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DOI 10.1140/epjp/i2019-12821-9
Regular Article
Eur. Phys. J. Plus (2019) 134: 436 THE EUROPEAN
PHYSICAL JOURNAL PLUS
Experimental design methodology as a tool to optimize the
adsorption of new surfactant on the Algerian rock reservoir:
cEOR applications
Seif El Islam Lebouachera1,3, Rachida Chemini1, Mohamed Khodja2, Bruno Grassl3, Mohammed Abdelfetah Ghriga3,4,
Djilali Tassalit5, and Nadjib Drouiche6,a
1Laboratoire des Sciences du G´enie des Proc´ed´es Industriels, Facult´edeG´enie M´ecanique et du G´enie des Proc´ed´es Universit´e
des Sciences et de la Technologie Houari Boumediene, Bab-Ezzouar, 16111 Alger, Algeria
2SONATRACH, Direction Centrale Recherche et D´eveloppement, Avenue 1 Novembre, 35000, Boumerdes, Algeria
3Institut des Sciences Analytiques et de Physico-chimie pour l’Environnement et les Mat´eriaux, IPREM, UMR 5254, CNRS
Universit´e de Pau et des Pays de l’Adour, 2 avenue P. Angot, Technopˆole H´elioparc, 64000 Pau, France
4Laboratoire de G´enie Physique des Hydrocarbures, Facult´e des Hydrocarbures et de la Chimie, Universit´e M’Hamed Bougara
de Boumerdes, Avenue de l’Ind´ependance, 35000 - Boumerdes, Algeria
5Unit´edeD´eveloppement des Equipements Solaires, UDES/EPST, Centre de D´eveloppement des Energies Renouvelables,
Route Nationale no. 11, BP386, Bou Isma¨ıl, 42400, Tipaza, Algeria
6CRTSE-Division CCPM- No. 2, Bd Dr. Frantz FANON- p.o.box 140, Alger sept merveilles, 16038, Algeria
Received: 24 January 2019 / Revised: 6 June 2019
Published online: 10 September 2019
c
Societ`a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019
Abstract. In this research work, a new surfactant called surf EOR ASP 5100 used in the SWCTT (single
well chemical tracer test) in the Algerian oilfield and sodium dodecyl sulfate (SDS) were used for static
adsorption tests. The Algerian rock reservoir has been characterized by different techniques such as SEM,
XRD, XRF, BET analysis. The equilibrium was successfully verified by Langmuir isotherm and second-
order (R2>95%) models for all concentrations and temperatures to predict the adsorption process.
Furthermore, the adsorption process was found to be exothermic (ΔG◦<0). To quantify the minimal
adsorbed quantity, a full factorial design of 23(8 experiments) was applied to analyze the individual
effects and interactions of operational parameters using variance analysis (ANOVA), desirability method
and response surface methodology. The optimal conditions obtained are as follows: the Qevalue was
2.3291 mg/g for the SDS surfactant at a concentration of 200 ppm and temperature of 25 ◦C, and Qewas
3.894513 mg/g for EOR ASP 5100 for the concentration of 200 ppm and temperature of 80 ◦C.
1 Introduction
Oil production from mature reservoirs is declining nowadays and is often low compared to the growing oil demands
around the world, leading to an increased interest toward Enhanced Oil Recovery (EOR) technologies such as surfactant
flooding, polymer flooding, etc. Surfactants with their complex chemical structures consisted of hydrophobic and
hydrophilic groups are used in various applications such as foaming, detergency, dispersion and solubilization of the
oils [1–5]. They are injected in oil reservoirs followed by a mixture of viscous polymer pumped into the porous medium
with an adequate pressure [6–8]. Surfactants are mainly injected to reduce the oil-water interfacial tension (IFT) to
values around 0.001mN/m, which consequently reduces the saturation of the residual oil. The oil trapped by the
capillary forces can be then displaced [9]. In litterature, it was reported that a quarter of the world’s reservoirs are
sandstone type, where the industrialists have tried to apply surfactant polymer formulation methods to recover more
oil from these reservoirs [10,11].
