Prediction of Asphaltene Precipitation for Kuwaiti Crude Using

2748

Ind. Eng. Chem. Res. 2001, 40, 2748-2756

Prediction of Asphaltene Precipitation for Kuwaiti Crude Using Thermodynamic Micellization Model M. A. Fahim,* T. A. Al-Sahhaf, and A. S. Elkilani Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

A thermodynamic micellization model is used in this work to describe asphaltene precipitation from Kuwaiti crude oil. The model is based on asphaltene and resin micelle formation and then destruction by addition of an alkane. A coin-like aggregate of asphaltene surrounded by resin molecules constitutes the micellar phase. The rest of the asphaltene and resin are dissolved in the bulk phase. A group contribution method was used to predict the critical properties for the asphaltenes, resin, and oil. The Peng-Robinson EOS was used to predict the onset point and to perform flash calculations. The onset point and the amount of asphaltene precipitated were measured. Hexane, heptane, octane, and decane with varying volumes and temperatures were used. The model also was tested using high-pressure data. In both cases, the model could describe the experimental data reasonably well with a mean square error of 0.57%. Introduction

Modeling Approaches

A variety of substances of diverse chemical natures constitute petroleum fluids. These include paraffinic, naphthenic, and aromatic hydrocarbons and polar polyaromatic materials that contain nitrogen, oxygen, and sulfur. Crude oil is a mixture of these compounds, and its concentration varies with the source. Thus, some crude oils have higher proportions of the lower-boiling constituents, whereas others have higher proportions of the heavy, polar, nonvolatile end of the crude, referred to asphaltene and resin. Under certain conditions, asphaltene and resin precipitate from a petroleum fluid. The asphaltene precipitation phenomenon is wrapped in great mystery because of the lack of asphaltene precipitation data available in the literature. The occurrence of precipitation in both underground petroleum reservoirs and production facilities is undesirable. Therefore, information regarding the optimum conditions for asphaltene precipitation is needed to deal with this phenomenon and avoid problems of plugging in processing facilities. Because the problem of asphaltene deposition can start at any point along the crude production process where the equilibrium of the stabilizing asphaltenes has been upset, modeling can estimate the destabilizing forces that most often cause the deposition problem. The asphaltene precipitation data that have been published so far provide little information about the effect of temperature and pressure on asphaltene precipitation conditions. The experiments of the present study were undertaken at three temperatures to gain information about the influence of the temperature at which asphaltene precipitation is first seen when a paraffin is added to an oil sample. The work also focuses on the effects of temperature, pressure, and solvent ratio on asphaltene precipitation. In this paper, we apply the model of Victorov and Firrozabadi1 to predict asphaltene precipitation upon addition of a light alkane. The effects of the model parameters on the amount of asphaltene precipitation are investigated.

A literature survey indicates that previous models of asphaltene precipitation can be classified into solubility, solid, colloidal, and micellization models.2 The first important approach in modeling asphaltene precipitation is the solubility model due to Hirschberg et al.3 Vapor-liquid equilibrium (VLE) calculations were first applied. The liquid was then divided into four components: asphaltene, resin, deasphalted oil, and solvent. The fugacities, molar volumes, and solubility parameters of oil, resin, and asphaltene were included in the model to estimate asphaltene precipitation. This approach matched experimental data with a limited degree of success. The simplest model for the precipitated asphaltene is the single-component solid model. The precipitated asphaltene is treated as a single component modeled as a solid phase, while oil and gas phases are modeled with cubic equations of state (EOSs). The solid model can require many empirical parameters and excessive tuning to match experimental data.4 The first colloidal model used to describe asphaltene precipitation was developed by Leontaritis and Mansoori.5 In this model, a VLE calculation is first performed using an EOS to estimate the liquid composition in which asphaltene can flocculate. Then, the critical chemical potential, which is calculated using FloryHuggins theory,6,7 is used to predict the onset of precipitation. The colloidal model is more applicable to situations in which dissociation of the asphaltene occurs.8 In the micellization models, the asphaltenes are assumed to aggregate, forming a micelle core, with resin molecules adsorbed on the surface of the core to stabilize the micelle. Victorov and Firrozabadi1 formulated this model through aggregation equilibrium and the standard free energy of micellization. The polydispersity of asphaltene aggregates was taken into account by Victorov and Smirnova.9 Their approach was then revised and combined with a more detailed description of the precipitated phase.10 Concentration is determined in this approach by the minimization of the Gibbs free

* Corresponding author. E-mail: [email protected].

