Experimental Study and Mathematical Modeling of Asphaltene Deposition Mechanism in Core Samples

In this work, experimental studies were conducted to determine the effect of asphaltene deposition on the permeability reduction and porosity reduction of carbonate, sandstone and dolomite rock samples using an Iranian bottom hole live oil sample which is close to reservoir conditions, whereas in the majority of previous work, a mixture of recombined oil (a mixture of dead oil and associated gas) was injected into a core sample which is far from reservoir conditions. The effect of the oil injection rate on asphaltene deposition and permeability reduction was studied. The experimental results showed that an increase in the oil injection flow rate can result in an increase in asphaltene deposition and permeability reduction. Also, it can be observed that at lower injection flow rates, a monotonic decrease in permeability of the rock samples can be attained upon increasing the injection flow rate, while at higher injection rates, after a decrease in rock permeability, an increasing trend is observed before a steady-state condition can be reached. The experimental results also showed that the rock type can affect the amount of asphaltene deposition, and the asphaltene deposition has different mechanisms in sandstone and carbonate core samples. It can be seen that the adsorption and plugging mechanisms have a more important role in asphaltene deposition in carbonate core samples than sandstone core samples. From the results, it can be observed that the pore volumes of the injected crude oil are higher for sandstone cores compared with the carbonate cores. Also, it can be inferred that three depositional types may take place during the crude oil injection, i.e., continuous deposition for low-permeability cores, slow, steady plugging for high-permeability cores and steady deposition for medium-permeability cores. It can be seen from the experimental results that damage to the core samples was found to increase when the production pressures were increased. The experimental results show that the amount of remaining asphaltene in carbonate core samples is higher than those in sandstone core samples. Also, SEM (Scanning Electron Microscopy) micrographs of carbonate core samples showed the formation of large clusters of asphaltene in comparison with sandstone core samples during natural depletion. It can be seen from the modeling results that the proposed model based on the multilayer adsorption equilibrium mechanism and four material balance equations is more accurate than those obtained from the monolayer adsorption equilibrium adsorption mechanism and two material balance equations, and is in agreement with the experimental data of natural depletion reported in this work and with those reported in the literature.

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Abstract -Experimental Study and Mathematical Modeling of Asphaltene Deposition Mechanism in Core Samples -In this work, experimental studies were conducted to determine the effect of asphaltene deposition on the permeability reduction and porosity reduction of carbonate, sandstone and dolomite rock samples using an Iranian bottom hole live oil sample which is close to reservoir conditions, whereas in the majority of previous work, a mixture of recombined oil (a mixture of dead oil and associated gas) was injected into a core sample which is far from reservoir conditions. The effect of the oil injection rate on asphaltene deposition and permeability reduction was studied. The experimental results showed that an increase in the oil injection flow rate can result in an increase in asphaltene deposition and permeability reduction. Also, it can be observed that at lower injection flow rates, a monotonic decrease in permeability of the rock samples can be attained upon increasing the injection flow rate, while at higher injection rates, after a decrease in rock permeability, an increasing trend is observed before a steady-state condition can be reached. The experimental results also showed that the rock type can affect the amount of asphaltene deposition, and the asphaltene deposition has different mechanisms in sandstone and carbonate core samples. It can be seen that the adsorption and plugging mechanisms have a more important role in asphaltene deposition in carbonate core samples than sandstone core samples. From the results, it can be observed that the pore volumes of the injected crude oil are higher for sandstone cores compared with the carbonate cores. Also, it can be inferred that three depositional types may take place during the crude oil injection, i.e., continuous deposition for low-permeability cores, slow, steady plugging for high-permeability cores and steady deposition for medium-permeability cores. It can be seen from the experimental results that damage to the core samples was found to increase when the production pressures were increased. The experimental results show that the amount of remaining asphaltene in carbonate core samples is higher than those in sandstone core samples. Also, SEM (Scanning Electron Microscopy) micrographs of carbonate core samples showed the formation of large clusters of asphaltene in comparison with sandstone core samples during natural depletion. It can be seen from the modeling results that the proposed model based on the multilayer adsorption equilibrium mechanism and four material balance equations is more accurate than those obtained from the monolayer adsorption equilibrium adsorption mechanism and two material balance equations, and is in agreement with the experimental data of natural depletion reported in this work and with those reported in the literature.

