Determining the Kinetics of Asphaltene Adsorption from Toluene: A

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Determining the kinetics of asphaltene adsorption from toluene; a new reaction-diffusion model Sophie Campen, Luca di Mare, Benjamin Smith, and Janet S. S. Wong Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01374 • Publication Date (Web): 25 Aug 2017 Downloaded from http://pubs.acs.org on August 25, 2017

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Energy & Fuels

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Determining the kinetics of asphaltene adsorption from toluene; a new reaction-diffusion model

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Sophie Campen , Luca di Mare , Benjamin Smith , Janet S. S. Wong

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*Corresponding Author: [email protected]

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Keywords: asphaltene adsorption, QCM-D, kinetics, polydispersity

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Abstract

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Department of Mechanical Engineering, Imperial College London, UK SW7 2AZ

BP Exploration Operating Company Limited, Chertsey road, Sunbury on Thames, Middlesex, UK TW16 7BP

Fouling by asphaltene, which constitutes the densest, most polar fraction of crude oil, poses a serious problem for the oil production industry. In order to obtain a fundamental understanding of asphaltene deposition it is necessary to determine both the thermodynamics and kinetics that govern this process. In recent years, there have been numerous studies of the kinetics of asphaltene adsorption, however, a consensus on the model that best describes asphaltene adsorption remains elusive. In this paper the adsorption of asphaltene from solution in toluene onto a gold surface is investigated using a quartz crystal microbalance inside a flow cell. The kinetics of adsorption depends on the state of asphaltene in solution and the adsorption behaviour alters with long-time aging of asphaltene solutions. A model is developed that links the kinetics of asphaltene adsorption to the bulk solution properties in terms of coexisting monomer and multimer states. A large portion of deposited asphaltene is effectively irreversibly bound and not easily removed by rinsing with toluene. The model suggests that asphaltene-asphaltene interactions play an important role in the formation of irreversibly bound deposits, which could lead to fouling problems.

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Fouling by asphaltene poses a serious problem for the oil production industry. Asphaltene is the densest, most polar fraction of crude oil. Although generally stable in liquid crude oil under the conditions present in the reservoir, changes in pressure, temperature, composition and shear rate may result in the precipitation and subsequent deposition of asphaltene. Deposited asphaltene can build up at many places along the oil production system, for example, inside wellbores, pumps, tubing, wellheads, safety valves, flowlines and surface facilities [1]. These deposits reduce the efficiency of oil production and in extreme cases they can completely plug the wellbore. Removal of deposited asphaltene costs both time and money. Fundamental studies of the kinetics of asphaltene deposition can help determine new and more effective strategies for dealing with asphaltene related issues.

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Asphaltene is defined by its solubility: soluble in aromatics like toluene, but insoluble in n-alkanes like heptane. Since asphaltene is a solubility class of materials and not a single molecular species, its chemistry is not unambiguously known. However, attempts have been made to determine the chemical structure of asphaltene molecules [2,3,4,5]. This has led to two leading molecular architectures: island and archipelago [6]. The island structure with one polycyclic aromatic core, forms the basis of the YenMullins hierarchical model of asphaltene self-assembly [7,8,9]. Whilst the archipelago structure has two or more smaller polycyclic aromatic groups linked by aliphatic chains [10]. Heteroatoms including

Introduction

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nitrogen, sulphur and oxygen are reported to be found in various functional groups [11]. The least stable asphaltene molecules tend to contain a greater proportion of oxygen-containing groups [12]. Cooperative polar and hydrogen-bonding interactions between asphaltenes are responsible for aggregation and are the likely cause of fouling in pipes [13].

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The Langmuir and Freundlich adsorption isotherms have been used to describe the adsorption of asphaltene onto surfaces with different studies finding evidence for both monolayer and multilayer adsorption [11,14]. There have also been numerous studies of the kinetics of asphaltene adsorption/deposition onto both solid surfaces and porous materials. Acevedo et al. investigated the adsorption of asphaltene from solution in toluene onto silica by measuring the decrease in the absorbance of the solution as a function of adsorption time [15]. For initial solution concentrations of 0.005 to 0.05 gL⁻¹, the rate of adsorption with respect to concentration of asphaltene was first order and had a rate constant of 1.17 x 10⁻³ min⁻¹. At higher concentrations of 0.2 and 0.4 gL⁻¹ the initial rate constant was similar, but decreased at long adsorption times. The rate of diffusion to the outer surface of the silica was found to be the rate-limiting step at initial adsorption times and it was proposed that adsorbed asphaltene provided a fresh site for further adsorption. At long adsorption times, there was a decrease in the rate of adsorption; it was suggested that the rate-limiting step was now the lateral diffusion of asphaltene across the surface to find a vacant site within the multilayer [15]. Aggregates existing in solution were found to adsorb at a similar initial rate to single asphaltene molecules.

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Nassar used both the pseudo-first and pseudo-second order sorption models to fit the adsorption of asphaltene onto γ-alumina nanoparticles from solution in toluene [14]. It was found that the pseudosecond order model provided a good fit for the experimental data whilst the pseudo-first order model did not. The equilibrium adsorbed masses obtained by the pseudo-second order model were in good agreement with the experimentally measured values (R² = 1.0). The pseudo-second order rate constant, k₂, is strongly dependant on the experimental conditions and unlike rate constants derived from typical rate laws, decreases with concentration. Similar behaviour was observed by Franco et al. for the adsorption of asphaltene from solutions in toluene onto nickel oxide nanoparticles supported on alumina. However, a clear correlation between the rate constant and the nickel oxide content of the sorbent could not be found [16].

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Behbahani et al. developed a new kinetic model for asphaltene adsorption onto porous media in a dynamic flowing system [17]. They modified the Langmuir model to take into account multilayer adsorption and derived a two-step model for adsorption: the first being adsorption of asphaltene onto the porous material and the second being the adsorption of asphaltene onto already adsorbed asphaltene. The multilayer model fitted the data better than monolayer adsorption models.

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The quartz crystal microbalance (QCM) has proven a useful technique for investigating the adsorption and deposition of asphaltene onto solid surfaces [20-25]. It is also being adapted to investigate asphaltene deposition under extreme conditions. For example, a quartz crystal resonator has been used to determine the effects of pressure, temperature and CO₂/methane injection on the onset of asphaltene precipitation from dead oil [18].

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In a QCM, the frequency and dissipation (or resistance) of an oscillating quartz crystal are monitored; from this, information about the adsorbed mass and also the material properties of the film can be obtained. Originally developed for measuring adsorption from the gaseous phase, modifications for use in liquid environments made QCM suitable for a wide range of applications. The high sensitivity (< 1 ng cm⁻²) of QCM means that it can monitor sub-monolayer films in situ. In 2002 Ekholm et al. published a paper on the use of QCM with dissipation monitoring (QCM-D) for studying the adsorption of asphaltenes

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and resins onto a gold surface [19]. In this study they successively exchanged the solution in contact with the surface by injecting new solutions of similar or higher concentration. The overall frequency and dissipation shifts from that of the baseline values in heptane/toluene were recorded. In this manner they were able to obtain an adsorption isotherm for asphaltene on gold.

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Dynamic measurements where the liquid in contact with the surface is flowing have been carried out and the kinetics of adsorption for these systems determined. Rudrake et al. investigated the adsorption of asphaltene from solution in toluene onto a gold surface [20]. They found that the initial rate of adsorption increased with increasing asphaltene concentration and could be fitted by diffusion-limited kinetics. Tavakoli et al. used QCM-D to research adsorption from extracted asphaltene [21] and crude oil [22] in heptane/toluene. A wide range of different experimental conditions were covered including the effect of heptane/toluene ratio, flow rate and surface chemistry. It was found that the deposited mass of asphaltene increased with increasing volume ratio of heptane to toluene up to the precipitation point which was determined to be 76 vol% heptane.

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Intuitively surface chemistry should play a role in asphaltene adsorption. Dudasova et al. investigated the deposition of asphaltene from solutions in toluene and 50:50 heptane-toluene onto silica, alumina, titanium oxide and iron oxide surfaces [23]. It was found that the source of the asphaltene had a greater effect on the deposited mass than the surface type. Asphaltene from Brazil adsorbed to the greatest extent and the highest adsorbed mass was observed on silica, whilst asphaltene from the Gulf of Mexico tended to adsorb to a lesser extent and the highest adsorbed mass was observed on alumina. This suggests selectivity of asphaltene from different sources to particular surfaces and perhaps indicates that a one-suits-all solution may not be possible with regard to selection of pipe and engineered surface materials as a means to mitigate fouling.

