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Sharif University of Technology Scientia Iranica Transactions C: Chemistry and Chemical Engineering www.sciencedirect.com

Modeling the kinetics of asphaltene flocculation in toluene–pentane systems for the case of sonicated crude oils M. Hamedi Rad a , M. Tavakolian a , I. Najafi b , M.H. Ghazanfari a,∗ , V. Taghikhani a , M. Amani b a b

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Petroleum Engineering Program, Texas A & M University at Qatar, Doha, Qatar

Received 23 January 2012; revised 24 July 2012; accepted 19 September 2012

KEYWORDS Asphaltene flocculation; Kinetic model; Formation damage; Ultrasound wave; Smoluchowski model; Reversibility; Shattering.

Abstract This work is concerned with the monitoring of ultrasound effects on inhibition, as well as the reversible kinetics modeling of asphaltene flocculation in toluene-n-alkane systems, which has been rarely reported in the literature. A crude oil sample was exposed to ultrasound waves, and then the colloidal structural evolutions of flocculated asphaltene particles induced by addition of n-alkane were studied, using a confocal microscopy. Observations confirmed that radiation of ultrasound can change the irreversibility of asphaltene flocculation in crude oil. To interpret the kinetics of asphaltene flock aggregation, the Smoluchowski model was used, and the time dependent size distribution of asphaltene flocks was predicted. Fractal analysis was applied and the parameters of the kinetic model were determined. The values for the regressed parameters of the kinetic model show that for sonicated oil, the formation coefficient decreases, while the disintegration coefficient did not considerably change. The reason might be that sonication prevents flocks from aggregating rather than disintegrating them into smaller flocks. It might be the reason for its lingering effect on flocculation. This work illustrates the successful application of the Smoluchowski model for predicting the kinetics of asphaltene flocks under the influence of ultrasonic radiation for the entire range of reversible flocculation processes. © 2013 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction Deposition of asphaltene existing in crude oil may cause severe problems, such as formation damage, leading to large economic losses [1]. Recently, ultrasonic wave technology has been greatly involved in industrial applications, such as the removal of asphaltene particles from near wellbore regions. However, monitoring of its inhibition effect on asphaltene flocculation is not well understood. In addition, few attempts have been made to develop a reversible kinetic model to predict the flocculation behavior of ultrasonic radiated asphaltene particles in toluene-n-alkane mixtures. Since the size of the flocks plays an important role in precipitation rate [2], monitoring the

∗

Corresponding author. Tel.: +98 21 66166413. E-mail address: [email protected] (M.H. Ghazanfari). Peer review under responsibility of Sharif University of Technology.

evolution of asphaltene flock size can reveal crucial information in studying the kinetics of flocculation. Although there are several observations regarding the reversibility of asphaltene [2,3], it is generally regarded as an irreversible process [4,5]. Asphaltene exposure to ultrasonic waves can change its molecular and structural properties. Further, according to observations reported by Najafi et al. [6] sonication can reverse the formerly irreversible kinetics of asphaltene flocculation. They found that the size of the flocks increases during the process of flocculation, but, after a while, the mean diameter of asphaltene flocks starts to decrease. Accordingly, Reaction Limited Aggregation (RLA) and Diffusion Limited Aggregation (DLA) models, which have been proposed for irreversible flocculation processes [4], could not be applied to sonicated crude oils. Looking for a predictive model for reversible flocculation, the Smoluchowski model, which is mainly used for modeling the coagulation process of inorganic compounds [7], was considered as an appropriate choice, and the kinetics of the flocculation of asphaltenes particles in ultrasonic treated crude oil has been predicted. Since the shape of asphaltene flocks is not completely determined, fractal analysis was implemented to quantify observations on asphaltene particle shapes, the relationship between their

1026-3098 © 2013 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved. doi:10.1016/j.scient.2012.12.018

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Symbols Ci & Cj concentrations of species i & j di measured diameter di and dj the diameters of the flocks dp diameter of the individual particle Df fractal dimension dflock measured diameter fi number frequency of the ith flock Fi,j & Di,j reaction rates for flocculation and disintegration i, j, k, & N number of particles in flock Kd shattering reaction constant Kf flocculation reaction constant nf number of individual particles in the flock Nf total number of flocks Pa fractional precipitation W separation distance

diameters and the number of individual particles which form the flocks. By analysis of model parameters, which has been rarely considered in the literature, we aim to reveal the inhibition role of sonication in asphaltene flock aggregation. 2. Experimental