C sf
Mass of suspended asphaltenes per mass of the oil phase C Experimental concentration (in this case, in mol/L) C A Volume fraction of the suspended asphaltene precipitates in the liquid phase D pt Average pore throat diameter D ptcr Critical pore throat diameter, assumed constant E A Volume fraction of the deposited asphaltene in the bulk volume of the porous media E ad Fractional pore volume of asphaltene adsorbed f Fugacity K a Ratio of adsorption/desorption rate constants K Permeability k 1 First adsorption step parameter (in our case, this step is taken to be adsorption of asphaltenes in solution to the surface of the rock) k 2 Second adsorption step parameter (in our case, this step is taken to be the adsorption of asphaltenes in solution to those asphaltenes already adsorbed to the rock) R Gas constant S oi Initial oil saturation S wi Initial water saturation n Mean aggregation number of the adsorbed asphaltenes (in the modified model) u Internal energy u L Flux of the liquid phase v Molar volume v L Interstitial velocity of the liquid phase

INTRODUCTION
Asphaltenes and resins are the polar fractions of crude oil that can be separated by addition of low-molecularweight n-alkanes. By definition, asphaltenes are the fraction of a crude oil that is soluble in toluene and insoluble in an n-alkane, typically pentane or heptane. These fractions are formed by molecules with a polyaromatic structure containing paraffinic and naphthenic chains, as well as oxygen, nitrogen and sulfur as functional groups or heteroatoms. On the other hand, asphaltenes are heavy hydrocarbon molecules that are in colloidal suspension in the oil, stabilized by resins adsorbed on their surface [1]. Asphaltenes can reduce the hydrocarbon effective mobility by plugging pore throats, thus reducing the rock permeability, altering the formation wettability from water-wet to oil-wet and increasing the reservoir fluid viscosity by forming a colloidal solution in the oil phase [2]. The processes of asphaltene precipitation and deposition in porous media have various effects on oil flow during primary oil production and enhanced oil recovery processes. The natural depletion of a reservoir may cause the precipitation and deposition of asphaltenes, decreasing the productivity of wells during primary oil recovery. The majority of existing work studies the asphaltene deposition during core flooding using the injection of recombined oil (a mixture of dead oil and associated gas) into the core and/or with static systems and in the absence of reservoir rocks [3][4][5]. Therefore, such results are not applicable to the dynamic conditions which are related to the complex interactions between the asphaltenes and the rock surface. Asphaltene precipitation and deposition are two different processes and are governed by different mechanisms. The asphaltene deposition is governed by four mechanisms; surface deposition, entrainment, plugging and adsorption (surface excess or Langmuir theory) [6][7][8][9][10][11][12]. When precipitation occurs, asphaltene particles are aggregated and a new solid phase is generated in the oil flow, whereas when deposition takes place on the rock, this can change the wettability of the reservoir formation and reduce oil production [13]. The asphaltene deposition phenomenon is described using several mathematical models that have been proposed for the prediction of porosity and permeability reduction of porous media [14][15][16][17][18][19]. These models are based on two different parallel pathways with small and large pore sizes [20]. Most models are capable of correlating the permeability reduction experimental data using adjustable parameters and include the flow continuity equation, a mass balance equation and a kinetic equation. Other models based on network modeling theory have also been developed to describe the deposition of asphaltene in reservoir rock [21,22]. In short, due to the complexity of asphaltene deposition on the rock surface, very few experimental results currently exist on asphaltene deposition under dynamic conditions using live reservoir fluid in porous media. The majority of existing work addresses the deposition of asphaltenes using dead residual oil or recombined oil [6,[23][24][25], while it is well-known that the asphaltene in bottom hole live oil is different than that of recombined oil [26]. In this work, an Iranian bottom hole live oil sample was used under dynamic conditions in porous T. Jafari Behbahani et al. / Experimental Study and Mathematical Modeling of Asphaltene Deposition Mechanism in Core Samples media for investigation of the effect of several parameters and different production conditions such as crude oil type, the flow rate of the oil, rock type and production pressure on asphaltene deposition. Also, the performance of the proposed model based on the multilayer adsorption equilibrium mechanism was studied in more detail and compared with the Wang and Civan [7] model based on the mechanical plugging mechanism and the asphaltene deposition model based on the monolayer adsorption equilibrium mechanism.
1 EXPERIMENTAL SECTION

Materials
In the majority of previous work, a mixture of recombined oil (a mixture of dead oil and associated gas) was injected into a core sample which is far from reservoir conditions. In this work, a bottom hole live oil sample from an Iranian reservoir in the Southeast region of Iran which is close to reservoir conditions was used. This reservoir has a serious asphaltene deposition problem during production conditions. The oil density and viscosity of the bottom hole live oil sample were measured to be 0.7674 g/cc and 4.35 cP at the reservoir pressure, respectively. The asphaltene content of the live reservoir fluid was measured to be wasp = 16.3 wt% using the SARA analyses. The compositional analysis result of this crude oil was obtained using the gas chromatography method and is given in Table 1. A reservoir brine sample was collected from the same oilfield, cleaned, and analyzed. Its detailed physical and chemical properties are listed in Table 2.  Various carbonate and sandstone cores with a cylindrical shape with lengths ranging from 4 to 6 cm and constant diameter equal to 4 cm were extracted at various depths of the Iranian wells, then characterized and tested in the EOR Research Center laboratory, Research Institute of Petroleum Industry (RIPI). All the cores investigated were cleaned prior to their use, by using various solvents (Soxhlet extraction with xylene, methanol and chloroform) according to the ASTM D2172 procedure. Their characteristics, including their porosities, permeabilities and pore volumes, were measured and are shown in Table 3.

