Mostafa Lashkarbolooki*,Shahab Ayatollahi

1 School of Chemical Engineering,Babol Noshirvani University of Technology,Babol,Iran

2 School of Chemical and Petroleum Engineering,Sharif University of Technology,Tehran,Iran

1.Introduction

The capillary forces acting in the interface region between crude oil and water entrap the oil ganglia in a complex network of underground capillary pathways keep the oil unrecovered in the reservoir[1,2].The magnitude of capillary force is directly proportional to the interfacial tension(IFT)of fluids which means that lower interfacial tension value,higher capillary number means.In addition,since the IFT is directly related to the capillary force,more oil recovery is possible as the IFT reaches to a specific level[3,4].

Although using aqueous solutions only containing ions is not able to achieve this ultra low IFT value,the IFT of aqueous solution containing different ions and crude oil have received increasing consideration over the recent years.Nevertheless,aqueous solution containing ions with different concentration can be used as smart water and low salinity water flooding as an EOR method beside as a transfer fluid of EOR agents.Therefore,investigation of the IFT of aqueous solutions/crude oil is an important parameter.Generally,there are several methods to reduce the IFT including using surface active agents,addition of salts to the aqueous solution,etc.Among these possible options,addition of salts into the aqueous solution has gained an increasingly attention during the past decades due to unique advantages on the reduction of IFT[5].In the light of these advantages,although,several investigations have been performed to formulate the effect of salinity on the IFT,no one can address this issue in general.The existence of several contradicting results and mechanisms[5-13]is the sign of this claim.But the clear point is that there is not a straightforward relation between the composition and type of crude oil and saline water quality and IFT variation.In the light of this fact,the influences of aqueous ions including NaCl,KCl,CaCl2,and MgCl2on the equilibrium IFT of an asphaltenic crude oil with high acidic compounds were previously investigated by coauthors[14]for concentrations ranged between 0 and 45,000 mg·kg-1and ambient conditions.

The results obtained by the coauthors revealed similar trends for the IFT at different salt concentrations with homolog systems including NaCl/KCl,and MgCl2/CaCl2[14].Besides,another investigation performed by the coauthors demonstrated that the effects of resin and asphaltene presented in the crude oil on the IFT of acidic crude oil/aqueous phase[15,16].The results showed that there are three dominant parameters which affect the IFT,including(a)the presence of surface active agents in the oleic phase,(b)the type of salts,and(c)salt concentration.According to the findings,it was concluded that the presence of resins and asphaltenes has a dual effect in the presence of divalent salt concentrations.In more details,for the case of low divalent salt concentrations,the asphaltene content leads to a greater decrease in the IFT compared with the resins,while for the elevated salt concentration solutions,the effect of resin for IFT reduction is dominant[15].In addition,the results demonstrated that the lowest equilibrium IFT values were obtained if the concentration of all the used ions reaches to about15,000 mg·kg-1[14,15].The noteworthy pointis thatinvestigation on the dynamic behavior of IFT has been largely ignored despite the dynamic behavior(raised from adsorption kinetics of surface active molecules at the liquid interfaces)being more important than static behavior in enhanced oil recovery applications[17].The reason behind this adsorption kinetic is controlled by transport processes in the bulk and the transfer of molecules from a solution state into an adsorbed state or vice versa[5,11].

The short-time approximation equation(Eq.(1))was used to calculate the diffusivity of surface active components from bulk to the crude oil/brine interface[18,19]:

where R is the universalgas constant(8.314 J·mol-1·K-1),T is temperature(K),D is diffusivity(m2·s-1),t is time(s),C is surface active agents(natural surfactant)concentration(mol·m-3),γtis the IFT of the system at surface age(time),γ0is the clean interfacial tension at time t=0,and Г is surface excess concentration(mol·m-2).

