A New Model for Describing the Adsorption of Asphaltenes on Porous

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A New Model for Describing the Adsorption of Asphaltenes on Porous Media at a High Pressure and Temperature under Flow Conditions Nashaat N. Nassar, Tatiana Tatiana Montoya, Camilo A. Franco, Farid B. Cortés, and Pedro Rafael Pereira-Almao Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b00693 • Publication Date (Web): 28 May 2015 Downloaded from http://pubs.acs.org on May 31, 2015

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A New Model for Describing the Adsorption of Asphaltenes on Porous Media at a High Pressure and Temperature under Flow Conditions

Nashaat N. Nassar1, *, Tatiana Montoya1, Camilo A. Franco2, Farid B. Cortés2,* and Pedro PereiraAlmao1 1. Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada. email: [email protected] 2. Grupo de Investigación en Yacimientos de Hidrocarburos, Facultad de Minas, Universidad Nacional de Colombia Sede Medellín, Kra 80 No. 65–223, Medellín, Colombia. email: [email protected]

ABSTRACT Asphaltenes may generate production loss in oil reservoirs due to several factors related to the interaction between the asphaltene molecules, aggregates and the reservoir rock. Consequently, this could alter the wettability of the rock surface, increase the viscosity of the crude oil and reduce the permeability of the porous media. In a previous study, we have developed the solid–liquid equilibrium (SLE) model based on chemical theory to describe the adsorption behavior of asphaltenes onto porous and non–porous solid surfaces. However, the SLE model neglects the effect of pressure on the interactions of asphaltene– asphaltene and asphaltene-aggregate–solid surfaces of the reservoir rock primarily at reservoir conditions (RC). Thus, in this study, to account for the effect of pressure, a modification to the previously developed SLE equation is presented. In this study, a novel and original model called the SLE–RC model of adsorption has been proposed to describe the adsorption mechanism mainly at reservoir conditions, for which the pressure and temperature effect has been evaluated. This model describes the temperaturepressure–dependent adsorption isotherms with five parameters: the maximum amount adsorbed, the constant of the i–mer reactions, Henry´s law constant, the molar volume and the solubility parameter of the asphaltenes. The proposed model has been validated with adsorption tests on porous media under flow conditions at different pressures and temperatures. The dynamic adsorption experiments were performed at different asphaltene concentrations, pressures and temperatures from 100 to 2000 mg/L, 6.89 to 17.24 MPa, and 313 to 353 K, respectively. The SLE–RC model was successful validated using more than five experimental data describing the adsorption isotherms of the asphaltene onto a packed bed of silica sand at a high pressure and temperature and following a type III behavior with root mean–square errors (RMSE%) below 2%. In addition, the packed sands used in the adsorption tests were analyzed based on surface and color changes using SEM, EDX analysis and Polarized Light Microscopy (PLM); the results were in agreement with the SLE–RC model parameters. KEYWORDS: Adsorption, Asphaltene, High Pressure, Isotherm, Self–Association, SLE–RC model.

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INTRODUCTION

The variations in crude oil reservoir conditions of temperature, pressure and compositions during its productive life may cause precipitation/deposition of high-molecular-weight compounds such as asphaltenes,1,

2

which may influence oil recovery processes and reservoir productivity.3 The adsorption

and/or deposition of asphaltenes onto formation grains is one of the primary causes of formation damage in oil reservoirs, which has been one of the major unresolved flow assurance problems in the oil industry.4-7 Asphaltenes, which are the heaviest and most polar compounds in crude oil, are typically defined as the solubility class obtained from crude oil by fractionation using solvents.8 Asphaltenes may also contain nonmetallic heteroatoms, such as nitrogen, oxygen, and sulfur, as well as metals, such as vanadium, iron, and nickel. 9, 10 Due to its complex chemical structure and amphiphilic behavior, asphaltenes exhibit a self– associating feature that promotes aggregation.11-15 This aggregation behavior of asphaltenes is also highly dependent on the chemical nature of the crude oil, temperature, compositions and the true vertical depth of the well that is directly associated with the reservoir pressure.16 For instance, the asphaltenes in condensate oils with an average gas–oil–ratio (GOR) of 350 m3/m3 behave as molecules with a size of 1.5 nm based on the Yen–Mullins model.17, 18 In black oils with a GOR of 90–180 m3/m3, asphaltenes behave as aggregates with an approximate size of 2 nm; however, for low GOR oils, such as heavy and extra heavy crude oils, asphaltenes may behave like clusters with a minimum size of 5 nm.16 This asphaltene aggregation behavior has typically been studied to describe the stability of asphaltene and its interactions with each other and solid surfaces. Understanding asphaltene adsorption behaviors over solid surfaces is of practical significance mainly for monitoring fluid-property variations that commonly occur during oil production. Several experimental studies of asphaltene adsorption onto solid surfaces have been reported in the literature19-25 to describe the influence of the origin of asphaltenes,26, 27 the solvent used,28, 29 the surface chemistry, 27, 29-31 the temperature,6,7, 25, 32,26,25, 29, 33,34, etc. For example, Pernyeszi et al.21 studied the adsorption of n-C7 asphaltenes from mineral oil on to several hydrophilic clays minerals.


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The authors found that the adsorption is mainly due to the interactions of the polar parts of the asphaltenes with the polar parts of the surface resulting in a hydrophobic shell of asphaltenes and allowing the adsorption of a second layer of asphaltenes that is more hydrophilic for the buildup of outward-facing polar functional groups.19, 21 Several studies21, 35-37 have shown that kaolinite and calcite are very active minerals for asphaltene adsorption and that kaolinite have the highest adsorption capacity. Dudášová et al.26 studied the adsorption of asphaltenes obtained from five different sources over a series of mineral sorbents. The authors correlated the adsorption capacities with the polar interactions with the solid surface and found that the amount adsorbed follow the order hydrophilic silica > TiO2 > kaolin > Fe3O4 ≈ FeS > CaCO3 > hydrophobic silica. Nassar et al.38 reported that asphaltene adsorption increased with increasing acidity of the adsorbent. Because of their high adsorption affinity and excellent catalytic potencies, metal oxide nanoparticles have promising solutions for problematic asphaltenes.19,

