Article pubs.acs.org/EF
Modeling Asphaltene Phase Behavior: Comparison of Methods for Flow Assurance Studies Xiaohong Zhang,* Nuno Pedrosa, and Tony Moorwood Infochem Computer Services Limited, Unit 4 The Flag Store, 23 Queen Elizabeth Street, London, SE1 2LP, United Kingdom ABSTRACT: Asphaltenes are the heaviest and most highly polarizable and polydisperse petroleum fractions in crude oils. The solubility of the asphaltenes in crude oils is usually affected by the reduction of pressure, temperature, and/or oil composition change as a result of commingling with other crude oils or gas injection. This may lead to asphaltene precipitation and deposition, decline in permeability, blockage of well and surface facilities, and finally, production decrease or termination, which has a substantial economical impact. Therefore, the ability to understand and predict asphaltene phase behavior is essential for both up- and downstream processing, so that appropriate strategies can be implemented for prevention and remediation. In our study, we present the capability and advances of the equations of state approach by applying the cubic-plus-association (CPA) and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation to model asphaltene stability in live oils and compare the predictions to the various types of measured asphaltene precipitation data over wide ranges of temperature and pressure.
1. INTRODUCTION Any form of solid formation during the production, transportation, and processing of oil and gas streams can cause severe blockages of flow tubes, pipelines, and production facilities, leading to substantial economic loss for the oil and gas industries. The major concerns in terms of solid formation by the oil and gas industries are gas hydrates, waxes, and asphaltenes. The latter is the one that still need more studies in terms of both its experimental determination and theoretical modeling. Unlike other solids, asphaltenes form at several stages from production, transportation, to refining. When they form and deposit, it not only causes blockages but also increases the oil viscosity because of the entrained asphaltenes in oil, leading to a challenging operational situation. Asphaltenes are the heaviest and highly aromatic petroleum fractions in crude oils. Their actual chemical structures are very difficult to define because of the lack of volatility, the complex and continuous variation in their chemical structures, and selfaggregation. However, most researchers agree that asphaltenes are a polydisperse mixture of molecules containing polynuclear aromatics, aliphatic rings and chains, and small amounts of dispersed heteroelements, such as oxygen, sulfur, vanadium, and nitrogen. Operationally, the asphaltenes are defined as a solubility class that are soluble in aromatic components, such as toluene and benzene, but are totally immiscible with paraffinic solvents, such as n-alkanes. As a solubility class, the amount of asphaltenes in oils or gas condensates is conventionally determined by titration of the stabilized oil with n-pentane or n-heptane. Because of the characteristic nature of the chemical structure, asphaltenes have a strong tendency not only to self-associate but also to cross-associate with other aromatic components, such as resins in crude oils.1,2 The nature of asphaltenes and resins and the mechanism causing precipitation are still open to debate. However, the largest and highly aromatic asphaltenes are usually dispersed in oils by resins, the second largest most aromatic groups in crude oils.3−5 This asphaltene−resin © 2011 American Chemical Society
dispersion is dissolved in the crude oil hydrocarbon phase by smaller aromatics that are asphaltene solvents but opposed by saturates that are non-solvents for asphaltenes. Thus, asphaltenes are held in the crude oil in a delicate balance that, once disturbed, can lead to precipitation. The phase behavior of petroleum mixtures is quite complex because of such a large diversity of asphaltene molecules present, and it may have some properties of a colloidal dispersion and some properties of a solution. A simplified physical model of asphaltenic crude oils is illustrated by Figure 1.
Figure 1. Simplified model of asphaltenic crude oil.
The consequence of such a complex structure of asphaltenes is that their theoretical modeling still remains a big challenge for the petroleum industry and that many theoretical approaches and models have been developed over the years. However, dependent upon the hypothesis on the mechanism of asphaltene precipitation and stabilization, the models are mainly classified into two categories: the colloidal approach and the true solution approach. The colloidal approach mainly includes the solid colloidal model by Leontaritis and Mansoori,6 Special Issue: 12th International Conference on Petroleum Phase Behavior and Fouling Received: September 13, 2011 Revised: December 9, 2011 Published: December 13, 2011 2611
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the reversible micellization model by Victorov and Firoozabadi,7,8 and the McMillan-Mayer-SAFT model by Wu and Prausnitz.3 This approach based on the statistical thermodynamics and colloidal science assumes that asphaltenes are insoluble solid particles that are stabilized in oils by an outer layer of resin molecules. The resins are adsorbed on the surface of asphaltene solid particles, and asphaltenes and resins form micelles. The asphaltene precipitation is determined by the chemical potential of resins in both liquid phase and that in asphaltene micelles. The decrease of the chemical potential of resins in the liquid phase because of pressure depletion or gas injection results in asphaltene precipitation, and the separated asphaltene phase is treated as a solid phase containing asphaltenes and resins. The true solution approach includes the solubility models2,9 and equations of state, such as cubic-plus-association (CPA)1,10,11 and perturbed-chain statistical associating fluid theory (PC-SAFT).12−18 In this approach, the asphaltenes are assumed to be in a true solution with oil constituents. Asphaltene precipitation is a result of the reduction of their solubility because of the change of pressure, temperature, and oil compositions, and the precipitated asphaltene phase is treated as either a liquid phase that contains pure asphaltenes or a liquid phase that contains all of the constituents of the oil, with the asphaltenes as the dominate components. Among all of those theoretical models, the current popular and practical approaches with great potential are the equations of state, such as CPA and PC-SAFT, because these models are fully compositional, able to overcome the limitation of other approaches, and capable of simultaneously modeling all of the fluid phases, other solid phases (waxes and gas hydrates), as well as the asphaltene phase within a unified framework. The objective of this study is to demonstrate the capability and potential of two well-developed equation of state models, CPA and PC-SAFT, for modeling the complex asphaltene phase behavior and the effect of gas injection on the asphaltene stability in reservoir fluids. These two distinctive models use quite different strategies to characterize the fluid with different levels of complexity and experimental data input.
