Energy & Fuels 2007, 21, 1243-1247
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Simplifying the Thermodynamic Modeling of Asphaltenes in Upstream Operations† Sebastiano Correra* and Daniel Merino-Garcia Eni S.p.A., R&M DiVision, Via Maritano, 26, 20097 San Donato Milanese, Italy ReceiVed August 11, 2006. ReVised Manuscript ReceiVed January 15, 2007
The development of a thermodynamic model to predict the onset of asphaltene precipitation is usually hindered by the complexity of the mixture under consideration. In an attempt to simplify asphaltene modeling, a model related to the Flory-Huggins theory had been previously proposed. The model is based on the fact that asphaltene stability depends upon the quality of the surrounding medium, expressed in terms of the solubility parameter. Moreover, the model only takes into account the first asphaltenes that come out of the solution. This allows the theoretical determination of one of the parameters starting from the concept of infinite dilution, as described in this work. This paper also presents a discussion about the optimal way of determining the parameters of the proposed model.
Introduction Asphaltenes comprise the most polar components of crude oil, because they concentrate the majority of the heteroatoms (N, O, and S)1 and metals (mainly Ni and V).2 Asphaltenes combine this polarity with a high molecular weight and also a high aromaticity (carbon/hydrogen ratio around 1.1 or 1.2).1 This composition gives them a great potential for association; this association increases the potential for precipitation, and this precipitation can be followed by flocculation and possibly deposition. In live oil conditions, asphaltenes may separate spontaneously by depressurization during production; in the laboratory, starting from stabilized (stock tank) oil, asphaltenes are separated by adding a relatively high excess of n-paraffins. However, several difficulties hinder the isolation and study of asphaltenes in a non-ambiguous way: asphaltenes are not a single, well-defined compound; instead, they (and their properties) depend upon the modality of separation and purification.1 This has a significant effect on the ability of the model to extrapolate from the behavior of laboratory asphaltenes to field conditions. Present analytical standards3 recommend the use of n-heptane, followed by washing in a Soxhlet extractor to remove the non-asphaltic material that is embedded in the solid.4 A debate is still ongoing in the scientific community to determine the optimal way to separate asphaltenes in the laboratory. Asphaltene phase separation is an important issue in oil production. It leads to the formation of heavy organic deposits † Presented at the 7th International Conference on Petroleum Phase Behavior and Fouling. * To whom correspondence should be addressed: Eni S.p.A., R&M Division, via Maritano, 26, 20097 San Donato Milanese, Italy. Telephone: 39-02520-46333. Fax: 39-02520-36116. E-mail:
[email protected]. (1) Speight, J. G. The Chemistry and Technology of Petroleum, 3rd ed.; Marcel Dekker: New York, 1999. (2) Yen T. F. In Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998; p 6. (3) Asphaltene (Heptane Insolubles) in Petroleum Products, IP 143/90; Standards for Petroleum and Its Products; Institute of Petroleum: London, U.K., 1985; p 143.1. (4) Alboudwarej, H.; Beck, J.; Svrcek, W. Y.; Yarranton, H. W.; Akbarzadeh, K. Energy Fuels 2002, 16, 462.
from the reservoir to the refinery, entirely reducing or blocking the flow of oil into the well bore,5 inside the well, during flow through pipelines, etc. For this reason, considerable effort has been dedicated to shed light on the factors that govern asphaltene stability and the development of descriptive/predictive models. Previous Work As stated above, the isolation of asphaltenes to study their properties is not a simple issue; it always remains dubious whether the separated asphaltenes are truly the ones that create problems in live oil or not. In any case, the main interest in upstream operations is on the physical conditions (T and p) of the separation of asphaltenes and not on the characteristics of separated asphaltenes. With this in mind, the focus is usually placed on the study of the behavior of asphaltenes inside the oil, without previous physical separation between the asphaltenes and the rest of the components. As reported in previous papers and presentations, a noticeable amount of onset data has already been collected in our laboratories by means of flocculation onset determinations.6-8 On a semiempirical basis, Correra and Donaggio attempted to put the experimental evidence together by developing a model [onset-constrained colloidal asphaltene model (OCCAM)].9 This model successfully fits experimental data on stock tank oil, by assigning values to the parameters of the model. After this fitting procedure, the model is used to predict the behavior of asphaltenes in live oil, as explained in the Appendix. Before describing the model, a brief re-examination of the main theories of asphaltene behavior in oil is presented, with the aim of shedding some light on the physics of asphaltene precipitation. (5) Leontaritis, K. J.; Amaefule, J. O.; Charles, R. E. SPE Prod. Facil. 1994, 9, 157, SPE paper 23810. (6) Donaggio, F.; Correra, S.; Lockhart, T. P. Pet. Sci. Technol. 2001, 19, 129. (7) Correra, S.; Capuano, F.; Panariti, N. Proceedings of the 5th International Conference on Petroleum Phase Behavior and Fouling; Czarneki, J., Ed.; Syncrude Canada: Edmonton, Canada, 2004. (8) Correra, S. Pet. Sci. Technol. 2004, 22, 917. (9) Correra, S.; Donaggio, F. Proceedings of the International Symposium on Formation Damage; Society of Petroleum Engineers (SPE): Richardson, TX, 2000; SPE paper 58724.