Gas and Liquid Chromatography
When the live reservoir fluid sample was flashed in atmospheric conditions, vapor and liquid phases were analyzed by means of the High-Temperature Gas Chromatography (HTGC) technique. To analyze the lighter fraction up to C9 (including CO 2 , H 2 S and N 2 ) a high-temperature gas chromatograph (three packed columns and one capillary column) with thermal conductivity and flame ionization detectors was used, while the residual liquid was analyzed up to C12 with another high-temperature gas chromatograph (a capillary column) that included a flame ionization detector.

SARA Analyses of the Crude Oil
The constituents of crude oils are typically classified by solubility: Saturates, Aromatics, Resins and Asphaltenes (SARA) [27]. For SARA fraction analysis, the asphaltene fraction was extracted from crude oil by precipitation with n-heptane as described by the ASTM D3279-97 procedure. Subsequent elution with a series of increasingly polar solvents as the mobile phase yields saturates (eluted with a nonpolar solvent such as hexane), followed by the elution of aromatics with toluene, and the resins are separated with a more polar solvent.
The SARA analysis results of live reservoir fluid are shown in Table 4.

Live Reservoir Fluid Viscosity
To determine the viscosity behavior of the reservoir fluid, at the studied temperature and different pressures, a constant force electromagnetic viscometer (maximum working pressure of 137.9 MPa, maximum temperature of 463.2 K) was used. The viscosity behavior of the live reservoir fluid is shown in Figure 1.

The PVT and Phase Behavior of the Live Reservoir Fluid
To determine the PVT and phase behavior of the live reservoir fluid, various experiments were conducted on the reservoir fluid, including constant mass expansion, differential vaporization and a separator test (DBR, VINCI PVT Cell). In these experiments, saturation pressure, relative volume, oil compressibility, the solution gas-oil ratio, the liberated gas-oil ratio, the oil formation volume factor and oil density were determined. In Tables 5 to 7, the PVT characteristics and phase behavior (constant mass expansion and differential vaporization results) of the studied live reservoir fluid are shown.
Also, the variation of relative volume, oil compressibility, the solution gas-oil ratio, the liberated gas-oil ratio, the oil formation volume factor and oil density with pressure are shown in Figures 2-4.  Figure 5 shows the schematic of the experimental setup used in this work in order to determine the effect of asphaltene deposition on the properties of a reservoir rock. This setup consists mainly of the following devices: -an automatic displacement pump (Vinci, p = 70 MPa, accuracy = 0.000687 MPa) was used to displace the crude oil and reservoir brine through the composite reservoir core plugs inside a core holder (Temco); -three high-pressure stainless steel cylinders (500-10-P-316-2, DBR, Canada) were used to store and deliver The viscosity behavior of the studied live reservoir fluid.   Variation of compressibility of liquid phase versus pressure for the studied live reservoir fluid. the live reservoir fluid, dead residual oil and reservoir brine, respectively (DBR, capacity of 500 mL); -the core holder (Temco, p = 70 MPa, T = 150°C) holds a core through a sleeve. A constant overburden pressure was applied around this sleeve, which was always kept 5 MPa higher than the inlet pressure of the core holder. The inlet and outlet ports of the core holder were connected to the pressure transducer. The inlet ports of the core holder were also connected to the positive displacement pump. Two cylinders containing the live reservoir fluid sample allowed injection of samples inside the core holder. The positive displacement pump was operated at a constant rate or in pressure mode. The outlet port of the core holder was connected to the fractional collector through a back-pressure regulator for collection of produced fluids from the core.

Experimental Apparatus
The pressure drop during the core flood tests was measured with a digital pressure indicator. The core flooding system was thermoregulated by means of an air-bath oven. An important feature was the possibility of continuous measurement of the pressure drop along sections of the porous medium. The annular space between the sleeve and the body was filled with paraffin oil through which the confining pressure is applied on the external surface of the sleeve. The advantage of this setup is the uniform pressure in both axial and radial directions: -a pressure transducer (Jumo, accuracy = 0.05); -a back-pressure regulator (Jeafer DBR, p = 70 MPa, T = 250°C). The regulator was used to maintain the prespecified injection pressure inside the core holder during each flooding test; -an overburden pump (Enerpac, p = 70 MPa); -an air-bath oven (Vinci, T = 200°C); -rigid valves; -a data acquisition system (Logger screen 500 Jumo: pressure, temperature, volume).

