Article pubs.acs.org/IECR
Process Design of Industrial Triethylene Glycol Processes Using the Cubic-Plus-Association (CPA) Equation of State Alay Arya, Bjørn Maribo-Mogensen, Ioannis Tsivintzelis,† and Georgios M. Kontogeorgis* Center for Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark ABSTRACT: The Cubic-Plus-Association (CPA) equation of state (EoS) has already been proven to be a successful model for phase equilibrium calculations for systems containing glycols. In the present work, we interface a thermodynamic property package (ThermoSystem), based on CPA, with Aspen HYSYS through the CAPE-OPEN standards. We, then, simulate certain binary and multicomponent systems where experimental data are available in the literature and which are critical for process design of natural gas dehydration units by triethylene glycol (TEG). We also demonstrate the potential of CPA for the process design of liquid−liquid extraction of aromatic hydrocarbons by TEG. Comparisons between simulation and experimental results are presented in order to illustrate the reliability of ThermoSystem while it is used in a process simulator for industrial applications. Detailed analysis on selecting TEG pure compound parameters and on calculating TEG−water binary parameters is shown. Missing binary interaction parameters are regressed and presented for various binary systems, and a relationship between the interaction parameters and alkane molecular weight is obtained for TEG−alkane binary systems. A simulation case study of a typical natural gas dehydration process is also presented.
1. INTRODUCTION There are two major industrial applications of triethylene glycol (TEG) in oil and gas industries. First, TEG is used as an absorbent in natural gas dehydration units to remove the water from the natural gas before it is transported through pipelines. With more natural gas fields being explored, there will be more TEG dehydration units online. In addition to water, glycol also absorbs small amounts of methane, volatile organic compounds, and hazardous air pollutants, which are ultimately emitted into the atmosphere from the glycol regenerator unit.1,2 Larger TEG recirculation rate will result in more emissions, higher operating cost and more heat energy for regeneration. The thermodynamic model should describe accurate phase equilibria ranging from absorber conditions (low temperature and high pressure) to regenerator conditions (high temperature and low pressure) in order to design/optimize the dehydration unit accurately. Second, TEG is also used as a solvent in liquid−liquid extractor unit to absorb the aromatic hydrocarbons from reformed naphtha and pyrolysis gasoline.3 However, in this work our main focus is TEG application for dehydration and very limited results are shown for liquid−liquid equilibria between TEG and alkanes with aromatics. Glycols form hydrogen bonds or similar strong interactions with themselves and with other components that have proton donor/acceptors, for example water and aromatic hydrocarbons. Without accounting for the hydrogen bond effects, cubic equations of state cannot accurately describe the phase equilibria.4 One way to account for this effect is, indirectly, through EoS/GE models like Soave−Redlich−Kwong (SRK) with the Huron−Vidal mixing rule,5,6 while a more direct approach is via the use of an equation of state (EoS) coupled with association theory, for example based on Statistical Associating Fluid Theory (SAFT)7 or Cubic-Plus-Association (CPA) like that proposed by Kontogeorgis et al.,8−10 which includes terms explicitly accounting for the hydrogen bonds. © 2014 American Chemical Society
There are a few simulation software packages which provide thermodynamic property packages for glycol applications. Typical simulator packages are mentioned in Table 1. Table 1. Process Simulators for Glycol Applications process simulator
base method
Aspen HYSYS TST EoS/AE (NRTL) model ProII SRKM CHEMCAD K-value method (empirical equations) ProMax PR/UNIQUAC
application
ref
dehydration with TEG
11
dehydration with TEG dehydration with TEG
12 13
dehydration/hydrate inhibitor system with MEG, DEG, and TEG
14
We have at the Center of Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering of the Technical University of Denmark (DTU), developed a thermodynamic property package based on CPA.15 The software package can directly be used in any process simulator that supports the CAPE-OPEN standard. In this work, we use Aspen HYSYS to simulate relevant experimental systems and compare the simulation results with experimental results. At the end, we give an example of the sensitivity analysis of the natural gas dehydration process by simulating the flowsheet with the CPA EoS. Received: Revised: Accepted: Published: 11766