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The process of asphaltene adsorption is complex. While numerous studies have been conducted investigating the adsorption of both extracted and model asphaltenes on various surfaces, as described above, the factors governing the adsorption process and the nature of the films remain unclear. The link between the properties of asphaltene in bulk solution and its adsorption behaviour is largely unknown. Focusing on adsorption kinetics, we aim to provide an understanding of how asphaltene adsorption and surface film formation is affected by its solution conditions. The adsorption of extracted asphaltene onto a gold surface from solution in toluene is investigated using a quartz crystal microbalance inside a flow cell. The rate of asphaltene adsorption onto gold is determined for a wide range of asphaltene concentrations and the kinetics are fitted using existing models. A new model is developed to describe the kinetics of asphaltene adsorption based on the properties of asphaltene in solution. This model provides a direct link between the states of asphaltene in bulk solution with the surface adsorption process.

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In this paper a new reaction-diffusion model for asphaltene adsorption is proposed. The model describes the adsorption of asphaltene in terms of three concurrent processes: the equilibrium in bulk between aggregates of different mass; the diffusion of the aggregates towards a solid surface; and the adsorption process on the surface.

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The model idealises the bulk of the asphaltene solution as a solution of species . The concentration of these species is uniform in the direction tangential to the wall (x-direction), but varies in the direction normal to it (y-direction), Fig. 1. The species are in equilibrium with each other through recombination and dissociation reactions. Adsorption takes place in a layer of small thickness compared to the thickness of

Kinetic Reaction-Diffusion Model

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the liquid film. The bulk species diffuse towards the layer where they take part in adsorption reactions and become bound to the wall.

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The mass balance for the -th species in the bulk solution reads [ ] [ ] = + [ ], [ ], … , [ ] 1

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where is the net production rate for the species , as a result of the dissociation and recombination dynamics in the bulk. is the diffusivity of species in the mixture.

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At a large distance from the wall the concentrations are uniform [ ] = 0 at → ∞ 2

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Near the wall the diffusive flux of the species matches its net adsorption rate .

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[ ] = [∗ ], … [∗ ], ["], [ ], … , [ ] at = 0 3

The net adsorption rate for species is a function of the bulk and surface concentrations of the species as well as the surface concentration of adsorption sites ". The mass balance for the adsorbed layer and the adsorption site balance finally read: $[∗ ] = [∗ ], … [∗ ], ["], [ ], … , [ ] 4 $ $["] = [∗ ], … [∗ ], ["], [ ], … , [ ] 5 $

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where [ ] is the concentration of the -mer in solution, [∗ ] is the surface concentration of the adsorbed mer and ["] is the surface concentration of adsorption sites (all -mers compete for the same sites).

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The net formation rates and the net adsorption rates can be modelled by postulating a reaction network and using mass action laws to relate the forward and backward reaction rates to the bulk and surface concentrations of the species involved in the model for a set of rate constants. On one hand, given a set of species, a reaction network with rate constants and a set of initial concentrations, the model can be integrated in time using standard finite difference methods to predict the variation in time of the adsorbed mass. On the other hand, the experimental results can be used to determine the values of the rate constants, for a postulated reaction network. In the present work, rate constants are determined as best fits of a set of experimental data using a genetic algorithm. The initial estimates for the rate constants are determined via an initial parametric study. In this way likely reaction paths can be formulated to model asphaltene adsorption.

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Brief descriptions of experimental methods are provided in this section. Note for the rest of the paper, tables, sections, equations, figures with labels started with ‘S’ can be found in the Supporting Information.

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3.1

Experimental section

Materials

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A crude oil sample from a source with a known history of asphaltene fouling problems was provided by BP. Asphaltene was extracted from the crude oil using heptane as a precipitant. Two stock solutions were -1 prepared with 10 and 1 gL extracted asphaltene in toluene (99.9 %, CHROMASOLV, used as supplied). Stock solutions were stored under ambient conditions (21°C) in a dark cupboard. Asphaltene solutions for testing were prepared by dilution of these stock solutions. Details of the asphaltene extraction process are given in section S.2. The physical properties and the particle size distribution of the asphaltene solutions can be found in sections S.3 and S.4 respectively. The viscosity and density of the concentrated asphaltene solution were slightly higher than those observed for toluene. Dynamic light scattering (DLS) shows that the mean size of asphaltene in aged asphaltene solutions was 2, 9 and 14 nm at concentrations of 0.01, 0.1 and 1 gL⁻¹ respectively, see Fig. S3. In all cases the size distribution was monomodal. The size distributions by volume were positively skewed. These results are in reasonable agreement with those reported in the literature [24].

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The QCM-D technique has been explained in detail by others previously [21,23,25,26]. In this work, the adsorption of asphaltene from solution in toluene onto a gold-coated quartz sensor was investigated using QCM-D. Dynamic measurements were carried out in a flow cell where toluene, followed by asphaltene solution (adsorption), then toluene again (rinsing) flowed through the cell sequentially. The adsorption and rinsing times were both 1 hour. Experiments were carried out at 20°C and a flow rate of 6 µLs⁻¹. A preliminary study showed that this flow rate was sufficiently fast to prevent mass transport-limited adsorption at short times, see section S.9. Changes in the resonance frequency ∆( (Hz) and dissipation ∆) were recorded. This data was used to extract the Sauerbrey mass and model the Voigt viscoelastic mass. For all adsorption experiments the error in the calculated adsorbed mass is approximately 27 ngcm⁻² at an adsorption time of 1 h. This error is calculated for the maximum expected background drift in the frequency and dissipation baselines and is typically caused by experimental instabilities such as O-ring creep and slight temperature fluctuations. Details of the principle of QCM-D, the experimental setup and how adsorbed mass is estimated can be found in section S.1.

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Note that ∆( and ∆) obtained during QCM-D experiments are affected by various factors including the adsorbed mass, changes in solution viscosity/density (liquid loading), and liquid trapping. The liquid loading shifts, ∆(*+,- *./-0 and ∆)*+,- *./-0 , were calculated using equations (S3) and (S4) given in section S.1.1. It was found that the liquid loading effect was very significant for the 10 gL⁻¹ solution, slight for 1 gL⁻¹ and negligible for the 0.1 gL⁻¹ solution, see Fig. S2. This is expected since the viscosity and density of asphaltene solution in toluene both increase with increasing asphaltene concentration, resulting in a greater deviation from the pure toluene baseline. The liquid trapping effect, ∆(*+,- 12/330 , was assumed to be zero owing to the use of sensors with a smooth Au surface (RMS roughness 1.1 nm at a scan size of 10 µm, see Fig. S4).

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The adsorption of asphaltene onto gold from solution in toluene was investigated for a concentration range of 0.001 to 1 gL⁻¹. For these experiments we used the same QCM sensor (Sensor X), which was cleaned thoroughly before each experiment and all experiments were completed within 3 days of preparing the asphaltene solutions. Typical QCM-D responses are illustrated in Fig. S5. The two main criteria for use of the Sauerbrey mass are (i) ∆) = 0 and (ii) that ∆( and ∆) are constant with respect to the observed overtone , particularly in ∆(. It is found that these criteria are not met since in all cases

QCM-D experiments

Results Adsorption of asphaltene onto gold


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∆) > 0. Spreading of the overtones is also observed and is most pronounced at high concentration. To account for the effect of liquid loading, the viscosity and density parameters of the bulk liquid were set to those of the asphaltene solution for viscoelastic modelling of the adsorbed asphaltene layers. We extracted both the Sauerbrey mass and the Voigt viscoelastic mass and found that the two results were similar, except at concentrations of 1 gL⁻¹ and over. In subsequent analysis we elect to use only the Voigt mass.