10.1021/ie000405s CCC: $20.00 © 2001 American Chemical Society Published on Web 05/17/2001

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2749

on the solid asphaltene precipitated from hexanetoluene solutions. At low concentration, regular solution behavior can be assumed. Consequently, the asphaltene density can be determined indirectly from a plot of the inverse mixture density versus the asphaltene mass fraction. The details of this procedure are given by Yarranton and Masliyah.13 Measurement of the molecular weight of asphaltene is problematic because, at higher concentrations, asphaltene molecules tend to aggregate. Also, adsorbed resin material leads to discrepancies in molecular weight determinations. Therefore, precipitated asphaltenes should be reprecipitated under reflux prior to the determination. Dilute solutions were also used to avoid aggregation. Thus, careful precipitation and careful choice of the determination method are both very important in obtaining meaningful results. The molar masses were determined with a vapor pressure osmometer (VPO) manufactured by Knauer and calibrated with chloroform. Measurements in chloroform were made at 50 °C. Molar masses of asphaltene in chloroform were determined over a range of 1.5-4.5 g of asphaltene per liter of solvent. Elemental Analysis. The compositions of STO, deasphalted oil, resins, and asphaltene were determined using an elemental analyzer. For this purpose, the precipitated asphaltenes in different solvents were analyzed using a Perkin-Elmer elemental analyzer (LECO CHNS-932) using method ASTM D5291. The analysis of asphaltene indicates the presence of sulfur, oxygen, nitrogen, carbon, and hydrogen. The elemental analyses with this instrument are accurate to (2%.

Table 1. Crude Oil Molar Composition of Reservoir Oil component

crude mol %

N2 CO2 H2S C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7+

0.69 2.00 1.51 29.77 14.40 9.46 0.93 4.37 1.32 2.63 3.38 29.54

energy of the crude oil bulk phase and the precipitated phase. The results of the micellization model agree well with experimental data. Experimental Methodology One Kuwaiti crude sample was used in this study. The reservoir crude oil molar compositions are given in Table 1. The stock tank oil (STO) composition and properties of the same crude are given in Table 2. The experimental program consisted of using STO for all precipitation experiments, in which several alkanes were added gradually to the oil to determine the onset point of asphaltene precipitation and the amount of asphaltene precipitated at different solvent/oil ratios. Precipitation Experiments. The solvents used for the purpose of precipitation were n-hexane, n-heptane, n-octane, and n-decane. Asphaltene is insoluble in these solvents to varying levels. The parametric study of precipitation includes analyses of the type of solvent, the solvent-to-crude ratio, the contact time of agitation of the mixture required to precipitate out the asphaltene, and the temperature of the precipitating medium. The amount of asphaltene present in the crude residue was determined by the standard IP 143 procedure. The onset point was determined by the spot test,11,12 which allowed for an accurate and rapid determination in terms of the amount of n-alkane added to the crude oil. The amount of asphaltene precipitated was determined gravimetrically. The precipitated asphaltenes were refluxed in heptane to ensure removal of all resins. The asphaltene was then dissolved in toluene, which was then evaporated in an oven at a temperature of 100-110 °C. The remaining solid (asphaltene) was accurately weighed, and the results were recorded on the basis of weight percent of the tank oil. Physical Properties of Asphaltene. The densities of the liquids were measured with a digital densiometer (PAAR DMA48 density meter) calibrated with demineralized water and toluene. Density measurements with this instrument are accurate to (0.003 kg/m3. All measurements were carried out at 25 ( 0.5 °C. The asphaltene densities were calculated indirectly from the densities of mixtures of different known concentrations of asphaltene in toluene. Experiments were carried out

Model Equations Mechanism of Micellar Formation. Asphaltenes are a complex organic material that are thought to be arranged in stacked, multi-ring structures. They contain nitrogen, oxygen, and sulfur atoms in addition to carbon and hydrogen atoms within the repeating unit.14 Asphaltenes are not truly soluble in most crude oils. They exist as 35-40-µm platelets and are maintained in suspension by materials called maltenes and resins.15-17 The chemical structure of asphaltene is not well understood. Asphaltenes are defined as the fraction of crude oil that is insoluble in excess normal alkanes but soluble in excess aromatics such as benzene and toluene at room temperature. Because asphaltene and resin are polar species, they can associate. Association between asphaltene molecules in different diluents results in aggregations of different molecular weights ranging from 800 to 50 000 or even higher. Storm et al.18 suggested that the asphaltene micelles have a spherical shape. Other shapes have also been assumed. The asphaltene molecules can be found as monomers (that is, single molecules) in the bulk phase and in the micellar core. The resins are also found in the monomeric state both in the bulk phase and in