March 25, 2014 June 16, 2014 June 24, 2014 June 24, 2014 dx.doi.org/10.1021/ie501251d | Ind. Eng. Chem. Res. 2014, 53, 11766−11778
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Article
2. DESCRIPTION OF CPA The CPA EoS is a combination of the SRK EoS16 (to account for repulsion effects and van der Waals attractive forces) with an association term derived from the first-order thermodynamic perturbation theory by Wertheim.17,18 CPA reduces to SRK in the absence of associating components. The cubic EoS is still a standard model in oil and gas applications. The association term adds a new set of internal variables, the fractions of association sites that are not occupied, which are functions of the mixture density. A robust approach for finding the density would typically involve nested loops, where the fractions of free sites are calculated at a fixed density in an inner loop, with density being modified in the outer loop to match a specified pressure.19 However, Michelsen19,20 showed that the numerical implementation of the association term ensures that the computation time is not much higher than that of SRK and other simple models. CPA has three pure component parameters (a0, b, c1) in the SRK term and two parameters (ε, β) in the association term. Thus, there are in total three parameters for nonassociating components and five parameters for associating components. These parameters can simultaneously be regressed either from vapor pressure and liquid density data or from vapor pressure, liquid density, and LLE data of binary mixtures containing the components of interest. We typically use one or two binary adjustable parameters (kij, βij): one in the energy parameter of the attractive term of SRK (kij) and another in the association strength of the association term (βij). For many binary mixtures only one binary interaction parameter (the one in the SRK term) is sufficient for fitting the CPA results to the experimental data and the cross-association energy and volume are estimated from combining rules. Generally, βij is fitted when only one component is self-associating and there is the possibility for cross association with the other component. The CPA EoS and related combining rules can be found in the work of Kontogeorgis and Folas,4 and they are also briefly repeated in Appendix B. As shown by Derawi et al.,21,22 Folas et al.,1,5,6 Afzal et al.,23,24 Breil and Kontogeorgis,25 and Tsivintzelis et al.,26 CPA can successfully be applied to glycol−water, glycol−aliphatic hydrocarbons, glycol−aromatic hydrocarbons, and glycol−acid gas systems. In most of these studies glycols have been modeled using the 4C scheme (also used for water), in the terminology of Huang and Radosz.27 Association schemes for different glycols are depicted in the work of Afzal.24
Figure 1. Role of the CAPE-OPEN interface as a standard for interprocess communication.
properties that must be accessible from the process simulator. A thermodynamic PP does not have to support all properties defined by the CAPE-OPEN standard, and ThermoSystem only supports the calculation of a limited list of properties, which are mentioned in Table A.3. In addition, ThermoSystem supports only two phase PT flash but can use the built-in flash from the process simulator (in this case, the HYSYS Flash).
4. TEG PURE COMPOUND PARAMETERS AND TEG−WATER BINARY PARAMETERS Systems of TEG that are relevant to the oil and chemical industry were studied by Breil and Kontogeorgis.25 The authors made a thorough investigation of the thermodynamic modeling of mixtures that contain TEG with water, aliphatic, or aromatic hydrocarbons using the CPA equation of state. The TEG molecule was modeled as a self-associating fluid using the wellknown 4C association scheme (where two proton donors and two proton acceptors are assumed on every molecule), as well as the newly developed 6D scheme (where two proton donors and four proton acceptors, all equivalent for simplicity, were assumed on every TEG molecule). Based on such association schemes three pure fluid parameter sets (sets 1−3) are reported for TEG, which are shown in Table 2. The parameter set 1, estimated previously by Derawi et al.,21 was obtained by fitting the predictions of the model to vapor pressure and liquid density data of the DIPPR correlations and, subsequently, it was tested for TEG-n-heptane VLE. The parameter sets 2 and 3, reported by Breil and Kontogeorgis,25 were obtained by including the binary data for vapor−liquid equilibrium of TEG−methane and the liquid−liquid