In general,the surface excess concentration is defined as the concentration of a species in the interfacial region which is in excess of the concentration of that species in the bulk[5].The crude oils are composed of four main components known as:saturates,aromatics,resins and asphaltenes[20].Resins and asphaltenes are important compounds in the crude oils which are in close relation to high molecular weight polycyclic hydrocarbons[14,15].On the other hand,asphaltenes and resins are natural surfactants making them interesting compounds for many researchers.The N,S and O elements existed in asphaltene structure distinguishing it from the hydrocarbons.In other meaning,being polar in nature,asphaltenes are surface-active substances which are able to significantly modify the properties of interfaces by adsorption[15,21].

At the last part of the adsorption process,as the adsorption has nearly attained its equilibrium value and the subsurface concentration varies little with time following equation is used[5,11,22]:

where γeand Γeqare the equilibrium IFT and the equilibrium surface excess concentration,respectively.The γ0(Eq.(1))and γe(Eq.(2))are obtained by the interceptofthe IFT versust1/2and t-1/2plots,respectively.

Therefore,at the start of the adsorption process,the short-time approximation would be used while at the end of the process the longtime approximation model is replaced.The short-time approximation is expected to become worse with increasing times and the long-time approximation with decreasing times[23].

The simplest way to evaluate the diffusion relaxation time,τ,is to use the mono-exponential decay model[5,24]:

Based on this equation,as the affinity and concentration ofthe active material increase,the adsorption time and reaching of the mesoequilibrium region reduce(when the change in dynamic IFT is reduced as a function of time).

In addition,the results reported in different literature demonstrated the high capability ofthe empiricalequation to describe the IFTbehavior[25,26]:where n and t*are constants whose values depend upon the nature of surfactant.The values of t*and n can be calculated by transforming Eq.(4)to its linear form:

The measured dynamic interfacialtension(DIFT)can be divided into four different regions including induction region,fast fall region,mesoequilibrium region,γm,(where γtshows only a small change with time),and equilibrium region[26]when the DIFT was plotted versus

In general,most of the previous published literature measured a single IFT value by assuming the equilibrium status of two fluids while the time-dependent IFT(DIFT)of crude oil/brine solutions which is a crucial parameter remains largely unexplored.

Due to the aforementioned facts,in the currentinvestigation a series of systematic experiments are conducted to draw a complete picture about the interfacial properties of asphaltenic-acidic crude oil followed by modeling.

Since the optimal salinity is a crucial parameter in EOR processes,the first objective of this study is to experimentally measure the crude oilaqueous ions dynamic IFT for aqueous ions including NaCl,KCl,MgCl2,and CaCl2at 15,000 mg·kg-1(optimum concentration for equilibrium IFT)and pressure of 500,1000,2000,and 4000 psi(1 psi=6.895 kPa)while the temperature held constant at 30°C.Finally,measured dynamic IFT of all systems is modeled using three different models namely diffusion-controlled,mono-exponential decay models,and empirical equation.With the assist of these models,induction,rapid fall(relaxation or adsorption),meso-equilibrium and equilibrium times,the diffusivity of surface active agents in the crude oil to the crude oil/aqueous phase surface and the surface excess concentration of surface active agents of deionized water(DW)systems are compared to brine solution systems.

2.Experimental

2.1.Experimental apparatus

The IFT between two fluid phases is defined as an enhancement in the Gibbs energy per unit increase in interfacial surface area while the pressure,temperature and number of mole are kept constant[27].Throughout the years,different IFT measurement methods have been proposed by differentresearchers forimmiscible fluids[28,29].Amonograph by Rusanov and Prokhorov[30]provided a broad review of the technical literature on the IFT techniques with detailed discussion of the theoretical bases and instrumentations.In general,the purpose and experimental environment are two parameters which dictate what kind of IFT measurement technique must be used.

Pendantdrop tensiometry has been shown to be a useful tool for the experimental measurement of the relaxation in IFT due to the adsorption of surfactantata fluid interface[31].Since in the currentinvestigation the IFT range is between 1 and 50 mN·m-1,the pendant drop method is utilized due to its good unique capabilities.For example,it is possible to perform this measurement at the elevated temperature and pressure.In the light of these advantages and considering its accuracy and suitability[11],the pendant drop which is based on the equilibrium of static force is the preeminent method suited for the current investigation[32,33].Measurement of dynamic IFT using the pendant drop method is based on the reality thatthe drop changes its shape as a resultofinterface relaxation[19].In brief,pendant oil drop is injected into a high pressure/high temperature vie wcell that is already filled with brine atdesired condition.

