CC BY
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BecTHHK Cn6ry. Cep. 4. 2013. Bun. 1
G. M. Kontogeorgis
ASSOCIATION MODELS FOR PETROLEUM APPLICATIONS
Introduction. Thermodynamics plays an important role in many applications in the petroleum industry, both upstream and downstream, ranging from flow assurance, (enhanced) oil recovery and control of chemicals to meet production and environmental regulations. There are many different applications in the oil and gas industry, in the broader terms, that thermodynamic data (phase behavior, densities, speed of sound, etc) are needed for a very diverse range of compounds beyond petroleum (CO2, H2S, water, alcohols, glycols, mercaptanes, mercury, asphaltenes, waxes, polymers, electrolytes, biofuels, etc) and over a very extensive range of conditions, up to very high pressures. Actually, the petroleum industry was one of the first industrial sectors which has used extensively thermodynamic models and has even contributed to the development of several of the most popular and still widely used approaches. While traditional thermodynamic models like cubic equations of state have been and largely still are the dominating tools in the petroleum industry, the focus of this review is on the association models. Under this name we include models belonging to the SAFT/CPA family (and others) which explicitly take into account hydrogen bonding and other complex interactions. Such association models have been, especially over the last 20 years, shown to be very successful in predicting many thermodynamic properties of interest to the oil and gas industry. They have not as yet fully replaced cubic equations state but the results which have been presented are in many cases, e. g. for gas hydrate related systems, CO2/H2S mixtures, water/hydrocarbons and others, very impressive. This review will highlight both the major successes of these association models but also some of their limitations which we believe should be addressed in the future.
Petroleum applications where thermodynamics plays a key role and the need for new approaches. Phase behavior (and other thermodynamic properties) of oil — gas (CO2, H2S, N2, ethane, methane, etc.) — water — chemicals (e. g. gas hydrate inhibitors) is of crucial importance in many applications in the petroleum industry. For example, when methanol and MEG are used as gas hydrate inhibitors, a significant problem, especially for the volatile methanol, is their loss in hydrocarbon phase(s). Successful estimation of inhibitor loss enables optimizing the injection of the inhibitors at the various conditions. Thus, predicting the distribution of water and inhibitors (methanol, MEG) in various phases at high pressure and low temperature is very important.
Actually the list of applications of interest to the oil industry is very broad. A recent presentation during the SAFT Conference in Barcelona (September, 2010) delivered by Dr. Francois Montel (from TOTAL) was entitled "A single predictive thermodynamic model for all the needs of Oil and Gas Exploration, Production, Refining and Petrochemical industries" . In this presentation, an impressively large number of applications are mentioned: in addition to those stated above, flow assurance (hydrate inhibitors, wax, asphaltenes), the effect of electrolytes (e. g. brine), sulfur compounds like mercaptanes, trace compounds e. g. mercury, complex chemicals used in diverse applications, biofuels and in general oxygenated compounds. Of course, thermodynamic properties are needed up to high pressures but these
Georgios M. Kontogeorgis — professor, Center for Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering. Technical University of Denmark. © G. M. Kontogeorgis, 2013
are not limited to phase behavior. Derivative properties like speed of sound and interfacial properties are also very important.
When thermodynamics is so important for the petroleum industry, it is not surprising that this industry has been in the forefront in the use and actually often in the development of thermodynamic models that can meet its needs. As high pressures are frequent in the oil and gas industry, equations of state are most useful and especially the simple, fast and often reliable cubic equations of state like SRK [1] and Peng—Robinson [2] have been extensively used and they still are. In 1986, Tsonopoulos and Heidman [3] concluded that "Cubic equations of state are simple, reliable models and allow for direct incorporation of critical conditions. We, in the petroleum industry, continue to find that such simple EoS are very useful high-pressure VLE models, and we found as yet no reason to use complex non-cubic equations of state". Ten years later, Jack Heidman (IVC-SEP discussion meeting, 1998) proclaimed that "Cubic EoS are here to stay". Even now, in a recent review by Eric Hendriks from Shell [4] we read "the general philosophy is to use standard and proven methods such as the Peng—Robinson equation of state...". An investigation carried out by the European Federation of Chemical Engineering (Working Party of Thermodynamics and Transport Properties) [5] on industrial needs reveals the same; industry continues to use in many applications "traditional" models like cubic Equations of State and activity coefficient models such as UNIFAC. And why not? Sometimes we feel that such traditional models are somewhat misunderstood and are even called "completely empirical" whereas the reality is often different. Recent reviews [6, 7] illustrate many capabilities of cubic equations of state, which when carefully used and with suitable mixing rules can be widely applicable even for size-asymmetric and polar systems, especially for high pressure vapor—liquid equilibrium applications. These reviews and recent monographs [8-10] outline many of the capabilities, applications and limitations of cubic equations of state. We will not focus further on these traditional models' strengths which are well documented. But we will say a few words on their limitations which justify why new thermodynamic approaches are needed in some cases.