39

Nassar et al.29,

31, 38, 40-46

performed several

experiments to investigate the role of metal-based nanoparticles on the adsorptive removal of asphaltenes followed by post-adsorption decomposition. The authors concluded that asphaltene adsorption and postadsorption decomposition are metal oxide specific, which utilized different degree of interactions between the asphaltene molecules and nanoparticle surface. Other work31 showed that basic and amphoteric oxide nanoparticles can adsorb more asphaltenes than acid oxides.31 Recently, we have shown that Ni-Pd bimetallic nanoparticles supported on different oxides, such as SiO2,6, 30, 34, 47, 48 Al2O3 6, 49 and TiO2 49 have higher adsorption affinity and catalytic activity toward adsorption and post-adsorption decomposition of asphaltenes compared to the support without functionalization. This was attributed to the synergistic effect of PdO and NiO that resulted in combined selectivities, intermolecular forces between the functional groups, heteroatoms present in the asphaltene molecule, metal-support interactions and electronic and geometric effects on the surface of the adsorbent.49


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However, most asphaltene adsorption studies reported in literature have been performed in a batch-mode experiment at atmospheric pressure and room temperature; thus, actual reservoir conditions have been neglected. Experimental studies regarding asphaltene adsorption are limited due to the complexity of asphaltene structures,50,

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which strongly depends on the pressure, temperature and asphaltene

concentration. It is well documented that asphaltenes can be adsorbed onto solid surfaces as molecules, micelles, monomers, dimers and nano–aggregates.19 The complexity of asphaltene adsorption at reservoir conditions requires a careful design of experiments in a porous media that operates at a high pressure and temperature. Further, thermodynamic modeling that promotes the understanding of the asphaltene– asphaltene and asphaltene-aggregate–solid-surface interactions is of the highest importance.33 The mathematical modeling of asphaltene adsorption is commonly studied based on two different types of isotherms, namely Langmuir52 and Freundlich53 isotherms, using experimental data obtained primarily under batch adsorption tests.29 The two models indicate the “effective” monolayer coverage of asphaltene on the solid surface19, 22, 31, 54, 55 and multisite and/or multilayer adsorption,53 respectively. The latter model indicates the aggregate formation and self–association of the asphaltene molecules as well as further formation of hemimicelles,19, 23, 25, 56 although the basis of this is not phenomenologically defined. Other models have also been proposed for describing the interaction of asphaltene and solid surfaces based on the molecular thermodynamics approach

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and the adsorption potential, as described by the Polanyi–Dubinin

theory.58 Castro’s et al. 57 model provides a good insight on the impact of both asphaltenes and adsorbent characteristics on adsorption process. However, the molecular thermodynamic approach model proposed by Castro et al.57 requires the determination of ten molecular parameters related to the size of the asphaltene aggregate and the square–well potentials that describe the asphaltene−surface and asphaltene−asphaltene interactions in both the bulk and adsorbed phases. Recently, our research group59 has used the Dubinin−Ashtakhov (DA) model based on the Polanyi theory60 to describe the adsorption of asphaltene onto surfaces of micro and nanoparticles. The proposed model


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requires the determination of three molecular parameters based on the energy of the interactions between the surface and adsorbate, the maximum adsorbed uptake and the heterogeneity parameter. However, this DA model is not appropriate to describe the mechanism of the adsorption of auto–associative molecules such as asphaltenes, particularly at low loads and when considering a uniformly dense region at moderate loads. More recently, our research group has developed a thermodynamic SLE model,33, 48 based on the Chemical Theory61 to describe the adsorption behavior of auto–associative asphaltene molecules onto different solid surfaces. This SLE model is related to the thermodynamic equilibrium of asphaltenes sorption onto solid surfaces while considering the i–merization of the asphaltenes and its interaction with a solid surface at different temperatures but neglecting the pressure effect. Actually, the pressure dependence is typically ignored in most adsorption models used to describe the asphaltene adsorption behavior. It should, however, be noted that the pressure may have a profound effect on the adsorption process, particularly in the flow mode. To the best of our knowledge, experimental and theoretical studies of the flow-mode adsorption isotherms of asphaltene onto solid surfaces at reservoir conditions have not been reported; therefore, for the first time, this study introduces a novel and original adsorption model to describe the asphaltene adsorption onto solid surfaces at a high pressure and temperature. This study revisits the previous SLE model33 and includes the pressure dependence in the SLE equation. Hence, a modification to the SLE model that outperforms the previous model and provides thermodynamic consistency under typical reservoir conditions is presented. For model validation, experimental adsorption tests were performed under a flow-mode process on porous media at different pressures, temperatures and initial concentrations of asphaltenes.

2. THEORETICAL CONSIDERATIONS In a previous study, we have developed the SLE model33 and validated it at low pressures, following the theoretical considerations described by Talu and Meunier61 based on the Chemical Theory that describes


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the behavior of solutions when the interaction forces are strong due to non-ideal circumstances.12, 33 In this study, a modification to the SLE model that outperforms the previous model and provides thermodynamic consistency under typical reservoir conditions (i.e., high temperature and pressure) is presented. Accordingly, in this study, the adsorption isotherm equation of the SLE model that is capable of describing the adsorption behavior at reservoir conditions (SLE–RC) is developed based on a) the chemical equilibria, 2) the equation of state (EOS) and 3) the phase equilibrium. Figure 1 shows a schematic representation for the derivations of the SLE–RC model. From the chemical equilibria, as we have shown in a previous study,

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the asphaltene cluster formation

reactions can occur on a solid surface due to the i–mer formation of asphaltenes after sequential chain reactions that first involve the formation of dimers, trimers, etc. until “i” reactions have occurred. Hence, the cluster size is approximated by the number of “i” reactions of the asphaltene monomer that forms an i– mer ( bi ) per Equation 1:

bi = ib1

(1)

where b is a monomer of the asphaltenes. From the equation of state, we used Volmer’s EOS62 because it considers the molecular volume (i.e., cluster formation) but depreciates the lateral interaction between the molecules. Additionally, the deviation from ideality can be perfectly described by this equation due to the consideration of the pressure effects in the volume correction term ( b ) per Equation 2:

π ( v − b ) = RT

(2)

where π is the spreading pressure, v is the molar volume, b is a volume correction factor that the volume occupied by the cluster size, R is the universal gas constant, and T is the temperature. The fugacity correlation that follows Van Ness’ equation63 is introduced as follows:


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π   d ( nv )  fi RT  d π RT ln = ∫  −  π xi 0  dni T ,π ,n ≠ i π  j  

(3)

where fi is the fugacity, xi is the molar fraction and ni is the mole number of the component i on the surface. By substituting Equation 2 into Equation 3 and integrating, the fugacity can be written as:  bπ f i = exp  i  RT

  ib1π  π xi = exp   RT 

  π xi 

(4)

Modifying our previous SLE model is accomplished primarily in the equilibrium phase because the effect of high pressure has important consequences on the chemical potential of a liquid phase, where it deviates from ideality at high-pressure conditions. Based on Le Chatelier’s principle64 at low pressures, the association of self–associative molecules can be neglected, leading to the suppression of the formation of new complexes, which depends on the chemical nature of the molecules, solvents, concentrations and temperatures present. However, as the system pressure increases, the forces between the molecules could be considered to be chemical but not physical in nature.12 In this regard, the strength of intermolecular interactions such as hydrogen bonds, dispersion forces, induction forces and electrostatic forces between the asphaltenes molecules would increase with the pressure, resulting in the increase of the degree of selfassociation. Accordingly, the activity coefficient can now be calculated. The phase equilibrium is expressed at a given pressure and temperature, and the chemical potential for each component is equal in all of the phases involved:

µi s = µi l

(5)

where the chemical potential of the solid and the liquid phases are defined as shown in Equations 6 and 7, respectively:

µi s = Γ s + RT ln f i

(6)


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µi l = Γ l + RT ln aas

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(7)

Where Γ s and Γ l are the phase solid and phase liquid constants integrations, respectively, and aas is the activity associated with the asphaltenes in the bulk phase and can be expressed as a function of the activity coefficient ( γ as ) and the concentration ( C ) of asphaltenes, as shown below:

aas = γ asC

(8)

 Γ s − Γl  Substituting Equation 8 into Equation 7, equalizing with Equation 6, and letting H ' = exp  ,  RT 

Equation 9 is obtained: C=

(9)

H ' fi

γ as

The asphaltenes activity coefficient can now be calculated with the Flory Huggins expression12 as follows:

ln γ as = ln C + 1 − C +

vas 2 [δ as − δT ] RT

(10)

Considering − ln C ≅ 1 − C , Equation 10 can be written as:

2  vas [δ as − δT ]   RT 

γ as = exp 

(11)

After substituting Equations 11 and 4 into Equation 9, and following the procedure proposed for the SLE model,33 the isotherm equation of the SLE–RC model can be obtained as follows: C=

ψ ΨH exp  1+ KΨ  Nm

 2  vas [δ as − δ T ]   exp  −  RT  

(12)

where the definitions of K and Ψ are given by:33


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K=

KT RT SA

(13)

Ψ=

−1 + 1 + 4 K ξ 2K

(14)

where ξ is a constant defined as ξ =

Nm ; N (g/g) is the amount adsorbed, N m (g/g) is the maximum Nm − N

adsorption capacity, K T is the reaction constant for dimer formation, SA (cm2/g) is the specific surface area of the adsorbent, vas (cm3/mol) is the asphaltene molar volume, δ as (MPa1/2) is the solubility parameter for asphaltenes, and δ T (MPa1/2) is the solubility parameter for the dissolvent reported in the literature.65 Equation 12 represents the new adsorption model that considers the effects of the temperature and pressure.


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Chemical Theory At low uptake, adsorption occurs on the high-energy sites. At medium uptake, adsorbate molecules form clusters around the high-energy sites. At high uptake, the finite volume available for adsorption becomes crowded with adsorbate molecules.

Chemical Equilibria

Equation of state

Phase Equilibria

Eq. 1

Eq. 2 and eq. 4

Eq. 5, 6 and 7

The activity of the bulk phase is introduced to describe the non-ideality of the system as a function of the activity coefficient and the bulk phase concentration.

The bulk surface properties and the surface phase properties are linked. The behavior of the surface phase is described.

Eq. 8 and 11

Adsorption Isotherm Equation A novel and original adsorption model is introduced for describing the adsorption process of self-associative molecules on solid surfaces at a high temperature and pressure conditions. Eq. 12 Figure 1. Schematic representation of the derivations of the SLE–RC model

3. EXPERIMENTAL Dynamic adsorption experiments of n-C7 asphaltenes on Ottawa sands were performed at typical reservoir conditions (i.e., high temperature and pressure) to validate the proposed SLE–RC model.


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3.3 Materials 3.3.1

Asphaltenes and solvents

Solid n-C7 asphaltenes were obtained from an extra heavy crude oil sample from a field located in the Meta department in the central region of Colombia. The estimated API gravity and viscosity of the selected crude oil were 7.2°API and 5.9 × 105 cP at 289 K, respectively. The n-C7 asphaltenes were extracted from the crude oil by a standard procedure described in previous works29,

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using n–heptane (99%, Sigma–

Aldrich, St. Louis, MO) as the precipitant; this process produced an approximate asphaltene content of 11.5 wt%. n-C7 asphaltenes were carefully washed with n-heptane using a Soxhlet setup. n–heptane was used instead of other precipitants because the resins content of the precipitated asphaltenes could be lowered to the minimum. The elemental analysis of the prepared n-C7 asphaltenes is presented in Table 1. Before beginning the displacement tests, heavy oil model solutions of asphaltenes in toluene (99.5%, MerkK GaG, Germany) were prepared at concentrations between 100 and 2000 mg/L. In addition, toluene, methanol (99.8%, Panreac, Spain) and HCl (37%, Panreac, Spain) were used for porous media cleaning.