equilibrium for TEG−nheptane systems in addition to the vapor pressure and liquid density data in the parameter estimation. The argument for including these two binary systems in the pure fluid parameter estimation, was that the experimental results of such binary mixtures cannot be reproduced accurately when they are excluded (especially the TEG−methane VLE). Thus, the binary interaction parameters for TEG−methane and TEG−n-heptane were estimated simultaneously with the TEG pure component parameters. As it is shown in Figure 2, the parameter set 1 presents the lower deviations from vapor pressure data obtained from the DIPPR correlation (13%),25 while the other two sets present relatively higher deviations (up to 50%).25 However, as it is shown in Figure 3 for the TEG−methane binary mixture VLE, all the TEG pure fluid parameter sets successfully describe the liquid phase compositions; however, only parameter sets 2 and 3 accurately describe the TEG content of the vapor phase. For this reason, the set 2 was suggested for TEG by Breil and Kontogeorgis,25 despite the fact that this set presents very high deviations from experimental vapor pressure data for pure TEG. There could be one
3. INTERFACING THE CPA PROPERTY PACKAGE CPA is a rather recently developed model, and it is not available in commercial process simulators. To use it for process design, as mentioned in the Introduction, CERE has developed the thermodynamic CPA property package (PP; called ThermoSystem), which supports the CAPE-OPEN standard maintained by the CO-LaN consortium.28 The CAPE-OPEN standard specification presents a set of interfaces that enables communication between a CAPE-OPEN compliant process simulator and ThermoSystem, and it can be visualized in Figure 1. In other words, one can use a user-defined thermodynamic PP (e.g., CPA) for process design instead of using built-in thermodynamic models (e.g., Peng−Robinson) available in process simulators. Almost all of the process simulators, used by various industries, by now support the CAPE-OPEN standard interface. The CAPE-OPEN standard defines different types of 11767
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Table 2. TEG Pure Compound Parameters set 1 set 2 set 3
Tc (K)
b (L/mol)
a0/Rb(K)
c1 (−)
ε/R (K)
β
association scheme
ref
769.5 769.5 769.5
0.1321 0.1289 0.1289
3562.48 3622.49 3622.49
1.1692 0.9676 0.9100
1724.44 1697.13 1420.00
0.0188 0.0198 0.0200
4C 4C 6D
21 25 25
carefully designed setup and procedure. A serious error can originate from small details of the procedure or the used apparatus. For this reason, it is suggested that some new experimental data have to be obtained in order to confirm the existing data sets for the TEG content of a methane vapor phase. Also, some new reliable experimental data are needed for pure TEG vapor pressures at low temperatures.29 This suggestion is also based on the fact that similar problems are not observed in the CPA modeling of other glycol systems, such as the MEG−methane mixture. However, until this problem is resolved and in contrast with Breil and Kontogeorgis,25 we decided to use the TEG pure fluid parameters, estimated by Derawi et al.,21 which more accurately describe the vapor pressures of pure TEG, despite the fact that this set fails to describe the TEG content in vapor phase of the TEG−methane VLE at low temperatures. Furthermore, the binary parameters for TEG−water mixture were revised in this study in order to satisfactorily describe all the available experimental data for this mixture, which include activity coefficients at 298 and 333 K,33 VLE data at 0.85 bar,34 excess enthalpies at 298 K,35 and activity coefficients at infinite dilution at 300−378 K.36 In order to obtain satisfactory description of all the aforementioned properties, three binary parameters were optimized by the experimental data: two of them were used for the temperature dependency of the binary interaction parameter, kij (kij = a + b/T), and one for the cross association parameter, βcross (only the cross association energy of this binary was obtained from CR-1 combining rule). Such binary parameters, which were obtained using the pure fluid parameters of Table A.1, are presented in Table A.2 Here it is worth mentioning that Breil and Kontogeorgis25 used two adjustable binary parameters for this system, but their approach fails to describe the experimental data for the activity coefficients at infinite dilution. On the other hand, as it is shown in Figure 4, at the expense of an additional adjustable binary parameter (βcross), the approach of this study results in a more satisfactory description of the experimental data.