In practice, cubic equations of state are correlative models. Adjustable parameters are needed for gas/hydrocarbon systems (but can be ignored if only hydrocarbons are present). These parameters are fitted to some data e. g. vapor—liquid equilibria at one temperature and are extrapolated at other conditions and especially for multicomponent systems. The results are often good but for high accuracy, sometimes temperature-dependent interaction parameters are needed. And indeed many such correlations for the interaction parameters of different gas/hydrocarbon mixtures have been developed (see e. g. in [8]). When two interaction parameters are used in cubic equations of state e. g. for H2S/water or solid—gas systems, they appear to have arbitrary values, highly specific which cannot be generalized. These problems of cubic equations of state become much more pronounced when polar and especially hydrogen bonding compounds are present. Whereas vapor—liquid equilibria of e. g. water/alcohols and other similar systems is described well especially when local composition mixing rules are used, this is not the case for liquid—liquid equilibria. Simultaneous description of vapor—liquid and liquid—liquid equilibria for methanol—alkanes or ethanol—alkanes is not possible with cubic equations of state using the classical van der Waals one fluid mixing rules and a single interaction parameter. Neither is it possible to describe both solubilities in highly immiscible systems like water—alkanes or glycol—alkanes. As expected, lack of representation of these binary systems results in even more severe problems for predicting multicomponent systems containing e. g. hydrocarbons (oil), water and polar chemicals like methanol and glycols. In such cases, it is often multiphase (vapor—liquid—liquid) equilibria which must be represented.
Successful representation and prediction of complex phase equilibria for mixtures containing hydrogen bonding fluids is not the only limitation of cubic equations of state but it is a serious one as such phase behavior is important in many applications in the oil industry e. g. for flow assurance, dehydration using glycols, water content in mixtures containing acid gases and developments of blends of gasoline containing oxygenated compounds like ethanol.
It appears that some fundamental phenomena present in many mixtures are not well represented by cubic equations of state. While, many such phenomena are "absorbed" by the semi-empirical terms and the adjustable interaction parameters, it appears that strong association effects caused by hydrogen bonding and other enhanced interactions have a profound effect on phase behavior and should be best accounted for explicitly in thermodynamic models, at least those aiming at accurate prediction of multiphase and multicomponent equilibria for a wide range of complex systems.
This and other needs led many researchers (both from academia and industry) to develop and use of advanced association models which explicitly account for hydrogen bonding interactions. Roughly these models are often divided into chemical, lattice (quasi-chemical) and perturbation theories. There are many reviews and books for all these types of models e. g. [8-11]. In this work we will focus on the perturbation theories especially those based on SAFT/CPA-type of approaches, as we consider that these have already gained some acceptance in the petroleum industry. SAFT stands for Statistical Associating Fluid Theory and CPA stands for Cubic Plus Association.
SAFT models for petroleum applications — overview. This section is intended as a critical application-oriented review focusing exclusively on the petroleum industry needs. The theoretical development of the models, details on the parameterization and wide ranges of applications are presented in recent monographs [8-11] and three review articles exclusively focusing on SAFT [12-14].
The origin of the development of SAFT lies in the four articles of Michael Wertheim [15-18] in the late 80s, but especially as studied and implemented in an engineering equation of state by Chapman et al. [19] and Huang and Radosz [20]. The general form of the model is given by the equation:
Z Zattr(disp) + Zrepuls(hs) + Zchain + Zassoc- (1)
Eq. (1) illustrates that SAFT is a theory which accounts explicitly for physical (dispersion, repulsion), chain and association interactions. The latter two terms in Eq. (1) originate from Wertheim's theory, while the reason for the many SAFT variants is partially explained by the various possibilities which have been used for representing the physical interactions. SAFT is a segment-based model and typically five pure component parameters are needed for hydrogen bonding compounds. All of these parameters have a clear physical meaning: segment size (diameter), energy and number of segments, energy and volume of association. They are typically estimated based on vapor pressure and liquid density data over extensive temperature ranges. Two SAFT-variants which have been used extensively for oil systems are the PC-SAFT model developed by Gross and Sadowski [21] and SAFT-VR by Jackson and co-workers [22, 23].
In our view, the major achievement of SAFT is the hydrogen bonding term, permitting the model to be used for water and a large variety of other complex chemicals. Nevertheless, even though SAFT was proposed in late 80's most applications up to 2000 ignored this association term! Among the numerous articles illustrating various applications of SAFT in the 20th century, only very few considered associating fluids and the results were not
very convincing either [24]. Most successful results presented with SAFT up to 2000 were for polymer systems, where the importance of the chain term of SAFT is illustrated. Only after the advent of CPA and the systematic implementation, validation and use of the association term of SAFT in CPA, have we seen many applications of SAFT to complex polar/associating fluids; largely all these articles have been published in the 21st century.