Table 2. Measured and Estimated Properties for Asphaltene and Resin Obtained from Kuwaiti STO

C%

H%

N%

O%

S%

measured molar mass MW

81.17 83.72 79.65

11.69 11.44 8.31

0.61 0.141 0.768

1.31 2.59 3.79

4.5 2.11 7.48

384 480 1520

measured elemental analysis aromatics + saturates resin asphaltene

estimated critical properties

measured molar composition (mol %)

measured molar volume va (m3/kmol)

estimated molar volume va (m3/kmol)

Tc (K)

Pc (atm)

Vc (cm3/g)

90.816 6.372 2.812

0.417 0.506 1.265

0.396 0.502 1.235

757 903 997

15.7 8.6 8.9

2.3 2.9 2.7

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Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001

the micellar shell. The nonpolar asphalt-free species are also found in the bulk phase and in the micellar shell. Equilibrium thermodynamics requires that, in a system of molecules that form aggregated structures in solution, the chemical potentials of all identical molecules in different aggregates must be the same. This condition can be expressed by19

µ ) µ°1 + kT ln c1 ) µN ) µ°N +

kT cN ln ) constant N N (1)

where µ1 is the mean chemical potential of a monomer; µN is the mean chemical potential of an aggregate of aggregation number N; µ°N is the standard part of the chemical potential µN; and cN is the concentration (or activity) of molecules in aggregates of number N, with c1 corresponding to isolated molecules (monomers) in solution. The aggregation of asphaltene monomers from the bulk phase of crude oil begins with the formation of a core that is called a micelle. Resin molecules are then adsorbed on the micelle core because of their polarity. As a result of changes in composition, pressure, and temperature to a lesser degree, the micellar size might change.20 The equilibrium between the precipitated phase and the bulk-liquid phase will be affected by the micellar size. The balance between the amount of asphaltene solubilized within the micelles and the amount remaining in the form of monomers is governed by the aggregation equilibrium, which can be written as21,22

µm ) naµa + nrµr

(2)

where µm is the chemical potential of a micelle consisting of na asphaltene molecules and nr resin molecules and µa and µr are the chemical potentials of monomeric asphaltene and resin molecules, respectively. The chemical potentials of asphaltene (µa) and resin (µr) can be expressed using eq 1. Assuming a dilute solution

µm ) G°m + kT ln xm

∞ ∆Gbending ) 4πσo(1 - θ)l2[1 - (r + l)/(ro + l)]2 (5)

where r is the aggregate core radius, ro is the core radius related to the resin molecule shape by the packing constraint, l is the resin shell thickness, σo is the asphaltene core/crude interface tension, and θ is the surface coverage fraction. Assuming rod-shaped micelles (cylindrical cores), resin molecules are bonded next to each other, forming a rod of length l, which is equal to the resin molecule diameter multiplied by the number of resin molecules. In this case, the fractional coverage θ of the asphaltene molecule with resins must be equal to 1.0; otherwise, the rod will be disassembled. Therefore, eq I.8 in Appendix I, ignoring the effects of coverage, will be

f(θ) )

∆Ur RT

(6)

where ∆Ur is the resin desorption energy. Upon solvent addition to crude oil at constant temperature and pressure, the process can be described by os (xos a φa )solvent ) (xaφa)initial

(7)

where xos a is the mole fraction of asphaltene monomers in the crude in equilibrium with the asphaltene precipitated phase. It is the maximum concentration of monomeric asphaltene in a crude at given temperature and pressure. Initially, xa, which is the asphaltene monomer mole fraction, can be assumed to be the amount of asphaltene initially present in the crude, which is determined experimentally. The fugacity coefficient φa for asphaltene monomers, initially, is calculated based on xa. Then, the solvent will affect xos a , as the fugacity coefficient φos a , calculated from the EOS, will vary depending on the solvent amount and type. Asphaltene Precipitation. With the precipitation of the asphaltene phase, the material balance equations should include the amount of the precipitate (phase s)

(3)

Noa ) Nsa + Na + naNm(na,nr)