The visual cell is equipped with three heating elements,a PT100 thermocouple,a PID controller with an accuracy of 0.1 K and a pressure transmitter with a fullscale accuracy of0.25%.To eliminate the heatloss,the visual cell is equipped with a jacket.After a period of time which introduced into the system to be assure about the stabilization of pressure and temperature,the crude oil was gradually discharged into the visual cell chamber[34].As soon as the produced drop at the tip of the nozzle reaches the maximum volume which could stabilize for sufficient time,the crude oil injection was stopped.

Once the proper drop at the tip of the nozzle generated the system is isolated during the video recording stage.At this point,the fully automated software(Axisymmetric Drop Shape Analysis)was started to monitor the drop and analyze it each 2 s at least for 1 h.In brief,the tendency of an interface between two immiscible phases to create the smallest surface area,gives rise to a pressure difference between the two fluids on either side of a curved interface:

whereΔP is the capillary pressure,γis the interfacialtension and R1and R2are the principal radii of curvature.

Ifthe drop is assumed to be axisymmetric aboutits verticalaxis,then ΔP at any given point on the interface curve can be written with reference to the apex point where R1=R2=R0[35]:where R0is the radius of curvature at the origin of the x-z coordinate(apex point),Δρ is the difference in the densities of the two phases,g is the gravitational acceleration,z is the vertical height measured from the datum plane and φ is the turning angle measured between the datum plane and the tangent to the interface at the point(x,z).R1is defined as the inverse of the rate of change of the turning angle,φ,with respect to the arc-length parameter,s.

In this way,the shape of the pendant drop has to be analyzed and the fluid densities have to be known in order to determine the IFT.Avibrating tube densitometer(Anton-Paar,Austria)worked at high pressure and temperature was used to measure the density of the fluids.A detailed description of the employed experimental setups is illustrated elsewhere[10,33].

2.2.Crude oil and salt properties

The properties of the used crude oil supplied from one of the Iranian oil reservoirs are presented in Table 1.The results of comprehensive chemical analysis of the crude oil including gas chromatography(GC)analysis,infrared(IR)spectroscopy(PerkinElmer Spectrum RX1)and totalacid number measurement(ASTMD 664-1989[36])are presented elsewhere[14,15].In brief,the used crude oil had a high acid fraction(TAN=1.46 mg KOH·(g oil)-1)and high asphaltene(11 wt%)and resin contents(13 wt%)consist of sulfoxide,sulfone,and carbonyl functions as well as small amounts of phenolic,amine,and amide functionalities.It is noticed that the crude oil is considered as an acidic crude oil if the TAN number of an oleic phase is higher than 0.5 mg KOH·g-1[37].All of the salts including NaCl,KCl,MgCl2and CaCl2were supplied from Merck,Germany and the properties of them are listed in Table 2.

Table 1 Crude oil properties

Table 2 Salt properties

3.Results and Discussion

The repeatability of the measurement for the used oil and two aqueous solutions is shown in Fig.1.The results of these measurements revealed an average deviation of1.3%and 2.9%for KCland MgCl2aqueous solutions,respectively,for dynamic IFT measurements.The obtained results showed that repeatability of dynamic IFT measurements was satisfactory despite the slight change of volume of crude oil drop.The relation between ions and distribution of surface active components of oil phase into the crude oil/aqueous phase interface are examined using dynamic IFT measurement.Fig.2 showed that dynamic IFT of 15,000 mg·kg-1of KCl/crude oil as a function of pressure had a similar trend if they were plotted versus time.As can be seen,the IFT decreases as a function of time,because of the adsorption of polar components such as asphaltene and resin at the crude oil/aqueous phase interface.This observed trend strengthens the hypothesis of natural surfactant activation at the fluid/ fluid interface.Besides,a close examination of the obtained results revealed that although no significant effect is introduced by pressure into the dynamic behavior of IFT,it is able to slightly increase the value of IFT.