For this reason, the SAFT applications for systems containing polar/hydrogen bonding compounds will be presented later and in this section we focus on SAFT applications for other types of oil-related systems.
Two major applications of SAFT in this respect are mixtures of hydrocarbons and gases as well as asphaltenes. Both the original SAFT and PC-SAFT have been used with success for size-asymmetric systems such as mixtures with alkanes e. g. [25, 26] and gas/alkanes e. g. [27-30]. It has been shown for these systems that the results are often excellent using a single system-dependent interaction parameter. It is very reassuring that without interaction parameters, PC-SAFT can predict very well the infinite dilution activity coefficients of alkane systems with diverse chain lengths [30]. This success can be attributed to the successful chain term of the model.
The references mentioned above and others present extensive results of SAFT for many systems of interest to petroleum, e. g. mixtures containing various gases (nitrogen, methane, ethane, CO2, CO, ethylene, H2S) with (heavy) alkanes. The vapor—liquid equilibrium results are very satisfactory up to high pressures using small values of temperature-independent interaction parameters, which often depend more on the gas rather than on the alkanes used.
Another significant application where SAFT may turn out to be a promising approach is in the prediction of the behavior of asphaltenes. Asphaltenes are solid, polar (polyaromatic) high molecular weight compounds which can plug reservoir wells and they can precipitate during production, transportation, refining and processing of crude oil. Despite the fact that there is significant uncertainty about their actual structure, they have been subject to SAFT modeling. Original SAFT [31, 32] and SAFT-VR [33] have been used in their full version, i. e. including the association term whereas the modeling with PC-SAFT [34-39] has been presented without the association term. It has thus not been established as yet whether the association term should be included or not in these applications for asphaltenes. There are, in general, few data for such systems but it is shown that the SAFT approach can be used for correlating asphaltene precipitation data but much more investigation is needed; including access to more measurements.
A different type of application where SAFT models have the potential of outperforming cubic equations of state is the field of derivative properties, for example speed of sound. There have been several investigations, especially over the last ten years, with soft-SAFT [40], PC-SAFT [41] and SAFT-VR [42-44] models. A typical result for PC-SAFT is shown in Fig. 1. The main conclusions from the investigations on the speed of sound is that SAFT models do perform better than cubic equations of state and can qualitatively capture the shape of speed of sound curves over extensive pressure ranges. However, from the quantitative point of view, improvements are needed.
It has also been shown that improved speed of sound results cannot be obtained by simply putting this data into the pure compound parameter estimation (at least not for hydrocarbons). These investigations have pointed out that derivative properties, like speed of sound, offer a much stringent test (than phase behavior) for evaluating the performance of thermodynamic models. They also show that none of the "classical" SAFT models perform for these properties as satisfactorily as for phase behavior. And new developments are needed. One promising such approach is the SAFT-VR Mie proposed by Lafitte et al.
Fig. 1. Speed of sound with PC-SAFT, CPA and SRK for n-octane at 300 K:
experimental data are from NIST; the values in parentheses indicate percentage deviations between model and experimental data; from X. Liang, personal communication
[42-44]. This model is a modification of the SAFT-VR equation of state using the Mie intermolecular potential and treating the repulsive exponent of the potential as an adjustable parameter. Satisfactory representation of speed of sound for alkanes, alcohols and other compounds has been obtained without loss of accuracy in the representation of vapor pressure and density. It remains to be evaluated whether this successful performance is due to additional adjustable parameters used or the theoretical significance of the model.
The CPA theory in petroleum applications. The Cubic-Plus-Association (CPA) equation of state has been proposed by Kontogeorgis et al. [45] and is described in detail in a recent monograph [8]. CPA combines the SRK (or another cubic) equation of state with the association term of SAFT:
Zcpa = ZSRK + ZASSOC- (2)
In this way the model combines a standard for oil applications thermodynamic model with an explicit association term which accounts for the complex physical-chemical interactions when polar chemicals like water, methanol and glycols are present. Thus, when no polar compounds are present, CPA reduces to SRK.
CPA started as an industrially supported project (Shell, Infochem) with well defined targets. The original target behind the development of CPA was to predict the thermody-namic properties of hydrocarbons (oil), gases, water and other polar chemicals, i. e. systems of interest to the oil industry. Emphasis was put on prediction, i. e. the model should perform well for the prediction of multiphase, multicomponent equilibria for mixtures with a minimum number of adjustable parameters per binary system (preferably one).
As mentioned previously, when CPA was proposed very few investigations of the association term of SAFT have been published. Thus, the major challenges of the CPA project was i) to validate and develop the association term of SAFT and ii) to test its combination with a cubic equation of state — and all these in a predictive way.
Over the last 15 years, CPA has been systematically developed for many types of associating compounds (water, alcohols, glycols, amines, acids, alkanolamines, glycolethers, etc)
and the most appropriate association schemes for the different hydrogen bonding compounds have been developed [8].