10.1021/ef060371m CCC: $37.00 © 2007 American Chemical Society Published on Web 02/24/2007
1244 Energy & Fuels, Vol. 21, No. 3, 2007
Physical-Chemical Nature of the Deposition Process To estimate the conditions at which asphaltenes separate as a second phase, it is obviously necessary to start from the assessment of the physical-chemical mechanisms involved. An early physical model of asphaltenes in oil10 described asphaltenes as solids insoluble in the oil but dispersed by another oil fraction (resins) adsorbed on their surface. Resins were considered to be the compounds chemically intermediate between the oil and asphaltenes. This picture constitutes the so-called lyophobic colloid model, in which solid formation is believed to be the result of resin desorption from the surface of the asphaltene particles. This desorption may be due to live oil depressurization or the addition of a paraffin solvent in the laboratory. A different approach, in which the separation of asphaltenes was described as a traditional liquid-liquid or solid-liquid phase equilibrium, was proposed by Hirschberg et al.11 Asphaltenes and oil constitute a true solution with some analogy with polymer solutions, because of the large difference in dimensions between asphaltenes and the oil matrix.11 This approach has been termed the lyophilic colloid model. In it, destabilization is the result of a reduction in the solvating power of the hydrocarbon matrix, caused by a change in pressure or the addition of poor solvents. Some of the evidence that supports this approach with respect to the lyophobic model are listed:6 (1) The lyophobic model is based on the assumption that asphaltenes are insoluble in oil, even though laboratory and field experiences have shown the opposite.12 (2) It has not been experimentally confirmed that the interaction between asphaltenes and resins occur at the surface of asphaltene aggregates, in an adsorption-like process.13,14 (3) Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) studies revealed that asphaltenes form aggregates of the same dimensions when they are dissolved in toluene in the absence of resins, because they are ones in the presence of resins in crude oil. Therefore, resins do not play a specific role in asphaltene stability. A more detailed discussion of this topic can be found elsewhere.6,14 However, it is evident that the asphaltene precipitation should be described as a liquid-liquid equilibrium (LLE). Because of the large size difference between the asphaltene molecules and the other ones, a polymer solution theory (similar to the Flory-Huggins one) is typically adopted as the starting point in asphaltene modeling. Moreover and for the sake of simplicity, the mixture is commonly described as a pseudo-binary one. If 2 represents the asphaltenes and 1 stands for the remaining oil, the following equation expresses the free energy of mixing:
In this expression, the free energy of mixing is obtained as the sum of two terms: the entropy and the enthalpy of mixing. (10) Nellenstein, F. I. The Colloidal Structure of Bitumens, The Science of Petroleum; Dunstan, A. E., Ed.; Oxford University Press, London, U.K., 1938. (11) Hirschberg, A.; deJong, L. N. J.; Schipper, B. A.; Meijer, J. G. Soc. Pet. Eng. J. 1984, 24, 283. (12) Porte, G.; Zhou, H.; Lazzeri, V. Langmuir 2003, 19, 40. (13) Espinat, D.; Ravey, J. C. Proceedings of the SPE International Symposium on Oilfield Chemistry; Society of Petroleum Engineers (SPE): Richardson, TX, 1993; SPE paper 25187. (14) Cimino, R.; Correra, S.; Del Bianco, A.; Lockhart, T. P. In Asphaltenes: Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; pp 97-130.