Experimental Procedure
The reservoir core plugs were cleaned with toluene, methanol and chloroform in sequence to remove hydrocarbons, salts and clays, respectively. Then, the reservoir core plugs were dried and vacuumed at 0.7 bar for one hour, and the reservoir brine was imbibed to measure the pore volume of the reservoir core plugs. Afterward, the reservoir brine was injected at different rates (1-30 cc/h) to determine the water permeability of the core plugs. As listed in Table 3, the measured porosity was in the range of u = 13.15-26% and the measured absolute permeability was in the range of k = 2.7-106.6 mD. Then, reservoir brine was displaced by the live reservoir fluid until irreducible water saturation. After the core plugs were fully saturated with the crude oil, the live reservoir fluid was injected into the core plugs and several flooding tests were conducted. Then, the differential pressure (DP) between the inlet and outlet of the core holder was measured by a digital pressure indicator and was indicated by the data acquisition system at preset time intervals.
To study the effect of production pressure, the production pump was adjusted to 15 MPa and the injected pump to various pressures. The live reservoir fluid was injected into the core and attained stabilized conditions within a few minutes. Then, the procedure of gradual pressure reduction was followed throughout the experiment. The injection pressure used in this experiment was in the range of 50-41 MPa with temperature at 70°C using live reservoir fluid. There was no flow of    Table 8 shows the experimental conditions. Samples of the core, after the flooding, were inspected by Scanning Electron Microscopy (SEM) (Scanning Electron Microscope, VEGA, TESCAN). The core samples that were damaged in the process mentioned previously would develop a layer on their surface. A thin section of the damaged core was then cut at a thickness of one centimeter. These samples were then dried and viewed under the electron microscope. The SEM image enabled a three-dimensional view of the core sample at a microscopic level.
During this experiment, permeability was calculated from the measured pressure drop along the core through Darcy's law. According to Darcy's equation (Eq. 1), the permeability is dependent on the interfacial surface area, the viscosity, etc.:

MATHEMATICAL MODELING OF ASPHALTENE DEPOSITION IN POROUS MEDIA
The asphaltene deposition modeling is not only according to the mechanical plugging mechanism but also according to the asphaltene adsorption mechanism.
In the majority of previous models, the asphaltene Schematic of core flooding apparatus.  The first adsorption step parameter (this step is taken to be adsorption of asphaltenes in solution to the surface of the rock, the second adsorption step parameter (this step is taken to be the adsorption of asphaltenes in solution to those asphaltenes already adsorbed to the rock, the mean aggregation number of the adsorbed asphaltenes (in developed model), the maximum possible adsorption for the whole isotherm, surface deposition, entrainment of deposits, mechanical plugging, snowball-effect deposition constant and critical interstitial velocity of liquid phase parameters deposition is based only on the mechanical trapping mechanism and it is different from the asphaltene adsorption mechanism. Also, the majority of previous work used two material balance equations based on the oil and asphaltene phases for core samples. In order to develop asphaltene deposition modeling including the asphaltene adsorption mechanism, a new model based on multilayer adsorption equilibrium theory and four material balance equations (oil, asphaltene, gas and water phases) was developed to account for asphaltene multilayer adsorption on core samples, as presented in our previous publication [28]. In this work, the results of asphaltene deposition in core samples during natural depletion were predicted using our proposed model based on the multilayer adsorption equilibrium mechanism and compared with those obtained using asphaltene deposition modeling based on the monolayer adsorption equilibrium mechanism [8], and obtained by Wang and Civan's [7] model based only on the mechanical plugging mechanism.

Asphaltene Precipitation Model
Solid modeling treats the precipitating asphaltene as a single component residing in the solid phase, while the oil and gas phases are modeled with a cubic EOS. Solid models may require many empirical parameters and excessive tuning to match experimental data. In this study, the Nghiem model [29] was used; the fugacity of asphaltene in the solid phase is given by: In a mixture, when the vapor, liquid and asphaltene phases coexist, the following thermodynamic equilibrium equations should be satisfied [29]: A three-phase flash algorithm is used to solve the above equations by using SRK EOS for the liquid and vapor phases. The existence of a solid phase satisfies the following criterion [29]: In this model, the only parameter that should be adjusted from the experimental data is the referenced pressure, P*. Also, according to our previous publication [30], Permeability reduction for studied live reservoir fluid and dead residual oil versus the injected pore volume for a sandstone core sample.  Permeability reduction for studied live reservoir fluid and dead residual oil versus the injected pore volume for a carbonate core sample.  Permeability reduction versus the injected pore volume for studied live reservoir fluid.
the asphaltene precipitation in this bottom hole live oil was calculated based on the Flory-Huggins theory.