Currently, surfactant injection triggered an increased interest due to rising oil prices [12]. In the literature, many
influencing parameters on EOR injection were taken into account by researchers to quantify the retention quantities
of surfactants during its flow in the consolidated and unconsolidated reservoirs [13–17], as is the case for media
heterogeneities, surfactant types and reservoirs parameters effects. The adsorption could involve many mechanisms,
ae-mail: nadjibdrouiche@yahoo.fr (corresponding author)
Page 2 of 15 Eur. Phys. J. Plus (2019) 134: 436
such as electrostatic and non-polar chain-solid interactions, salvation and desolvation of adsorbates and adsorbents
materials, hydrogen bonding or van der Waals interactions between hydrocarbon chains of the adsorbed surfactant [18].
The surfactant retention on porous media can be related to many factors, such as the mineralogical composition of
rocks, the concentration, the dosage of the surfactant [19,20], the temperature [21, 22], the pH, the adsorption dose, the
ionic strength and the electrolyte concentration [4,23]. On the other hand, in order to optimize an adequate process
for EOR injection, adsorption equilibrium and kinetics are very practical laboratory tests for studying the surfactant
adsorption on a rock surface and to understand the interactions between them. Equilibrium results could facilitate the
determination of adsorption rate and predict the fate of surfactant in order to establish beneficial injection strategies.
Owing to the use of different surfactants with different compositions during the laboratory studies, a systematic
comparison among the adsorption of commercial surfactant is fairly impossible. The type of the employed surfactant,
the mineralogical and morphological properties of the rock and the types of the electrolytes existing in solution are the
most effecting parameters on the adsorption isotherm nature [20,24,25]. It was also found that the rock surface charge
and the fluid-solid interfaces have their own importance in the case of surfactant adsorption. According to studies done
by Wayman (1963) and Scamehorn (1980) about the adsorption of a dilute solution of sodium alkyl benzene sulfonate
on a variety of clay minerals, it was emerged that the Langmuir equation fits well with adsorption isotherms which
are capable of expanding with the usage of Truber diagram [24, 26–36].
Several recent studies have been conducted in order to investigate the retention of surfactants. Recently Rahul
Saha et al. [19] studied the effects of mineralogy and temperature on adsorption characteristics of SDS surfactant,
the results indicated that Langmuir isotherm and pseudo-second order were the models for describing the adsorption
phenomena which follows the order of illite >feldspar >montmorillonite >kaolinite. Ali Ahmadi analyzed the
influence of nanosilica particles on both adsorption and ultimate oil recovery when he used sodium dodecyl sulfate
as surfactant. The author showed that the incorporation of nanoparticle in both hydrophilic and hydrophobic states
could reduce the SDS loss due to the adsorption phenomena [37]. Scamehorn and Wayman studied the adsorption of
a dilute solution of sodium alkyl benzene sulfonate (SABS) as a surfactant on various clay minerals. They concluded
that the adsorption isotherms correspond to the Langmuir equation [24]. Ahmadi and Shadizadeh [18,19] reported
the adsorption kinetics behavior of the natural surfactant Zyziphus Spina Christi on real samples of shale-sandstone
reservoir, where the effect of temperature on the kinetics and equilibrium of adsorption process was experimentally
done. The results indicated that the Freundlich model was more acceptable for the adsorption equilibrium of this
natural surfactant after analyzing the related data for four models [11]. Bera et al. modeled the adsorption of three
different surfactants namely anionic (SDS), cationic (CTAB), and nonionic (Tergitol 15-S-7) on clean sand particles,
which were investigated with a variation of some parameters such as salinity, adsorbent dose, temperature, and pH.
Pseudo-second order and Langmuir were the most appropriate ones for predicting the adsorption process [4].
Other studies using optimization techniques have also been investigated. The statistical design of experiments in
which each factor was involved and simultaneously varied. It allows together aplenty information with a minimum
number of experiments [38–40]. Zhang et al. [41] studied the kinetics and equilibrium of acid dyes on chitosan/surfactant
adsorption. The main and interaction effects between different parameters, such as surfactant concentration, initial
dye concentration and temperature on adsorptions of two adsorbents were analyzed by 23full factorial designs. Cheng
et al. [42] reported four processes variables (i.e. surfactant concentration, temperature, and initial dye concentration)
of adsorption in which Congo red and direct red 80 AC/surfactant were optimized by response surface methodology
(RSM). Radnia et al. have evaluated the adsorption behavior of graphene oxide which represents an important factor
of chemical enhanced oil recovery methods onto sandstone surface at various levels of GO concentration. In this study,
the salinity and pH were assessed by surface response methodology [43]. Lebouachera et al. investigated experimentally
the effect of concentration, salinity and temperature of SDS adsorption onto an Algerian sandstone reservoir rock to
quantify the adsorbed quantity [44].