(8)

where xm is the mole fraction of micelles and G°m is the Gibbs free energy of formation of a micelle, which is the sum of standard chemical potentials of asphaltene and resin. In a dilute solution, the difference between the standard free energies determines the distribution of micelles in terms of size and composition. Substituting eq 2 into eq 3 and using the definition for chemical potential in eq 1 to solve for the mole fraction of the micelles in crude, one obtains

Nor ) Nsr + Nr + nrNm(na,nr)

(9)

xm ) xna axnr r exp(∆G∞m /kT)

(4)

where xa and xr are the monomeric mole fractions of asphaltene and resin, respectively, in the bulk phase and ∆G∞m is the free energy of micellization. Thus, contributions to ∆G∞m include resin head adsorption, surface tension, and surface repulsion terms. Victorov and Firrozabadi’s1 equation for ∆G∞m, assuming a coin-like micellar shape, is detailed in Appendix I. For a spherical micellar core, Victorov and Smirnova9 suggested an additional term for ∆G∞m to account for the bending or curvature correction term for spherical types of micelles

in which Noa is the initial number of molecules of asphaltene in the crude, Nsa is number of molecules of asphaltene precipitated with resin molecules that were in the micelle when precipitation occurred, Na is the number of molecules of monomer species in the bulk phase, Nm is the number of micelles that contain asphaltene covered with resin, Nsr is the number of molecules of resin precipitated with asphaltene, and Nr is the number of molecules of resin still dissolved in the bulk phase. The above equations assume that all of the micelles are of the same size. This assumption can be justified in the case of small colloid particles. Results and Discussion Model Implementation. The calculation procedure for estimating the asphaltene onset point is described in Figure 1, in which all input parameters for the PR EOS calculations are listed for the crude, asphaltene, resin, and added solvent. The asphaltene and resin critical properties calculations are based on the Joback group contribution method and are discussed in the next


(NMSE) is minimized. Finally, the material balance equations are used to calculate the mole fraction of asphaltene precipitated. Parameters of PR EOS. Although the asphaltene and resin chemical structures remain unclear, some researchers tried to elucidate the issue using either elemental analysis or nuclear magnetic resonance (NMR) spectra. Ali et al.23 suggested three chemical structures for asphaltene based on NMR spectral analysis. The relatively high percentage of sulfur (characteristic of asphaltenes in heavy crude oils) might be distributed among aliphatic and thiophenic moieties and might be in forms such as sulfides, disulfides, polysulfides, and mixed aliphatic-aromatic compounds. Nitrogen is most likely to be incorporated in condensed aromatic and porphyrinic structures, whereas oxygen, because of its low percentage, might be fractionated between more than one unit sheet. In other words, oxygen might play a major role in binding unit sheets.24 Although the exact structure of the asphaltenes and resin is the scope of active research, there is enough information in the literature to identify the functional groups that might constitute them. Therefore, we use a group contribution method to calculate the critical constants, which, in turn, are used in the EOS calculations. In the present work, the Joback group contribution method25 is used to find the group frequencies constituting the resin or asphaltene molecules using elemental analysis along with the measured molecular weights of aspaltene and resin. Five groups from the Joback group contribution method, shown in Table 3, are assumed to exist in the asphaltene23 and resin26 monomers, each with a frequency number from a1 to a5 and r1 to r5, respectively, representing the number of times that each group is repeated in the molecule. The selection of five groups from the Joback group contribution method was restricted by the number of equations obtained from the measured data. The five equations are solved simultaneously for the five unknowns. The critical properties, listed in Table 2, are estimated by the Joback group contributions. Details for estimating the frequency numbers in Table 3 and the Joback group contribution equations used to calculate criticals (Table 2) are described in Appendix II. The calculation of the critical properties was tested by estimating the molar volumes of asphaltene, resin, and the deasphalted crude oil using the PR EOS and comparing these values with the experimental results. The comparison was quite favorable, as shown in Table 2. Solvent Type and Solvent Ratio. In our calculations, we assumed that the asphaltene micelles could be either coinlike (plate), spherical, or rodlike in shape. For the coinlike shape, eqs I.7 and I.8, with σo ) 0.037 N/m and a ) 45 A2 (close to the values reported by Victorov and Firrozabadi1) were used to calculate ∆G∞m.