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The adsorbed areal mass is plotted vs. time, see Fig. 2(a). The initial rate of adsorption is fast and increases with increasing asphaltene concentration. At longer times, the rate of adsorption slows and the adsorbed mass appears to be reaching a plateau. This suggests that the adsorbed mass is reaching an equilibrium adsorbed amount, however it may be a quasi-equilibrium mass rather than a true equilibrium mass (i.e. the relative change in mass with time is small, such that the system may be described as approaching a steady state, although if left for a much longer time, the mass may further increase). At the lowest concentration of 0.001 gL⁻¹ (solid circles, Fig. 2(a)) where the rate of adsorption is slower, equilibrium is not reached. After an adsorption time of 1 hour, pure toluene is flowed through the QCM cell and it is observed that the adsorbed mass decreases (see Fig. 2(b)). The decrease in mass upon toluene-rinsing is due to asphaltene desorption from the gold surface. The rate of desorption varies with the concentration of asphaltene used during adsorption. The initial rate of desorption is similar to the initial rate of asphaltene adsorption onto the clean Au surface. The rate of desorption decreases with rinsing time. The removal of asphaltene is slow and continues beyond the rinsing time of 1 hour. It is not known whether a new equilibrium adsorbed amount is reached or whether complete desorption of all adsorbed asphaltene will be achieved at infinitely long rinsing times. However, since the rate of removal is very slow at long rinsing times, it may be assumed that a quasi-equilibrium state is reached and that the mass remaining on the surface can arguably be described as irreversibly-bound. Hence, a proportion of the film is easily removed by solvent rinsing whilst a greater portion is more strongly bound.

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The adsorbed mass after 1 hour, 56 , is approximated to be the equilibrium adsorbed mass, 57 . A plot of 57 (ngcm⁻²) vs. concentration of asphaltene in the bulk at equilibrium, 87 , (gL⁻¹) indicates that the adsorption follows a type I isotherm and that only monolayer adsorption occurs, see Fig. 3(a). The data is fitted using the Langmuir adsorption model: 57 = 59

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:; 87 6 1 + :; 87

where 59 is the adsorbed mass for a complete monolayer (ngcm⁻²) and :; is the equilibrium constant for Langmuir adsorption (Lg⁻¹). Since our experiments are carried out in a flow cell, 87 is constant with time and is equivalent to 8= , the initial concentration of asphaltene in the bulk solution. The linear form of the Langmuir model, which is plotted in Fig. 3(b) is given by the following equation: 87 87 1 = + 7 57 59 59 :;

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It is observed that the Langmuir adsorption isotherm provides a good fit for the data and exhibits a high linear correlation coefficient of 1.000. The values of 59 and :; are found to be 790.51 ngcm⁻² and 203.39 Lg⁻¹ respectively. n.b. Using the equilibrium mass predicted by the kinetic models in section 4.3 instead of 56 yields 59 and :; of 804.12 ngcm⁻² and 201.23 Lg⁻¹ respectively. To illustrate the goodness of fit of the Langmuir isotherm for the entire concentration range a log-log plot is shown in the insert in Fig. 3(b). It is observed that there is a monomial relationship where 87 ⁄57 depends on 87 =.AB , the power of which is

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close to unity. Note analyses based on the Freundlich and Temkin isotherms do not achieve as good a fit as the Langmuir isotherm (see section S.7) and thus are not pursued further.

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= For a system at equilibrium, the Gibbs free energy of adsorption, ∆C/-D , is given by: = ∆C/-D = −FG ln : 8

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where F is the ideal gas constant (8.3144 Jmol⁻¹K⁻¹), G is the temperature (293.15 K) and : is the equilibrium constant (dimensionless). The equilibrium constant, :, can be obtained by: : = :; ×

LD 9 MD

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where :; is the equilibrium constant for Langmuir adsorption in Lmol⁻¹, LD is the density of the solvent in gdm⁻³ and MD is the molar mass of solvent in gmol⁻¹ [14]. Assuming a molar mass for asphaltene of 750 gmol⁻¹, :; is determined to be 150920 Lmol⁻¹. For toluene at 20°C (293.15 K), LD and MD are 867.0 gdm⁻³ and 92.14 gmol⁻¹ respectively. The Gibb’s free energy of asphaltene adsorption onto gold from toluene at 20°C is thus calculated as -34.53 kJmol⁻¹. This value is very close to the value of 34.3 kJmol⁻¹ reported by Balabin et al. for an iron surface [27]. It also falls within the ranges reported for alumina and aluminasupported-nickel oxide nanoparticles [14,16]. However, our value is significantly more negative than that previously reported for a gold surface, which was -27 kJmol⁻¹ [20]. This is likely due to the fact that oxygen plasma cleaning rendered our gold surfaces hydrophilic.

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Interestingly, it has been shown that the average free energy of asphaltene association in toluene is -32 kJmol⁻¹ per asphaltene-asphaltene interaction for nanoaggregates of up to 5.2 molecules [28]. The similarity between the free energies of association in the bulk and adsorption at a surface is striking, however the significance of this finding is unclear. It may suggest that the thermodynamic driving force for adsorption largely comes from the formation of favourable asphaltene-asphaltene interactions rather than asphaltene-surface interactions. However the Gibb’s free energy of adsorption in this study was calculated from the Langmuir isotherm, a model which assumes that there are no lateral interactions between adsorbed molecules and that there is monolayer adsorption only. i.e. a model that is incongruous with a conclusion that adsorption is driven by asphaltene-asphaltene interactions.

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We used Filippov’s model for kinetic-diffusive-convective adsorption in flow cells [29], described in section S.8, to investigate whether our results could be fitted by the asymptotic solution for diffusion-controlled adsorption at short times. The adsorbed mass was plotted vs. the square root of time, see Fig. 4(a). If the rate of adsorption is diffusion-controlled, this relationship should be linear with slope (ℎ) given by:

Kinetics of adsorption inside a flow cell

) ⁄ ℎ = 28= P R 10 Q 29 30 31 32 33 34 35

where ) is the diffusion coefficient (m²s⁻¹). It is observed that at long times there is a deviation from linearity as the system approaches equilibrium. At very short times the relationship is non-linear, indicating that the initial rate of adsorption is not diffusion-controlled. (Note that the chosen flow rate in this work, as shown in section S.9, is sufficiently high to ensure that our adsorption process is not governed by mass transport.) This result is in agreement with Tavakkoli et al. [21] but in disagreement with other studies [26,30]. The disagreement with [30] might be due to differences in solvent quality (they used a 50:50 mixture heptane-toluene) and hence the asphaltene aggregation state in solution. As noted

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by Zahabi and Gray [31], Abudu and Goual [26] failed to account for lag time when calculating the diffusion coefficient and this explains the large discrepancy between their results and those obtained in our and other studies.

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At intermediate times the relationship between adsorbed mass and square root of time does appear linear. For the sake of comparison, the diffusion coefficients at different asphaltene concentrations were tentatively calculated by taking the slope of this linear portion of the graph, Fig. 4(b). The mean particle diameter was calculated by rearranging the Stokes-Einstein equation: )=

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ST T 11 6QV

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where ST is the Boltzmann constant (1.38 x 10⁻²³ m²kgs⁻²K⁻¹), T is temperature (K), V is the viscosity of the liquid (kgm⁻¹s⁻¹) and is the radius of the hard sphere (m). It is observed that, based on the assumption that the initial rate of adsorption is diffusion-controlled, the mean adsorbing particle size increases across the concentration range, see Fig. 4(c). The nominal values for the critical nanoaggregate concentration (CNAC) and the critical clustering concentration (CCC) as proposed by the Yen-Mullins model are also indicated on the graph. According to the Yen-Mullins model, the size of particles should not vary across the nanoaggregate range and it should only be the number of nanoaggregates that increases with increasing concentration. We do not observe this behaviour. Elsewhere, a similar trend of increasing particle diameter with concentration has been observed, i.e. the predicted diameters are not quantized for the different states of aggregation [31]. This is not surprising, particularly for extracted asphaltene which is made of molecules of various chemistry and thus is likely to exhibit a distribution of size even at the molecular level. We note that there are numerous sources of error associated with asphaltene particle size determination by the above method including: (i) incorrect supposition of diffusion-limited adsorption and (ii) approximating the hydrodynamic radius of asphaltene by that of a hard sphere, since asphaltene particles may be greatly solvated [32] and thus exhibit larger than expected diffusion coefficients.

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4.3

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The initial rate of adsorption provides important information that can be used to determine a rate law for asphaltene adsorption. For each concentration the initial period of the mass vs. time plot was fitted by a straight line, Fig. 5(a). The gradients of these lines were taken as the initial rates of adsorption. A log-log plot of initial rate vs. concentration of asphaltene was created, Fig 5(b). Such analysis, typically gives a linear relationship with gradient equivalent to the rate order with respect to concentration of the adsorbing species and y-intercept equivalent to log S/ , the rate constant for adsorption. In our case, however, this plot was not linear. We used a fourth degree polynomial equation to fit the data. The apparent rate order with respect to concentration of asphaltene, which corresponds to the instantaneous slope of the fit, decreases with increasing concentration. At low concentration, the value is 1.30, however, at high concentration the rate order is fractional, falling to 0.26 at the highest concentration of 10 gL⁻¹. This suggests that a simple rate equation cannot be used to describe the rate of adsorption for the entire concentration range tested.