The CPA Equation of State has been applied with success, over an extensive temperature and pressure range including very high pressures, to a large variety of mixtures containing hydrocarbons (including reservoir fluids), gases (CO2, H2S, etc) and polar chemicals. We will outline below the most characteristic results of relevance to the oil industry. First of all, the outline of calculations is presented. In agreement to the targets set, typically one temperature-independent binary interaction parameter is used which is always estimated from experimental data of binary systems. Sometimes two binary parameters are needed for the so-called "solvating" systems such as water or glycol with aromatic hydrocarbons. Then, CPA is used for extrapolations at other conditions and most importantly for predictions of multicomponent mixtures for which relatively few data are available. These predictions include often multiphase equilibria i. e. presence of vapor, solid and various liquid phases which may be present when we have polar chemicals.
At its first stages of its development (1996-1999), CPA has been applied to mixtures containing methanol (possibly the most important gas hydrate inhibitor), other alcohols, water and hydrocarbons. It has been shown that CPA can correlate with one interaction parameter both vapor—liquid and liquid—liquid equilibria for methanol—hydrocarbons and water—hydrocarbons. Details of the phase diagrams are well represented e. g. the azeotropic behavior of methanol/propane at very low methanol concentrations, for the existence of which there is industrial evidence. A typical example of the capability of CPA over extended temperature and pressure ranges is shown in Fig. 2 for methanol/methane [46]. A single temperature independent interaction parameter is used.
The success of the model, especially for water—hydrocarbons, is unprecedented. It can correlate over extensive temperature and pressure conditions both of the very low solubilities, of water in oil and oil compounds in water. Even the prediction (which means no use of interaction parameters) is very satisfactory. For example, without any interaction parameters, CPA can predict the water solubility in methane (and other alkanes) over a 1000-bar pressure range and diverse temperatures [8].
We believe that the water-hydrocarbon phase behavior results obtained with CPA are the best results with a thermodynamic model for aqueous hydrocarbon mixtures to-date. A typical result for a system containing water and an aromatic hydrocarbon is shown in Fig. 3.
Moreover, CPA can correlate water/alcohols VLE over a 100 bar pressure range and 250 degrees temperature range with just one adjustable parameter. Then, it has been shown that CPA can predict multiphase (vapor—liquid—liquid) equilibria of multicomponent mixtures containing water, methanol (and other alcohols) and hydrocarbons. The results are very successful, rendering CPA an excellent predictive model when no data are available. The success is due to the successful representation of the association phenomena, especially the hydrogen bonding nature of the complex polar compounds involved (alcohols, water). The correct physical representation of hydrogen bonding and other phenomena has been verified by comparing the model's predictions and parameters against spectroscopic data such as monomer fractions and theoretical values for the enthalpies/entropies of association which have not been used in the parameter estimation.
The development of advanced association models like CPA and SAFT can be time consuming as care should be exercised for establishing the appropriate way to represent the complex association phenomena and estimate the necessary parameters. However, once this has been accomplished and the parameters are available the models can be readily used by scientists and engineers.
300 т
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я
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0.001
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♦ 283.15 K exp.
■ 348.15 K exp.
323.15 K CPA
• 298.15 K exp.
• 298.15 K exp.
348.15 K CPA
• 298.15 K exp.
— 283.15 K CPA
A 323.15 K exp.
-- 298.15 K CPA
Fig. 2. Experimental and calculated methanol content in gas phase of methane + methanol system using the CPA equation of state with kij = 0.01: the experimental data are indicated as points and the CPA calculations as lines; from Riaz [46]
100000 -e
10000 -E 1000-E 100 -E 10 -t 1
♦ Ethylbenzene in water (Exp.) --Ethylbenzene in water (CPA)
• Water in ethylbenzene (Exp.) --Water in ethylbenzene (CPA)
300 310 320 330 340 350 360 370 380 T, K
Fig. 3. Mutual solubilities (in mole fraction, x) of ethylbenzene + water:
the experimental data are indicated as points and CPA calculations as lines using a solvation scheme with kij = —0.0165 and Across = 0.051; from M. Riaz, personal communication
x
These first successful results of CPA have made this modeling approach popular both in industry and academia and there are now many corporate users especially in the petroleum industry and groups in academia which has further developed the model in various applications. We will illustrate hereafter the most characteristic results which are of relevance to the oil and gas sectors.
Glycols. Extension of CPA to glycols was somewhat delayed due to lack of experimental data, even for the relevant binary systems. The most important glycols of interest to the oil industry are MEG (monoethylene glycol) and TEG (triethylene glycol). Thanks to a collaboration project with Statoil and the efforts of a few research groups in Europe, we have now available experimental LLE data for several binary glycol—hydrocarbon mixtures as well as for a few water — MEG — hydrocarbon ternary systems. These data have been used for modeling (binary systems) and validating (multicomponent systems) the CPA equation of state. It is shown that CPA can correlate very well MEG—hydrocarbon LLE, in all cases CPA has been also combined with a solid hydrate model and in this way hydrate curves have been calculated, also in the presence of inhibitors like methanol and
glycols. The representation of hydrate equilibria is very satisfactory, even at large inhibitor concentrations. One example is shown in Fig. 4.