To our knowledge, no research in the literature has examined the adsorption of EOR ASP 5100 and SDS surfactants
in an Algerian sandstone reservoir using experimental design methodology. In this article, the adsorption behavior of
the new surfactant ASP EOR 5100 on the Algerian rock under the effect of different parameters, such as surfactant
concentration, contact time and temperature, were evaluated. The Adsorption isotherms models of Freundlich, Lang-
muir and Temkin have been analyzed. The kinetics were verified by pseudo first and pseudo second orders. Different
characterizations, such as XRD, SEM, XRF, BET analysis, were used to identify the mineralogy of this rock. The in-
troduction of the novel concept of full factorial design was used to optimize the adsorption quantity for an appropriate
surfactant selection in EOR processes.
2 Materials and methods
2.1 Surfactants
An anionic SDS surfactant with a purity of 98% and molecular weight equal to 288 g/mol purchased from Merck
Company alongside a commercial EOR ASP 5100 surfactant, purchased from Solvay company, were used during the
experiments.
Eur. Phys. J. Plus (2019) 134: 436 Page 3 of 15
2.2 Rock sample
Rock samples were obtained from Hassi Messaoud sandstone reservoir, which is located in south of Algeria. Crushed
rock samples were sieved into fractions of 4 μm to obtain a uniform geometric size for the experiment. The grains were
washed with distilled water and dried in an oven at 150 ◦C for 24 h.
2.3 XRD, XRF, SEM and BET analysis
PANalytical X-ray diffractogram was used to evaluate the semi-quantitative composition of the Hassi Messaoud crushed
cores. The X-ray was applied in a wide range of Bragg angles (2◦≤2θ≤70◦). The data were analyzed using a data
collector and treated with High score Plus PANalytical measuring instrument with CuKα(λ=1.54186 ˚
A). The
minerals composition results are evaluated based on the sequential spectrometer Bruker-Axs: S8 TIGER as shown in
table 1. Our results have been treated using the Spectra Plus software. In addition, we examined the sample by SEM,
looking for crystal morphology with Thermo Fisher Scientific under the name FEI-Quanta 650. The BET surface of
rock was measured using a Quanta chrome Autosorb-3bsurface analyzer based on nitrogen adsorption. The sandstone
powder was dried in an electric convection oven at 120 ◦C overnight to eliminate water and further adsorbed substances.
2.4 Preparation of surfactant solutions
The surfactant solutions were prepared with distilled water and the concentration of SDS and EOR ASP 5100 was in
the range of 200–800 ppm.
The first solutions of SDS and EOR ASP 5100 were prepared with concentrations varying between 200 and 800 ppm
by dissolving the adequate amounts in 100ml distilled water. The surfactant was dissolved slowly in distilled water
under stirring using a magnetic stirrer to completely homogenize the solution.
2.5 Adsorption procedure
Batch adsorption tests were carried out in the laboratory by contacting a certain volume of surfactant solution
with Hassi Messaoud rock under stirring at 130 rpm for few hours to ensure equilibrium. Knowing the equilibrium
concentration and the initial concentration of surfactant, the amount of surfactant adsorption can be calculated using
Adsorbed surfactant =msolution ∗(C0−C)
msandstone ×10−3,(1)
where qis the surfactant adsorption on rock surface (mg/g of rock); msolution represents the total mass of solution in
original bulk solution (g); C0indicates the surfactant concentration in the initial solution before equilibrium (mg/L);
Cdenotes the surfactant concentration in the aqueous solution after equilibrium (mg/L); msandstone is the total mass
of the crushed sandstone. This method represents accurate results with an error of 4% for all experiments [45].
2.6 Evaluation of thermodynamic parameters
The fundamental thermodynamic parameters, such as enthalpy, entropy and Gibbs free energy can be calculated using
Langmuir isotherm constant, which depends on the system temperature [18, 44,46,47].
The Gibbs free energy change (ΔG◦) is a key parameter for determining the spontaneity of a process which can
be calculated according to the following equation:
ΔG◦=−RT ln(KL),(2)
where Ris the universal gas constant (8.314Jmol/K), Tis the temperature (K) and KLis the Langmuir constant.