The thermodynamic concepts and the main features involved in this CPA model are as follows: (1) Generally, we believe that high-pressure asphaltene precipitation from live oils is thermodynamically reversible but probably kinetically slow.23 (2) Asphaltene molecules exist mainly as monomers in crude oils. (3) Self-association of asphaltene molecules and cross-association of asphaltenes and resins are the two competing mechanisms of asphaltene precipitation. (4) Maximum asphaltene precipitation occurs at bubblepoints. (5) Asphaltenes are assumed to be in a true solution with oil constituents and form an asphaltene-rich liquid phase, where all of the oil constituents may be present. (6) The model is fully compositional; all of the fluid phases and asphaltene phase are modeled within a unified framework. (7) When no associating components are present, the model reduces to the standard SRK equation of state. In the framework of the CPA approach, the general expression of the reduced residual Helmholtz free energy Ares/RT in terms of (T, V, n⃗) is expressed as
Ares(T , V , n ⃗)/RT = ASRK (T , V , n ⃗) + Aassoc(T , V , n ⃗)
(1)
where T is the absolute temperature, R is the universal gas constant, and V and n⃗ are the total volume and molar amount of the components in the mixture, respectively. In eq 1, ASRK represents the repulsive and attractive contribution expressed by SRK equation of state as follows:
⎛ V ⎞ ⎛ V ⎞ a ⎟ + ⎟ ASRK = N ln⎜ ln⎜ ⎝V − b⎠ RTb ⎝ V + b ⎠
(2)
where N and V are the total mole number and volume of the mixture, respectively. Conventionally, the energy and volume parameters a and b in the SRK equation are defined by the critical properties, such as critical temperature, pressure, and acentric factor. In our approach, the energy parameter ai of the pseudo-components (e.g., the petroleum fractions) is expressed by eq 3a and that of the well-defined components, such as methane and ethane, is defined by fitting to the saturation vapor pressure of the pure component with the parameters κi1−κi5 in eq 3b to improve the accuracy of the prediction on saturation pressure.
2. CPA The CPA equation is a thermodynamic model based on the wellknown Soave−Redlich−Kwong (SRK) equation of state with additional association terms to describe the self-association between the asphaltene molecules and the cross-association between the asphaltene and resin molecules. Our CPA approach for modeling asphaltene precipitation has been developed and refined over a number of years, similar to the method recently published by Firoozabadi et al.10,11 It is a rigorous thermodynamic model based on an extensive database of measurements of asphaltene precipitation from live oils. The model can handle all of the fluid phases, such as vapor, hydrocarbon liquid, and aqueous phase, as well as the asphaltene phase, within a unified framework and reproduces not only the asphaltene phase boundaries but also the amounts precipitated as a function of the temperature and pressure. The model also gives reasonable predictions of the effect of gas removal, gas injection, the effect of aromatics, and the composition change because of oil blending on asphaltene stability in crude oils. The association term used in CPA is based on the simplified version of the statistical association mechanism developed from the Wertheim work.19,20 The mathematical simplification in the association terms is applied to speed up the phase equilibrium calculations and turn the model into a robust and practical engineering tool.21,22
ai = aci(1 + (0.48508 + 1.5517ωi − 0.15613ωi 2) × (1 −
2
T /Tci ))
(3a)
ai = aci(1 + κ i1ti + κ i2ti 2 + κ i3ti 3 + κ i 4ti 4 + κ i5ti 5)2 , ti = 1 −
T /Tci
(3b)
aci = 0.42748R2Tci 2/Pci For the liquid density, the Peneloux density correlation in eq 4 is applied to improve the liquid density prediction.
ci = ci0 + ci1T + ci2/T , V = V ′−
∑ cini
(4)
where V′ is the calculated volume by SRK equation of state and the coefficients ci0, ci1, and ci2 are obtained by matching the saturated liquid density at reduced temperature around 0.7. 2612
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cross-association between resins and asphaltenes. Because the complexity of the asphaltene phase behavior strongly depends upon the geological location and the nature of crude oils, the two crossassociation model parameters are usually determined by fitting to the asphaltene precipitation onset data, ideally at two different temperatures. With the optimized cross-association parameters, the CPA model gives good predictions on not only the asphaltene phase boundary over an entire temperature and pressure range of interests but also the effect of gas injection on the asphaltene phase stability in crude oils, as demonstrated in section 4. In general, the model can give excellent results for a wide range of different types of precipitation envelopes.1 The CPA asphaltene model can simultaneously describe the gas, oil, aqueous, and asphaltene phases, making it possible to calculate the phase stability and phase equilibrium in a general and consistent way. 2.1. Fluid Characterization with CPA. Crude oil is a complex mixture typically containing not only the well-defined components, such as N2, H2S, CO2, and light hydrocarbons, but also thousands of imprecisely defined petroleum fractions. An appropriate fluid characterization method is therefore required to characterize the oils to reduce the number of components and define the physical properties of the fractions required by equation of states. For our CPA model, a well-known and widely used fluid characterization method in oil industries is applied to characterize the crude oils together with a robust regression method for fitting the compositional analysis of the fractions in crude oils. During the characterization, the full compositional distribution of the fractions from C6 upward is then regrouped into a few pseudo-components with the physical properties defined by the Lee−Kesler and Riazi correlations.25−28 In the characterization, the asphaltenes are defined as the heaviest fractions, followed by the resins as the second heaviest fractions. As a fully compositional model, several resins with varying physical properties can be present but the exact number depends upon the amount of resins and the compositional distribution of the fractions in crude oil. An example of the detailed characterization of oil 2 is summarized in Table 2, where the resins are the pseudo-components starting with “R” and other pseudo-components are with “C”.