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It must be noted that in these experiments S/ is not a rate constant for an adsorbing molecule or even nanoaggregate, but is an ensemble view of all adsorbing species present. It is expected that the ratio of nanoaggregates to molecules will increase with increasing concentration, however the exact distribution of asphaltene between molecule and aggregated states is not known. The aggregation of asphaltene was simulated using an equilibrium-based mathematical model developed by Acevedo et al. [33]. Using the

Initial rate of adsorption

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equations given in their paper and assuming a molecular weight of 750 Da, it is possible to estimate the concentration of free monomer (molecules) at different asphaltene concentrations, see section S.10 and Fig. S8. Interestingly, it is observed that plotting the initial rate of asphaltene adsorption vs. the concentration of monomer gives a straight line, see Fig. 5(c). The apparent rate order with respect to concentration of asphaltene monomer is 0.85.

6

4.4

The pseudo-first and pseudo-second order models

7 8 9 10 11 12 13 14 15 16 17 18

The adsorption of asphaltene onto gold was fitted using both the pseudo-first and pseudo-second order equations, see section S.8 for details. The linear forms of the pseudo-first and pseudo-second order equations, given by equations (S21) and (S23) respectively, are plotted in Figs. 6(a) and 6(b) respectively. In order to plot the pseudo-first order equation, the value of the equilibrium adsorbed mass, 57 , was approximated by the adsorbed mass at an adsorption time of 1 hour, 56 . The estimated values of 57 were subsequently improved by maximising the linear correlation coefficient, R² value. At the lowest concentration of 0.001 gL⁻¹ the data is suitably fitted by the pseudo-first order equation and a straight line is observed. The equilibrium adsorbed mass, 57 and the pseudo-first order rate constant, k₁, are found to be 510 ngcm⁻² and 9.11 x 10⁻⁴ s⁻¹ respectively. At higher concentrations the adsorption of asphaltene cannot be fitted by the pseudo-first order equation. It is observed that the plots are non-linear at initial time. Additionally, the values of 57 predicted by the model, being much lower than the experimentally measured mass after 1 hour, are clearly inaccurate, see Table 1.

19 20 21 22 23 24 25 26 27 28 29

The linear form of the pseudo-second order equation was also plotted, Fig. 6(b). Linear relationships are observed at concentrations of 0.01 to 1 gL⁻¹. At the lowest concentration of 0.001 gL⁻¹ the relationship is non-linear at initial times but linear at longer times. The initial non-linear part of this relationship was omitted during subsequent analysis to obtain the pseudo-second order rate constant S . Linear fitting of the lines gave correlation factors of 1.000 at high concentrations, see Table 1. It is concluded that at low concentration the kinetics of asphaltene adsorption are best described by the pseudo-first order equation, whilst at concentrations of 0.01 gL⁻¹ and over the pseudo-second order equation provides the best fit. The ratios of S ⁄S were determined for each concentration, see Table 1. It is observed that at a concentration of 0.001 gL⁻¹ the ratio of S ⁄S is greater than the equilibrium adsorbed mass, whilst at higher concentrations the opposite is observed. As noted by Liu and Shen [34], this explains why there is a change in the model that best describes the adsorption with increasing concentration.

30 31 32 33 34 35 36 37 38 39 40 41

We make the time at which rinsing the adsorbed film with toluene is commenced, trinse, equivalent to 0 s. The pseudo-first and pseudo-second order equations are thus plotted for the desorption of asphaltene from the gold surface. The pseudo-first order equation is unable to fit the data (not shown), whilst the pseudo-second order equation gives a good fit for all concentrations, see Fig. S9. The predicted equilibrium adsorbed masses before toluene rinsing (crosses) were found to be in good agreement with the experimentally measured values (solid circles), see Fig. 6(c). The only exception was at the lowest concentration of 0.001 gL⁻¹ where it is known that equilibrium was not reached within the adsorption time of 1 h. The predicted 57 values after toluene rinsing (pluses) are similar to those that were measured experimentally (open circles). It is noted that plotting mass lost as a function of rinsing time does not provide a linear relationship using the pseudo-second order equation. Hence, the rate of desorption is dependent on the adsorbed mass present at trinse and the adsorption history must be taken into account when fitting desorption data.

42 43

The calculated pseudo-second order rate constants for both the adsorption and desorption are plotted as a function of asphaltene concentration, Fig. 6(d). As the concentration of asphaltene increases from 0.001

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to 0.1 gL⁻¹ the rate constant for adsorption increases. However, when the concentration is further increased to 1 gL⁻¹, the rate constant decreases. The reason for this is not known, however, it is postulated that it may be due to a change in the state of the adsorbing species either from monomer to nanoaggregate or from nanoaggregate to cluster. It might also be a mixture of aggregates of various sizes. According to the Yen-Mullins hierarchical model for asphaltene assembly it is expected that the critical nanoaggregate concentration (CNAC) will be 0.1 gL⁻¹ and the critical clustering concentration (CCC) will be ~3 gL⁻¹ [7]. Hence, a change in state of asphaltene is likely for the range of concentrations investigated. The rate constants for desorption generally decrease with increasing concentration. However, the rate constant for desorption at 1 gL⁻¹ is similar to that at 0.1 gL⁻¹.

10 11 12

It has been shown that in cases where diffusion affects the rate of adsorption, there is deviation from linearity exhibited as a downward curvature at initial times in the ⁄51 vs. plot [35]. In our results we see no such behaviour which further confirms that the rate of asphaltene adsorption is not diffusion-limited.

13

4.5

14 15 16 17 18 19 20 21

The asphaltene stock solutions were stored in a dark cupboard at room temperature (21°C) for a period of 75 days. After this time, the adsorption experiments were repeated. As shown in Fig. 7(a), there is a change in the shape of the adsorption profile due to aging of the asphaltene stock solution (open squares); the kinetics of adsorption are slower as compared to adsorption observed with a freshly made solution (solid squares). However, further aging for a total of 127 days (crosses) caused no subsequent measurable change in the adsorption profile. The effect of solution aging is observed in all test solutions used. Notably, the initial rate of adsorption is significantly slower for aged solution of low asphaltene concentration (Fig. 7(b)).

22 23 24 25 26 27 28 29 30

Results in Figs. 7(a) and 7(b) suggest that solution aging is complete within 75 days, and indeed may occur within a much shorter time. During the 75-day incubation period, solution equilibration causing a redistribution of asphaltene between monomer and aggregated states is likely to have occurred. Other possible effects include chemical changes, for example oxidation or contamination by water or other impurities from the atmosphere. Solvent evaporation may occur, but this in itself cannot explain the observed effect since evaporation of toluene would lead to an increase in asphaltene concentration and the reverse trend would be expected, i.e. an increase in the rate of adsorption upon aging. n.b. Care was taken to tightly seal the bottles containing the stock solutions, yet some evaporation may occur, not least when the bottle is periodically opened to remove a sample.

31 32 33 34 35 36 37 38 39 40 41 42 43

Nine repeat experiments were made at a concentration of 0.01 gL⁻¹. It is found that the adsorbed mass depends on the sensor used, see circles for sensor Y vs. others from sensor X in Fig. 7(a). However, when different experiments made using the same sensor were compared, the repeatability was good, see for example data from Sensor X, 75 days and 127 days (open squares and crosses) in Fig. 7(a). This suggests that the observed discrepancies are not due to inconsistencies in sensor cleaning. The reproducibility of the results are further confirmed in Fig. 7(c) where the effect of adsorption time on the kinetics of asphaltene removal by toluene-rinsing was investigated using sensor Y. Elsewhere, similar analysis has permitted elucidation of adsorption kinetics for systems where the mechanism is 2-step involving reversible and irreversible binding or a molecular reorganisation (changing-footprint) [36,37]. It is observed that all four tests overlap during the asphaltene adsorption stage, supporting the experimental protocol gives good reproducibility. Note the rate of asphaltene removal from the sensor depends on the adsorption time. At a short adsorption time of 200 s (solid triangles, Fig. 7(c)) the rate of asphaltene removal is considerably slower than at longer adsorption times. This suggests that the composition or

Effect of asphaltene solution aging and sensor surface

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nature of binding within the asphaltene film changes with time. The observed behaviour is fitted by the kinetic reaction-diffusion model in section 4.6.