Asphaltene Adsorption and Deposition Models
There are two asphaltene deposition mechanisms on porous media, adsorption and mechanical plugging.
The asphaltene adsorption mechanism, which is related to the interactions between the asphaltene functional groups and the rock surface, involves surface polarity, affinity or other attractive forces. This process is reversible, with asphaltene desorbing from porous media when the concentration of suspended asphaltene in crude oil decreases. Asphaltene is a polar component; therefore, formations containing clay and carbonate formation have greater ability than sandstone formations to adsorb asphaltene.
In order to develop a new model for asphaltene deposition in porous media, a multilayer adsorption equilibrium term was included in the asphaltene flow rate and porosity relations, as presented in our previous publication [28]. In this model, two steps are considered for asphaltene adsorption. The first adsorption step is taken as the adsorption of asphaltenes in solution to the surface of the rock, and the second adsorption step is taken as the adsorption of asphaltenes in solution to those asphaltenes already adsorbed to the rock, as follows [31]: Also, by comparison, the asphaltene adsorption was modeled using a monolayer adsorption equilibrium term (Langmuir isotherm equation), as follows [8]:                                                    Experimental and simulated deposited asphaltene during primary deposition (Q = 10 cc/h) in carbonate core sample (live reservoir fluid).

T. Jafari Behbahani et al. / Experimental Study and Mathematical Modeling of Asphaltene Deposition Mechanism in Core Samples
The deposition rate for asphaltene is given by: where the first term represents the surface deposition, the second term represents the entrainment of asphaltene deposits by the flowing phase when the interstitial velocity is larger than a critical interstitial velocity, and the last term represents the pore throat plugging rate. The value of b is set as [7]: where v L is equal to u L // The value of c is described as [7]: Thus, the pore throat plugging deposition rate increases proportionally with the total deposits. When D pt is less than D ptcr , pore throat plugging deposition will occur. The details of these models are described else where [7].

Mass Balance Equations
The asphaltene precipitation and deposition problems are represented by mass balance equations for the liquid and asphaltene, the momentum balance equation, the asphaltene precipitation and deposition models, and the porosity and permeability reduction models [7]. The mass balance for asphaltene is given by [7]: The mass balance equation for the live oil phase is given by [7]: where O represents the oil component and L represents the liquid phase. The details of these models are described elsewhere [7]. The majority of previous work used two material balance equations based on the oil and asphaltene phases for core samples. The material balance equations are included for the water and gas components during flooding processes, and therefore the material balance equations are proposed as follows: Gas phase [28]: Experimental and simulated deposited asphaltene during primary deposition (Q = 1 cc/h) in carbonate core sample (live reservoir fluid). Water phase [28]: The momentum balance equation is given by Darcy's law [7]: The instantaneous local porosity during asphaltene deposition is equal to the difference between the initial porosity and the fractional pore volume occupied by the deposited asphaltene and adsorbed asphaltene [28]: The instantaneous, local permeability, k, is calculated by [7]: Table 9 summarizes the considerations and parameters for all the studied models. Experimental permeability damage due to asphaltene deposition in cores was correlated using the above model of asphaltene deposition and their coefficients were adjusted to achieve the best match with the experimental data. The partial differential equations were coupled and solved using a finite-difference method, backward both in time and space, in MATLAB software to determine pressure and asphaltene concentration in the core samples. The Runge-Kutta fourth-order scheme was applied to calculate the volume fraction of asphaltene deposition and adsorption. A fully implicit numerical model was performed and solved by iterations. Numerical simulation runs were conducted to obtain the best match between experimental and numerical results. Numerical simulation was carried out in a linear grid system of 90 grid blocks. Time was discretized with a Dt of 30 second. For optimization and determination of the model parameters, history matching was used. In this study, square roots of the summation of the differences between measured and calculated porosity data are defined as the objective function [28]: As a result, the model parameters obtained by the optimization procedure are C 1 , k 1 , k 2 , m, n, a, b, v c , c, K a , r and f p . The simulated data are not appreciably sensitive to time and space steps. 1.1 9 10 À4 6.1 9 10 À3 9.1 9 10 À3 4.6 9 10 À3 k 2 4.6 9 10 À9 5.9 9 10 À9 8.9 9 10 À8 9.6 9 10 À8 4.3 9 10 À8  Figures 6 and 7 show the permeability reduction of two sandstone and carbonate core samples versus the pore volume of injected live reservoir fluid and dead residual oil samples. As observed, higher permeability reduction is caused when injecting the live reservoir fluid samples in comparison with the results obtained by injecting the dead residual oil samples for the studied sandstone and carbonate cores. This observation can be justified by the fact that the C 12 + fraction in live reservoir fluid samples is heavier than the dead residual oil and contains more asphaltene content. Also, this difference may be from the state of asphaltene in live crude oil that is quite different from that in dead residual oil. It is clear that live and dead residual oil asphaltene show clear compositional differences, including [26]: -the dead residual oil asphaltene sample contains a lower amount of the nitrogen-containing species but is higher in rings plus double bonds in comparison with the live reservoir asphaltene sample; -the live reservoir asphaltenes are rich in sulfur and oxygen compared with the dead residual oil asphaltene; -the live reservoir asphaltene has less aromatic compounds compared with the dead residual oil asphaltene; -the live oil asphaltene contains more functional groups and less saturated groups in comparison with the dead oil asphaltene.    Deposited asphaltene in core sample versus pore volume of injected oil.     Based on these results, it was concluded that the propensity for the asphaltenes of live reservoir fluid to aggregate into larger particles and to deposit on the rock was higher than for asphaltenes of dead residual oil. Therefore, permeability reduction and formation damage by asphaltene deposition during live reservoir fluid flooding were higher than for the dead residual oil flooding. Figure 8 shows the variation of the permeability for different types of core samples at various pore volumes of the injected live reservoir fluid.