confocal microscopy. Nearly ten images were taken from different locations of the crude oil sample to obtain a statistically reliable size distribution of asphaltene flocks. More than 10,000 images were taken and analyzed to determine the time dependent size distribution of asphaltene flocks as a function of time. Figure 1 shows images of flock evolution at different time steps. 2.2. Measurement of the size distribution In order to survey the flocculation process, a thorough understanding of the asphaltene flocks size distribution is required. There are several methods for investigating size distribution; the two most convenient and widespread being laser and confocal microscopy [2]. The laser method is inaccurate because its induced heat can disintegrate the asphaltene flocks. Confocal microscopy does not have this disadvantage and is introduced as a reliable method for analyzing flock size distribution [1,4,9]. According to Najafi et al. [6], the diagram of the mean flock size versus flocculation time for Samples 1 and 2 is depicted in Figure 2. The average radius for Sample 1 (the non-sonicated sample) has an increasing trend, while, for Sample 2 (the sonicated sample), a change in trend is observed, which can be justified due to the reversibility of flocculation caused by sonication. 3. Modeling of asphaltene flocculation

2.1. Procedure

3.1. Irreversible models

Najafi et al. [6] reported an optimum value, ten minutes, for sonication time, at which the viscosity and flocculation rate of asphaltenic crude oils reduces to its minimum. Therefore, experiments on Sarvak oil were performed at this optimum exposure time. A set of confocal microscopy experiments was conducted for investigating the size distribution of asphaltene flocks of sonicated and non-sonicated Sarvak crude oil samples. The stages in the experiments are as follows: (A) 100 ml of crude oil sample were placed in a 300 ml vessel and sonicated for 10 min. For the sake of simplicity, a similar non-sonicated sample and the sample sonicated for ten minutes were named as sample numbers 1 and 2, respectively. (B) As asphaltene is insoluble in light saturated hydrocarbons [8], e.g. n-Pentane, it should be added to the above crude oil samples in order to study the kinetics of the flocculation process. Also, toluene was added to the samples to enhance the transparency for confocal microscopic observations. The overall composition of the solution was 2% oil, 60% pentane and 38% toluene. During the process of flocculation, the samples were placed in an enclosed area between two transparent plates to avoid pentane evaporation and, at specified time intervals, were observed by the

Several models have been presented for prediction of the flocculation process. Kawanaka et al. [10] presented a thermodynamic model to predict the size distribution of asphaltene flocks at equilibrium, and Browarzik et al. [11] modeled the average molar mass of asphaltene in the solution. Since the aim of this work is to monitor size distribution as a function of time, thermodynamic models cannot be used, because they only give the size distribution at infinity. One of the most popular models used for modeling of asphaltene flocculation is Derjaguin–Ladau–Verwey–Overbeek (DLVO), which consists of two parts: RLA and DLA [4]. DLVO models can predict size distribution as a function of time with good accuracy. However, as they can only be used for modeling irreversible flocculation, their accuracy for the prediction of reversible flocculation of asphaltenes induced by sonication is poor. Another model is a statistical model. Smoluchowski presented a model to predict the kinetics of reversible coagulation of inorganic compounds [7,12]. Considering the similarity between flocculation and coagulation, since asphaltene flocculation in ultrasonic treated oil, shown in Figure 2, confirmed reversibility, the Smoluchowski model, explained in detail in the next section of the paper, was used to predict the kinetics of asphaltene flocculation in sonicated crude oil.

Figure 1: Evolution of asphaltene flocks at different experiment times: (a) 20, (b) 30, and (c) 90 min.

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from 2 to 3. The flocculation was not predicted with acceptable accuracy by implementing this equation and better predictions were observed by assuming the smaller flock as the reaction controlling reactant [13]. The following equation was obtained by modification of Eq. (4):

Fi,j = Kf

Figure 2: Overall trend of mean particle size as function of flocculation time.

ni ni + nj

1/Df

The classical approach to studying coagulation was first developed by Smoluchowski, who proposed Eq. (1) to describe time evolution for the concentration of clusters of k particles, Ck , under the assumption of binary collisions. According to the Smoluchowski model, which predicts the kinetics of coagulation for colloidal and polymer substances, reversible flocculation can be given as follows: dC k 1 = Fi,j Ci C j − Di+j Ci+j dt 2 i+j=k

−

N −k (Fk,j Ck Cj − Dk+j Ck+j ),

where indices i, j, k and N represent the count of particles in each flock, D and F are disintegration and formation constants, respectively, and their unit is the number of reactions per unit volume per unit time [7]. In the Smoluchowski equation, the first summation consists of two parts; the formation of flocks with size k from smaller flocks, and the disintegration of flocks with size k to smaller ones. The second summation, however, takes into account the consumption of flocks with size k to form larger ones, and also the disintegration of larger flocks forming ones with size k. According to Ball et al. [13], if asphaltene particles are assumed to be spherical, the reaction rate will be proportional to the flock boundary volume, Vc , which is given by: Fi,j ∝ Vc = π di + dj