3

4.6

4 5 6 7

Numerical experiments are carried out using the reaction-diffusion model described in section 2. The computations simulate the aging of the solution from 1 gL⁻¹ stock solution, the adsorption experiments and the effect of rinsing with pure solvent simultaneously. The concentration and running times correspond to the experiments presented in section 4.5.

8 9 10

The model is exercised with two different mechanisms, corresponding to different hypotheses on the behaviour of the system studied and on the steps of the adsorption process. Both mechanisms studied involve only two bulk species, with molecular mass ratio 2. The corresponding reaction is

Numerical Prediction of Asphaltene Adsorption

2 ⇌ 12 11 12 13

and describes the equilibrium between lighter and heavier aggregates in the bulk solution. The existence of a bulk equilibrium with a characteristic time in the order of 10Z seconds is suggested by the effect of solution age on adsorption histories.

14 15 16 17 18 19

The mechanisms postulate the existence of two adsorbed forms of the species , namely the species ∗ and the species [∗ . A similar hypothesis is applied to the adsorption of the species : which can exist on the surface in two forms, ∗ and [∗ . The ∗ and the [∗ species although chemically identical are bound to the surface in different ways and their adsorption and desorption take place over different time scales. The existence of species with different release time constants is suggested by the drastically different rates of adsorption and desorption in the rinsing experiments (Fig. 7(c)).

20 21 22

An additional species [ ∗ is introduced to represent the growth of a bi-layer on top of a tightly adsorbed monolayer. The existence of a multi-layer is required by the results of the high-concentration experiments which suggests the adsorbed mass value is affected by bulk concentration, see Fig. 2.

23 24 25 26 27

The upper limit for the adsorption site concentration ["] is set by assuming that adsorption sites correspond to the size of lattice cells. If a cell area of 0.17 nm² is used, the maximum site concentration is approximately 1 nmolcm⁻². QCM data suggest that 0.6 nmolcm⁻² for sensor X and 0.45 nmolcm⁻² for sensor Y are appropriate values. This difference can be justified by differences in the gold plated area of the two crystals.

28 29 30 31 32 33 34

Two surface mechanisms are proposed, denoted hereafter as M1 and M2, shown in Tables 2 and 3. The mechanisms postulate similar dynamics for the bulk and for the adsorption of the light compounds, but postulate different paths for the adsorption of heavier compounds. In mechanism M1, the adsorption of takes place in two sequential steps, first R5, then R6, similarly to the adsorption of the lighter aggregates . Mechanism M2 allows two parallel paths (R5 and R7 concurrently) for the adsorption of . One leads eventually to the formation of a strongly bound layer (R7), the other stops with the formation of a loosely adsorbed layer (R5).

35 36

In addition to mechanisms M1 and M2, alternative mechanisms have been considered containing the surface recombination reaction in addition to reactions R1-R6: R8

2∗

⇌

∗

Surface recombination

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1 2

This mechanism, however, does not result in realistic predictions of the post-rinse adsorbed mass and will not be discussed further.

3 4 5 6 7 8

The forward and backward rate constants, S\ and S] respectively, for the two mechanisms M1 and M2 are obtained as best fits to the experimental data and are reported in Tables 4 and 5. The fit is based on a genetic algorithm by minimising the mean-square error between the predicted and measured adsorbed mass over the entire histories of all available experiments. The constants for all reactions of each mechanism are optimised simultaneously. For the purpose of parameter fitting, the QCM data are lowpass filtered.

9 10 11 12 13

The simulations also produce histories of surface and bulk concentrations of each species and adsorption site concentration. Histories of adsorbed mass are presented in Fig. 8 (lines) together with the corresponding experimental histories for various solution concentrations and stock ages (symbols). Detailed histories showing the composition of the adsorbed layer with time during the experiments are presented in Fig. 9.

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

The two mechanisms produce similar predictions for the adsorbed mass, but rather different predictions for the composition of the layer adhering to the crystal. The adsorption path for the species and its subsequent fixation is responsible for the shape of the adsorption curves for aged, low concentration -1 (0.01 g L ) solutions see Figs 9(a) and (b). The adsorption mechanisms predict that the species is quickly adsorbed to form a loosely adsorbed species ∗ (pluses). The loosely adsorbed species ∗ then is transformed into the strongly adsorbed species [∗ (crosses). For most experiments, only a relatively small quantity of ∗ is found on the crystal after approximately 10^ seconds from the start of the adsorption experiment. The different time constants for the adsorption of ∗ (R1) and the fixation reaction (R3) cause the surface concentration of ∗ to reach a maximum and then to decrease gradually. Upon rinsing, the remaining loosely bound species ∗ is released back into the pure solvent stream. The desorption time of the loosely bound species is in the order of 10 seconds. The gradual decrease in the amount of ∗ explains why in experiments at the same concentration, but rinsing at different times, the drop in adsorbed mass is sharper when the crystal is rinsed earlier, see Fig. 10. Mechanism M2 predicts that part of the adsorbed film is a bilayer (solid squares, Fig. 9(b)). Mechanism M1 predicts that no bilayer forms, and the heavy species in the adsorbed films are adsorbed dimers (open squares, Fig. 9(a)).

29 30 31 32 33 34 35 36 37 38 39 40

At higher concentrations (0.1 g L ), Figs. 9(e) and (f), a significant amount of heavier compounds are present in the solution and these compounds contribute the largest portion of the adsorbed mass. Furthermore, the rapid adsorption of heavier compounds (∗ and [∗ for M1 and M2 respectively) also accounts for the high initial adsorption rate seen at high concentration solutions. It is interesting to note that mechanisms M1 and M2 provide two different explanations for the drop in adsorbed mass upon rinsing. Mechanism M1, Fig. 9(e), predicts that the species ∗ (asterisks), the main component of the adsorbed film, is strongly bound to the surface and slowly converted into [∗ (open squares). Neither ∗ nor [∗ are released from the surface of the sensor upon rinsing and the drop in adsorbed mass is attributed to the removal of the bilayer [ ∗ (solid squares). Mechanism M2, Fig. 9(f), on the contrary, shows that [∗ is the main component of the adsorbed film with ∗ and [∗ reaching an equilibrium quickly during adsorption. The loss in adsorbed mass during rinsing is attributed to the removal of the species ∗ and predicts the formation of very small amounts of bilayer.

41 42 43

Both mechanisms reproduce the correct effect of aging on the initial adsorption rate and adsorbed mass prior to rinsing, Figs. 8 and 10. The effect of aging is shown clearly by comparing the adsorption and -1 desorption histories for experiments at concentration 0.01 g L and using stocks aged for 89 days (Figs.

-1

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9(a) and (b)) and 6 days (Figs. 9(c) and (d)) on sensor X. For low-concentration experiments, models M1 and M2 produce fairly close results in terms of adsorbed mass but return different pictures for the composition of the adsorbed layer. When applied to younger stock, the adsorbed mass is dominated by the compounds ∗ (asterisk, Fig. 9(c)) for mechanism M1; and [∗ (open squares, Fig. 9(d)) for mechanism M2. The momomers (∗ and [∗ , pluses and crosses respectively) as well as the bilayer ([ ∗ , solid squares) seem to contribute little. Neither model predicts complete saturation of the surface during experiments with young stock (see concentration of sites, open circles). In general asphaltene adsorption from a young, low concentration solution resembles that from high concentration solutions (Fig. 9(e) and (f)). Adsorption from aged low concentration stock produces closer behaviour between the models, mainly because the adsorption rates are dominated by the lighter species (∗ and [∗ , pluses and crosses respectively in Figs. 9(a) and (b)). These findings show that the observed sensitivity of the adsorption experiments to the age of the solution can be attributed to a bulk equilibrium between species which are adsorbed at different rate. It also shows that, if the measured results are a consequence of such equilibrium, the lighter species become more abundant in the bulk of the aged stock keeping concentration constant. Both models predict that the equilibrium in toluene is favourable to the monomer species (:7+ ≈ 10B at low concentration and is established in approximately 10Z seconds. A summary of the predictions of asphaltene adsorption behaviour based on mechanisms M1 and M2 is presented in Table 6.