Figure 1. Flow chart for calculation procedure. NMSE ) [(xa - xanew) + (xr - xrnew)]2/[(xa + xr)(xanew + xrnew)]

section. The fugacity coefficient φa of the asphaltene monomers in the crude is calculated on the basis of an initial guess for asphaltene monomer mole fraction xa. Then, upon addition of a certain amount of solvent, the fugacity coefficient of the asphaltene monomers was calculated using the critical properties of the added solvent. Then, eq 7 was applied to calculate the mole fraction of asphaltene at onset point in equilibrium with asphaltene monomers. Consequently, the fractional coverage θ of an asphaltene core covered by resin is calculated by finding a root for eq I.10 using the Newton-Raphson technique. The numbers of molecules of asphaltene (na) and resin (nr) are estimated on the basis of the fractional coverage θ, as shown in the flowchart (Figure 1). Then, the standard Gibbs free energy change and the mole fraction of micelles are estimated. The numbers of moles of asphaltene monomers and resin monomers were recalculated using the material balances eqs 8 and 9. A comparison between the initial guess and the estimated mole fractions is made using the technique of error minimization. The actual values for xa and xr are obtained when the normalized mean square error Table 3. Joback Group Contribution for Critical Properties properties

no. of repetitions of groups

group

Tb

Tc

Pc

Vc

MW

asphaltene

resin

crude

dC-H ring dC< ring -SdN-OH >CH2 -CH2 ring

26.73 31.01 52.10 57.55 31.22 22.88 27.15

0.0082 0.0143 0.0019 0.0085 0.0098 0.0189 0.0100

0.0011 0.0008 0.0051 0.0076 0.0048 0 0.0025

41 32 38 34 13 56 48

13 12 32 14 17 14 14

a1 ) 32 a2 ) 75 a3 ) 4 a4 ) 2 a5 ) 3 -

r1 ) 0.31 r2 ) 0.05 r3 ) 0.76 r4 ) 20.5 r5 ) 12.0

c1 ) 7.8 c2 ) 0.54 c3 ) 0.17 c4 ) 0.31 c5 ) 18.4 -

2752


Figure 2. Effect of micelle shape on model estimation using heptane C7 solvent at 298 °C. (Symbols are experimental data; lines are predicted results.)

Figure 3. Asphaltene concentration as a function of dilution ratio indicating onset points for various solvents at 298 °C.

For the spherical shape, the bending contribution, eq 5, was added to calculate ∆G∞m. Simultaneously, for the rod-shaped micelles, eq 6 was used. The same calculation procedure, shown in Figure 1, was applied for the three shapes to calculate the weight of asphaltene precipitated. Figure 2 shows the effect of the assumed micelle shapes on the weight percentage of asphaltene precipitated by heptane at different dilution ratios. Comparison with experimental results shows that the coin-shaped micelles give the best results. Therefore, we adopt this shape for all subsequent calculations. The mole fractions of asphaltene at the onset, xos a , and the corresponding monomeric asphaltene mole fractions in the bulk, xa, are predicted upon addition of different solvents, at different solvent-to-crude ratios, and the results are shown in Figure 3. Before precipitation (i.e., before the onset point), as the solvent-to-crude ratio increases, resins in the micelle shell dissolve in the solvent, resulting in the destruction of some micelles. Hence, asphaltene and resin molecules are transported to the bulk. As a result, the mole fraction of asphaltene in the micelles decreases, whereas the mole fraction of asphaltene in the bulk phase increases. When the onset point is reached and precipitation starts, any addition of solvent leads to larger micelles and lower bulk asphaltene concentrations. Hence, the mole fraction of asphaltene monomer becomes very small. Therefore, the ratio between the fugacity coefficient of initial monomer and the fugacity coefficient of monomers at higher dilution ratios becomes constant. This clarifies the flat pattern in Figure 3 upon solvent addition after the onset point was reached. From model

Figure 4. Aggregation number as a function of dilution ratio of heptane at 298 °C.