Effect of Rock Type on Asphaltene Deposition
As can be seen from this figure, the permeability reduction in carbonate rock types is steeper than that observed in sandstone rock cores over the whole range of pore volume numbers. Also, it can be observed that the carbonate core samples can be plugged at lower pore volume numbers due to the higher rate of asphaltene deposition and permeability reduction. Thus, it can be found that the plugging deposition mechanism is very significant in asphaltene deposition in carbonate core samples.
The SEM images for both carbonate and sandstone rock types are given in Figures 9 and 10. As shown in these figures, a comparison of SEM images revealed that the carbonate core samples would develop a layer on their surface. Thus, the carbonate core samples experienced more particle plugging compared with sandstone core samples, and the carbonate core samples were severely plugged by aspaltene deposition. It can be seen that asphaltene deposition has different mechanisms in carbonate and sandstone core samples. Therefore, it can be concluded that the adsorption mechanism in asphaltene deposition in carbonate core samples is more significant than that in sandstone core samples.
The difference between the carbonate and the sandstone cores is related to the core structure, mineral composition and consolidation. Hence, the carbonate core's inner surface may contain polar groups, which can exert polar interactions with asphaltene surface groups. Therefore, it is likely that asphaltene deposition on the carbonate core's surface can involve p-interaction and hydrogen bonding between the asphaltene groups and core surface polar groups. Asphaltene is a polar component: therefore, formations containing clay and carbonate have greater ability than sandstone formations to adsorb asphaltene [23]. In fact, the existence of polar components makes the asphaltene molecules adhere more strongly to the surface, and hence increases the amount of asphaltene deposition on the surface of the carbonate rock samples. Figure 11 indicates the pressure drop versus pore volume for three rocks with different permeability.
It can be concluded that the formation damage caused by asphaltene deposition in low-permeability rock was more severe than that in higher-permeability rock for the same asphaltene content of the crude oil and under the same dynamic potential force. For low-permeability core samples, there may be a continuous deposition until complete plugging. In low-permeability cores, the plugging mechanism acts like a snowball growth that can be inferred from the sharp slopes of Figure 11 once plugging deposition is activated, leading to the first significant pressure variation. The results indicated that in low-permeability cores, the region of the asphaltene deposition was spread. There may also be a slow steady plugging for high-permeability cores. Furthermore, the deposition of asphaltene in the core was lower. In the high-permeability core, the region of the asphaltene deposition was limited in the inlet end of the core. Finally, a steady deposition can occur until interstitial velocity is high enough to not allow further mechanical plugging for medium permeability cores.

Effect of Oil Injection Flow Rate on Asphaltene Deposition
Figures 12-14 show the plot of the permeability reduction as a function of time for the cases of 1 to 30 cc/h injection rates for sandstone cores and 1 to 10 cc/h injection rates for carbonate cores. One of the most important results from this experiment is the permeability reduction of the core samples at the beginning of the injection, which shows that the plugging of the pore throats occurs immediately after asphaltene deposition. The results also show that the asphaltene deposition on the covered pore surface with asphaltene layers is less than that on the clean surface.
These plots clearly show that an increase in flow rate is followed by an increase in asphaltene deposition at low flow rates. At these flow rates, the permeability reduction took place in a steady manner. The reduction continued until a steady state was reached. At this point, the relatively low deposition rate leads to the development of a steady state in pores. Also, these figures show that reduction in permeability until a minimum value was observed, and then a reversal in permeability reduction took place at higher flow rates. At this point, the permeability increased and reached a steady state. For this case, flow begins with a speed higher than the critical speed but it declines steadily below the critical velocity and the asphaltene deposits. Because of asphaltene deposition, the pores are blocked and the speed increases beyond the critical speed and the entrainment phenomenon begins, resulting in an increasing permeability. Figure 14 shows that at a higher flow rate, 40 cc/ h, the asphaltene plugging process appeared to begin late.
However, as the flow continued, permeability reduction took place very quickly. For this case, a steady-state condition was never reached, and the injection pressure continued to rise until the injection had to be stopped. For this case, local speed values remain above the critical speed. Consequently, permeability reduction remains steady. This also means that most asphaltenes trapped would be in the vicinity of the wellbore, an area that can be treated with production stimulation operations [6]. Figure 15 shows the effect of production pressure on permeability reduction as a function of time.