Correra and Merino-Garcia
The entropy of mixing is calculated by means of a lattice model and expresses mainly the increase in the configuration entropy of the solvent, because of the presence of the macromolecular solute. The enthalpy of mixing is expressed essentially by means of a binary interaction parameter (χ), which can be further expressed in terms of the difference in solubility parameters between the solute and solvent. From this equation, it is possible to evaluate the chemical potentials of components in each phase and then construct the phase boundary of the system. However, this kind of model was conceived for a binary system constituted by two true compounds. In the study of asphaltenes, because of the ambiguity of definitions and experimental difficulties, it is almost impossible to estimate in an unambiguous way the molecular weight, and this fact has a tremendous impact on the performance of a model, because it renders the molar concentration uncertain. The empirical model (OCCAM) described previously was able to describe the onset of asphaltene precipitation. The aim of this paper is to show how this model is a limit case of the Flory-Huggins model and how to estimate its parameters. In this way, the simplicity and reliability of the empirical model are supported by a theoretical framework. OCCAM Model This model has the following characteristics: (1) A pseudobinary formulation is employed. The mixture is considered to be constituted by two pseudocomponents. The first one (asphaltene) is the component that separates at the onset, while all of the other components are lumped together as a single pseudocomponent (mixture), with average properties.9 (2) Upon the addition of the precipitant in flocculation experiments, two phenomena occur simultaneously. First, the mixture is diluted, and second, the overall solvent quality of the mixture is worsened. The first factor favors the stabilization of asphaltenes in solution, so that only the worsening of the solvent power of the mixture may explain the separation. Therefore, asphaltene precipitation is ruled by the overall quality of the surrounding medium toward asphaltenes. If the medium (the oil) has a good quality, asphaltenes remain in solution. If the quality of the medium is decreased (either by a pressure decrease or by the addition of an anti-solvent), asphaltenes start to separate as a second phase. (3) The model focuses on the onset of the asphaltene separation, i.e., on the first asphaltenes that come out of solution. That is to say, the model only says if there is asphaltene instability or not. This restriction is largely balanced by the fact that in this way (i) there is no need to know the asphaltene molecular weight and concentration and (ii) it is possible to employ onset data measured on stock tank oil to tune the model and predict the behavior of the live oil. The model is based on the concept of the interaction parameter (χ)
χ)
V1 (δ - δ1)2 RT 2
(2)
where R is the universal gas constant, T is the absolute temperature, Vl is the molar volume of the mixture of oil, solvent, and alkane, δ2 is the solubility parameter of asphaltenes, δ1 is the solubility parameter of the mixture of oil, solvent, and alkane. At the onset, the following equation holds:
χ ) χC
(3)
Simplifying Modeling of Asphaltenes Upstream
Therefore, separation occurs when a critical value of the interaction parameter is reached. Because of a pressure and temperature decrease or a compositional change, the molar volume of the mixture and the solubility parameter δ1 are increased, leading to an increase in χ. When χ reaches the critical value χC, asphaltenes separate. Using a similar approach, Porte et al. found that the onset conditions are proportional to the product between the molar volume (of asphaltenes, in this case) and the difference in solubility parameters.12 When eqs 1-3 are compared, it is noticed that the use of a critical interaction parameter as the onset criterion implies that only the enthalpic term in eq 1 plays a role. The consequences of this will be explained below. It is important to notice that the concept of the critical interaction parameter (χC) is not the same as the critical solubility parameter (δC) that had been proposed in the past.15 δC only works in particular cases; to have a more general validity, the variation in molar volume has to be considered.16 Model Parameters The model is based on the determination of a few variables. The model allows for the determination of the values of these variables by means of experiments on dead oil samples. In this way, the model is tuned to a particular oil and then it is employed in a predictive way to evaluate the asphaltene stability at different conditions or compositions in live oil. An example is described in the Appendix. In this section, a detailed discussion of the determination of OCCAM variables is presented. Oil Molar Volume. The oil molar volume is usually evaluated from density and average molecular-weight measurements; both of these values are currently available in pressurevolume-temperature (PVT) standard reports. With respect to live oil, the PVT characterization of the oil is typically used as the starting point. Then, the traditional procedure of composition