parameter estimation, the micelles become bigger upon solvent addition. The material balance calculations show that, as the solvent-to-crude ratio increases, the bulk concentration of asphaltene decreases and the asphaltene concentration in the micelles increases, so precipitation increases. For example, the number of asphaltene molecules in the micelle core is na ) 40, and the number of resin molecules in the shell is nr ) 200 at a heptaneto-crude ratio of 4.0 cm3/g. Increasing this ratio to 5.0 cm3/g, na becomes 50, and nr becomes 238. Figure 4 shows the relation between the number of molecules in the micelle as the solvent-to-crude ratio increases. This figure shows that the critical micelle concentration is reached at the solubilization ratio na/nr ) 0.2, which agrees with the value reported by Victorov and Firrozabadi.1 The intersection of each corresponding pair of lines in Figure 3 is the onset point of the oil when a certain solvent is used. The dotted lines show the mole fraction of asphaltene monomer xa in the bulk solution before precipitation. Once xa reaches xos a , precipitation starts. The onset point (volume of solvent) increases as the number of carbon atoms in the corresponding solvent increases. Four solvents, hexane (C6), heptane (C7), octane (C8), and decane (C10), were tested. For the highest solvent carbon number (C10), we needed a greater amount of solvent (around 7 cm3/g) to start precipitation, whereas for C6, we needed only 4 cm3/g of crude. Earlier, we explained that the onset point depends on the type of solvent, because the fugacity coefficient depends on the solvent type and dilution ratio. Figure 5 shows the weight percentage of asphaltene precipitated using different solvents. Measurements were conducted at different solvent-to-crude ratios in the range from 10 to 50 cm3/g solvent. The comparison between the measured and estimated weight percentages was based on calculations of the normalized mean square error (NMSE). The average NMSE is 0.0033, which indicates that the estimated points are in good agreement with the experimental values. Figure 6 shows a linear correlation between the amount of asphaltene precipitated and the solvent density. Note that, at constant dilution ratio, as the solvent density increases, precipitation decreases. This figure shows that benzene and toluene do not cause precipitation, as their densities at 25 °C are about 0.88 g/cm3. This figure also implies that C2-C5 should result


Figure 5. Effect of solvent type on asphaltene precipitation with the assumption of coin-shaped micelles at 298 °C. (Symbols are experimental data; lines are predicted results.)

Figure 6. Effect of solvent density on the amount of asphaltene precipitated at a solvent/oil dilution ratio of 40 cm3/g of oil using atmospheric crude oil and atmospheric residue at 298 °C. (- - - -, extrapolated; (, experimental).

in greater precipitation. One reason for the greater precipitation is that C2-C5 might cause precipitation of resins in addition to asphaltenes.24 Effect of Temperature. For normal alkane solvents with carbon numbers above 5, the precipitated amount of asphaltene falls with increasing temperature.27,28 This agrees well with the model, as the micellar size decreases when the temperature of the crude or the crude/ solvent mixture increases. This trend is shown in Figure 7 for n-heptane. The predicted results are in good agreement with measurements, with NMSEs ranging from 0.0005 to 0.0132. Effect of Pressure. The effect of pressure on the fugacity of asphaltene in the asphalt solid phase (s) is expressed by8

(

ln f sa ) ln f os a + va

)

P - Pos RT

(10)

where f sa and f os a are the fugacities of pure asphaltene in the solid phase at pressures P and Pos, respectively, where Pos is the onset pressure, and va is the molar volume of pure asphaltene. Equation 10 is rearranged to allow for calculation of the onset concentration

Figure 7. Effect of temperature on asphaltene precipitation at atmospheric pressure as a function of heptane dilution ratio. (Symbols are experimental data; lines are predicted results.)

[(

os os xos a φa P ) vaφaP exp va

)]

Pos - P RT

(11)

At high pressures P . Pos, the exponential part is highly negative, and eq 11 does not predict any change in fugacity coefficients. The high pressure keeps the resin associated with the asphaltene aggregates, thus, keeping the micelles suspended. At the saturation pressure, light gases are evolved from the oil, changing its composition, which can be calculated by flash calculation. Asphaltene precipitation between the onset point and the bubble point occurs because of transfer of some resin molecules from the micelle phase to the oil phase. Accordingly, more asphaltene surface sites become bare, and more precipitation occurs, as described by the model. When the mole fraction of asphaltene in the bulk phase becomes greater than the onset mole fraction, precipitation occurs. A material balance is performed to subtract the amount of precipitation and restore the equilibrium between the micelles and the bulk asphaltene concentration. Reducing the pressure to a value less than the onset pressure lowers the onset mole fraction, which means that precipitation can occur at lower values as soon as the mole fraction of the asphaltene micelles passes the onset point. The same calculation procedure as in Figure 1 is followed, with the exception that eq 11 is used instead of eq 7. The same phenomenon occurs until the saturation pressure is reached. At that point, light paraffinic gases are evolved, thereby upsetting the equilibrium. Flash calculations are carried out using the PR EOS to calculate the new liquid composition that will equilibrate the micelles and the bulk. The same procedure is then used to calculate the onset point and asphaltene precipitation. The model described in the present work was used to study the effect of pressure in comparison with data extracted from Nghiem and Coombe.29 Pure solid was assumed for pressure application in Nghiem and Coombe.29 They reported an onset pressure of 5173.4 psia. Figure 8 shows this comparison starting from 5173.4 psia (Pos), where no precipitation appears, and lowering the P, thereby enhancing precipitation until a maximum is reached at around 2000 psia. At pressures below 1000 psia, the liquid phase does not show any asphaltene change. The results of the model and measured data are in good agreement, especially at the