For mixtures, the standard (van der Waals one-fluid) mixing rules are applied to obtain the energy and volume parameters a=
∑
aiaj (1 − kij)ninj , b =
ij
N=
∑ nibi ,
bi = 0.08664
i
RTci Pci
∑ ni
(5)
i
where kij is the binary interaction parameters, which is usually determined by fitting the vapor−liquid equilibrium (VLE) experimental data of the binary component mixtures, ni is the mole number of component i, ωi is the acentric factor, and Tci and Pci are the critical temperature and pressure, respectively. Aassoc is the association contribution accounting for the effect of association between the associating components, such as asphaltenes−asphaltenes and resins−asphaltenes
Aassoc =
⎛
∑ ni ∑ ⎝ln X Ai − ⎜
i
Ai
1 1⎞ X Ai + ⎟ 2 2⎠
(6)
where ni is the molar amount of component i in mixtures and XAi is the mole fraction of component i not bonded at association site Ai, which is defined as21
X A i = (1 + ρ ∑ nj ∑ X BjΔA iBj )−1 j
Bj
(7)
The general expression for the association strength, Δ
AiBj
is defined as
⎤ ⎡ ⎛ ε A iBj ⎞ ⎟ − 1⎥bijβ A iBj ΔA iBj = g (ρ)⎢exp⎜ ⎥⎦ ⎢⎣ ⎝ RT ⎠
(8)
where bij = (bi + bj)/2 and g(ρ) is the average radial distribution function. To reduce the computation time, a simplified-hard sphere form based on the expression proposed by Elliott et al. is applied.21,24 ΔAiBj is the association strength between two association sites belonging to two different molecules, and εAiBj and βAiBj are the association energy and association volume of interaction between site Ai of molecule i and site Bj of molecule j, respectively. For simplification, the association sites of asphaltene and resin molecules are assumed to be identical to the number of association sites, Nasp and Nresin, respectively. This leads to four possible association parameters accounting for the self-association between asphaltene molecules and cross-association between resin−asphaltene molecules, given in Table 1. The total number of association sites considered for asphaltenes is 4 and 2 sites for resin molecules in our approach.
Table 2. Physical Properties of the Pure Components and Pseudo-components of Oil 2 for CPA
Table 1. Summary of the CPA Model Parameters asphaltenes−asphaltenes asphaltenes−resins
association energy
association volume
ε εasp−resin
βasp−asp βasp−resin
asp−asp
The CPA asphaltene model was validated with a large set of experimental asphaltene onset data of live oils ranging from heavy oils to light condensates. Extensive comparisons on the experimental measurements of asphaltene precipitation, including both proprietary and public domain data, have demonstrated that it is possible to use the same form of asphaltene−asphaltene association energy, εasp−asp/R = 3000 K, and the association volume, βasp−asp = 0.05, for all cases with good results.1 Using the universal asphaltene−asphaltene association parameters εasp−asp and βasp−asp, the model parameters are reduced to two accounting for the 2613
components
Mw (g/mol)
specific gravity
critical T (K)
critical P (bar)
acentric factor
nitrogen CO2 H2S methane ethane propane isobutane n-butane isopentane n-pentane C6−17 C17−27 C27−38 C38−48 C48−52 R52−80 R80+ asphaltenes
28.01 44.01 34.08 16.04 30.07 44.10 58.12 58.12 72.15 72.15 139 296 438 586 695 865 1173 1245
0.281 0.837 0.799 0.146 0.366 0.516 0.562 0.584 0.624 0.630 0.799 0.890 0.927 0.951 0.963 0.978 0.997 1.035
126.19 304.13 373.10 190.56 305.33 369.85 407.85 425.16 460.45 469.70 631.17 805.65 890.99 950.29 982.94 1020.5 1038.8 1040.1
33.96 73.77 90.00 45.99 48.72 42.48 36.40 37.96 33.77 33.67 25.12 14.38 10.46 8.25 7.21 6.14 5.02 15.44
0.037 0.223 0.101 0.010 0.099 0.152 0.184 0.199 0.227 0.251 0.559 0.873 1.100 1.263 1.349 1.463 1.529 1.535
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referred as to “lights”. The relative amounts of the gas components are found by flashing the original oil to stock tank conditions and performing a compositional analysis of the released gas. The liquid fraction is characterized in terms of saturates, aromatics + resins (A + R), and asphaltenes and is based on the stock tank oil liquid composition analysis and the SARA analysis. The saturates represent the normal alkanes, branched alkanes, and cycloalkanes in oil. The aromatics and resins are lumped into a single component defined by the degree of aromaticity, γ, which defines the ratio of resins and aromatics. It varies between γ = 0, implying that the pseudo-component behaves as a derivative of benzene, and γ = 1, which means that it behaves more like a polynuclear aromatic (PNA). In the fluid characterization, the aromaticity is adjusted, so that the saturation point and liquid density predicted by PC-SAFT matches the experimental ones. For asphaltenes, the molecular weight (MW) used in this work is the same as that used in previous works.12−18 The detailed description of the characterization procedure for PC-SAFT can be found elsewhere.16 The PC-SAFT parameters for the gas components, methane, CO2, N2, ethane, and propane, are directly taken from the work by Gross and Sadowski,31 which are summarized in Table 3. In