The experimental data are from [47-49].
Acid gases (CO2, H2S) and other sulfur compounds (mercaptanes). CPA has
been developed over the last 5 years for mixtures containing acid gases (CO2, H2S) with hydrocarbons, water and other polar chemicals (methanol, glycols) [50-54]. For these and other developments, it has been necessary to extend CPA to include the effect of "solvation" which is also responsible e. g. for the higher solubilities of aromatic hydrocarbons (compared to aliphatic ones) in water and glycols (see also Fig. 3). The association term of CPA permits a natural extension of the model to include the "solvation phenomenon" which ensures a very successful representation of these systems as well. Modeling the solvation with CPA requires two adjustable parameters, one in the physical (SRK) term and one in the association term (cross association volume). However, using the concept of "homomorph", only one adjustable parameter is needed in many cases. According to the "homomorph concept", the interaction parameters for physical interactions are obtained from "similar systems" e. g. for water—hexane in the case of water—benzene and using this approach only the cross-association volume parameter is fitted.
The conclusion from the extensive acid gas investigations [50-54] is that CPA is an accurate model for the description of densities and phase equilibria of systems containing acid gases (CO2, H2S), water, methanol, glycols and hydrocarbons. Very good results are obtained over extensive temperature and pressure ranges and for both binary and multicompo-nent systems. We have considered about 30 multicomponent CO2/H2S-water-hydrocarbons-alcohols/glycols systems where phase equilibrium (VLE, VLLE) data are available, but not all results have as yet been published. The interpretation of the results for multicomponent acid gas containing systems is not easy, as the experimental uncertainty is often not reported and because the solubilities of certain compounds may be very small in some phases e. g. for glycols in the gas phase or for hydrocarbons in the aqueous phase. Nevertheless, having
3.0-,
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Pm
§ 1.51
1.0-
0.5
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■ 14.99% EG, Bishnoi et al., 2000
▲ 30% EG, Bishnoi et al.,2000
X 10% EG, Richon & Mohammadi, 2010
- 20% EG, Richon & Mohammadi, 2010
♦ 35% EG, Richon & Mohammadi, 2010 O 50% EG, Richon & Mohammadi, 2010
• 25% EG, GPA RR-92, 1985 A 50% EG, GPA RR-92, 1985
--CPA
O
245
250
255
260
265 T, K
270
275
280
285
Fig. 4. Hydrate curve for ethane at different monoethylene glycol concentrations: points are experimental and lines are CPA predictions; from E. Karakatsani, private communication
these parameters into consideration, CPA performs overall satisfactorily with deviations for the multicomponent systems being a bit higher than those obtained for the corresponding binary systems. A typical example is shown in Fig. 5 for the water solubility in pure CO2, pure methane and a gas mixture. The CPA results are favorably compared to those obtained from a successful classical model (SRK with Huron—Vidal mixing rules) which contains, however, more binary adjustable parameters than CPA.
It has been shown that overall equally good results are obtained by treating the acid-gases as self-associating molecules (three-sites for H2S and four sites for CO2) and as solvating molecules (with polar compounds), when the same number of adjustable parameters are used. When the solvation approach is used, the cross-association energy for CO2-water or CO2-methanol can be obtained from spectroscopic or other theoretical approaches.
Recently, using also newly measured experimental data, CPA has been applied to the important for oil applications family of mercaptanes [55, 56]. It has been shown that CPA can correlate well mixtures of various organic sulfur species including mercaptanes in mixtures with water and hydrocarbons. A typical example is shown in Fig. 6. The calculations are predictions with CPA using parameters obtained from binary data alone.
Other chemicals. While methanol and glycols are very important due to the role as gas hydrate inhibitors, they are not the only chemicals of importance. Oil industry uses a variety of other chemicals with many functions e. g. as emulsion breakers, antifoamers and corrosion inhibitors. Alkanolamines are important also in connection to CO2 capture from coal-fired power plants. Environmentally sustainable and economic production and transportation of oil requires careful control of these chemicals both in terms of type and amount used. And thermodynamics plays a key role in this as it is directly related for
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Fig. 5. Solubility of H2O in pure CO2, in pure CH4 and in CO2 with 5.31 mol. % CH4: experimental data (points) while the calculations are denoted as lines (solid for CPA and dotted for SRK—Huron Vidal); SRK-HV calculations are from [57], from I. Tsivintzelis, personal communication
■ Exp. data, mixture, 298 K
Exp. data, pure CO2, 298 K
O Exp. data, pure CH4, 298 K
- CPA, (solid lines)
........ SRK-HV (dot lines, Austegard et al. 2006)
1 Pure CO2
1 .................................................... ■ Mixture
■ .........■ ■ ■........