19 20 21 22 23 24 25 26 27 28

A change in the properties of the adsorbed layer with time can also be inferred by the ratio Δ) /Δb for -1 the overtones = 3,5,7,9, as shown in Fig S10. The conditions shown are (a) 0.01 g L , 133 days stock, -1 -1 -1 sensor X; (b) 0.1 g L , 5 days stock, sensor X, (c) 0.01 g L 6 days stock, sensor X; (d) 0.01 g L 133 days stock, sensor Y. In all sets of data, Δ) /Δb varies with time. This phenomenon can be interpreted as indicating a gradual change in the properties of the adsorbed layer. Such a change, in the numerical models, takes place because of the rearrangement reactions ∗ → [∗ and because of the formation of multilayers at a rate different from the formation rate of the monolayers. Furthermore, it can be seen that data obtained with stocks of similar age, e.g. graphs (a),(d) and graphs (b),(c) have similar shape, but this shape changes with age. This is further confirmation that the properties of the solution vary with time, and that the properties of the solution influence both the adsorption rate and the nature of the adsorbed layer.

29

5.

30 31 32 33 34 35 36

Since asphaltene is not a single molecular species but a class of molecules containing different chemistries in different states of aggregation from monomer to nanoaggregates to clusters, determination of the kinetics of processes such as surface-adsorption is more complicated than typically encountered in simple systems containing only one species. The possibility of diffusion-limited adsorption further complicates kinetic analysis. Fortunately, in our test conditions, the observed rate of adsorption is not diffusion-limited. This means that we are able to draw some insightful conclusions on how the state of asphaltene affects its adsorption behaviour.

37 38 39 40 41 42 43 44

The initial rates of adsorption were determined for a concentration range of 0.001 to 1 gL⁻¹. A log-log plot of initial rate vs. concentration revealed a non-linear relationship, effectively suggesting that the rate order with respect to concentration of asphaltene decreases with increasing concentration. It is postulated that a change in the state of asphaltene in the bulk was responsible for this observed behaviour. Let’s assume that at a concentration of 0.001 gL⁻¹ all the asphaltene exists as monomer. We then double the concentration of asphaltene to 0.002 gL⁻¹. If there is no change in the state of asphaltene we expect that the rate of adsorption will be doubled, since the concentration of monomer is two times its original value. If we now assume that at a concentration of 0.002 gL⁻¹ all the asphaltene forms dimer we can only expect

Discussion

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that the rate of adsorption will be equivalent to that observed for monomer at the same bulk concentration if the rate at which a dimer adsorbs is equivalent to the rate at which a monomer adsorbs. This is owed to the fact that there will be half the number of adsorbing species but that each species will contribute two times the mass. Since the rate order with respect to concentration of asphaltene decreases with increasing concentration, see Fig. 5(b), we conclude that the rate at which aggregates adsorb is slower than the rate at which monomers adsorb. Other studies have found a similar trend [15,38]. Furthermore, plotting the initial rate of adsorption vs. the predicted concentration of monomer on a log-log plot, Fig. 5(c), yields a straight line suggesting that the initial rate of adsorption depends on the concentration of free monomer.

10 11 12 13 14 15 16 17 18

The reason why a nanoaggregate would adsorb at a slower rate than a single molecule is not clear. It is postulated that within the asphaltene molecular structure there will be particular groups capable of forming specific asphaltene-surface interactions. These surface-active groups will likely contain heteroatoms such as oxygen, nitrogen and sulphur. Alternatively, surface interaction may be via the π electrons of the polycyclic aromatic core. At higher concentration the asphaltene molecules will selfassociate. Self-association is expected to occur principally via π-π stacking of the central polycyclic aromatic cores, however, it is possible that polar interactions may form between the heteroatom containing groups [39]. These intermolecular interactions could limit the availability of these groups for forming surface interactions which may reduce the propensity for surface adsorption.

19 20 21 22 23 24 25 26 27 28 29 30

It is also not known whether an adsorbing nanoaggregate will hold its structure or will disassociate at the surface to yield a monolayer. In fact, a ‘monolayer’ of nanoaggregates may or may not be a monolayer of molecules. Arguably adsorption of the nanoaggregate ‘side-on’ with long-axes of the polycyclic aromatic cores perpendicular to the surface would yield a true monolayer of molecules. On the other hand, adsorption of the nanoaggregate with the planar polycyclic aromatic cores parallel to the surface, as in a stack of pancakes, would yield a multilayer film with number of layers equivalent to the number of molecules within the nanoaggregate. Rudrake and Rudrake et al. reasoned from QCM and XPS data that, given an apparent film thickness of 6–8 nm, the likely arrangement was edge-on or ‘vertical’ [40,20]. Based on reported literature values [41,42,43,44,45], we adopt an asphaltene density of 1.2 gcm⁻³ and estimate that the thickness of the adsorbed asphaltene film in our study varies with concentration from 47 nm, see Table 7. This assumes that the density of asphaltene in the thin adsorbed film is similar to its value in the bulk.

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

The area per molecule can be estimated by assuming a molecular mass of 750 gmol⁻¹ (this value is taken from the Yen-Mullins model [7]). For a monolayer film, the area per molecule is determined to be 15.5 Å². This value is significantly lower than the values reported in the literature for extracted asphaltenes, which range from 100 to 400 Å² [46,47,48]. It has been observed that the area per molecule of asphaltene at the hydrocarbon-water interface is constant with increasing concentration, whilst the apparent molar mass of asphaltene increases with concentration, suggesting higher degrees of self-association [46]. This suggests that associated or “aggregated” asphaltenes stack parallel to the surface, since the area occupied by an edge-on species would depend on the number of molecules within the aggregate. Studies of model asphaltene molecules with known chemical structures at the oil-water and air-water interfaces have shown that the preferred orientation depends on the chemistry of the asphaltene molecules [49,50,51]. One perylene bisimide model asphaltene displayed an apparent area per molecule that was much smaller than expected based on all possible orientations. Additionally, the surface pressure-area isotherm exhibited distinct steps; this indicated that the molecules were stacking with their polycyclic cores parallel to the surface, i.e. multilayer formation [49]. Given, the unacceptably small area per molecule, we can conclude that despite the fact that the Langmuir adsorption isotherm provides a good fit

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Energy & Fuels

for the experimental data, we in fact have a multilayer film. In light of this the question then becomes: what is the significance of the maximum adsorption capacity, 59 ? Assuming a molecular area of 100 Å² the number of layers on the surface at 59 is calculated to be 7, similar to the number of asphaltenes within a nanoaggregate. Whilst potentially coincidental, we find an argument that 59 corresponds to the mass of a complete ‘monolayer’ of nanoaggregates very attractive. At even higher solution concentrations, beyond those tested in this study, there will likely be further growth beyond the value of 59 reported here, as observed previously [52].

8 9 10 11 12 13 14

It is interesting to note that in addition to the proportion of free monomer decreasing with increasing concentration (Fig. S8 and [33]), the ensemble chemical make-up of free monomer may also change with increasing concentration. It has been shown that asphaltene molecules containing polar groups are the most unstable, i.e. precipitate with the smallest volume fraction of heptane [13]. In a similar way a particular subset of asphaltene structures with specific functionality may be the first to self-associate at high concentration. These molecules would preferentially form nanoaggregates and clusters meaning that the chemistry of the residual free monomer fraction is altered.

15 16 17 18 19 20 21 22 23

It may be expected that the activity of the free monomer fraction would decrease with increasing concentration. However, this view is very simplistic and the real behaviour may be further complicated by additional effects such as co-solubilisation [53,10]. In particular, a decrease in the chemical heterogeneity of asphaltene monomer with increasing total asphaltene concentration would lead to an increased thermodynamic driving force for aggregation and surface adsorption [54]. The striking difference in the solubility of chemically monodisperse and chemically polydisperse samples of asphaltene has been observed previously, with the former undergoing a sharp and complete precipitation near the onset of precipitation and the latter undergoing a very gradual precipitation with increasing volume fraction of precipitant [55].

24 25 26 27 28 29 30 31 32 33 34 35

In this study we find that determination of the kinetics of asphaltene adsorption is convoluted by the fact that there is a change in the adsorption behaviour with aging of the stock solutions. At low concentration the initial rate of adsorption is significantly reduced by aging, see Fig. 7(b). Whilst at a high concentration of 1 gL⁻¹, the aged solution displays a slightly higher initial rate of adsorption. The explanation for this behaviour is that aging of the stock solution resulted in a redistribution of asphaltene between monomer and aggregated states. Given the previously drawn conclusion, that monomer adsorbs at a faster rate than aggregates, it follows that the aged solutions at low concentration contains a smaller proportion of monomer and larger proportion of aggregates. However, we must instinctively question whether this seems plausible. Whilst it is readily accepted that the aged solution will be fully equilibrated whereas the young solution is not, we do not know the respective distributions of asphaltene for these two cases. We must therefore question whether it is more likely that the degree of aggregation is either increasing or decreasing with time.