The experimental data required to parametrize the model are gas chromatography (GC) compositional analysis for live or stabilized oil and the amount of asphaltenes and resins in stock tank oil. The measured bubblepoints of live oils are optional. However, if bubble point data are available, the physical properties of pseudocomponents, such as acentric factors or the Mathias−Copeman parameters, are tuned to reproduce the experimental bubblepoints. For the association model parameters of resin−asphaltene, three types of data can be applied: (1) measured asphaltene precipitation upper onset points, (2) titration onset data of n-heptane (amount of n-heptane for initializing the onset of asphaltene precipitation), and (3) reservoir conditions (only valid for live oils). Using reservoir conditions, on the basis of the de Boer et al.29 screening technique, it is assumed that the reservoir fluid is nearly saturated with asphaltenes at reservoir conditions.
3. PC-SAFT MODEL The statistical association fluid theory (SAFT) has been increasing in popularity since its original development by Chapman et al.30 Since then, several versions have been developed, such as PC-SAFT,31 SAFT-VR,32 and soft-SAFT.33 The PC-SAFT version has been demonstrated to be particularly good in predicting the phase behavior of various polymers.34 Because of the similarity of asphaltenes to large-size, heavy components, the PC-SAFT has been explored to predict the complex phase behavior of asphaltenic oils.12−18 The SAFT model is usually defined as a sum of contributions to the residual Helmholtz free energy.
Ares = Ahs + Achain + Adisp + Aassoc
Table 3. SAFT Parameters for Discrete Components31
(9)
In the case of PC-SAFT, the expressions used in each of the terms are published in the original development work.31 To model a non-associating component using PC-SAFT, three parameters are needed: m, representing the number of segments per molecule, σ, representing the segment diameter, and ε/k, representing the segment dispersion energy. Contrary to other equations of state used in the oil and gas industry, the characterization of oils with SAFT is not wellestablished. In the works by Ting et al.12,13 and Gonzalez et al.,14−17 while modeling the phase behavior of asphaltenic oils, a procedure to characterize the petroleum fluids was also developed. The same procedure is used in this work. 3.1. Fluid Characterization with SAFT. Similar to other equations of state, PC-SAFT equation requires the petroleum mixtures to be characterized, so that the physical properties of all of the components are defined before any thermodynamic phase equilibrium calculations. In this section, a brief description of the characterization procedure used for the model is given as follows. The characterization procedure used in this work follows the procedure proposed by Ting12 and later improved by Gonzalez.16 The characterization procedure makes extensive use of the values reported by the saturates, aromatics, resins, and asphaltenes (SARA) analysis and the compositional analysis of the flashed oil gas and liquid phases at standard conditions. The characterized system is composed of a gas and a liquid that are recombined in the appropriate gas/oil ratio (GOR) to simulate the original live oil. The components used to characterize the gas stream are usually methane, CO2, and N2. To improve the modeling of gas injection in some cases, ethane and propane are also included to add a more fine control of the model binary interaction parameters. The remaining gas components are then grouped into a pseudo-component,
component
Mw (g/mol)
m
σ (Å)
ε/k (K)
N2 CO2 methane ethane propane
28.0 44.0 16.0 30.1 44.1
1.205 2.073 1.000 1.607 2.002
3.313 2.785 3.704 3.521 3.618
90.96 169.21 150.03 191.42 208.11
the PC-SAFT approach, the molecular size difference and the van der Waals interaction are thought to be the dominant mechanism for asphaltene precipitation in crude oils, the same mechanism assumed by the published works.12−18 There are published works where the association between asphaltenes and resins is considered in the SAFT context by BuenrostroGonzalez et al.35 and Wu et al.,3,36 and the results obtained do not differ from the results obtained where association is not included. Therefore, the cross-association between the asphaltenes and resins is not considered, making the model simpler, and no extra parameters are required. This approach is quite different to the approach applied in CPA, where the selfassociation of asphaltene molecules and the cross-association of the asphaltenes and resins are the two competing mechanisms for asphaltene precipitation. The SAFT parameters for the light oil components (“lights”) follow the n-alkane correlation with MW. The MW of the light fractions is assumed to be the one of the corresponding alkanes for which parameters were originally developed by Gross and Sadwoski.31 The SAFT parameters for saturates and aromatics + resins also follow a correlation with MW, which was developed by Ting et al.13 and later improved by Gonzalez.16 The asphaltene parameters are more or less fixed because the MW is always taken to be 1700 g/mol, the value of pre-aggregate asphaltenes.13 For a complete reference, the improved correlations are shown in Table 4 and the range of the asphaltene model parameters is listed in Table 5. For a typical crude oil, the asphaltene SAFT parameters are initially set to m = 29.5, σ = 4.3 Å, and ε/k = 395 K, the values developed by Ting et al.13 The binary parameters, kij, are 2614
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pressure (AOP) and that predicted by SAFT. The AOP is the point where the oil starts to split into two liquid phases: a light hydrocarbon-rich liquid phase and asphaltene-rich liquid phase.