Table 1. n-C7 asphaltenes elemental analysis and molecular weight. Sample n-C7 asphaltenes

3.3.2

C (wt%) H (wt%) N (wt%) O (wt%) S (wt%) 71.1

7.32

1.22

18.3

2.06

H/C

MW (g/mol)

1.24

1830

Porous media

A horizontal porous bed of silica sand was constructed to study the behavior of asphaltene adsorption at reservoir conditions. Clean silica sand (Ottawa sand, US sieves 100–120 mesh) was purchased from Minercol S.A., Colombia and was used as an adsorbent. Silica sand surface area was estimated to be 2.67 ± 0.08 m2/g by N2 physisorption at 77 K using an Autosorb-1 from Quantachrome. Before use, the prepared porous bed was initially cleaned with a solution 1:1 of toluene and methanol at 10 mL per 5 g of sand. Then, the sand was washed with excess deionized water and HCl at 10% v/wt to remove any dust or ACS Paragon Plus Environment

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surface impurities. Rock cleaning using HCl is a technique commonly used to remove any impurities on the surface of siliceous rocks at both laboratory and field scale without the risk of altering or dissolve aggressively the components of the porous media66 or induce drastic changes in the rock physical properties.67 Nevertheless, the acid treatment could induce the formation of Si-Cl end-groups or the increase in the Si-OH,19 resulting in the increase of the amount of adsorbed asphaltenes. Sand packing was performed after drying the sand at 333 K for 12 h using a stainless steel column.6 The packed bed was 3.8 cm in diameter and 5 cm in length with a measured porosity of 27.1%. In addition, the porous media has an absolute permeability of 0.21Darcy, which was measured by injecting water at a flow rate of 0.5 mL/min.

3.4 Methods 3.4.1

Dynamic adsorption experiments

The dynamic adsorption experiments (DAEs) were performed using the flow-through method.68 Heavy oil model solutions at different initial asphaltene concentrations ( Ci ) were successively driven through the porous media, starting with the more dilute solutions and ending with the more concentrated solutions, for each condition of pressure and temperature. The experimental equipment used to perform the coreflooding displacements at reservoir conditions is shown in Figure 2. The experimental setup consisted

primarily of the following: a positive displacement pump (DB Robinson Group, Canada) for displacing the injecting fluid from a container tank into the porous media stored in a stainless steel reactor (i.e., the core holder); a commercial pump (Cole–Parmer Instrument Co., Canada) that was used to increase the system overburden pressure by pumping an incompressible fluid (i.e., mineral oil) into the core holder; and valves, thermocouples and pressure transducers that were installed along key points of the setup to control the experiment variables. The system was maintained at the desired temperature by isolating the reactor column with a fiberglass casing and covering it with heating tape. In addition, tests tubes at the outlet of the setup were used for sample collection to measure the changes in the asphaltene concentration produced by adsorption onto the porous media. To study the effect of pressure on the adsorption process, tests were


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performed at a fixed temperature of 313 K and at three different overburden pressures of 6.89, 10.34 and 17.24 MPa. The temperature effect on the adsorption process was investigated at a high fixed pressure of 17.24 MPa and at different temperatures of 313 K, 333 K and 353 K. Before injecting the heavy oil model solutions, the sand bed was initially washed and equilibrated with pure toluene to remove any dust on the silica surface. The porous media was washed until no significant difference between the absorbance of the toluene at the outlet of the core and the blank sample could be detected using a Genesys 10S UV-vis spectrophotometer (Thermo Scientific, Waltham, MA) which has an uncertainty of ± 0.001 a.u. in the absorbance measurement. The adsorption experiment began by injecting heavy oil model solutions into the porous media at a constant flow rate of 0.5 mL/min and a fixed Ci ; any change in the absorbance was also analyzed at the outlet of the core with the UV-vis spectrophotometer29, 32

, each sample was analyzed in duplicate to confirm validity and reproducibility of the experimental

results. The run was conducted until saturation was reached (i.e., no significant change in the asphaltene inlet and outlet concentrations were measured). Once the breakthrough run was complete, a more concentrated solution was injected, and the outlet concentration was monitored. This sequence of different asphaltene concentration injections was performed for the initial asphaltene concentrations from 100 to 2000 mg/L.


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Figure 2. Schematic representation of the experimental setup: 1) the core holder, 2) the sand packed bed, 3) the displacement cylinder, 4) the displacement positive pump, 5) the mineral oil pump, 6) the pressure transducers, 7) the valves and 8) sample output. The determination of the adsorption isotherms was performed via mass balance; equation 15 was used to determine the amount of asphaltenes adsorbed “ N ” (g/g) onto the porous media:68 teq

N =∑ t =0

(Ci vi − Ct vo ) ∆t W

(15)

where Ci (mg/g) and Ct (mg/g) are the initial and outlet concentrations of the asphaltenes solution injected at a specified time t (min) when each sample was taken, respectively; teq is the time at which the adsorption equilibrium was achieved; vi (mL/min) and vo (mL/min) are the inlet and outlet volumetric flows, respectively; and W (g) is the dry adsorbent (i.e., silica sand) mass. The adsorption isotherm was


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obtained by plotting the calculated N against the equilibrium concentration ( C ) that was obtained at teq . The model parameters are obtained by minimizing the root–mean–square error (RMSE%, Equation 16) between the theoretical and experimental data points using the DataFit software, version 8.2.79 (Oakdale Engineering) and Microsoft Excel: m

∑C

exp erimental ,i

RMSE % =

− Cmod el ,i

i =1

m

×100

(16)

where Cexperimental,i (mg/g) and Cmodel,i (mg/g) are the experimental concentration and the concentration estimated by the SLE-RC model, respectively, and m is the number of observations performed during the experiment.