In addition,the results illustrated that KClaqueous phase introduces a similar electrostatic behavior as a function of pressure.In order to obtain the induction,adsorption,equilibriumand meso-equilibriumtimes,mono-exponential decay model and empirical equation were utilized.

In addition,Fig.3 shows the dynamic IFT of crude oil/15000 mg·kg-1of KCl aqueous solution at a pressure of 4000 psi(1 psi=6.895 kPa)as a function ofusing a semi-logarithmic scale.Induction,adsorption and equilibrium times are also depicted in Fig.3.As can be seen,the measured DIFT was divided into four different regions including induction region(I),fast fallregion(II),meso-equilibriumregion(III),and equilibrium region(IV).Due to low induction time,the fast fall region could be considered equal to adsorption time.The point that should be mentioned is that it is possible to calculate the meso-equilibrium time by subtracting the adsorption time from equilibrium time.

For the sake of a better comparison,standard deviation(SD)of measured equilibrium IFT of DW and monovalent salts as well as the employed constant parameters of models with AARD of predicted IFT to the experimental IFT are tabulated in Table 3.Comparing the AARD of the mono-exponential decay model with empirical equation(see Table 3)shows that mono-exponentialdecay model prediction is better than empirical equation for DW,NaCl and KCl in the entire range of studied pressure.Since the effect of the pressure on the DIFT is the same for all of the examined pressures,only one set of fitting parameters was used for all the examinations at constant temperature.In other words,the fitting parameters are obtained using regression method using the minimum error for a constant temperature and four constant pressures as an objective function.In general,although a slight deviation in the result of modeling is observed,a good capability of the empirical equation was recorded.This result showed that dynamic IFTis satisfactory decay based on the exponential function.

Fig.1.Dynamic IFT repeatability of the used crude oil and KCl and MgCl2 at 15000 mg·kg-1 and 1000 psi(1 psi=6.895 kPa).

Fig.2.Time-dependent behavior of IFT at different pressure for 15000 mg·kg-1 of KCl aqueous solutions(1 psi=6.895 kPa).

Fig.3.Generalized dynamic IFT versus lg on empirical equation for crude oil/15000 mg·kg-1 of KCl aqueous solution at T=30 °C and P=4000 psi(1 psi=6.895 kPa).

Table 3 Errors of equilibrium IFT measurement and the used models for prediction of dynamic IFT of monovalent salts(1 psi=6.859 kPa)

A closer examination in Figs.4 and 5,one can observe that the dynamic IFTs of 15,000 mg·kg-1of divalent salts including CaCl2and MgCl2solutions nearly increase as the pressure increases.Besides,these figures demonstrate that the dynamic IFTs of both systems are considerably independent of pressure.Also,it can be seen that the IFTs of brine+crude oil systems were reduced to～6.6 and～16.7 mN·m-1for MgCl2and CaCl2,respectively.The depicted results demonstrated that the IFT of divalent ions(i.e.CaCl2and MgCl2)experienced a sharp reduction in the early stage of measurements.For the sake of comparison,adsorption,equilibrium,and meso-equilibrium times of used crude oil/different aqueous solutions as a function of pressure are shown in Fig.6(a),(b),and(c),respectively.As can be seen in Fig.6(a),addition of 15000 mg·kg-1of monovalent salt reduces adsorption time(～1950 and～2330 for KCl and NaCl,respectively)compared with DW(～2500 s).It should be noticed that the lower adsorption time is needed if the rate of movement of the surface active agents towards the interface is higher.In more details,the concentration ofthe surface active agents at the interface approaches maximum affinity to the interface in the lower time when monovalent salts were added to the solutions compared to DW.In addition,the attained results revealed that the adsorption time significantly reduces if the addition of 15000 mg·kg-1of divalent salts to the aqueous solution occurs(～500 and 410 s for MgCl2and CaCl2,respectively)compared with monovalent ions.In other words,the following conclusion can be extracted for the adsorption time:

Fig.4.Time-dependent behavior of IFT at different pressure for 15,000 mg·kg-1 of CaCl2 aqueous solutions(1 psi=6.895 kPa).