Table 4. SAFT Parameter Correlation for Saturates and Aromatics + Resinsa saturates
aromatics + resins
m = 0.0257Mw + 0.8444
m = (1 − γ)(0.0223Mw + 0.751) + γ(0.0101Mw + 1.7296)
σ = 4.047 − (4.8013 ln(Mw)/Mw)
σ = (1 − γ)(4.1377 − (38.1483/Mw)) + γ(4.6169 − (93.98/Mw))
ln(ε/k) = 5.57 − (9.523/Mw)
ε/k = (1 − γ)(0.00436Mw + 283.93) + γ(508 − (234100/Mw1.5))
a
4. RESULTS AND DISCUSSION In the current study, six live oils are considered. Table 7 provides the details of the properties and compositions for the crude oils, including the MW, specific gravity (SpG) of the C6+, and the amounts of asphaltenes and resins in stock tank oils. For the CPA model, the physical properties, such as the critical temperature, pressure, and acentric factor, of the pseudo-petroleum fractions are defined from the standard Lee−Kesler and Riazi correlations25−28 and the MW and SpG are defined from the extended Whitson table.28 Among those properties, the MW and SpG of the pseudo-components of individual oils may be adjusted to reproduce the measured MW and SpG of the stock tank oils in the characterization and the acentric factors or the equivalent temperature-dependent Mathias−Copeman parameters are adjusted to improve the predictions on the saturation line. For the asphaltenes, the critical properties are derived on the basis of the asphaltene solubility parameter ranging from 18.2 to 20.7 MPa1/2.37 For the six live oils, the cross-association CPA model parameters between asphaltenes and resins were optimized with the experimental asphaltene precipitation upper onset or the asphaltene titration onset data. The cross-association energy and volume parameters for all six oils are summarized in Table 8. To determine the SAFT parameters for each fluid, the procedure derived by Ting12 and Gonzalez16 was used. As described
γ is the aromacity factor. Equations are from the work by Gonzalez.16
Table 5. SAFT Parameter Range for Asphaltene Component16 Mw (g/mol)
m
σ (Å)
ε/k (K)
1700
19−39
4.1−4.5
296−504
asphaltene
initially set to the values obtained by Gonzalez,16 which are given in Table 6. In the case that ethane and propane are considered in the characterization, the binary interaction parameter used, as a first estimate, is the one for methane. Later, some of the binary interaction parameters, such as N2−asphaltene or methane−asphaltenes, are adjusted to improve the predictions on the effect of gas injection on asphaltene stability. For each fluid, the aromaticity parameter is adjusted to match the saturation pressure and liquid density experimental data after characterization. Then, the asphaltene parameters are tuned to minimize the error between the measured asphaltene onset Table 6. SAFT Binary Interaction Parameters16 component
N2
N2 CO2 methane lights saturates A+R asphaltene
CO2
methane
lights
saturates
A+R
asphaltene
0.0
0.03 0.05
0.06 0.1 0.00
0.12 0.13 0.03 0.01
0.11 0.09 0.029 0.01 0.007
0.11 0.1 0.029 0.010 0.007 0.00
oil 56 (mol %)
oil 62 (mol %)
Table 7. Properties of the Six Oils Used in This Study
a
components
oil 138 (mol %)
oil 239 (mol %)
oil 340 (mol %)
N2 H2S CO2 methane ethane propane isobutane n-butane isopentane n-pentane C6+ MW of C6+ SpG of C6+ saturates (wt %) aromatics (wt %) resins (wt %) asphaltenes (wt %)
0.088 0.048 1.022 42.42 10.8 6.918 0.957 3.518 1.213 2.086 30.93 204.43 0.840 63.3 24.9 11.3 0.5
0.490 3.220 11.369 27.357 9.409 6.699 0.810 3.170 1.220 1.980 34.277 236.34 0.873 57.4 30.8 10.4 1.4
0.17 2.04 1.75 16.47 8.66 8.21 1.35 4.84 1.88 3.15 51.48 205.22 0.848 47.98 44.42 6.29 1.32
oil 441 (mol %) 1.261 0.228 40.000 9.099 8.875 1.341 4.217 1.459 1.927 31.593 207.046
0.616 40.767 7.08 5.272 0 2.59 0 1.841 0.418 0.616 40.767 297.17
2.8 0.9
31.2a 3.6a
1.246 37.079 8.544 7.149 1.316 3.819 1.486 1.765 37.597 242.39 0.860
16.1 1.9
The amounts are estimated from the published compositions of the resins and asphaltenes. 2615
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Table 8. Cross-association Energy and Volume between Asphaltenes and Resins for the Six Oils with CPA ε /R (K) βasp−resin asp−resin
oil 138
oil 239
oil 340
oil 441
oil 56
oil 62
2124 0.16
2032 0.32
1959 0.62
1999 2.33
2523 0.02
2194 0.15
in section 3, the experimental data required are the GC analysis of the fluid when flashed at standard conditions (60 °F and 1 atm). 4.1. Oil 1: Live Oil from the Magwa Area in South Kuwait. Oil 1 in Table 7 is a live oil from the Magwa area of the Greater Burgan field in south Kuwait published by Kabir et al.38 This is a fairly paraffinic crude with little asphaltenes, 0.5 wt % in stock tank oil, but the field suffered severe asphaltene problems ranging from plugging of tubulars and flowlines to separators. To implement a suitable operating procedure for minimizing the asphaltene precipitation and deposition in the field, a comprehensive review using the gravimetric technique was carried out to establish the asphaltene precipitation onsets at various temperatures in terms of asphaltene contents in the oil solution as a function of the pressure. With the CPA model as mentioned in the previous section, the two model parameters accounting for the crossassociation between asphaltenes and resins are adjusted using the asphaltene upper onset data at two different temperatures. Then, the same model parameters are used to predict the entire asphaltene phase boundary and the amounts of asphaltene in solution as a function of the pressure at other temperatures. For the PC-SAFT model, the asphaltene model parameters are found according to the procedure described in section 3. The SAFT parameters are shown in Table 9. The SAFT binary
Figure 2. Asphaltene phase boundaries, for oil 1:38 solid line predicted by CPA, dashed line predicted by PC-SAFT, ■ for the asphaltene onset data, and ● for measured bubblepoints.