2

w,

(2)

where dj is the diameter of the jth flock and w is the distance within which the flocculation occurs. It is obvious from Eq. (1) that the summations are on the size of flocks; therefore, the relationship of F and D to flock size must be determined, so that the summations can be calculated. For this purpose, fractal analysis is implemented and a relation between flock diameter and number of individual particles is obtained. Diameter, dflock , and the number of individual particles, ni , are related by fractal dimension, Df , as:

ni =

dflock dp

Df

.

(3)

Substituting in Eq. (2) results in: Fi,j = Kf ni 1/Df + nj 1/Df

λ

,

(4)

where Kf is the flocculation constant, which is dependent on the properties of asphaltene and flocculation temperature and is independent of flock size, and λ is a tuning parameter; ranging

ni + nj

1/Df nj

λ

.

(5)

1/Df β

+ nj

) ,

(6)

where Kd is the disintegration constant and β is the tuning parameter, ranging from 0 to 3. 3.3. Fractal analysis of asphaltene flocks Calculation of fractal dimensions is a delicate issue and has some complications due to the intangibility of the concept and the fact that it has to be calculated indirectly by statistical calculations. Rastegari et al. [2] derived an equation from which the fractal dimensions of the flocks can be determined relying on size distribution, the mass of precipitated asphaltene and some other tangible and measurable parameters as:

(1)

j =1

+

nj

Eq. (4) will be obtained by setting ni = nj in Eq. (5). Shattering, the breakage of larger flocks into smaller ones, and erosion, the removal of tiny flocks from the surface of the mother flock, are believed to be the reasons for the disintegration of asphaltene. Wei et al. [14] observed that disintegration is mainly due to shattering, and erosion can be neglected without imposing considerable error. The shattering reaction rate is given by: Di+j = Kd ( ni

3.2. Reversible flocculation modeling

1/Df ni

PA =

Df π ρA Nf d3p di 6mA

fi

dp

,

(7)

where PA is the fractional precipitation; the fraction of the whole asphaltene which is precipitated, fi is the number frequency of the ith flock, Nf is the total number of flocks, ρA is the density of the asphaltene, dp is the diameter of an individual particle, assumed to be 1 µm in this work, and mA is the total mass of asphaltene flocks in the solution obtained by IP-143 testing. By implementing this equation and measuring its parameters, the fractal dimension is readily calculated. 3.4. Algorithm As seen in the flowchart shown in Figure 3, the inputs to the model are the initial concentration and the diameter of the individual particles, the fractal dimensions of the flocks, the reaction constants, and the reaction exponents. F and D are calculated using Eqs. (5) and (6), respectively, and are substituted into the Smoluchowski equation (Eq. (1)). The rate of change in concentration is calculated for each time step and, consequently, the size distribution is calculated as a function of time. The reaction constants and exponents are employed as tuning parameters, while the fractal dimensions of the asphaltene flocks, calculated using Eq. (7), 1.53, consider constants, the assumption made by Rastegari et al. [2], as well. The mass balance was checked at each step to avoid miscalculation and the time step was decreased in case of any noticeable mass balance error. 4. Results and discussions The model predictions (Eq. (1)), and experimental data of the size distribution of asphaltene flocks after 20, 30 and 90 min

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Figure 4: Comparison of model and experiment after (a) 20, (b) 30, and (c) 90 min of flocculation for sonicated oil. Figure 3: Flow chart of the model.

Table 1: The parameters of Smoluchowski kinetic model for sonicated and non-sonicated oil.

of flocculation time are shown Figure 4(a)–(c). It is obvious from the figure that the Smoluchowski model predictions are in reasonable agreement with the experimental data, while, based on the data given in Figure 2, after 60 min of flocculation time, the RLA and DLA models could not be applied in the case of sonicated oil. In order to quantify the accuracy of the model predictions, the error was calculated as: N

E=

|Cmodel − CExperiment |

1

N

.