36 37 38 39 40 41 42 43 44

Given that the starting point of the stock solution was dissolution of an asphaltene solid precipitated with an excess of heptane, we believe it is most likely that the degree of aggregation is decreasing with solution age. This casts aspersions on the validity of the conclusion that monomers adsorb at a faster rate than aggregates. Perhaps thinking in terms of the respective numbers of monomer and nanoaggregate is too simplistic. We cannot really assign a rate constant for an adsorbing monomer nor a nanoaggregate. The nature of asphaltene tells us that not all monomers are equivalent. Neither are all nanoaggregates. The chemical make-up or composition of the monomer and nanoaggregate fractions is a function of concentration as are their respective numbers. The log-log plot of initial rate vs. predicted monomer concentration gives straight lines for both the young (non-equilibrated) and aged (equilibrated) solutions,

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insert of Fig. 7(b). However, the equations for these lines are very different; the apparent rate order with respect to concentration of monomer increases from 0.85 to 1.54 with solution equilibration. We believe that the initial rate of adsorption is not only dependent on the concentration of free monomer, but also on other factors that are inherently linked to this variable.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Our reaction-diffusion model shows that at high concentration, both heavier species and lighter species adsorb simultaneously at initial times, see Figs. 9(e) and (f). Hence, the initial rate of adsorption would depend on the concentrations of both these species. Use of the predicted monomer concentration, as defined by Acevedo [33], simply allows us to adjust for the observed effect that the activity of asphaltene does not increase linearly with its concentration. The kinetic reaction-diffusion model describes how the kinetics of adsorption are affected by polydispersity of adsorbing species. The rate constants do not provide real values for adsorption of monomer and dimer, but are representative of a lighter particle and a heavier particle with different adsorption rate constants. The two different mechanisms proposed in section 4.5 are both able to reasonably describe the adsorption histories, however M1 provides a better fit (see Tables S6 and S7). This model suggests that the initial weakly adsorbed species, ∗ , quickly undergoes a transition to form a strongly bound species, [∗ . This may be a rearrangement, reorientation or change in the binding mechanism. Upon rinsing with toluene, a fraction of the adsorbed mass is readily removed from the surface. One of the species responsible is the loosely adsorbed monomer ∗ . The other species are the bilayer [ ∗ (in mechanism M1) or the dimer ∗ (in mechanism M2), see Fig. 9. This emphasises the role of asphaltene-asphaltene interactions within adsorbed films and how this can contribute to formation of strongly and irreversibly adsorbed films which lead to fouling problems. The model allows us to explain observed adsorption histories in terms of a redistribution of asphaltene in the bulk solution due to aging. This indicates that the time required for equilibration of asphaltene in toluene is c. 12 days, an important observation for future studies.

24 25 26 27 28 29 30

Finally, we find that different gold QCM sensors acquired from the same supplier and cleaned using the same method display different adsorption behaviours. The reason for this not known, however, in our model it can be explained by a change in the surface concentration of adsorption sites. Of course this observation would have implications if this work were to be extended to investigate the effect of surface type. For such a study it would be difficult to firmly conclude that changes in the kinetics of adsorption and maximum adsorption capacity are truly due to surface chemistry, particularly if the effect of surface type/chemistry is relatively small compared to the inherent variability of sensors.

31 32 33 34 35 36 37 38 39 40 41 42 43

In summary, asphaltene aggregation and surface adsorption are complex phenomena due to the heterogeneity of asphaltene’s chemical makeup, geometry and size. As asphaltene solution ages, the distribution of aggregates in the bulk, both in terms of size and chemistry, evolves. This means that the surface reactivity of monomers and aggregates, and aggregate stability in solution change with time. These dynamics and the effect of bulk asphaltene distributions are reflected in this work as the initial rates of asphaltene adsorption vary with the age of low concentration asphaltene solutions. Our reactivekinetic model, which simplifies the bulk asphaltene distribution to only two species that have a mass ratio of 1:2, supports that our experimental results are indeed altered by the bulk asphaltene distribution. Our model also suggests that the bulk asphaltene distribution impacts on the nature of the adsorbed layer, with younger and more concentrated asphaltene solutions giving rise to adsorbed layers that are composed of heavier species. The ease of removal of adsorbed asphaltene depends on the asphalteneasphaltene interactions within the adsorbed film and these interactions contribute to the formation of strongly and irreversibly adsorbed films.

44

6.

Conclusion

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A quartz crystal microbalance was used to monitor in situ the adsorption of asphaltene from solution in toluene onto a gold surface inside a flow cell at ambient temperature and pressure. For these experiments a flow rate of 6 µLs⁻¹ was sufficient to prevent mass-transport-limited adsorption. The initial rate of adsorption and the maximum adsorbed mass increased with increasing concentration. It was found that the rate order with respect to total concentration of asphaltene was not constant across the concentration range, decreasing from unity at low concentration to 0.3 at high concentration. On the other hand, the rate order with respect to concentration of asphaltene monomer was 0.85 and constant across all tested concentrations. The decrease in rate order with respect to total concentration of asphaltene with increasing concentration indicates that the rate of monomer adsorption is greater than that of aggregates.

10 11 12 13 14

A portion of the adsorbed asphaltene was easily removed by rinsing with toluene. However, a larger proportion was strongly (or irreversibly) bound, and the rate of desorption of this portion was very slow and continued beyond the toluene-rinsing time of 1 hour. The maximum adsorption capacity based on experiments over a wide concentration range from 0.001 to 1 gL⁻¹ suggests a monolayer coverage by aggregates of c. 7 molecules.

15 16 17 18 19 20 21

A kinetic reaction-diffusion model was used to model the adsorption of asphaltene onto gold and its subsequent desorption via toluene-rinsing. The model indicates that initially asphaltene monomer adsorbs to form a loosely bound state. These loosely bound molecules are relatively short lived, either being immediately desorbed or participating in further reactions to yield a strongly bound state. These reactions may be adsorbed monomer-monomer interactions or a molecular rearrangement. The rate of desorption of strongly bound asphaltene is very slow and explains why a large portion of the adsorbed asphaltene film cannot be easily removed by rinsing with toluene.

22 23 24 25 26 27

Long-time aging of the asphaltene stock solutions in toluene led to a decrease in the initial rate of adsorption, changing the observed kinetics. This was captured by the kinetic reaction-diffusion model and could be explained by an equilibration between monomer and multimer (aggregated) species in the bulk liquid, which affects the adsorption kinetics. This study shows that asphaltene aging in pure toluene, i.e. without the presence of an asphaltene precipitant such as heptane, does occur and must not be overlooked.

28 29 30 31

Acknowledgement The authors would like to acknowledge the funding and technical support from BP through the BP International Centre for Advanced Materials (BP-ICAM) which made this research possible.

32

Supporting Information. Supporting information is provided as one document with the following content:

33

S.1 Details of the QCM experiments

34

S.2 Extracted asphaltene solution preparation

35

S.3 Determination of the physical properties of the asphaltene solutions

36

S.4 Asphaltene size distribution in toluene solutions

37

S.5 Sensor surface characterisation by AFM

38

S.6 Typical QCM response

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1

S.7 Fitting with Freundlich adsorption isotherm

2

S.8 Existing models to describe adsorption kinetics

3 4

S.9 Preliminary study of asphaltene adsorption in flow cellS.10 Estimation of monomer concentration in asphaltene solution

5

S.11 Modelling asphaltene desorption with pseudo second order equation

6 7

S.12 Root mean square (RMS) error for models M1 and M2 with respect to the experimental measurements

8

S.13 A change in the properties of the adsorbed layer with time as shown by the ratio Δ) /Δb

Page 18 of 28

9 10

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Energy & Fuels

1 2

Figures and Tables for “Determining the kinetics of asphaltene adsorption from toluene; a new reaction-diffusion model”

3

Sophie Campen , Luca di Mare , Benjamin Smith , Janet S. S. Wong

4

1

5 6

2

7

*Corresponding Author: [email protected]

1

1

2

1*

Department of Mechanical Engineering, Imperial College London, UK SW7 2AZ

BP Exploration Operating Company Limited, Chertsey road, Sunbury on Thames, Middlesex, UK TW16 7BP

8

9

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1 2

Page 22 of 28

Figure 1. Schematic of the reaction-diffusion adsorption mechanism. For details of the reactions see section 4.6.