Figure 3. Asphaltene content in solution as a function of the pressure, for oil 1:38 solid line predicted by CPA, dashed line predicted by PCSAFT, and ◆ for the measured values.
Table 9. SAFT Parameters Used To Characterize Oil 1 N2 CO2 methane lights saturates A+R asphaltenes
m
σ (Å)
ε/k (K)
Mn
amount (mol)
1.205 2.073 1.000 1.955 4.949 4.512 29.00
3.313 2.785 3.704 3.973 3.894 4.123 4.230
90.96 169.21 150.03 211.97 248.96 390.10 373.0
28.01 44.01 16.04 43.20 159.73 222.28 1700
0.00094 0.01023 0.42567 0.23172 0.25175 0.07950 0.00019
but, when production occurs from the reservoir state to surface conditions, asphaltene precipitation and deposition become more probable. To avoid the asphaltene risk area, sufficient asphaltene inhibitors and dispersants were reported to be used in the field and the asphaltene precipitation upper onsets were successfully suppressed below the wellbore flowing temperature and pressure conditions. The predicted asphaltene phase envelopes by the two models are quite different; this is due to the fact that the mechanism responsible for the asphaltene precipitation is distinctively different between the two models. The predicted phase envelope by PC-SAFT tends to be open at the high-temperature side, whereas that by CPA is closed along the bubblepoint line. Figure 3 presents the predicted and measured asphaltene content in solution as a function of pressures at a given temperature. It is clearly shown that the prediction by both models on the maximum asphaltene precipitation occurring at the bubblepoint is consistent with the experimental observation but the CPA model gives better prediction on the absolute asphaltene content in solution. 4.2. Oil 2: Asphaltene Phase Boundary with Nitrogen Injection. Oil 239 also comes from a reservoir suffering operational problems because of asphaltene precipitation during the primary production. Before any planned enhanced oil recovery (EOR) with nitrogen to maintain the reservoir pressure, a comprehensive study was carried out to assess the possible mechanism and enhancement of asphaltene precipitation
interaction parameters used are the parameters reported in Table 6 without change. The predicted asphaltene phase envelopes by both CPA and PC-SAFT are summarized in Figure 2, together with the measured asphaltene onset data, the predicted and measured bubblepoints. The asphaltene upper and lower onset data in Figure 2 were established from the measured asphaltene content as a function of the pressure at various temperatures, one of which is presented in Figure 3. As shown in Figure 2, the predicted asphaltene phase boundary by CPA is in very good agreement with the asphaltene upper and lower onset data over the entire temperature range applied in the measurements. The PC-SAFT model gives reasonable prediction of the asphaltene lower boundary, but the asphaltene upper boundary is slightly off the trend. Knowing that the asphaltene precipitation boundary is critical for implementing appropriate strategies for preventing the asphaltene precipitation and deposition along the production line. As shown in Figure 2, the initial reservoir condition is just above the asphaltene upper boundary 2616
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characterization procedure generated values that were different from the values by Gonzalez et al.15 The SAFT parameters generated in this work are listed in Table 10 for reference. It was
arising from contacting nitrogen gas with the reservoir fluid. The laboratory experiments using the transmittance of an optimized laser light in the near-infrared (NIR) wavelength were used to investigate the asphaltene upper onset regions of the original reservoir fluid with and without nitrogen contact. Similar to oil 1, the asphaltene−resin association model parameters for the CPA model are optimized using two of the measured asphaltene upper onset data of the original reservoir fluid, and then the same model parameters are used to predict the asphaltene phase boundary for all of the cases, including the reservoir fluid with nitrogen injection. For the PC-SAFT model, the three asphaltene model parameters are adjusted to reproduce the asphaltene phase boundary for the original reservoir fluid. Then, the same parameters are applied to predict the N2 injection cases. In the SAFT case, a good prediction is achieved but is only possible when the binary interaction parameter between nitrogen and asphaltenes is changed from 0.11 to 0.2. The predicted asphaltene precipitation regions for the original reservoir fluid are presented in Figure 4, and those of the nitrogen
Table 10. SAFT Parameters Used To Characterize Oil 2 N2 CO2 methane lights saturates A+R asphaltenes
m
σ (Å)
ε/k (K)
Mn
amount (mol)
1.205 2.073 1.000 1.957 5.805 5.577 29.5
3.313 2.785 3.704 3.973 3.916 4.172 4.3
90.96 169.21 150.03 212.9 251.53 389.36 377
28.01 44.01 16.04 43.30 193.0 283.0 1700
0.0050 0.1137 0.2735 0.2516 0.2389 0.1165 0.000764