(8)

Error values for 20, 30 and 90 min of flocculation are equal to 5.28, 4 and 6.4, respectively, which is in an acceptable average deviation range from the experimental data. Based on the algorithm given in Figure 3, values of the kinetic model parameters for non-sonicated and ten minute-sonicated crude oils are calculated and compared in Table 1. The figures in the table show that sonication caused no noticeable change

Input Reaction constant, Kf Shattering reaction constant, Kd Flocculation reaction exponent, λ Shattering reaction exponent, β Fractal dimension, Df

Non-Sonicated 5.23 × 10−5 4.95 × 10−5 2.6 1.5 1.65

Sonicated 5.02 × 10−6 5.04 × 10−5 3 1 1.53

in the disintegration constant; however, the reaction constant has become approximately ten times smaller. It is concluded that sonication has almost no influence on the disintegration of asphaltene flocks and the reduction in the mean diameter is due to the decrement in their formation. Consequently, based on the conclusions made from the comparison of sonicated and nonsonicated samples, the reason ultrasonic radiation decreases the mean diameter is that it inhibits flock growth, rather than disintegrating them into smaller flocks, therefore, it acts as an inhibitor in the flocculation process [9]. The figures in the table also show that the fractal dimension has reduced for sonicated

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macro structures and, consequently, reduces precipitation of asphaltene in well-bores and inside pipelines, which prevents tremendous economic loss. Acknowledgment The authors would like to express their gratitude to Mr. Mohammad Reza Mousavi for his assistance in the confocal microscopy experiments. References

Figure 5: Comparison of experimental data, DLVO and Smoluchowski model.

oil, which indicates that the flocks are smoother. This might be the reason for decreasing the reaction constant, as smoother flocks are less prone to flocculate. This effect of ultrasound could be helpful for inhibition of formation damage near wellbore regions. In this work, by implementing model and statistical experiments, the microscopic effect of ultrasound on the flocculation process is understood, and it was verified that the flocculation behavior of asphaltene particles in alkane mixtures can be predicted by the mentioned model with proper accuracy. To calculate the model parameters, only two confocal microscopy asphaltene flock size analysis tests are required. By implementing the discussed model, a size distribution of asphaltene flocks as a function of time was obtained. However, the previously developed model, namely; the DLVO model, only yields the average radius of the flocks. To compare the precision of the DLVO model with the Smoluchowski model, the average radius of the asphaltene flocks is calculated from the size distribution and compared with the DLVO model [6] and experimental data, as depicted in Figure 5. It is shown in the plot that the Smoluchowski model has predicted the reversibility of the flocculation of sonicated oil. 5. Conclusions Previous irreversible kinetic models, RLA and DLA, suffer from inadequate accuracy for prediction of the size distribution of asphaltene flocks formed in ultrasonic treated crude oils. However, in this work, an understanding of the size distribution of asphaltene flocks, as a function of time, for reversible asphaltene flocculation in sonicated crude oils, was obtained. According to the results obtained in this study, radiation of ultrasonic waves changes the irreversibility of asphaltene flocculation in crude oil. The changes in flocculation rate are not limited to sonication time. It was also observed that among the kinetic model parameters, the formation coefficient decreased in the case of sonicated oil, while the disintegration coefficient did not considerably change. It might be due to the fact that sonication prevents flocks from aggregation rather than disintegrating them into smaller flocks. This is believed to be the reason for its lingering effect on flocculation. The model presented here can predict both size distribution and average radius of asphaltene flocks at different time intervals, and is applicable to the whole range of the flocculation process, rather than DLVO models. The results of this work can be helpful in a better understanding of the fact that the flocculation rate for the case of sonicated oil inhibits the formation of