Other parameters related to ΔG◦, which are important in the feasibility and spontaneity of a process, are entropy
(ΔS◦) and enthalpy (ΔH◦) obtained according to
ΔG◦=ΔH◦−TΔS◦.(3)
By combining the equations, we get
ln(KL)=ΔS◦
R−ΔH◦
RT .(4)
By plotting ln(KL)versus 1/T , the values of ΔH◦and ΔS◦coincide with the slope and the intercept, respectively [48,
49].
Page 4 of 15 Eur. Phys. J. Plus (2019) 134: 436
Fig. 1. XRD model of the Hassi Messaoud rock.
Table 1. Constituents of the Hassi Messaoud rock.
Constituent (%)
Na2OMgO Al2O3SiO2P2O5SO3K2OCaO TiO2MnO Fe2O3PAF
0.53 0.24 9.13 84.64 0.04 0.03 1.44 0.11 0.08 0.02 1.25 2.44
2.7 Full factorial design experiments
In this work, a full 23factorial design requiring 8 experiments was used to study the importance of the individual
effects and interactions of SDS and ASP EOR 5100 surfactants on the Hassi Messaoud rock [50,51]. This design
was used to reduce the number of experiments and the time to reach the appropriate model for the optimization
process [52, 53], where 2krepresents the number of experiments, kthe number of factors [54]. Three input variables,
such as surfactant “X1”, the concentration of each surfactant “X2” and temperature “X3” have been varied and one
response (experimental adsorption capacity in equilibrium (Qe)) was evaluated.
Note that the factors used in this work have never been investigated simultaneously using a full factorial design,
and were chosen for their important influence on the predicted response (Qe). The results of the factorial design
were studied and interpreted using the JMP8 software by analysis of variance (ANOVA), and the determination of
coefficient R2[50]. The significance of the regression coefficients parameters was discussed by the student’s test [55].
3 Results and discussion
3.1 Characterization of Hassi Messaoud rock
The Hassi Messaoud rock contains different quantities of quartz, kaolinite, illite, siderite and hallite, which are illus-
trated in fig. 1.
The composition of chemical compounds is indicated in table 1
The major elements of the constituent of the Hassi Messaoud rock were determined by XRF analysis, which
confirms the presence of Quartz with a composition of 84.64%. The specific BET surface area of the Hassi Messaoud
rock was measured under a nitrogen environment and was found to be equal to 5.71 m2/g.
The micro structural morphology of Hassi Messaoud rock was observed using SEM technique with secondary
electron option as shown in fig. 2.
The SEM image indicates that the surface is a mutual mixture of groove and pores, these spots could be an effective
adsorption site of SDS and EOR ASP 5100 surfactants.
Eur. Phys. J. Plus (2019) 134: 436 Page 5 of 15
Fig. 2. SEM image of the Hassi Messaoud rock.
Fig. 3. Concentration and contact time effect on EOR ASP 5100 adsorption kinetics (T=25◦C, speed = 130 rpm).
3.2 Effect of surf EOR ASP 5100 concentration and contact time
Figure 3 illustrates the effect of concentration and contact time for ASP 5100 surfactant on the Hassi Messaoud rock.
The adsorption amount increases with time and concentration. The kinetics of adsorption was rapid initially due
to the possible contacts of the surfactant with the available sites in the free surface. The adsorption reaches gradually
equilibrium due to the uptakes of ASP EOR 5100 molecules in the pores of adsorbents. The adsorbed quantities for
the surfactant were 1.75, 3.12, 5.52 and 5.85mg/g for 200, 400, 600 and 800 ppm respectively, where equilibrium was
reached after 45 minutes for all initial concentrations.
3.3 Effect of temperature on surf EOR ASP 5100 adsorption
The other important parameter that affects adsorption phenomena is the temperature, which is shown in fig. 4.
The quantity adsorbed for the surfactant at 80◦C was 1.56, 4.53, 7.00 and 8.98 mg/g for 200, 400, 600 and 800 ppm,
respectively, indicating a higher adsorption.
Page 6 of 15 Eur. Phys. J. Plus (2019) 134: 436
Fig. 4. Effect of temperature on surf EOR ASP 5100 adsorption kinetic (temperature 80 ◦C, speed 130 rpm).