not possible to reproduce the results from the work by Gonzalez et al.15 with the SAFT parameters presented in their work. The results obtained with the parameters from this work are generally in good agreement with the results obtained by Gonzalez et al. The bubble points are slightly overpredicted in this work when injecting N2, but a better prediction on the asphaltene onset phase envelope is made. As shown in the graphs, both models give good predictions of not only the asphaltene phase boundary for the original reservoir fluid but also the effect of injected N2 on the asphaltene onset pressure. Between the models, the prediction on the asphaltene boundary by PC-SAFT is slightly better than that by CPA, whereas CPA gives better predictions on the bubblepoints. As demonstrated in Figure 5, both models are capable of predicting the enhancement of asphaltene precipitation in the reservoir because of the nitrogen injection. 4.3. Oil 3. This case is a reservoir fluid from an offshore carbonate oil field in the Arabian Gulf, recently published by Yonebayashi and co-workers.40 The field exhibits asphaltene precipitation and deposition problems inside tubing of some production wells. Before the future planned full-field EOR development, Yonebayashi et al. carried out a comprehensive study to assess the likely enhancement of the asphaltene problem because of gas injection and the oil blending from different wells in the area. The NIR light scattering technique was used to measure the asphaltene upper onsets for several fluids from different wells. The fluid presented here is well 3 from the upper reservoir. The detailed gas titration experiments (GTEs) with a gas mixture containing 40 mol % of methane at four different temperatures were carried out with the fluid from well 3. On the basis of the asphaltene onset pressures as a function of the molar amounts of injected gas at a given temperature by GTE, it is possible to estimate the asphaltene onsets for the original reservoir fluid, well 3, by extrapolating the onset pressure to the zero amount of gas at the given temperature. The estimated possible asphaltene onset data for well 3 are presented in Figure 6, together with two of the several measured asphaltene onsets for the cases with gas injection. Two CPA asphaltene model parameters for the original reservoir, well 3, are obtained using two of the asphaltene onsets derived from the GTE, and then the same model parameters are used to predict the asphaltene phase boundary for the cases with gas injection. The asphaltene model parameters for PC-SAFT were tuned to reproduce the same set of asphaltene onsets for the original fluid, well 3. However, we found that it was quite difficult to find a suitable set of asphaltene model parameters or binary interaction parameters to improve the prediction of the asphaltene phase boundary for
Figure 4. Asphaltene phase boundaries, for oil 2:39 solid line predicted by CPA, dashed line predicted by PC-SAFT, ■ for the asphaltene onset data, and ● for measured bubblepoints.
injection cases are presented in Figure 5. In Figure 5, 20% N2 injected means 0.2 mol of N2 added to 1 mol of original fluid. This
Figure 5. Asphaltene upper onset pressures and bubblepoints as a function of the nitrogen concentration (mol %), for oil 2.39
oil has been analyzed in a previous work with PC-SAFT;15 therefore, it was a good case to test whether the characterization procedure was being carried out correctly or not. In this work, the 2617
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Figure 6. Asphaltene phase boundaries of the reservoir fluid with and without gas injection, for oil 3:40 solid lines predicted by CPA, dashed lines predicted by PC-SAFT, dotted line for the predicted bubblepoint line by CPA, and ◇ for the experimental bubble point pressure.
Figure 8. Asphaltene onset pressures as a function of molar amounts of gas injected at 91.85 °C: solid line predicted by CPA and dashed line predicted by PC-SAFT, for oil 4.41
separated from the “lights” fraction, enabling the adjustment of their binary interaction parameters with the asphaltene component. 4.5. Oil 5: Asphaltene Precipitation. In comparison to the four oils presented above, this oil is fairly heavy with a MW of C6+ of 297 g/mol, which was published by Leontaritis at the American Institute of Chemical Engineers (AIChE) 1993 conference.6 The origin of the oil and the details of the experimental technique for measuring the bubblepoints and the asphaltene precipitation onsets were not reported in the paper, but it is one of several live oils that we have in our databank that demonstrates an asphaltene solubility decrease with an increasing temperature in the range of operational interest. The asphaltene stability in the oil was fully investigated experimentally with detailed measurements for the asphaltene precipitation upper and lower onsets and several bubblepoints, as shown in Figure 9. On the basis of the published oil
both the original fluid and the cases with gas injection, as shown in Figures 6 and 7. On the other hand, the CPA model
Figure 7. Asphaltene onset temperatures as a function of molar amounts of gas injected at a pressure of 278 bar, for oil 3.40
gives good predictions on the asphaltene phase boundaries for both the original reservoir fluid and the cases with gas injection. 4.4. Oil 4: North Sea Crude with Gas Injection. The three oils presented above are mainly from the Middle East area. In this section, the oil studied is from a North Sea reservoir, published by Fotland et al.41 For this crude oil, there was no reported asphaltene precipitation and deposition problems at reservoir conditions but the contact of gas with the reservoir fluid demonstrates the potential of asphaltene precipitation with 35 mol % or more of gas injection. Because there was no asphaltene problem with the original reservoir fluid, both the CPA and PC-SAFT model parameters were tuned to the measured asphaltene onset for the case of the 35 mol % gas injection. Then, the same model parameters are used to predict the asphaltene onset pressures for the other cases with much higher amounts of gas injected. As shown in Figure 8, both CPA and PC-SAFT give good prediction on the asphaltene onset pressures as well as the bubblepoints but with the prediction by CPA slightly better. In this case, the SAFT model was more fine-tuned in the sense that ethane and propane were
Figure 9. Asphaltene phase boundaries of the reservoir fluid oil 5:6 solid lines predicted by CPA, dashed lines predicted by PC-SAFT, and dotted line for the predicted bubblepoint line by CPA.