lumping is applied. The properties of the plus fraction can be adjusted to match the experimental data of the bubble point and stock tank oil density, as explained elsewhere.17 Then, V1 at any pressure and temperature can be estimated by means of an equation of state. Oil Solubility Parameter. In previous work, it was shown that the solubility parameter of the oil follows a linear relationship with respect to density.18 Angle et al.19 found a similar relationship. Therefore, if the density of the stock tank oil is known, its δ can be directly estimated. The temperature dependence can be estimated using the correlations presented previously.18 In onset tests with an anti-solvent, δoil can be weighed by the volume fraction and added to δ of the antisolvent to give δ1. Asphaltene Solubility Parameter. δ2 is obtained as a fitting parameter from onset flocculation experiments. Experiments are performed at different conditions to allow for the determination of the temperature and pressure dependence of δ2.17 In this way, δ2 and δ1 are estimated separately. This solves the problem that arose when the two parameters where calculated from one single set of experiments.20 (15) Andersen, S. I.; Speight, J. G. J. Pet. Sci. Eng. 1999, 22, 53. (16) Buckley, J. S.; Wang, J. X.; Creek, J. L. Solubility of the least soluble asphaltenes, in Asphaltenes, HeaVy Oils and Petroleomics; Mullins, O., Sheu, E., Hammami, A., Marshall, A., Eds.; Springer, New York, 2006; Chapter 16. (17) Merino-Garcia, D.; Correra, S. J. Dispersion Sci. Technol., manuscript accepted for publication. (18) Correra, S.; Merlini, M.; Di Lullo, A.; Merino-Garcia, D. Ind. Chem. Eng. Res. 2005, 44, 9307. (19) Angle, C. W.; Long, Y.; Hamza, H.; Lue, L. Fuel 2006, 85, 492.
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Figure 1. OCCAM model fit (χ ) 0.5 and 1). MarsPink Oil, experimental data were from Wang. Experiments were at ambient conditions.
Critical Interaction Parameter. With respect to the value of the critical interaction parameter, it was at first assumed to be constant and equal to 0.5. This came from assuming a molar volume of asphaltenes much greater than the molar volume of the oil. Flory21,22 showed that a polymer j and a liquid i are completely miscible through the entire composition range provided that
χ
0
(6)
where x2 represents the molar fraction of asphaltenes. With a bit of algebra, the free energy of the Flory-Huggins model (eq 1) becomes
∆Gmix ) RT[ln(1 - φ2) + φ2χ x2[ln(1 - φ2) + lnφ2 - φ2χ]] (7) χ is the same as in eq 2. When mixing volume effects were neglected and r was taken as the ratio between the molar volumes of the asphaltenes and the oil (r ) V2/V1), the volume fraction of asphaltenes becomes
φ2 )
rx2 rx2 ) x1 + rx2 1 - x2 + rx2
(8)
The logarithm can be approximated with a polynomial expansion
1n(1 - y) ) 1n(1 - y0) - (y - y0)(1 - y0) (1 - y0)2 y2 (y - y0) = -y (9) 2 2
Therefore, the critical interaction parameter is equal to 1, when asphaltenes are considered to be at infinite dilution. The consequences of this result are 2-fold: (1) The maximum of the volume of anti-solvent as a function of the carbon number is correctly fitted with only one fitting parameter (δ2). (2) The derived value of 1 is in agreement with the previously reported experimental results,17,20 which said that the optimal χC is closer to 1 than to 0.5. This result has however been obtained by a theoretical approach that contains some assumptions. The validity of these assumptions is discussed. (i) Given that r is much greater than 1, x2 goes to 0 faster than φ2 at infinite dilution of asphaltenes, because of the fact that the molar volume of asphaltenes is greater than the one in the solution. (ii) This leads to a simplification of eq 7; the terms multiplied by x2 are considered negligible. This holds when the ratio V2/V1 is large enough. That is to say, this assumption holds for large enough values of the asphaltene MW2. The calculations show that a MW2 greater than 3000 g/mol is enough to fulfill this premise. Because interest is focused on the heaviest molecules of the asphaltene fraction (those that precipitate first are believed to be the molecules with the largest MW of the oil), this assumption is taken to be true. (iii) The polynomial expansion of the logarithm has been truncated at the second term. Calculations have shown that this assumption is again correct, as long as φ2 is lower than 0.3. Because the asphaltenes of interest are those that precipitated first, their volume fraction is much lower than 0.3. With this, the result of eq 14 has been validated. When asphaltenes are taken to be at infinite dilution, the critical interaction parameter is equal to 1. This has an important consequence. This statement implies that, at infinite dilution, the onset criterion of the Flory-Huggins model is reduced to an expression in which only the enthalpic contribution appears. This is actually the main assumption that was made in the development of the OCCAM model. In other words, the FloryHuggins and OCCAM models are identical when the solute is at infinite dilution. This gives further validity to the model proposed herein as a valid alternative to the use of the complete Flory-Huggins equation to describe asphaltene instability.