3.4.2

Sands characterization

Sand samples were characterized before and after using the DAE process to observe the differences in the asphaltene adsorption at different pressure conditions. Samples of virgin silica sand and the sands used for the DAE at 10.34 and 17.24 MPa at a constant 313 K were selected for these characterizations. After the DAE analysis, samples were dried at 323 K to remove any remaining solvent. A JSM–6490LV scanning electron microscope (JEOL, USA) coupled to an INCA PentaFET –x3 detector (Oxford Instruments, Russia) was used to determine the energy–dispersive X–rays (EDX) spectra for elemental analysis; a RPL3B optical microscope with a rotating stage, a Bertrand lens, mica and gypsum plates and a 10X objective lens (Microscopes INDIA, India) was used to provide images of the three selected samples. The micrographs were taken with the same luminosity and photographic distance and were processed by an in– house programed Matlab® algorithm to determine the differences among the selected samples via changes in the average values of the colors red, green and blue (RGB). Additionally, the RGB values were transformed into the perceptually uniform color space CIE 1976 L*a*b* (CIELAB) to avoid misinterpretations due to the instabilities and non-linearities of commercial cameras.69 The CIELAB space ACS Paragon Plus Environment

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is based on the opponent–color theory that assumes that the human eye perceives color in opposite pairs of light against dark (L*), red against green (a*) and yellow against blue (b*).70

4. RESULTS AND DISCUSSION The SLE–RC model is expected to provide insight into the asphaltene–asphaltene and asphaltene–solidsurface interactions at reservoir conditions (i.e., high pressure and temperature). To validate the model, the results and analyses were divided into four sections: i) the effect of system pressure, ii) the effect of system temperature, iii) image analyses to support the data obtained from the DAE testing and iv) sensitivity analysis.

4.3 Effect of pressure The pressure effect on the asphaltene adsorption under dynamic conditions was studied at the three different pressures of 6.89, 10.34 and 17.24 MPa at 313 K. Figure 3 shows the breakthrough curves obtained at different pressures and initial asphaltene concentrations. As expected, as the pressure increased from 6.89 to 17.24 MPa at different initial concentrations, the breakthrough curve shifts to the right, suggesting an increase in the adsorption efficiency. Accordingly, Figure 4 shows the adsorbed amount of asphaltenes obtained at different pressures along with the SLE–RC model fits for the adsorption. The estimated values of the model’s fitted parameters and their corresponding RMSE% values are listed in Table 1. Clearly, the asphaltene adsorption is pressure-dependent, and the adsorption isotherms exhibit Type III behavior, based on the classifications of the International Union of Pure and Applied Chemistry (IUPAC),

71

and deviate from the Langmuir Type I or Freundlich isotherms, as typically reported in the

literature. Type III isotherms are obtained in systems with low adsorbate–adsorbent affinity, leading to the formation of multiple layers of asphaltenes on the silica sand surface.72, 73 These results agree with those reported by Mendoza de la Cruz et al.50 for adsorption of n-C7 asphaltenes, obtained from Mexican heavy crude oil, onto Berea sandstone at concentrations below 5000 mg/L, and those reported by M. Castro et


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al.57 for adsorption of n-C7 asphaltenes, extracted from a Mexican crude oil, onto limestone, dolomite and Berea minerals at concentrations between 10 and 30000 mg/L. As shown in Figure 4, the isotherm curves shift to the left as system pressure increases, indicating that the amount of asphaltenes adsorbed increased as the system pressure increased; this difference was more noticeable at higher concentrations (>0.35 mg/g) because the asphaltene-asphaltene and solid-surface– asphaltene interactions presumably increased.64 The association/clustering process of the asphaltenes and the subsequent presence of highly surface–active components on the asphaltene structures are typically enhanced at a high pressure and high concentration.57 The multilayer trend of the adsorption isotherms also could be due to the adsorbent being fixed in the DAE throughout the experiment, leading to a reduction in the available active sites and therefore, the reduction of the surface area of the silica sand, which favors the self–association process of asphaltenes and the subsequent formation of multiple layers. Nitrogen and oxygen functional groups can be found in the asphaltenes molecule according to the elemental analysis presented in Table 1. The heteroatoms content is an important parameter in the adsorption process31, 38, 74-78 and also for the modeling of the asphaltene adsorption thermodynamic and kinetic behavior, because the heteroatoms can have different affinities for different adsorbents. In this order, besides hydrogen bonding, van de Waals forces and π − π stacking, the asphaltene–asphaltene interaction can be explained due to acid-base interactions between the oxygen–, sulfur– and/or nitrogen–containing functional groups.19 In addition, it is worth to mention that asphaltenes with high aromaticities are more prone to form strong multilayers19, 56, 79 and hence one can anticipate that the use of asphaltenes with a higher H/C ratio than the one reported in Table 1 would result in lower amount adsorbed and vice versa. According to the YenMullins theory,17,

18, 80

the island-type architecture is the most common asphaltenes structure with an

average of 7 fused rings in the PAH core and about ~ 750 g/mol of molecular weight. In this order, according to the value of the n-C7 asphaltenes molecular weight (Table 1) it can be inferred that the architecture of the molecule could be more like continental-type than the typical island type, which gives


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special importance to π − π stacking as the PAH core could be composed by more than 10 fused rings. It is expected that as the adsorption process does not provides the energy enough for molecule cracking, the architecture of the asphaltenes adsorbed remained unchanged after adsorption on the silica surface. The adsorption process of asphaltenes onto the silica surface occurs mainly due to the Si-OH functional group on the material surface. The theoretical value of the point of zero charge (pHpzc) for pure silica corresponds to a pH value of 2.0,81 and generally for commercial silica the pHpzc < 3.5.82 This indicates that the nature of the adsorbent surface is acidic and would be more prone to attract hydroxyl groups present on the asphaltene molecules.83 In some studies,19, 54 it was reported that asphaltenes adsorbed onto kaolinite showed a 6-fold increase in the N/C and S/C ratios in comparison with the oil source. In another study, 37 it was found that the capacity of adsorption of asphaltenes onto illite has a linear correlation with increasing the content of C and S. It has been also reported84 that for the asphaltenes adsorbed onto basic surfaces present higher concentration of sulfur, however the total adsorbed amount of the asphaltenes was lower compared with the adsorbed amount over acid surfaces which bind more quickly or strongly to lower sulfur-containing species.19, 84 According to Curtis et al.,85 the adsorption of model asphaltenes compounds onto dry silica followed the order phenylsulfoxide > quinoline > phenol > benzoic acid > benzophenone > benzylbenzoate > pyrene.


