EoS

DEG

Diethylene glycol

DIPPR

Design Institute for Physical Properties

EoS

Equation of State

GC

Glycol cooler

GPA

Gas Processing Association

HC

Hydrocarbons

HE-i

Glycol/Glycol Heat Exchanger, where i stands for 1,2

HV

Huron-Vidal mixing rules

JT

Joule-Thomson

LLE

Liquid – Liquid Equilibrium

MC

Mathias-Copeman expression for the alpha function (Eq. 8)

MHV2

modified Michelsen – HV mixing rule

NG

Natural gas



NGL

Natural gas liquids

NRTL

Non-random two liquid activity coefficient model

P-i

Glycol Pump, where i stands for 1,2

PR

Peng – Robinson EoS

Reb.

Reboiler of the TEG Regenerator

Si

Stream of the dehydration process, where i stands for 1-12

SG

Stripping Gas

SRK

Soave-Redlich-Kwong EoS

TEG

Triethylene glycol

TST

Twu – Sim – Tassone EoS

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TST/NRTL EoS/AE mixing rule combining the TST EoS with NRTL activity coefficient model UMR-PRU Universal Mixing Rule combined with PR and UNIFAC UNIFAC

UNIQUAC Functional-Group Activity Coefficients

VLE

Vapor – liquid equilibrium

VOCs

Volatile Organic Compounds

W

water

WS

Wong – Saddler mixing rule

Greek symbols αji

NRTL binary interaction parameter between the components i and j.

γ

activity coefficient

θ

UNIFAC surface fraction

τji

NRTL energy parameter between the components i and j.

φ

UNIFAC volume fraction

Ψmk ω

binary interaction parameter between the UNIFAC groups m, k for the UMR-PRU model acentric factor 40 ACS Paragon Plus Environment

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Superscripts and Subscripts c

critical property

Calc

Calculated value

E

excess

Exp

Experimental value

k,m,n

UNIFAC groups

l

liquid

p

points

r

reduced value of temperature (Tr=T/Tc)

res

residual term of the GE calculated through UNIFAC

s

saturation

SG

Staverman-Guggenheim contribution of the combinatorial term of UNIFAC

vdw

van der Waals

0

zero pressure

∞

infinite pressure

*

reduced property

References (1) Campbell, J. M.; Maddox, R. N. Gas conditioning and processing. Campbell Petroleum Series: 1970; Vol. 2. (2) Bahadori, A. Estimation of Hydrate Inhibitor Loss in Hydrocarbon Liquid Phase. Pet. Sci. Technol. 2009, 27, (9), 943-951. (3) Bahadori, A.; Vuthaluru, H. B. Rapid estimation of equilibrium water dew point of natural gas in TEG dehydration systems. J. Nat. Gas Sci. Eng. 2009, 1, (3), 68-71. (4) Bahadori, A.; Vuthaluru, H. B. Simple methodology for sizing of absorbers for TEG (triethylene glycol) gas dehydration systems. Energy 2009, 34, (11), 1910-1916. (5) Gandhidasan, P. Parametric Analysis of Natural Gas Dehydration by a Triethylene Glycol Solution. Energy Sources 2003, 25, (3), 189201. (6) Ghiasi, M. M.; Bahadori, A.; Zendehboudi, S.; Chatzis, I. Rigorous models to optimise stripping gas rate in natural gas dehydration units. Fuel 2015, 140, (0), 421-428. (7) Jacob, N. C. G. Optimization of Triethylene Glycol (Teg) Dehydration in a natural gas processing plant. Int J Res Eng Res Eng Technol 2014, 3, (6), 346-350. (8) Nemati Rouzbahani, A.; Bahmani, M.; Shariati, J.; Tohidian, T.; Rahimpour, M. R. Simulation, optimization, and sensitivity analysis of a natural gas dehydration unit. J. Nat. Gas Sci. Eng. 2014, 21, (0), 159-169.



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