[1] Shedid, A.S. and Attallah, S.R. ‘‘Influences of ultrasonic radiation on asphaltene behavior with and without solvent effects’’, SPE International Symposium and Exhibition on Formation Damage Control, 18–20 February, Lafayette, Louisiana (2004). [2] Rastegari, K., Svrcek, W.Y. and Yarranton, H.W. ‘‘Kinetics of asphaltene flocculation’’, Industrial & Engineering Chemistry Research, 43, pp. 6861–6870 (2004). [3] Anisimov, M.A., Yudin, I.K., Nikitin, V., Nikolaenko, G., Chernoutsan, A., Toulhoat, H., Frot, D. and Briolant, Y. ‘‘Asphaltene aggregation in hydrocarbon solutions studied by photon correlation spectroscopy’’, Physical Chemistry, 99, pp. 9576–9580 (1995). [4] Hung, J., Castillo, J. and Reyes, A. ‘‘Kinetics of asphaltene aggregation in toluene-heptane mixtures studied by confocal microscopy’’, Energy & Fuels, 19, pp. 898–904 (2004). [5] Pfeiffer, J. and Saal, R. ‘‘Asphalt bitumen as colloid system’’, Physical Chemistry, 44, pp. 139–149 (1940). [6] Najafi, I., Mousavi, S.M.R., Ghazanfari, M.H., Ramazani, A., Kharrat, R. and Ghotbi, C. ‘‘Quantifying the role of ultrasonic wave radiation on kinetics of asphaltene aggregation in toluene–pentane mixture’’, Petroleum Science and Technology, 29, pp. 966–974 (2011). [7] Family, F., Meakin, P. and Deutch, J.M. ‘‘Kinetics of coagulation with fragmentation: scaling behavior and fluctuations’’, Physical Review Letters, 57, pp. 727–733 (1986). [8] Thou, S., Ruthammer, G. and Potsch, K. ‘‘Detection of asphaltenes flocculation onset in a gas condensate system’’, European Petroleum Conference, 29–31 October, Aberdeen, United Kingdom (2002). [9] Amani, M. and Najafi, I. ‘‘Asphaltene flocculation inhibition with ultrasonic wave radiation: a detailed experimental study of the governing mechanisms’’, Advances in Petroleum Exploration and Development, 2, pp. 32–36 (2011). [10] Kawanaka, S., Leontaritis, K.J., Park, S.J. and Mansoori, G.A. ‘‘Thermodynamic and colloidal models of asphaltene flocculation’’, American Chemical Society, 396, pp. 443–458 (1989). [11] Browzik, D., Laux, H. and Rahimian, I. ‘‘Asphaltene flocculation in crude oil systems’’, Fluid Phase Equilibria, 154, pp. 285–300 (1999). [12] Branco, V.A.M., Mansoori, G.A., Xavier, L.C.D.A., Park, S.G. and Manafi, H. ‘‘Asphaltene flocculation and collapse from petroleum fluids’’, Petroleum Science & Engineering, 32, pp. 217–230 (2001). [13] Ball, R.C., Weitz, D.A., Witten, T.A. and Leyvraz, F. ‘‘Universal kinetics in reaction-limited aggregation’’, Physical Review Letters, 58, pp. 274–277 (1987). [14] Wei, J., Lee, W. and Krambeck, F. ‘‘Catalyst attrition and deactivation in fluid catalytic cracking system’’, Chemical Engineering Science, 32, pp. 1211–1218 (1977).

Mohammad Hamedi Rad received his B.S. degree in Chemical Engineering from Sharif University of Technology, Tehran, Iran, in 2012, and is currently a Ph.D. candidate at the University of Illinois at Urbana Champaign, USA. He has been a member of the Ultrasonic Research Group in the Chemical and Petroleum Engineering Department of Sharif University of Technology since 2010. His research interests include: mathematical modeling and studying the properties of ultrasonic treated matter. Mandana Tavakolian received her B.S. degree from Sharif University of Technology, Tehran, Iran, in 2012. She joined the Ultrasonic Research Group in the Chemical and Petroleum Engineering Department of Sharif University of Technology in 2010. Her research interests include: process control and design. Iman Najafi graduated from the Chemical and Petroleum Engineering Department of Sharif University of Technology, Tehran, Iran, in 2010, and is currently a Ph.D. degree student at Texas A&M University, USA. He received the Society of Petroleum Engineers certificate in 2010 for his research work at the international SPE paper contest in Italy. Prior to that, his studies on ultrasonic stimulation technology were awarded first rank in the Middle East, India and North Africa regions by the Society of Petroleum Engineers referees at the Oman SPE Student Paper contest. His research interests include: ultrasonic stimulation technology and right now he is involved in the ultrasonic research studies group of Texas A&M University in Qatar.

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Mohammad Hossein Ghazanfari received his B.S. degree from Isfahan University of Technology, in Iran, and Ph.D. and M.S. degrees from Sharif University of Technology, Tehran, Iran, all in Chemical Engineering. He is currently Assistant Professor in the Chemical and Petroleum Engineering Department at Sharif University, and head of the Enhanced Oil Recovery Laboratory. His research interests include: modeling of transport in porous media, micro/core scale EOR studies, and asphaltene precipitation/deposition in static/dynamic conditions.

Tehran, Iran, and is currently responsible for the academic affairs of the whole department. He has supervised more than 50 B.S., 70 M.S., and 10 Ph.D. theses in both Chemical and Petroleum Engineering, and has published more that 70 technical articles in this area in prestigious journals. He has delivered more than 60 presentations at national and international Chemical and Petroleum Engineering conferences, and has been invited to give more than 10 lectures at different universities and academic institutions around the world.

Vahid Taghikhani received B.S., M.S. and Ph.D. degrees in Chemical Engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran. Since 2000, he has been working as full time faculty member in the Department of Chemical and Petroleum Engineering at Sharif University of Technology,

Mahmood Amani is Associate Professor at Texas A&M University in Qatar. He has broad experience of working in academia and industry and has two patents. His research interests include: drilling fluid, cement and acoustic stimulations.