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2100

100 mg/L 6.89 MPa 300 mg/L 6.89 MPa 500 mg/L 6.89 MPa 1000 mg/L 6.89 MPa 2000 mg/L 6.89 MPa 100 mg/L 10.34 MPa 300 mg/L 10.34 MPa 500 mg/L 10.34 MPa 1000 mg/L 10.34 MPa 2000 mg/L 10.34 MPa 100 mg/L 17.24 MPa 300 mg/L 17.24 MPa 500 mg/L 17.24 MPa 1000 mg/L 17.24 MPa 2000 mg/L 17.24 MPa

1800 1500 C (mg/L)

1200 900 600 300 0 0

0.2 0.4 Pore Volumes Injected

0.6

Figure 3. Breakthrough curves for different initial concentrations of n-C7 asphaltenes at different test pressures at 313 K.

0.009

17.24 MPa 10.34 MPa 6.89 MPa

0.006

SLE-RC

N (g/g)

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

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0.003

0 0

0.5

1 1.5 C (mg/g)

2

2.5

Figure 4. Adsorption isotherms of n-C7 asphaltenes at different test pressures and temperature of 313 K. The symbols represent the experimental data and the solid curves are from SLE–RC model (eq 12).

As shown in Figure 4 and Table 2, there is excellent agreement between the SLE–RC model and the experimental results with RMSE% values < 2%. As shown in Table 2, the solubility parameter δ as increased


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as the pressure increased; this is not surprising because the asphaltene solubility is a function of the pressure and is highly dependent on the bubble point of the solvent.86 Hence, a system pressure above the bubble point exhibits a constant fluid composition, and increasing the system pressure would lead to an increasing fluid density, resulting in a higher solubility.

87

However, for systems below the bubble point,

due to solvent expansion, the density and thus the asphaltene solubility decrease.86 Because the bubble point pressure of the solvent (i.e., toluene) is 0.007 MPa, which is significantly less than the system pressures considered in this study, it is expected that the solubility parameter increases as the system pressure increases; this is in agreement with the values reported in the specialized literature.88-90 By definition, the solubility parameter is inversely proportional to the molar volume; thus, it is expected that as the solvent power required to solubilize asphaltenes increases, the molecular weight of the asphaltenes in the solvent decreases; this supports the decrease in vas with pressure, as shown in Table 2. The decrease in

H indicates that as pressure increases, the number of active sites on the adsorbent would be easily accessible by the asphaltenes, thus increasing the preference of asphaltenes for attaching to the adsorbent surface rather than being present in the bulk phase.33 The affinity between the solid surface and the asphaltenes increases as the intermolecular forces between asphaltenes and the silica sand surface such as

π − π stacking, van de Waals forces and acid-base interactions increase by augmenting the system pressure. Conversely, the increase in K as the pressure increases suggests that the pressure has a significant influence on the self–associative behavior of the asphaltenes on the adsorbent solid surface, indicating that the degree of asphaltene self–association on the adsorbent sites increases as the pressure increases. However, the self-association of asphaltenes is strongly dependent on their molecular structure and the interaction that occurs between them and its strength.56,

91-93

Additionally, the increasing trend of N m

shown as the pressure increases agrees with the experimental results.


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Table 2. Estimated parameters of the solid-liquid model at reservoir conditions in the SLE–RC model for different test pressures at 313K.

6.89

Test Pressure 94 10.34

17.24

H (mg/g)

8086.42

7030.61

3321.65

K (g/g)

1259.76

1440.82

1473.52

N m (g/g)

0.00668

0.00708

0.00879

δ as (MPa )

16.56

16.64

16.80

v as (cm /mol)

1040.4

1025.28

743.74

RMSE %

1.70

0.04

0.63

Parameter

1/2

3

4.4 Effect of the temperature The effect of the temperature on the asphaltene adsorption under dynamic conditions was studied at three different temperatures of 313, 333 and 353 K and a fixed pressure of 17.24 MPa. Figure 5 shows the breakthrough curves obtained at the different temperatures and different initial asphaltene concentrations. As expected, as the temperature increased from 313 to 353 K, the breakthrough curves shift to the left at different initial concentrations, suggesting a decrease in the adsorption efficiency. Figure 6 shows the adsorbed amount of asphaltenes obtained at different temperatures along with the SLE–RC model fits. The estimated values of the obtained model parameters and their corresponding RMSE% values are shown in Table 3. Again, the asphaltene adsorption isotherms exhibit Type III behavior.71 From Figure 6, it is shown that the amount of adsorbed asphaltenes decreased with increasing temperature in the following order 313 K > 333 K > 353 K. These findings are in excellent agreement with previous studies pertaining to the asphaltene adsorption onto different solid surfaces at different temperatures.29, 30, 47, 49, 59, 95 These results indicate that the adsorption of asphaltenes onto silica sand is an exothermic process and that temperature has an influence on the adsorbent–adsorbate and adsorbate–adsorbate interaction forces. 47 In addition, the increase of the temperature could result in the reduction of Si-OH groups and consequently the number of sites available for adsorption is decreased.96


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2100

100 mg/L 353 K 300 mg/L 353 K 500 mg/L 353 K 1000 mg/L 353 K 2000 mg/L 353 K 100 mg/L 333 K 300 mg/L 333 K 500 mg/L 333 K 1000 mg/L 333 K 2000 mg/L 333 K 100 mg/L 313 K 300 mg/L 313 K 500 mg/L 313 K 1000 mg/L 313 K 2000 mg/L 313 K

1800 1500 C (mg/L)

1200 900 600 300 0 0

0.2 0.4 Pore Volumes Injected

0.6

Figure 5. Breakthrough curves for different initial concentrations of n-C7 asphaltenes at different test temperatures at 17.24 MPa.

0.009

313 K 333 K 353 K

0.006

SLE-RC model

N (g/g)

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

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0.003

0 0

0.5

1 1.5 C (mg/g)

2

2.5

Figure 6. Adsorption isotherms of nC7 asphaltenes at different test temperatures at 17.24 MPa. The symbols represent the experimental data obtained, and the solid curves are calculated by the SLE–RC model (Equation 12).