2
When the equation is substituted into eq 7,
1 ∆Gmix ) RT -φ2 - φ22 + φ2χ 2
[
]
(10)
The second degree can be eliminated because it approaches 0 more rapidly than the first degree terms
limx2f0[∆Gmix] ) RTφ2[-1 + χ]
(11)
Instability occurs when eq 6 is fulfilled. When eqs 6 and 11 are combined,
RTφ2[-1 + χ] > 0
(12)
Finally, the instability criterion is obtained
χ>1
(13)
When a model was applied as the one shown in eqs 2 and 3, the demonstration shown above leads to the final value of the critical interaction parameter (χC)
χC ) 1
(14)
Conclusions This work has presented the latest modifications to the OCCAM model that simplify the model without reducing the reliability of predictions of asphaltene instability. The initial assumptions are that asphaltenes are lyophilic colloids and that precipitation is at a LLE. The model focuses on the first asphaltenes that come out of the solution, to avoid the problems of the determination of asphaltene properties. These least soluble asphaltenes are at infinite dilution within the oil. Empirical and theoretical arguments support a value of 1 for the critical interaction parameter. For the infinite dilution case, where only the enthalpic term of the free energy is significant, the FloryHuggins and OCCAM models are equivalent. Optimal methods to determine the remaining model parameters are presented. The result is a simple model for estimation of the pressures and temperatures at which asphaltenes will precipitate using only a few experimental data points and only physically meaningful parameters. Appendix: Upstream Application The procedure to apply the OCCAM model is outlined: (1) Lump the C+ fraction into pseudocomponents to match the (p and T) behavior of the oil. (2) Check that the bubble-point curve
Simplifying Modeling of Asphaltenes Upstream
Energy & Fuels, Vol. 21, No. 3, 2007 1247
Nomenclature
Figure 2. Illustration of a phase diagram of asphaltenes at a fixed temperature.
and the density at ambient conditions are well-fitted with the equation of state chosen. The properties of the C+ fraction (F and MW) may be varied to obtain a better fit with the experimental data. (3) Determine δ1 from the density, by means of a density correlation.18 (4) Determine δ2 at ambient conditions by fitting onset flocculation experiments. (5) Estimate the constant K that allows for the estimation of δasp at other temperatures, following the equation,11 as described in a previous paper:17
δasp(T) ) δasp(T0)exp[Kasp(T - T0)]
(15)
(6) Determine the region of asphaltene instability (Figure 2) at each temperature of interest.
LLE ) liquid-liquid equilibrium MW2 ) asphaltene average molecular weight OCCAM ) onset-constrained colloidal asphaltene model p ) pressure R ) ideal gas constant r ) volume ratio (asphaltenes/mixture of oil, solvent, and alkane) SANS ) small-angle neutron scattering SAXS ) small-angle X-ray scattering T ) temperature Vi ) molar volume of the solvent Vj ) molar volume of the polymer Vl ) molar volume of the mixture of oil, solvent, and alkane V2 ) molar volume of asphaltenes x1 ) molar fraction of oil x2 ) molar fraction of asphaltenes ∆Gmix ) free energy of mixing ∆Hmix ) enthalpy of mixing ∆Smix ) entropy of mixing φ1 ) volume fraction of oil φ2 ) volume fraction of asphaltenes χ ) binary interaction parameter χC ) critical interaction parameter χonset ) interaction parameter at the separation onset F2 ) asphaltene density δ2 ) solubility parameter of asphaltenes δ1 ) solubility parameter of the mixture of oil, solvent, and alkane EF060371M