3

4 5 6

Figure 2. (a) Adsorbed mass vs. time for asphaltene in toluene on gold (sensor X), arrow at 3600 s indicates toluene-rinsing; (b) adsorbed mass before and after 1h toluene rinsing.

7 8 9

Figure 3. Adsorption of asphaltene onto gold from solution in toluene: (a) Type I isotherm; (b) Langmuir adsorption isotherm with insert log-log plot showing monomial fitting of Langmuir isotherm.

10

11

22


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1 2 3 4 5

Energy & Fuels

Figure 4. Consideration of diffusion-limited kinetics: (a) graph showing adsorbed mass vs. square root of time; (b) linear fitting of adsorbed mass vs. square root of time to obtain slopes for the calculation of diffusion coefficients; and (c) adsorbing particle size predicted by Stokes-Einstein equation with dashed lines indicating the critical nanoaggregate concentration (CNAC) and critical clustering concentration (CCC) suggested by the Yen-Mullins model [7].

6

7 8 9 10 11

Figure 5. (a) Adsorbed mass vs. time focusing on the linear region used to find initial adsorption rate; (b) the initial adsorption rate obtained from (a) is used to determine the rate order (i.e. the slope) with respect to total concentration of asphaltene; (c) log-log plot showing initial adsorption rate vs. predicted monomer concentration.

12

13

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1 2 3 4

Page 24 of 28

Figure 6. Adsorption of asphaltene onto gold is plotted based on (a) the pseudo-first order equation and (b) the pseudo-second order equation; (c) the experimentally observed mass and the equilibrium mass (57 ) predicted by the models before and after toluene rinsing; (d) calculated pseudo-second order rate constants, S against bulk asphaltene concentration.

5

6 7 8 9 10 11

Figure 7. Repeatability of QCM experiments: (a) effect of sensor and stock solution age on adsorption profile at a concentration of 0.01 gL⁻¹; (b) effect of aging of stock solutions on the relationship between the initial rate of adsorption and total concentration of asphaltene; insert shows the relationship between initial rate and concentration of monomer in log-log scale; and (c) experiments made at 0.01 gL⁻¹ with sensor Y showing effect of adsorption time on desorption behaviour.

12

13 14 15

Figure 8. Adsorbed mass histories for mechanisms (a) M1 and (b) M2. The age of the solutions are shown in brackets. Lines are from simulations and symbols are experimental results.

16 17

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1 2 3 4 5

Figure 9. Computed surface concentrations of adsorbed species from fitting of adsorption data by -1 -1 mechanisms M1 (left) and M2 (right): (a) and (b) 0.01 gL , 89 day stock, sensor X; (c) and (d) 0.01 gL , 6 -1 day stock, sensor X; (e) and (f) 0.1 gL , 5 day stock, sensor X. Black arrows indicate when toluenerinsing commenced.

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Page 26 of 28

1 2 3

Figure 10. Adsorbed mass histories for mechanisms (a) M1 and (b) M2. The time at which rinsing commenced is shown in brackets. Lines are from simulations and symbols are experimental results.

4 5

Table 1. Parameters predicted by pseudo-first and pseudo-second order models for sorption of asphaltene on gold Pseudo-first order C q1h (gL⁻¹) (ngcm⁻²)

Pseudo-second order -

k₁ (× 10 Gradient qₑ Intercept R² -4 (× 10 ) (ngcm⁻²) 4 s⁻¹)

Gradient Intercept -4 (× 10 )

R²

qₑ k₂ (× 10 (ngcm⁻² 5 k₁ / k₂ s⁻¹) )

1

787.2

-7.85

4.87

0.87 129.9

7.85

12.49

0.11

1.00

800.6

1.39

56.4

0.1

709.2

-23.4

5.16

0.93 173.4

23.4

13.91

0.05

1.00

718.9

3.77

62.0

0.01 597.7

-16.3

5.34

0.92 209.1

16.3

16.35

0.14

1.00

611.6

1.94

84.1

0.001 467.6

-9.11

6.23

1.00 509.8

9.11

11.92

2.39

0.99

839.1

0.059

1534. 4

6 7 8

Table 2. Adsorption reaction mechanism M1 R1 R2 R3 R4 R5 R6

2

" + ∗

+ [∗

∗ + 2"

⇌

Bulk equilibrium

⇌

[∗

Fixation of ∗

⇌ ⇌ ⇌ ⇌

∗

Site-specific adsorption of

[∗

Multi-layer formation

[∗

Site-specific fixation of ∗

∗

Site-non-specific adsorption of

9

26


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

Energy & Fuels

Table 3. Adsorption reaction mechanism M2 R1 R2

2

" +

R4 R5 R7

Bulk equilibrium

⇌

[∗

Fixation of ∗

⇌

∗

R3

⇌

∗ + [∗

⇌

⇌

+ 2"

∗


[∗

Multi-layer formation

[∗


∗

⇌

Site-non-specific adsorption of

2 3

Table 4. Rate constants for mechanism M1 kd

ke

R1

2.4

× 10f

nmolf cm^ s f

1.3

R2

3.4 × 10fk

nmolf cm s f

8.9 × 10f^ s f

R3

2.3

R4

1.9 × 10fB

nmolf cm s f

9.2 × 10fZ s f

R5

4.7 × 10=

s f

1.1 × 10fB s f

R6

2.7 × 10f^

nmolf cmk s f

2.5

× 10f^ s f

× 10fZ s f

1.9 × 10fk s f

s f

4 5

Table 5. Rate constants for mechanism M2 kd

ke

R1

9.3

× 10f

nmolf cm^ s f

7.2

× 10fl s f

R2

1.6

× 10fk

nmolf cm s f

1.4 × 10f^ s f

R3

1.2

× 10f^

s f

1.2 × 10fk s f

R4

1.4

× 10fB

nmolf cm s f

5.4 × 10fZ s f

R5

2.5

× 10f^

s f

5.4 × 10fZ s f

R7

2.0

× 10fB

nmolf cmk s f

1.6 × 10f s f

6 7 8

Table 6. Predictions of asphaltene adsorption behaviour based on models M1 and M2 Solution State Low

Mechanism M1

∗ slowly converts to [∗

Mechanism M2

∗ slowly converts to [∗

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concentration, aged solution

(Figs. 9(a), (b)) Low concentration, young solution (Figs. 9(c), (d)) High concentration

∗ is released upon rinsing. [∗ is the heavier species left on the crystal after rinsing; no bilayer [ ∗ observed.

∗ dominates the adsorbed mass. Adsorption behaviour resembles that of high concentration solution. " is not completely consumed.

slowly converts to Both ∗ and [∗ adsorb strongly. [ ∗ is removed upon rinsing.

(Figs. 9(e), (f))

∗

[∗ .

Page 28 of 28

1 2 3 4

∗ is released upon rinsing. [ ∗ is the main heavier species. It represents a bilayer grows on top of a monolayer of lighter species [∗ . [∗ dominates the adsorbed mass. Adsorption behaviour resembles that of high concentration solution. " is not completely consumed. ∗ and [∗ quickly reach equilibrium. [∗ remains while ∗ is removed upon rising. Only small amount of [∗ exists.

Table 7. Asphaltene film thickness and area per molecule calculated from areal mass Number of layers assuming area per molecule Area per molecule d d C qₑ Thickness 48.3 Å² 31.2 Å² d for a 130.6 Å² 100 Å² 400 Å² (gL⁻¹) (ngcm⁻²) (nm ) monolayer c c Edge-on End-on b Flat perylene (Å² ) perylene perylene qm*

804.1*

6.70

15.5

6.46

25.83

8.43

3.12

2.01

1

800.6

+

6.67

15.6

6.43

25.71

8.40

3.11

2.01

0.1

718.9

+

5.99

17.3

5.77

23.09

7.54

2.79

1.80

0.01

611.6

+

5.10

20.4

4.91

19.64

6.41

2.37

1.53

^

4.25

24.4

4.09

16.37

5.35

1.98

1.28

0.001 509.8 5 6 7 8 9 10 11 12

* Mass of complete monolayer predicted from Langmuir adsorption isotherm + Equilibrium mass obtained from pseudo second order fit ^ Equilibrium mass obtained from pseudo first order fit a Calculated assuming density of asphaltene is 1.2 gcm⁻³ b Assuming MW of asphaltene is 750 gmol⁻¹ c Upper and lower limits of area per molecule for real asphaltenes reported in literature [45,46,47] d Predicted molecular areas of perylene bisimide model asphaltene from Nordgård et al. [48]

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Determining the Kinetics of Asphaltene Adsorption from Toluene: A

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