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As shown in Figure 6 and Table 3, there is excellent agreement between the SLE–RC model fits and the experimental results, showing RMSE% values < 1.9%. From Table 3, it is shown that H increases (i.e., the adsorption affinity decreases) as the system temperature increases; this is an indication of the preference of asphaltenes for being in the bulk liquid phase rather than on the solid surfaces as the temperature increases.12, 33 This is also supported by the decrease in N m with the temperature. These findings are in excellent agreement with those reported by Franco et al.47, 55 on the adsorption of oil from fresh and salt water on alumina nanoparticles functionalized with a Colombian vacuum residue. The authors also examined a Type-III adsorption isotherm and found that based on the affinity parameters from the BET models, the adsorption affinity decreased as the test temperature increased. Based on K , the self– association of the asphaltene molecules onto the silica sand surface is inhibited as the temperature increases, suggesting a decrease in the intermolecular forces between the adsorbent and the adsorbate. Additionally, changes in temperature may influence the asphaltenes’ aggregate size in the solution and thus alter their spatial disposition on the adsorbent surface.29, 47

Table 3. Estimated parameters of the SLE–RC model for different test temperatures at 17.24 MPa. Test Temperature (K) Parameter 313 333 353

H (mg/g) K (g/g)

3321.65 1473.52

14927.37 1161.48

32700.27 982.41

N m (g/g)

0.00879

0.00801

0.00607

δ as (MPa )

16.80

15.90

15.64

743.74 0.63

837.84 1.90

925.31 0.81

1/2

3

v as (cm /mol) RMSE %

The values of vas and δ as correlate well with the temperature. The liquid density decreased with the temperature,87 suggesting that the power of the solvent to dissolve the asphaltenes decreased. This behavior is most common for solvents with a carbon number above 5(i.e., toluene),87 which directly affects their molar volume that tends to increase with temperature (Table 2). The results are also in agreement with ACS Paragon Plus Environment

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Energy & Fuels

Diallo et al.,97 who reported the molar volume and solubility parameters of an asphaltene model isomer and obtained linear trends as a function of the temperature. Panels a and b from Figure 7 show the relationship of a) vas and b) δ as as functions of the temperature. As shown, vas increases linearly with the temperature, while δ as shows the opposite linear trend. The thermal expansion coefficient of the asphaltenes can be estimated

97

from the slope of Figure 7a. Accordingly, for a fixed temperature of 300 K and a system

pressure of 17.23 MPa, the thermal expansion coefficient for the n-C7 asphaltenes used in this study, is calculated to be 6.62 x 10-3 K-1. This result could be useful for comparison purposes with the thermal expansion coefficients of pure polycyclic aromatic hydrocarbons, such as anthracene or phenanthrene, and determine their similarities with the evaluated asphaltenes.97

a 950

b

vas = 4.5393∙T - 675.94 R² = 0.99

900

δas (MPa1/2)

vas (cm3/mol)

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

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850 800 750 700

17

δas = 0.0008∙T2 - 0.5618∙T+ 114.27 R² = 1

16.6 16.2 15.8 15.4

300

320 340 Temperatue (K)

360

300

320 340 Temperature (K)

360

Figure 7. Relationship between the constants a) vas and b) δ as from the SLE-RC model and the temperature.

4.5 Micrographs and EDX analyses for silica sands before and after DAE To obtain complementary evidence for the modeling and experimental results observed in the adsorption isotherms, selected samples of silica sands before and after DAE testing were analyzed with Scanning Electron Microscopic (SEM), Energy Dispersive X-Ray Spectroscopy (EDX) and Polarized Light Microscopy (PLM). Panels a-c of Figure 8 show micrographs from an optical microscope at 10X ACS Paragon Plus Environment

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magnification with the respective average color variation for a) clean silica sand, b) sand after adsorption at 10.34 MPa and c) sand after adsorption at 17.24 MPa. From Figure 8, it is shown that the average color of the image varies in its brown intensity and changes by increasing the test pressure in the DAE test. This could be attributed to the different amount of asphaltenes adsorbed onto the sand surfaces at different pressures. RGB and Lab analyses were performed to determine the color variations present, and the results obtained are shown in Table 3. As shown, G and B were largest in the clean silica sand, followed by the sand after adsorption at 10.34 MPa and then the sand after adsorption at 17.24 MPa. This could be attributed to the increase in the adsorption and aggregation of asphaltenes onto the sand surface with increasing pressure, which is in agreement with the model and the DAE experiments. To further support this claim, the RGB analyses were translated into the CIELAB space; and it was found that L* follows the same order as G and B, indicating that the sample gets darker as the adsorption of asphaltenes increases. Conversely, a* is positive for red tones and negative for green tones, and b* is positive for yellow tones and negative for blue tones. The results of a* and b* indicate that the presence of yellow and red tones can be associated with the presence of asphaltenes on the adsorbent surface.

a

Average color variation

b



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c


Figure 8. Micrographs from an optical microscope at 10X magnification with the respective average color variation for a) clean silica sand, b) sand after adsorption at 10.34 MPa and c) sand after adsorption at 17.24 MPa.

Table 3. RGB and estimated values of L*, a*, and b* for micrographic analyses from an optical microscope for selected samples. 10X Magnification Sample R

G

B

L*

a*

b*

Clean silica sand

134

122

100

52

2

14

Sand after adsorption at 10.34 MPa

133

116

94

50

4

15

Sand after adsorption at 17.24 MPa

140

109

69

48

9

27

Because the micrograph analysis showed no significant difference on the surface or in the morphology of the selected samples, the SEM micrographs along with EDX spectra analyses were conducted to confirm the adsorption trend and quantity of the elements present in the selected samples. Panels a–c of Figure 9 show the SEM micrographs and EDX element C specific map image for a) clean silica sand, b) sand after adsorption at 10.34 MPa and c) sand after adsorption at 17.24 MPa. A compositional analysis was