... ■ ' *
.
'hV r >U O
T Pure CH = 298.15 K ^__ 4
40 60 80 P, MPa
100
Fig. 6. Solubility of DMS in the DMS + CH4 + H2O ternary mixture as a function of pressure:
solid line indicates the CPA prediction using parameters from binary data alone; modified from [55]
example to the amount of inhibitors injected for specific applications and the assessment of the chemicals' fate in the ecosystems, especially aquatic ones.
For this reason, we provide a short review of the major conclusions from the applications of CPA to diverse chemicals [8, 58-61].
CPA has been so far applied to amines (using two or three sites), organic acids (one site) and multifunctional chemicals of wide use such as alkanolamines and glycolethers (in both cases, typically four sites are used). Most of these applications have focused on binary systems. The correlation results are satisfactory for vapor—liquid and liquid—liquid equilibria in mixtures with hydrocarbons, but somewhat higher interaction parameters are needed when these complex chemicals are in mixtures with other polar compounds, especially water. Other "advanced" association schemes have been used for glycolethers and alkanolamines [58, 61] but no improvement over the standard "four-site" scheme is obtained, thus there is no need for additional complexities in the model.
We have identified some important limitations, especially for mixtures containing small organic acids (e. g. acetic acid/water) and aromatic acids (e. g. benzoic acid and tereph-thalic acid). Some of these problems e. g. for terephthalic acid can be attributed to lack of data, but for other acids they cannot! For example, for benzoic acid, reliable vapor pressures and liquid densities are available. Nevertheless, CPA cannot correlate satisfactorily phase behavior (vapor—liquid, liquid—liquid and solid-liquid) for benzoic acid-water over the whole temperature range for which data are available. Thus, it can be concluded that capturing the complex phase behavior of aromatic acid-water systems may require some fundamental improvement of CPA and other association models. We have not been able to identify any successful models in the literature which can describe the phase behavior of benzoic acid-water over the entire temperature range for which data are available.
Reservoir fluids. Of course, an important application of interest to the petroleum industry is to predict phase behavior in mixtures containing reservoir fluids and chemicals (water, methanol, glycols). A rather simple but efficient characterization procedure which can be used in CPA has been developed by Yan et al. [62]. Yan et al. have then applied CPA to the few cases for which data were available (oil/water and oil/water/MEG systems) and the agreement is satisfactory. However, none of the oil systems is particularly "heavy" and no reliable heavy oil/water or heavy oil/water/MEG data have been found for further testing of CPA with this characterization method. Lack of data in general for reservoir fluids has been a problem for testing CPA for "real oils" and thus during the last five years a significant experimental program for obtaining new data has been carried out in collaboration with Statoil (Norway). The data and modeling obtained are available in references [46, 63, 64].
In this collaborative research project experimental phase equilibria data for five North Sea reservoir fluids (three condensates and two so-called "light oils") in mixtures with MEG and MEG-water have been measured. Several "condensates + MEG + water" systems have been investigated and the liquid—liquid equilibrium data have been measured in the temperature range of 275.15 to 323.15 K at atmospheric pressure.
The five reservoir fluids have different PNA distributions (as shown in Fig. 7) and molecular weight/densities (as given in Table).
Using the same characterization method previously developed [62], CPA has been applied to all these reservoir systems together with water and MEG. The results are in good agreement with the measurements for all solubilities, even for the water and MEG solubilities in the condensate phase and the condensate solubilities in the polar phases which are rather low.
Overall Density, Molar Mass and C10+ Fraction of Condensates and Oils investigated in the collaborative research project between DTU (Denmark) and Statoil (Norway) in the period 2008-2011 (from [46])
Reservoir Fluid Density, g/cm3 Molar Mass, g/mol C'io+, mass %
Condensate-1 0.7562 112.70 40.77
Condensate-2 0.7385 106.90 27.96
Condensate-3 0.7210 97.37 12.49
Light-Oil-1 0.9060 266.00 91.45
Light-Oil-2 0.7784 135.20 57.41
More specifically, for the reservoir-fluid + MEG systems excellent correlations are obtained for the mutual solubility of reservoir fluids and MEG as a function of temperature using solely a single average, temperature independent interaction parameter for all MEG-hydrocarbon pairs. A typical example for Light Oil-2 is shown in Fig. 8 [46].
For the reservoir-fluid + MEG + water systems satisfactory predictions are obtained using an average temperature independent interaction parameter for all MEG-hydrocarbon pairs obtained from reservoir-fluid + MEG systems and a water—hydrocarbon interaction parameter which is obtained from a generalized correlation (as a function of carbon number). CPA can satisfactorily describe the trends in solubilities of reservoir fluids, MEG and water as a function of the MEG mole fraction in the polar phase and as a function of temperature.