Fig.5.Time-dependent behavior of IFT at different pressure for 15,000 mg·kg-1 of MgCl2 aqueous solutions(1 psi=6.895 kPa).

Fig.6.Comparison between(a)adsorption,(b)equilibrium and meso-equilibrium and(c)times of used crude oil/different aqueous solutions as function of pressure(1 psi=6.895 kPa).

Adsorption time of：DW＞NaCl＞KCl＞MgCl2＞CaCl2

An almostsimilartrend was observed for equilibriumtime,although equilibrium time of 15000 mg·kg-1of NaCl is slightly more than DW.But in the case of MgCl2interesting results are obtained considering its meso-equilibrium time.In more details,although adsorption and equilibrium times of MgCl2are considerably lower than DW and monovalentsalts,its meso-equilibrium time is higher than DWand is nearthe monovalent salts.This observed trend is related to this fact that the complex ion of Mg2+and polar organic component of asphaltene and resin[15]is rapidly formed,but the packing of these complex ions at the interface needs higher time.

The packing of the surface active agents at the interface in the meso-equilibrium region is the most important parameter to experience the lower meso-equilibrium region.As it was previously reported,the affinity ofMg2+to the resin molecules is higher than Ca2+while the affinity of Ca2+to the asphaltene molecules is higher than Mg2+[14].Therefore,the time of packing of the surface active agents is lower for Ca2+due to the higher polarity of asphaltene molecules and higher affinity of them to Ca2+cation.

The values of equilibrium IFT of crude oil with different solutions(with different concentration of salts)are demonstrated in Fig.7(a)as a function of pressure.According to the outcomes(see Fig.7),it can be concluded that the monovalent ions introduce a slight effect on the equilibrium IFT,whereas the effect of divalent ions on the equilibrium IFT is more apparent.

The point that must be mentioned is that the volume of drop is different from drop to drop for all of the examined salts.As can be seen from Fig.7b,for CaCl2and MgCl2smaller drop was used.Due to lower IFT of crude oil in these solutions compared to DW,KCl and NaCl(see Fig.7a),it was not possible to form a large drop.In other words,the smaller crude oil drop is needed for systems with lower IFT.In details,the increase of IFT for salt solutions containing the anion Cl-for pressure of 500 psi(1 psi=6.895 kPa)is as follows:

DW＞KCl＞NaCl＞CaCl2＞MgCl2

As the pressure increases,the rate of IFT enhancement for 15000 mg·kg-1of KCl solution is higher than that for DW.

Fig.7.Comparison between(a)equilibrium IFT of used crude oil/15000 mg·kg-1 of different brine solutions and(b)volume on crude oildrop as a function of pressure(1 psi=6.895 kPa).

Table 4 Errors of equilibrium IFT measurement and the used models for prediction of dynamic IFT of divalent salts(1 psi=6.895 kPa)

To understand which mechanism is dominant,dynamic adsorption models based on short and long term approximations were used.Comparisons between the error of fitting of short and long time approximations used for correlating the dynamic IFT values of crude oil/15000 mg·kg-1of different brine are tabulated in Table 4.The point that must be mentioned is that in Table 4,for diffusion-controlled models,AARDs/%of predicted IFT are given based on the adsorption time and the entire range of time.

Fig.8.Comparison between a)diffusivity of surface active agents to the crude oil/different aqueous solution interface and b)surface excess concentration of surface active agents atcrude oil/different aqueous solution interface as function of pressure(1 psi=6.895 kPa).