composition and the information on asphaltenes and resins, the fluid was characterized for both CPA and PC-SAFT models. With the CPA model, the two asphaltene−resin association parameters were easily adjusted using two of the asphaltene upper onset data to reproduce both the asphaltene upper and lower onsets very well. Then, the same model parameters were used to predict the entire asphaltene phase envelope, including the asphaltene lower boundary. For the PC-SAFT model, the three asphaltene model 2618
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including the asphaltene onset point. For the asphaltene onset, it was not possible to improve the SAFT prediction any further without decreasing the quality of the predictions on the rest of the precipitation curve.
parameters were tuned to the asphaltene upper onset data. The binary interaction parameters were also included in the fitting, but the results were not improved. However, it seems that, regardless of how the asphaltene model parameters change, it is not possible to change the trend of predicted asphaltene envelope by PC-SAFT to follow the shape of measured asphaltene precipitation onset, as shown in Figure 9. The measured asphaltene precipitation onset data show that the asphaltene solubility decreases with an increase of the temperature in the temperature range considered. Oils 3 and 5 are the fluids analyzed in this work that show the distinctive difference between both models. In oil 3, a suitable set of parameters was not found that made the SAFT-predicted asphaltene onset points describe the observed experimental data. For oil 5, the SAFT model is not able to describe the reverse tendency observed in this oil. It seems that PC-SAFT tends to predict asphaltene solubility increases with an increasing temperature at lower temperatures, indicating that the mechanism of asphaltene precipitation, including a large molecular size and van der Waals interaction, may be not enough to represent cases such as this. Following the work by Buenrostro-Gonzalez et al.,35 it would be of value to check what would be the predictions of the SAFT model when association is considered between asphaltenes and resins for the Leontaritis and Mansoori6 and Yonebayashi et al.40 cases. 4.6. Oil 6: n-Heptane Titration. The work presented in this section is to demonstrate the capability of the two models on modeling the asphaltene precipitation by n-heptane in stock tank oil. The oil considered is an Iranian crude with a n-heptane asphaltene content of 1.9 wt %, published in the work by Hirschberg et al.2 For this oil, a series of titration experiments on the stock tank oil were reported. The onset of asphaltene precipitation upon dilution of the crude with various liquid alkanes was measured together with the amount of asphaltene formed upon mixing stock tank oil with various amounts of liquid alkanes, as shown in Figure 10. The measured data in
5. CONCLUSION A comprehensive study of two compositional equations of state models, CPA and PC-SAFT, for modeling complex asphaltene phase behavior is presented in this work. The detailed comparison to six live oils demonstrates the capability and potential of the CPA approach as a practical engineering tool for modeling the asphaltene phase and the effect of gas injection on asphaltene stability in reservoirs and pipelines because of its simplicity, robustness, and reliability. Because it is based on the SRK equation, oils can be characterized using the standard oil industry techniques with straightforward extensions to pick out the resins and asphaltenes. With the universal asphaltene− asphaltene association parameters, the four model parameters are reduced to two accounting for the cross-association of asphaltenes−resins. As demonstrated in the six cases, the CPA model is able to give good predictions of the asphaltene phase boundary over an entire temperature and pressure range, the amount of asphaltene in solution, and the effect of the gas injection on the asphaltene stability in crude oils when the two cross-association model parameters of the original reservoir crude oils were obtained from the experimental asphaltene data. The PC-SAFT model gives good prediction of the asphaltene phase boundary for the type of oils as oil 2 and generally performs well when predicting the asphaltene onset phase boundary and how it changes with gas injection. However, the model shows that further work is still needed to make it applicable to more types of crude oils. The oils published by Leontaritis and Hideharu are good examples of systems where PC-SAFT needs further improvement.
■ ■
AUTHOR INFORMATION
Corresponding Author
*Telephone: +44-207-357-0800. E-mail:
[email protected].
ACKNOWLEDGMENTS The authors thank Dr. Francisco M. Vargas, Dr. Anjushri S. Kurup, and Prof. Walter G. Chapman for their valuable help and suggestion with the PC-SAFT model. All of the calculations were performed with the Infochem Multiflash program.
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REFERENCES
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