However, despite these preliminary satisfactory results, we are far from a full validation of CPA to real oil systems. Further work is needed in order to establish whether CPA with the proposed characterization method can perform satisfactorily also for heavy oils and/or when the aromatic/naphthenic content of the oil is high.
SAFT applications for associating systems and comparison to CPA. Following or parallel to the development of CPA for associating fluids, various variants of SAFT especially PC-SAFT and SAFT-VR have been applied to many similar systems, especially
70 60 50 40 30 20 f-10-E-0
s::i Condensate-1 ■ Condensate-2 ■ Condensate-3 ■ Light-Oil-1 ■ Light-Oil-2
r I
A
Fig. 7. PNA distribution of condensates (condensate-1, 2 and 3) and oils (light-oil-1 and 2) studied from [46]
10000T
♦ Light-Oil-2 in MEG exp.
--Light-Oil-2 in MEG CPA t. = 0.02
-Light-Oil-2 in MEG CPA k.. = 0.00
• MEG in Light-Oil-2 exp.
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300 305 310 315 320 325 T, K
Fig. 8. Mutual solubility (in mole fraction, x) of light-oil-2 and MEG as a function of temperature for light-oil-2 + MEG system: the experimental data are indicated as points and the CPA calculations as lines; from [46]
water/hydrocarbons and mixtures with alcohols, acids and glycols. Many results and relevant references are presented in a recent monograph [8]. In some cases, comparisons to CPA have been presented e. g. for alkanolamines, glycolethers and water/methanol/hydrocarbons [58, 61, 65]. In most of these applications, SAFT and CPA have been developed in similar ways for associating fluids i. e. the same type of association schemes and number of adjustable parameters used. Polar versions of PC-SAFT have also been applied extensively to methanol-alkane and water-alkane systems [10, 66].
A general conclusion is that, under these conditions i. e. when developed in the same way for the associating compounds, the performance of SAFT models (and especially PC-SAFT) is satisfactory and, in most cases, similar to CPA. We have not experienced, with one major exception, many cases where trends and performance of PC-SAFT and CPA are different. We have also observed that for both models several sets of adjustable parameters can be obtained alone from pure compound data (vapor pressures and liquid densities) and thus the optimum set should be identified based on additional data e. g. (liquid—liquid equilibrium) mixture data for the associating compound under investigation and an n-alkane. There have been only few studies of multicomponent systems with PC-SAFT, but the results shown for water/methanol/alkanes in [65] are good and overall similar to CPA.
There has been one important case where we have observed that CPA performs better than SAFT, at least based on the investigations done so far. This is water and especially water-alkane liquid—liquid equilibria where the overall performance of CPA is superior to SAFT using the same number of adjustable parameters. This may be due to the way the parameters have been estimated. Recently, very successful results for water/alkanes LLE have been presented with a polar version of PC-SAFT [66]. These results are similar to CPA, but it is unclear whether the good performance with this PC-SAFT version is due to the explicit inclusion of the polar term in the model or the parametrization which, in this recent work, is similar to CPA (use of liquid—liquid equilibrium data for selecting the best water parameter set).
Future challenges. We have shown that CPA and SAFT-type approaches are very promising models in the petroleum industry and there are many cases where they perform clearly better than cubic equations of state, when hydrogen bonding compounds are present and for multiphase, multicomponent equilibria. We have already discussed some challenging areas where more experimental data for model development/validation and improvements in the models are needed. These are derivative properties (e. g. speed of sound), asphaltenes, mixtures with organic acids as well as heavy oils of diverse types. The latter includes the
need for development of accurate characterization methods, suitable for association models. As the association models are still under development, new applications are presented continuously. For example, it can be mentioned that recently CPA has been applied successfully to asphaltenes [38].
In this section, we report some additional developments and challenges which should be met so that these models can really become widely used tools in the petroleum industry.
First of all, the models should be extended to those important compounds still not addressed (several sulfur compounds, diverse hydrocarbons, complex chemicals including surfactants) as well as those present in trace amounts such as mercury-type compounds. In most of these cases, additional experimental data are needed.
A second challenge is to develop group contribution (GC) or other predictive schemes for estimating in a reliable way both the pure compound and mixture parameters. There are several such GC schemes developed especially for PC-SAFT and SAFT-VR (see [8] for a review) whereas no such methods have been developed for CPA. Nevertheless, predictive schemes have been developed for CPA for some of the pure compound parameters [8] and for the interaction parameters in several families of compounds e. g. water/acids, mixtures with esters, etc. of relevance to biofuels [67]. One example of correlations of the CPA interaction parameter for water/alkanes and MEG/alkanes is shown in Fig. 9.
In addition to phase behavior, interfacial phenomena are also very important in many petroleum applications. Association equations of state like CPA and SAFT have been used for estimating surface and interfacial tensions using the gradient theory or the density functional theory [8]. Which framework is the best remains to be seen as well as whether the successful results reported for the surface tension of many compounds will be extended to liquid—liquid interfacial tensions of water-hydrocarbons and similar systems?