Table 2. Isotherms and their linear forms [41,56].
Isotherm Linear form Plot
Freundlich ln qe=lnKF+(1/n)lnCeln qevs. ln Ce
Langmuir Ce
qe=Ce
qmax +1
bqmax
Ce
qevs. Ce
Temkin qe=RT
BTln(KT)+ RT
BTln(Ce)qevs. ln(Ce)
Several previous works have proved that the increase in the temperature can cause the decrease in the quantity
adsorbed. However, in our experiments, the amount of adsorbed EOR ASP 5100 increased with a temperature (from
25 ◦Cto80◦C) for all concentrations. The equilibrium is reached after only 12 minutes at 80◦C compared to 45 minutes
at 25 ◦C. One can explain this result by temperature increasing the mobility of organic compound sand decreased the
energy activation that facilitated the contact between rock sample and the surfactant and cause a possible rapid
penetration into the Hassi Messaoud rock.
3.4 Equilibrium modeling
Once the equilibrium state is reached, the adsorption isotherms indicate the specific relationship between the equilib-
rium concentration of the bulk adsorbate and the amount adsorbed at the surface. The analysis of different data is an
important step to find the most suitable model for experimentation.
Several mathematical models can be used to describe the experimental data of adsorption isotherms. Three ad-
sorption isotherms, Langmuir, Freundlich and Temkin [19] were used to describe the equilibrium behavior of EOR
ASP 5100 on the Hassi Messaoud rock for the different concentrations and temperature. These isotherms are presented
with linear forms on table 2, where qe(mg/g) is the adsorption capacity at equilibrium; Ce(mg/l) is the concentration
of surfactant EOR ASP 5100 at equilibrium; KL(l/mg) is the Langmuir constant associated with the energy of ad-
sorption; qmax (mg/g) denotes the theoretical monolayer adsorption capacity; KFis the Freundlich constant (mg/g);
(l/mg)1/n while 1/n is a measure of the adsorption intensity or surface heterogeneity, BTis the Temkin constant re-
lated to the adsorption heat (kJ/mol); KTis the equilibrium binding constant (l/mol) corresponding to the maximum
binding energy; Ris the gas constant (8.314 J/mol K); Tis the absolute temperature (K).
The isotherm adsorption data was plotted in fig. 5 to obtain the Freundlich, Langmuir and Temkin models param-
eters that were summarized in table 3.
As can be seen from fig. 5, when comparing these results, the high R2values (>0.95) obtained using the Langmuir
linear isotherm indicate that this model describes very well the adsorption of EOR ASP 5100 at different temperatures
and concentrations. In the literature, the Langmuir isotherm model that was initially used to describe gas-solid
adsorption on activated carbon, is now usually preferred in the area of surfactant adsorption.
Eur. Phys. J. Plus (2019) 134: 436 Page 7 of 15
Fig. 5. Adsorption isotherms of EOR ASP 5100 on the Hassi Messaoud rock ((A) Langmuir, (B) Freundlich, (C) Temkin) at
different temperatures.
Table 3. Parameters of models at different temperatures.
Isotherm model Parameters Temperature
Freundlich KF(L/mg) T=25◦CT=80◦C
1/nf0.4566 0.0151
R20.3551 0.7389
0.912 0.868
KL(L/mg) 0.03300.0395
Langmuir qmax (mg/g) 2.1724 5.483
R20.985 0.995
KT(L/g) 0.0879 0.0136
Temkin BT0.086 0.401
R20.7667 0.819
The maximum adsorption capacity, qmax of the Langmuir model, was found to be 4.1754 mg/g and 7.9113 mg/g
for the temperature of 25 ◦Cand80
◦C, respectively. The low KLvalues (0.0051 L/mg and 0.0092 L/mg) in both
temperatures could indicate that probably the rock of Hassi Messaoud has low surface energy, indicating a possible
stronger bond between EOR ASP 5100 and Hassi Messaoud rock. Also,the first adsorbed layer leaves the hydrophobe
tails towards the solution (i.e. the tail is away from the rock surface). In that case, hemimicelle or bilayer structure
are more likely [57].
Page 8 of 15 Eur. Phys. J. Plus (2019) 134: 436
Table 4. Results of pseudo-first order application for different concentrations and temperatures.