As it is clear from Table 4,the short-time approximation showed a satisfactory prediction of the experimental IFT data before adsorption time while the prediction results experienced a worse deviation as time increases after adsorption time.Contrariwise,the long-time approximation correlates the experimental IFT data after adsorption time and prediction become worse with decreasing times before adsorption time especially for initial times.As suggested by Joos et al.[23],at the start of the adsorption process the short-time approximation was utilized in which diffusivity of surface active agents to the fluid/fluid interface was calculated(see Fig.8a).On the other hand,at the end of the process the long-time approximation was used and surface excess concentration of surface active agents at the interface was calculated(see Fig.8b).

As the results presented in Fig.8a and Table 5,the diffusivity values of asphaltenes and resins in the crude oil are between D～10-18and 10-19m2·s-1.These values of diffusion showed that the process is non-diffusion-controlled process as Pradilla et al.[40]reported for their findings regarding the Brij?-93(model demulsifier)and asphaltene in xylene.In these cases,a decrease in the IFT is not clarified through the diffusion of surfactant molecules to the interface,but as an alternative itis probable that an adsorption barrier is present[40].In addition,Rane et al.[41,42]using the oscillating pendant drop technique found that at water-oil interfaces,adsorption from largely aliphatic oils appeared to be governed at early times by molecular diffusion and at later times by molecular random sequential adsorption.

In addition,a close examination in Fig.8 a revealed that the effect of salt on the diffusivity of surface active agents follows the current sequence:MgCl2＞CaCl2＞NaCl＞KCl＞DW.The presence of divalent ions including Mg2+and Ca2+changes significantly the adsorption process.The presence of divalent ions in the aqueous solutions decreases adsorption time while increases diffusivity of surface active agents to the crude oil/aqueous phase interface.As it was expected,the surface excess concentration of surface active agents can be a positive parameter due to the presence of asphaltene and resin at the interface of aqueous solution and crude.Besides,this parameter is higher for CaCl2aqueous solution compared with DW and monovalent salts due to low equilibrium IFT.In particular,many complex ions constructed by divalent ions(calcium and magnesium salts)and of a polar organic component,which have N-and O-bearing moieties,are soluble in aqueous solutions,which can consequently enhance the surface excess concentration[15].Although positive values were obtained for surface excess concentration of surface active agents based on the dynamic adsorption model,surface excess concentration of surface active agents at CaCl2aqueous solution/crude oil interface is lower than DW and NaCl aqueous solutions(see Fig.8b).

Through the Gibbs adsorption isotherm,the IFT is linked to the composition of the system.The change in IFT as a function of chemical activity of the components can be obtained through the Gibbs equation[43-45]:

where dγis the change in IFT of the solution,R is the gas constant,T is the absolute temperature,and Гiand aiare the surface excess concentration and the activity of the i th component in the solution,respectively.

Equilibrium IFT of crude oil,8 wt%of extracted of asphaltene and resin in toluene and 15000 mg·kg-1of different brine solutions at ambient conditions[15]are shown in Fig.9.It is shown that equilibrium IFTs of aqueous solutions/crude oil conform the following sequence:

Fig.9.Effect of ion type and surface active component(8 wt%of extracted of asphaltene and resin in toluene)in equilibrium IFT of crude oil.

The measured IFT of toluene/deionized water,8 wt%extracted asphaltene and resin in toluene compared to deionized water were 35.4 mN·m-1,23.9 and 24.1 mN·m-1,respectively.It was also observed that ions especially divalent cations because of synergetic effect of asphaltene and resin with salt leads to more IFT reduction.

The IFT of crude oil/brine solutions and the surface excess concentration of the surface active agents(i.e.asphaltene and resin)did not follow the same trend.For more investigation,dynamic IFT of crude oil/15000 mg·kg-1of different brine solutions are at temperature of 30°C and pressure of 500 psi are depicted in Fig.10.A glance on the depicted results one can find out that initial IFTs of aqueous solutions/crude oil conform the following sequence:

Therefore,polar organic components of surface active agents(i.e.,asphaltene and resin)react with the Ca2+cations consequently producing complex ions[14,46,47]leading to an enhancement in the activity coefficient of the surfactant in the aqueous phase.Hence,based on the Gibbs adsorption isotherm(Eq.(8)),equilibrium IFTdecreases compared with DW as the activity of the surfactant in the aqueous phase increases.For MgCl2,two important parameters including surface excess concentration and activity of surface active agents increase compared with other studied salts consequently leading to a significant IFT reduction for MgCl2compared with the other salts.Although the equilibrium surface excess concentration of CaCl2case is obtained lower than DW,NaCl and KCl cases(see Fig.8),not only the higher activity of surface active agents(is equal to lower initial IFT(see Fig.10))in the aqueous solution containing CaCl2leads to lower equilibrium IFT for CaCl2solution but also the equilibrium time is considerably lower for CaCl2case(see Figs.6 and 10).In other words,the initial IFT of the used crude oil/CaCl2is obtained lower than DW,NaCl and KCl systems due to higher activity of resin and asphaltene in the Ca2+solution.Therefore,the activity of the surface active agents in the presence of Ca2+is dominant mechanism compared with the equilibrium surface excess concentration.Moreover,due to low impact of pressure on the equilibrium surface concentration(see Fig.8 b)and activity of surface active agent(see initial IFT on Figs.2,4 and 5),equilibrium IFTs(Fig.7 a)were not changed based on Eq.(8).In addition,based on the obtained results it can be concluded that the presence of salt,especially divalent cation,is able to alter the distribution of surface active agents between crude oil and aqueous phase and enhances the adsorption of them at the interface and consequently leads to the IFT reduction.

Table 5 Comparison of adsorption parameters of different systems with the current investigation

Fig.10.Comparison of dynamic IFT of crude oil/15000 mg·kg-1 of different brine solutions at T=30 °C and P=500 psi(1 psi=6.895 kPa)with exponential decay model(EDM).

As it is obvious in Fig.10,deviation between the dynamic IFTs calculated by mono-exponential decay model and the experimental values is higher for MgCl2compared with other studied salts.Digging on the result stabulated in Table 4 revealed that the empiric alequation for MgCl2leads to higher accuracy compared with the mono-exponential decay model.A closer examination in Tables 3 and 4 illustrated that for aqueous solutions which had low diffusivity of surface active agents including DW,NaCl,and KCl,not only short time approximation prediction in entire times is satisfactory but also it demonstrated higher accuracy than the long time approximation model.In contrast,the long-time approximation model predicts dynamic IFT better than the short time approximation for divalent cations including Ca+2and Mg2+which have high diffusivity.

4.Conclusions

The different models are used to predict the dynamic IFT of asphaltenic-acidic crude oil over aqueous phase containing chloride anion bonding to Na+,K+,Mg2+and Ca2+cations.In addition,the Gibbs adsorption is other mand dynamic adsorption model were utilized to describe the impact of activity and surface excess concentration of surface active agents(i.e.asphaltene and resin)in the IFT behavior of different ions.Totally,the following conclusions are extracted from the performed experiments and modeling:

?Although,pressure has no considerable effect on dynamic behavior of IFT for different saline solution/crude oil,the value of equilibrium IFT slightly increased as the pressure increased.

?The measured dynamic IFT properly qualified the variations on the crude oil/saline solution interface.

?The divalentions reduce the adsorption time more than monovalent ions.

?The short time approximation model experience more deviation at the end of the process as the activity of surface active agents at the fluid/ fluid interface increases.

?It was found that the aqueous solution containing Mg2+is more effective compared to others,however the arrangement of the surface active components at the interface,hence the IFT reduction needs more time for this case.

?Although the surface active agents surrounding Ca2+solution pose lower surface excess concentration than water,higher IFT reduction was observed due to the high activity of surface active agents for CaCl2.

?The next phase of this study would be design of experiments to investigate the effectof temperature,pHand crude oil type to clarify smart water injection applicability in the reservoir.Comparison of the crude oil sample from Iran with samples from other places(i.e.of different composition)may also be a subject of interest.

Acknowledgments

The authors express their sincere gratitude to Mr.Ali Zeinolabedini Hezave for his masterful guidance during the experimentation and organizing this manuscript.

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