Figure 2. TEG vapor pressures. The symbols represent experimental data from DIPPR.29
possibility that, since set 2 and 3 match the vapor pressure data at temperatures around 290−320 K, which are rejected by DIPPR, they are able to predict TEG−methane VLE data, which are also available at around same temperatures (298.15, 316.75 K). From a thorough study (which included the investigation of many parameters, such as the used association scheme, the fitting procedure, and others), it was clear that we cannot simultaneously obtain accurate description of the pure fluid vapor pressures and the TEG−methane VLE with the CPA EoS. Some sets of pure fluid parameters satisfactorily describe the pure fluid vapor pressures, but not the methane−TEG VLE, while other sets present the opposite behavior. In addition, very similar modeling results are obtained with other association theories, such as the NRHB model.32 Here it worth mentioning that the experimental mole fractions of TEG in the vapor phase of the TEG−methane VLE are of the order of 10−7 and 10−6 for 298 and 317 K, respectively.31 Such low concentrations are very difficult to measure, and the corresponding experiments require a very
Figure 3. TEG−methane VLE. (a) Solubility of methane in the liquid phase. Experimental data are from the work of Joo et al.,30 and lines are correlation by CPA. (b) TEG content in the vapor phase. Experimental data from the work of Dalibor et al.31 Lines are correlations by CPA. 11768
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Figure 4. Thermodynamic properties of the TEG−water binary mixture. Experimental data (points) and CPA correlation (lines). (a) Mixture pressures calculated from activity coefficients at different amount of water in TEG. Experimental data from Herskowitz et al.33 (b) Vapor−liquid equilibrium at 0.85 bar. Experimental data from Mostafazadeh et al.34 (c) Excess enthalpies at 298 K and 1 bar. Experimental data from Salah et al.35 (d) Activity coefficients at infinite dilution at 1 bar. Experimental data from Parrish et al.36
Table 3. Comparison between Simulation Results of the Binary System of TEG (1) + Solute (2) Using CPA/ThermoSystem and Experimental Results in Terms of MAPEb of Mole Fraction (x) of the Compound binary system
no. of data (N)
exp data ref
temp range (K)
press. range (bar)
MAPE x2 in Ia
MAPE x1 in IIa
TEG−water TEG−methane TEG−ethane TEG−propane TEG−n-hexane TEG−H2S TEG−CO2 TEG−benzene
18 51 59 40 27 40 40 11 5 10 8
34 38 38 38 39 38 38 40 1 40 1
371−417 298−398 298−398 298−398 473 298−398 298−398 355−429 280−288 385−443 279−345
0.85 1.1−202.0 1.1−204.8 0.2−64.5 0.1−18.1 0.1−94.3 1−202.5 1.0 1.0 1.0 1.0 avg
16.6 2.4 2.2 3.2
21.0
TEG−toluene
a
51.2 7.9 2.1 24.4 4.3 7.2 5.4 7.6
42.3 31.8 65.5 19.0 38.5
I = glycol rich phase. II = solute rich phase. bMAPE = mean absolute percentage error = ∑i=N i=1 (|yexp − ycal|/yexp)1/N.
All the pure fluid parameters used in this work are presented in Table A.1. Apart from TEG−methane and TEG−water, new binary parameters were also obtained for some other systems as shown in Table A.2, while for many investigated systems the corresponding binary parameters were adopted from the literature.
parameters are estimated from binary mixture data alone and then the model is used for predictions for ternary and multicomponent systems. Thus, in this work we first simulate binary experimental systems and then we present predictions for ternary and multicomponent systems. Diverse types of phase behavior (VLE, LLE, and VLLE) are considered. By comparing results with experimental data, we will make sure that CPA in ThermoSystem provides reliable phase equilibrium results at various conditions using the given pure component parameters and binary parameters. We also validate the robustness of the ThermoSystem algorithm, the predictive
5. SIMULATION RESULTS WITH THERMOSYSTEM Pure component parameters and adjustable binary parameters, used in this work, are listed in Tables A.1 and A.2, respectively. As in other equations of state, CPA is developed, i.e. interaction 11769
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Figure 5. (a) VLE of the TEG−n-hexane system at 473 K. (b) Bubble pressure and liquid composition relationship for TEG−n-hexane system at 343 K: symbols represent experimental measurements from the work of Rowley et al.;39 solid lines are correlations using the CPA EoS.
Figure 8. Trend of the CPA/ThermoSystem kij parameters of TEG− alkane binaries vs molecular weight of alkanes at 303 K.
Figure 6. VLE and LLE of the TEG−benzene system at 1 bar: symbols represent experimental measurements from the work of Gupta et al.40 and Folas et al;1 solid lines are correlations using the CPA EoS.
ability of CPA for multicomponent systems, and the application of CPA to various glycol systems. We use Aspen HYSYS to simulate these systems using ThermoSystem. 5.1. Binary Systems. Table 3 shows the different binary systems considered and the comparison of CPA/ThermoSystem results with the available experimental data in terms of average absolute deviation in equilibrium concentrations. Binary parameters are regressed using Aspen Plus with minimization of MAPE. Please note that experimental data are not checked with any thermodynamic consistency criteria, however, plots of CPA correlation with respect to experimental data are observed manually. Most of the systems show rather small deviations, (