2754


The solvophobic contribution can be related to the concentration of monomeric asphaltenes, xos a , in the crude at equilibrium with the asphaltene precipitate ∞ ∆Gads ) -na ln xos a

(I.4)

The excess energy can be lowered when resin molecules decrease the interfacial tension, σo, as follows

∆G°surf ) -nrσoa(1 - θ)/θ

Figure 8. Effect of pressure on asphaltene precipitation at 313 °C. (Symbols are experimental data; lines are predicted results.)

saturation pressure. Excellent agreement was obtained at the saturation pressure for Kuwaiti crude.

where θ is the fraction of micellar core surface covered by resins. The restrictions of the resins adsorbed on the asphaltene cores can be expressed as

∆G∞rep ) nr ln(1 - θ)

Acknowledgment The authors express their gratitude to Kuwait University Research Department for funding this project (EC083) and acknowledge the assistance of Mr. Magdi Abdel-Hameed for carrying out the experimental work.

∆G∞m ) nrf(θ) - na ln xos a RT

xm )

xna axnr r

exp(∆G∞m

/kT)

f(θ) ) ln(1 - θ) +

∞ + ∆G∞solv + ∆G∞surf + ∆G∞rep ∆G∞m ) ∆Gads

(I.2)

The major driving force for the resins to be adsorbed and form a shell around the asphaltenic core of the aggregate is the association of the resin molecule polar heads with the asphaltenes. The Gibbs free energy change for adsorption, in which nr is the number of resin molecules and ∆Ur is the energy of adsorption, estimated to be 18 kJ/mol,1 is defined as follows ∞ ) nr∆Ur ∆Gads

(I.3)

∆Ur σoa(1 - θ) RT RTθ

(I.8)

where ∆Ur/RT characterizes the difference between the interaction energy of a resin molecule head with the petroleum medium and the interaction energy of the resin molecule head with asphaltenes in a micellar core, and σoa/RT characterizes the interfacial tension between the asphaltene micellar core and the crude, where xos a is the equilibrium concentration of monomeric asphaltene coexisting with solid asphaltene phase. Equation 4 determines the concentration of micelles as a function of the aggregation numbers na and nr for given concentrations of monomeric asphaltenes and resins. The optimum composition of a micelle of a given size, n ) na + nr, is determined by

(

)

∂ ln xm ∂θ

n

)0

(I.9)

Using eq I.9 along with eqs 4, I.7, and I.8, one obtains

(I.1)

Several contributions in the ∆G∞m equation, corresponding to resin head adsorption, solvophobic, surface tension, and surface steric repulsion are defined.

(I.7)

where

Appendix I. Victorov and Firrozabadi Model1 The concentration of micelles can be related to the standard Gibbs free energy of aggregation ∆G∞m, as follows

(I.6)

Substituting the terms into eq I.2, one obtains

Conclusions A micellization/colloidal/aggregation model containing micelles of asphaltene colloidal aggregates surrounded by resin shell is used to describe crude oil containing asphaltene and resin monomers, along with the saturates and aromatics that constitute the bulk of the crude oil. Experimental data agreed well with the assumption that asphaltene aggregates are present in a coin-like shape. The critical properties of the asphaltene, resin, and crude oil were estimated using the group contribution technique. The effects of solvent type, temperature, and pressure were predicted and found to compare well with experimental values. The onset points and amounts of asphaltene precipitated were also predicted and found to compare favorably with experimental values.