Effect of Production Pressure on Permeability Reduction
It can be seen from this figure that the highest permeability reduction occurs at the highest production pressure at 50 MPa. The damage of the core sample was found to increase when the production pressures were increased. At higher production pressures, the asphaltene deposition in the core sample increased due to the increase in the driving force acting on the asphaltene particles. Greater asphaltene deposition caused severe blockage of pore throats, and thus greater reduction in permeability of the core sample induced.
Also, at high pressures, the asphaltenes are soluble in oil. However, during pressure depletion, the oil expands, reducing the oil solubility parameter, and it becomes a poor solvent for asphaltene. At a low pressure, asphaltenes begin to precipitate. Pressure depletion is the main reason for asphaltene deposition due to the destabilization of asphaltenes. This phenomenon occurred due to the decrease in the crude oil density, the vaporization of the light component and the decrease in the solubility of asphaltenes in the oil [32].
The flow rates of live reservoir fluid recorded for each injection pressure during the live reservoir fluid flooding experiment are shown in Figure 16.
It is seen that the recorded flow rates were in continuous response to the imposed pressure drops. In other words, a decrease in the system pressure was followed almost immediately or instantaneously, by a resulting increase in the system flow rate. This behavior indicates that an increase in injection pressure is followed by a constant production pressure.

Modeling Approach
In the majority of previous models, the asphaltene deposition is based on the mechanical plugging mechanism [7] and also, only two material balance equations were applied. Therefore, the previous models in the literature do not consider the adsorption mechanism, which is related to interactions between the positive polar component of asphaltenes and the rock surface.
Therefore, in the proposed asphaltene deposition model [28], in addition to the mechanical plugging mechanism term, a multilayer adsorption equilibrium mechanism term for asphaltene was included. Also, application of four material balance equations (oil, asphaltene, gas and water phases) instead of two material balance equations was considered. In this section, the results of asphaltene deposition in core samples during natural depletion were predicted using our proposed model based on the multilayer adsorption equilibrium mechanism and compared with those obtained using asphaltene deposition modeling based on the monolayer adsorption equilibrium mechanism [8] and obtained by Wang and Civan's [7] model based only on the mechanical plugging mechanism.
The proposed model was correlated using the natural depletion experimental data obtained in this work which are denoted as 1 to 12 in Table 8. Figures 17 to 35 show the results of permeability reduction, porosity reduction, pressure drop and deposited asphaltene in the sandstone, carbonate and dolomite core samples due to asphaltene deposition using the proposed model and compared with those obtained using asphaltene deposition modeling based on the monolayer adsorption equilibrium mechanism [8] and obtained by Wang and Civan's [7] model based only on the mechanical plugging mechanism. Figures 17 to 35 show that the proposed model can correlate the experimental data more accurately in comparison with the Wang and Civan [7] model and the model based on the monolayer adsorption equilibrium mechanism. These figures show that reduction in permeability until a minimum value was observed and then permeability increased in the experimental data. Because of asphaltene deposition, the pores are blocked and the speed increase beyond the critical speed and the entrainment phenomenon begins, resulting in increasing permeability. Figures 22 to 26 compare the results of porosity reduction due to asphaltene deposition in core samples using the proposed model with those obtained from the Wang and Civan [7] model and the model based on the monolayer adsorption equilibrium mechanism. It should be noted that the reduction of the porosity ratio is much lower than that of the permeability ratio. Figures 27 to 30 compare the results of pressure drop in core samples during oil flooding due to asphaltene deposition using the proposed model with those obtained from the Wang and Civan [7] model and the model based on the monolayer adsorption equilibrium mechanism. Figures 31 to 35 compare the results of deposited asphaltene in core samples during oil flooding using the proposed model with those obtained from the Wang and Civan [7] model and the model based on the monolayer adsorption equilibrium mechanism. Table 10 shows the Average Absolute Deviation (AAD) of the predicted permeability reduction from the experimental data due to asphaltene deposition using the proposed model, that of the Wang and Civan [7] model, and that of the model based on the monolayer adsorption equilibrium mechanism. These results also confirm that the proposed model based on the multilayer adsorption equilibrium mechanism of asphaltene can correlate the permeability reduction experimental data with AAD of 2.4-3.1%, whereas the Wang and Civan [7] model correlates asphaltene deposition less accurately with AAD of 4.2-5.6%. This suggests that the multilayer adsorption mechanism of asphaltene has an important role in asphaltene deposition on core samples.
The results show that modeling based on the monolayer adsorption equilibrium mechanism is less accurate in the modeling of asphaltene deposition during natural depletion with AAD of 3.1-3.8%. Therefore, the asphaltene adsorption behavior on core samples is far from the monolayer adsorption equilibrium mechanism and is closer to the modified model based on multilayer adsorption equilibrium behavior.
This phenomenon can be explained by the fact that the asphaltene adsorption mechanism, which is related to the interactions between the asphaltene functional groups and the core surface, involves surface polarity, affinity or other attractive forces. It is also known that asphaltene surface groups may have acidic (carboxylic, benzoic, phenolic), and/or basic (pyridine, pyrazine, dimethylsulfoxide) functionality [23]. Tables 11 to 13 show the adjusted parameter values of the proposed model based on the multilayer adsorption equilibrium mechanism of asphaltene, the model based on the Langmuir isotherm and Wang and Civan's [7] model during natural depletion in core samples. It should be noted that the adjusted parameters are affected by the nature of core samples (rock morphology, rock-surface characteristics, mineral composition, etc.). For example, the adjusted parameters in the proposed model such as the first adsorption step parameter (k 1 ) and the second adsorption step parameter (k 2 ) have different quantities in carbonate and sandstone core samples, which is related to different mineral composition and rock morphology. Also, the results show that the second adsorption step parameter (k 2 ) is much lower than the first adsorption step parameter (k 1 ). It was found that the tendency for asphaltene deposition on the pore surface that was covered with asphaltene is less than that for the clean surface of core samples.