A very significant challenge which calls for fundamental developments is when electrolytes are present. The presence of brine and the effect of salts in hydrate inhibition curves are two of the many cases why CPA and SAFT models should be extended to electrolytes in order to be able to handle such systems. There have been developed over 20 different electrolyte versions of CPA and SAFT (see [8, 9, 14] for a review) but we feel that the problem is far from being solved. The developed electrolyte versions of association models are largely correlative tools with little predictive value. Essentially none of these developed electrolyte association equations of state has been used for water-gas-mixed solvent—salt systems which are of interest to the petroleum industry.
Weak electrolyte systems such as CO2/water/alkanolamines or ammonia are also very important in CO2 capture processes. Thus, this is a major challenge for future work. In one recent contribution in this direction [68] it has been shown that the two major theories for electrostatic interactions, MSA (mean spherical approximation) and Debye—Huckel perform overall very similarly, in terms of the reduced Helmholtz energy, up to very high concentrations. The results are almost identical if the Debye—Huckel distance of closest approach parameter was set to 5/6 of the MSA diameter. Thus, any of these theories could be used in combination with CPA or SAFT. However, it remains to be investigated what is the importance of other electrolyte terms especially the Born term as well as the importance of the dielectric constant. For the latter, predictive and theoretically sound models must be developed for both water-salts and mixed solvent—salt systems.
Conclusions. Optimization of many applications in the petroleum industry (flow assurance, oil transport and production, enhanced oil recovery, etc) relies a lot on thermodynamics. Oil industry has been traditionally using cubic equations of state (either with the van der Waals or with local-composition based mixing rules). They are still very useful but
0.15 -r 0.10 0.05 0.00
-0.05 --
-0.10
0123456789 10 11
Carbon Number
Fig. 9. Correlation for binary interaction parameters for water-hydrocarbons and MEG-hydrocarbons (this work): 1 — kij = -0.0153NC +0.1503, R2 = 0.9973; 2 — kij = -0.0261NC +0.1929, R2 = 0.9986; from [46]
for applications involving hydrogen bonding fluids and mixtures with complex interactions, e. g. when water, alcohols, glycols, acids and alkanolamines are present, association models are particularly useful.
We have illustrated in this work that association equations of state in the form of SAFT and especially CPA are particularly successful in oil and gas applications. These models are relatively "young" compared to cubic equations of state but they have nevertheless gained some acceptance in both academia and industry. More than 20 research groups in academia (in Denmark, Greece, Portugal, France, UK, The Netherlands, USA, China, South Africa and other countries) are currently applying and further developing CPA for new applications. There are also many industrial users. In a recent article, Eric Hendriks [4] from Shell writes that CPA represents a pragmatic approach for industrial applications in the oil industry and performs better than cubic EoS for e. g. gas hydrate inhibition by methanol or glycol, water content in mixtures containing high levels of acid gases and dehydration using glycol.
In an almost 30 years old academia-industry Panel discussion published in Fluid Phase Equilibria [69], Prausnitz and co-workers predicted that in the years to come (semi) theoretical equations of state for complex mixtures will be developed, the quadratic mixing rules will be abandoned and equations of state for petroleum fractions and for polymers will be available. We believe that the three predictions became largely true with the advent of SAFT and CPA equations of state. On the other hand, other predictions-expectations from that panel discussion (scaling laws for the critical region of pure fluids and mixtures will appear; comprehensive framework for multicomponent mixtures containing aqueous electrolytes solutions with hydrocarbons and weak electrolytes as well (CO2, ammonia, acetic acid), unique models for many applications) remain challenges for future researchers.
We have also illustrated that there are many challenges remaining in the thermodynamics of importance for the petroleum sector and, despite Francois Montel's wish (SAFT Conference in Barcelona, September 2010) we feel we are quite far from having "a single predictive thermodynamic model for all the needs of Oil and Gas Exploration, Production, Refining and Petrochemical industries". The challenging issues with these advanced association mod-
els are not limited to the science but equally important is the implementation in the form of development of fast and accurate algorithms for these models and approaches e.g. based on the CAPE-OPEN framework for the efficient dissemination of these results to industry. While such dissemination and training of industrial users for these advanced models remains an issue, we believe that the CAPE-OPEN framework can facilitate the dissemination of these models by permitting them to be used in existing process simulators [70].
The author is grateful to the following researchers for providing material for this manuscript: Dr. Eirini Karakatsani, Dr. Ioannis Tsivintzelis, Dr. Muhammad Riaz, Dr. Javeed Awan and PhD student Xiaodong Liang. The author is also grateful to the companies Statoil (Norway), BP (UK), TOTAL (France), GASSCO (Norway), M^rsk Oil & Gas (Denmark), DONG Energy (Denmark) and Petrobras (Brazil) for funding the CPA development as part of the project CHIGP (Chemicals in Gas Processing).
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Статья поступила в редакцию 24 июля 2012 г.