26

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demonstrated in both atomic and weight percentages for the detected elements. EDX confirms that these samples are primarily composed of C, O, Si, Al, K, Fe and Ti. The quantified results of the elemental analysis of the images in Figures 9a-c are summarized in Table 3. As expected, Si and O are the most abundant elements in the samples with some traces of impurities such as Al, K, Fe and Ti, which represent the porous media. The presence of C in the clean sand sample could be due to the traces of remaining solvent remaining after the washing process. Most importantly, the detected C percentage, which accounts for the adsorbed asphaltenes, in the selected samples was lowest in the clean silica sand, followed by the sand after adsorption at 10.34 MPa and then the sand after adsorption at 17.24 MP. As the only source of Carbon in the sample are asphaltenes and as the most abundant element in the molecule, an increase in the Carbon content is a strong indicator of the increase of the amount adsorbed of asphaltenes. The absence of N, S, V and Ni on the elemental analysis by EDX could be due to the self-association over the adsorbent active sites that result in hindering the aforementioned heteroatoms and metals. In fact, in Table 1 it is shown that asphaltenes have a high content of oxygen, but the EDX analyses showed a decrease in the oxygen content. This is could be due the EDX detector is unable to detect buried elements, suggesting that most of the adsorption could be governed by the interaction between the functional groups of the adsorbent and the oxygen-containing groups of the asphaltenes. Additionally, a linear relationship between L* and the C atomic % on the selected samples is shown (Figure 10), indicating that a darker sample typically has a larger amount of adsorbed asphaltenes. These results are in agreement with the adsorption isotherms from the DAE experiments, the values of the SLE–RC model parameters (i.e., K , H , N m , vas and δ as ) and their variations with pressure.


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a

b

c

Figure 9. SEM micrographs (left) and EDX spectra analyses (right: specific map image of C element represented by red dots) at 60000X for a) clean silica sand, b) sand after adsorption at 10.34 MPa and c) sand after adsorption at 17.24 MPa.


28

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Table 4. Elemental EDX analysis for the clean silica sand and the sands after asphaltene adsorption at 10.34 and 17.24 MPa. Sample Element

Clean silica sand

Sand after adsorption at

Sand after adsorption at

10.34 MPa

17.24 MPa

wt %

Atomic %

wt %

Atomic %

wt %

Atomic %

C

3.1

5.8

17.0

27.7

42.8

56.71

O

30.0

42.1

28.7

35.2

26.3

26.16

Al

4.6

3.8

3.5

2.6

1.5

0.90

Si

57.4

45.9

47.0

32.9

27.6

15.62

K

1.2

0.7

0.9

0.5

0.3

0.11

Ti

1.7

0.8

1.6

0.6

1.3

0.44

Fe

2.0

0.8

1.4

0.5

0.2

0.07

52

L* = -0.0781∙Carbon + 52.347 R² = 0.99

51 50 L*

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49 48 47 0

10

20

30

40

50

60

Carbon (atomic %)

Figure 10. Relationship between L* and the C atomic% on the silica sand surface.


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Energy & Fuels

4.6 Sensitivity analysis A sensitivity analysis was performed to investigate the reliability of the SLE–RC model parameters. In this section, only the results for the isotherm at 313 K and 10.34 MPa are shown because the same trend is followed in the other experimental conditions. Panels a–e of Figure 11 show the results for the sensitivity analysis performed on the SLE–RC model parameters: a) H , b) K , c) N m , d) δ as and e) vas with an increase or decrease of 10% in each parameter. H , K and vas show similar degrees of sensitivity, while

δ as is the most sensitive to changes. In addition, N m does not exhibit sensitivity at low concentrations.

0.004

0.004

0.002

SLE-RC model H+10% H-10%

0

Nads (g/g)

b 0.006

N (g/g)

a 0.006

0.002

SLE-RC model K+10% K-10%

0 0

0.5

1 1.5 C (mg/g)

2

2.5

0

d 0.006

0.004

0.004

N (g/g)

c 0.006

N (g/g)

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

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0.002

SLE-RC model

0.5

1 1.5 Ce(mg/g)

0.002

Nm-10%

0

0.5

1 1.5 C (mg/g)

2

2.5

SLE-RC model δas+10% δas-10%

Nm+10%

0

2

0 2.5

0


1

2

3 4 C (mg/g)

5

6

7

30

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e 0.006

N (g/g)

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

Energy & Fuels

0.004

0.002

SLE-RC model Vas+10% Vas-10%

0 0

0.5

1 1.5 C (mg/g)

2

2.5

Figure 11. Sensitivity analysis of the SLE–RC model parameters for the n-C7 asphaltenes adsorption isotherms obtained from the DAE experiments at 313 K and 10.34 MPa. The symbols represent the experimental data, and the dashed lines represent the model predictions for a 10% increase or decrease in the model parameters.

5. CONCLUSIONS In this study, a modification to the previously reported solid-liquid-equilibrium model (SLE model) based on the chemical theory has been introduced to accurately describe the influence of high pressure and temperature on asphaltene adsorption. Using the new five–parameter SLE–RC model, excellent agreement between the model and experimental results with RMSE% < 2% was established. The proposed new model was used for the first time based on classic thermodynamics concepts to improve the understanding of the asphaltene–asphaltene and asphaltene–solid-surface interactions on the adsorption equilibrium process at typical reservoir conditions. The sensitivity analyses showed that the most sensitive parameter was δ as , suggesting that a slight variation in this parameter will cause a considerable variation between the experimental and calculated data. In addition, for the first time, Type III adsorption isotherms from dynamic adsorption experiments at high temperature and pressure conditions were reported. It was also observed that as the system pressure increased, the amount of adsorbed asphaltenes increased; the opposite was observed for the effect of temperature. These preliminary results based on the experimental data of ACS Paragon Plus Environment

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several systems are encouraging to the future development of the association theory with other solid surfaces, such as consolidated and other unconsolidated media at reservoir conditions.

6. ACKNOWLEGMENTS The authors acknowledge Universidad Nacional de Colombia for logistical and financial support and COLCIENCIAS and ECOPETROL for the support provided in the agreement 264 of 2013. The authors are also grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC), NexenCNOOC Ltd, and Alberta Innovates-Energy and Environment Solutions (AIEES) for the for the financial support provided through the NSERC/NEXEN/AIEES Industrial Research Chair in Catalysis for Bitumen Upgrading. Also, the contribution of facilities from the Canada Foundation for Innovation, the Institute for Sustainable Energy, Environment and Economy, the Schulich School of Engineering and the Faculty of Science at the University of Calgary are greatly appreciated.

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A New Model for Describing the Adsorption of Asphaltenes on Porous

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