(I.5)

ln

( ) xa

xrxos a

-

∆Ur σoa (1 + b) ) RT RT θ (1 + θb) (I.10) (1 - θ)

ln(1 - θ) where

b)

( )

va 8π a ans r

0.5

(I.11)

and b is the asphaltene molecular geometrical parameter, which is determined by the geometrical characteristics of the asphaltene and resin molecules and by the micellar radius, assuming that the micelles are coinlike in shape (platelike). Equation I.10 determines the


most probable fraction of micellar core coverage, θ, provided the total aggregation number, n is given.1

(S/C)c )

32c2 12c1 + 12c5

(II.16)

(O/C)c )

16c4 12c1 + 12c5

(II.17)

Appendix II. Critical Property Estimation The group frequency numbers are estimated on the basis of measured asphaltene properties, namely, molecular weight and elemental analysis, as follows:

MWa ) 13a1 + 12a2 + 32a3 + 14a4 + 17a5 (II.1) a1 + a5 (H/C)a ) 12a1 + 12a2

(II.2)

(N/C)a )

14a4 12a1 + 12a2

(II.3)

(S/C)a )

32a3 12a1 + 12a2

(II.4) (II.5)

nAa ) 2a1 + a2 + a3 + a4 + 2a5

(II.6)

The group definitions and their properties are given in Table 3. For example, a1 is the number of repetitions of the dC-H ring group in the asphaltene molecule, which has a molecular weight equals to 13 g/gmol. The hydrogen-to-carbon weight ratio (H/C) can be calculated from eq II.2, because the hydrogen atom is present in a1 and a5 groups with a weight equal to 1 g/gmole, whereas carbon atoms are present in a1 and a2 groups with a weight equal 12 g/gmole each. The number of atoms in the asphaltene monomer is nAa in eq II.6, made up of two atoms in the group a1 (carbon and hydrogen repeated a1 times), one atom in the a2 group, one atom in the a3 group, one atom in the a4 group, and two atoms in the a5 group. The same procedure is repeated to find the five groups existing in the resin monomer

MWr ) 32r1 + 14r2 + 17r3 + 14r4 + 14r5 (II.7) r3 + 2r4 + 2r5 (H/C)r ) (II.8) 12r4 + 12r5 14r2 (N/C)r ) (II.9) 12r4 + 12r5 (S/C)r )

32r1 12r4 + 12r5

(II.10)

(O/C)r )

16r3 12r4 + 12r5

(II.11) (II.12)

For the deasphalted crude oil, the following equations are used to estimate the frequency of Joback group contribution:

MWc ) 13c1 + 32c2 + 14c3 + 174 + 14c5 (II.13) c1 + 2c5 12c1 + 12c5

(II.14)

14c3 (N/C)c ) 12c1 + 12c5

(II.15)

(H/C)c )

(II.18)

The elemental analysis data and molecular weight experimental data shown in Table 2 are used to calculate the group frequency numbers for asphaltene, resin, and deasphalted crude, which are shown in Table 3. With the aid of these group formulations, the critical properties are estimated by the group contribution method of Joback30

Tc ) Tb[0.584 + 0.965

∑∆T - ∑(∆T)2]-1

Pc ) [0.113 + 0.0032nA -

16a5 (O/C)a ) 12a1 + 12a2

nAr ) r1 + r2 + 2r3 + 3r4 + 3r5

nAc ) 2c1 + c2 + c3 + 2c4 + 3c5

∑∆P]-2

(II.19) (II.20)

Vc ) 17.5 +

∑∆V

(II.21)

Tb ) 198 +

∑∆b

(II.22)

For molecules that do not differ greatly in size or chemical structure, the binary constant kij, which was used in the PR EOS mixing rules, can be set equal to zero. For binary mixtures in which both components fall into one of these categories hydrocarbons, rare gases, permanent gases, carbon monoxide, and perhalo carbons, kij can be estimated by

kij ) 1 -

8(VciVcj)0.5 (Vci0.33 + Vcj0.33)3

(II.23)

Upon estimation, kij for the crude oil constituents ranges from 0.06 to 0.14. Nomenclature a ) resin surface area b ) molecular geometrical parameter c ) concentration f ) fugacity G ) Gibbs free energy k ) Boltzmann constant MW ) molecular weight n ) number of molecules N ) number of aggregates P ) pressure Pc ) critical pressure R ) gas constant r ) micelle core radius T ) temperature Tb ) boiling point Tc ) critical temperature Ur ) interaction energy v ) molar volume Vc ) critical volume x ) mole fraction Greek Symbols φ θ µ σ

) ) ) )

fugacity coefficient fractional coverage chemical potential interfacial tension

2756


Superscripts o ) standard oo ) infinite os ) onset Subscripts a ) asphaltene m ) micelle n ) aggregates number r ) resin 1 ) monomer

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Received for review April 6, 2000 Revised manuscript received February 26, 2001 Accepted March 11, 2001 IE000405S

Prediction of Asphaltene Precipitation for Kuwaiti Crude Using

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