Case Study
In order to verify the accuracy of the proposed asphaltene deposition model, the model was run using the data given by Minssieux et al. [10], as denoted GF3. Figures  36 to 40 compare the results of the pressure drop, deposited asphaltene in the porous rock, remaining asphaltene concentration in the flowing oil, and permeability and porosity profiles at various times using the proposed model with those obtained from the Wang and Civan [7] model and the model based on the monolayer adsorption equilibrium mechanism. It should be noted that the deposition model constants given in Tables 11 to 13 are used in the above-mentioned models without using the GF3 experimental data.
The water and live oil saturation profiles were studied and the results are shown in Figure 41. The water saturation increases through the core sample. The water saturation increases from an initial value of 0.44 toward the value of 0.62. The oil saturation decreases through the core sample. The oil saturation reduces from an initial value of 0.56 toward the value of 0.4.

CONCLUSION
In this work, a set of experiments was conducted using bottom hole live oil samples under dynamic conditions in porous media with the purpose of investigation of asphaltene deposition and adsorption mechanisms involved in the interfacial interaction of the asphaltene/mineral rock. The effective parameters of porous media on asphaltene deposition, such as morphology of the surface, were studied in this work using SEM micrographs. Also, the experimental data obtained in this work were correlated by an asphaltene deposition model based on the multilayer adsorption equilibrium mechanism and four material balance equations (oil, asphaltene, gas and water phases) and the correlation results were compared with other models based on the mechanical plugging mechanism and the monolayer adsorption equilibrium mechanism to account for permeability reduction in porous media in dynamic conditions. While none of the studied models cover the experimental results with satisfaction, the proposed model correlates the experimental formation damage data due to asphaltene deposition better in comparison with the other studied models.
The experimental and modeling results of asphaltene deposition and adsorption during core flooding led to the following conclusions: -the proposed model, based on the multilayer adsorption equilibrium mechanism of asphaltene and four material balance equations, is found to be more accurate than Wang and Civan's [7] model based on the mechanical plugging mechanism with AAD of less than 3.2. Hence, the multilayer adsorption equilibrium mechanism of asphaltene has an important role in asphaltene deposition, permeability reduction and wettability alteration of reservoir rock; -the experimental results showed that an increase in flow rate is followed by an increase in asphaltene deposition; permeability reduction and porosity reduction took place in a monotonous manner until a steady-state condition was reached at low flow rates. At higher flow rates, initial permeability was reduced until a minimum value and then an increase in permeability was observed until a steady-state condition was reached; -the effect of rock type on asphaltene deposition was also studied. It can be seen that the asphaltene deposition has different mechanisms in carbonate and sandstone core samples. SEM micrographs of asphaltene deposition on the surface of carbonate core samples show the formation of large clusters and propose multilayer adsorption of asphaltene; -the experimental results showed that the permeability reduction rate using the live reservoir fluid samples obtained from wells can be different from that of the same dead oil samples in the same conditions due to higher asphaltene content; -as inferred, the experimental results indicated that three depositional types, continuous deposition for low-permeability cores, slow, steady plugging for high-permeability cores and steady deposition for medium-permeability cores, can be observed. The results showed that the values of pore volumes of the injected crude oil are higher for sandstone cores compared with carbonate cores; -also, the experimental results showed that the damage of the core sample was found to increase when the injection pressure was increased; -the proposed model was verified using experimental data reported in the literature.