Pseudo-first order Correlation R2K1(min−1)qe(mg/g)
Temperature 25 ◦C
200 ppm ln(qe−qt)=−0.0037t+1.4242 0.7582 0.0055 2.0063
400 ppm ln(qe−qt)=−0.0038t+1.5705 0.8963 0.0111 6.0465
600 ppm ln(qe−qt)=−0.0042t+1.7165 0.8679 0.0108 8.0892
800 ppm ln(qe−qt)=−0.0053t+1.7389 0.9063 0.0097 10.7871
Temperature 80 ◦C
200 ppm ln(qe−qt)=0.2594t+17.1895 0.7371 0.035 3.0585
400 ppm ln(qe−qt)=0.2351t+4.5505 0.9023 0.0121 4.2535
600 ppm ln(qe−qt)=0.1557t+3.2325 0.7111 0.0075 8.1472
800 ppm ln(qe−qt)=0.1162t+2.9237 0.859 0.0046 7.4973
Table 5. Results of pseudo-second order application for different concentrations and temperatures.
Pseudo-second order Correlation R2K2(g/mg min) qe(mg/g)
Temperature 25 ◦C
200 ppm t/qt=0.4858t+ 195.9879 0.951 0.0011 2.7225
400 ppm t/qt=0.2055t+16.2955 0.9953 0.0026 4.8662
600 ppm t/qt=0.1670t+18,4355 0.992 0.0045 5.9880
800 ppm t/qt=0.1240t+21.0058 0.9860 0.0070 7.0926
Temperature 80 ◦C
200 ppm t/qt=0.2594t+17.1895 0.951 0.035 3.895
400 ppm t/qt=0.2351t+4.5505 0.9757 0.0121 4.2535
600 ppm t/qt=0.1557t+3.2325 0.9897 0.0075 6.3171
800 ppm t/qt=0.1162t+2.9237 0.9840 0.0046 9.085
Also, Freundlich constants related to the adsorption potential, KF, and heterogeneity factor, 1/nf, were calculated
and found that KF(0.4566 and 0.0151) for 25 ◦Cand80
◦C, respectively, were higher than other two models. The
low values of the heterogeneity factor (1/nf<1.0) given in the table revealed the heterogeneity of the surface of the
Hassi Messaoud rock. On the other hand, it is clear that Temkin model is the least adapted among the isotherms used
for these experiments because it provides a low R2(0.7767 and 0.819) for 25 ◦Cand80
◦C, respectively. The Hassi
Messaoud field is known to be very heterogeneous and complex, so the adsorption plateau can vary under the same
conditions.
In addition, it can be concluded that the comparison of the models estimated is as follows: Langmuir >Freundlich >
Temkin.
3.5 Adsorption kinetics of ASP EOR 5100 on the Hassi Messaoud rock
The second important evaluation of data was the surfactant adsorption rate on the crushed sandstone which depends on
the interaction between adsorbate and adsorbent and the process conditions. The kinetics of ASP EOR 5100 adsorption
on the sorbent were analyzed by two models: pseudo-first- and second-order model. The forms and linearization of
these two models are cited in previous studies [19,58–60].
First, the parameters and R2values for the pseudo-first order model were calculated by plotting ln(qe−qt)versus
taccording to slope and intercept of straight lines. The calculated values for the rate constant (K1) and equilibrium
adsorption rate (qe), were given in table 4. Furthermore, the values of K2and (qe) for the second-order model were
calculated based on the slope and intercept of a plot curve t/qtversus tand are summarized in table 5. The correlation
coefficients of the first model were low (R2<92%) and the intercept indicate that the straight lines do not pass through
the origin. This deviation from the origin probably occurs because of the mass transfer rate in the initial and final
stages of adsorption were different. On the other hand, the high R2values (>95%) suggest the pseudo-second order
model describes well the adsorption phenomena and had a good fitness with the experimental data for surfactant EOR
ASP 5100 adsorption on the Hassi Messaoud rock for each concentration and temperature.
Eur. Phys. J. Plus (2019) 134: 436 Page 9 of 15
Table 6. Thermodynamics properties of ASP EOR 5100 adsorption on the Hassi Messaoud rock.
T(K) KL(L/g) ΔG◦(kJ/mol) ΔH◦(kJ/mol) ΔS ◦(kJ/mol)
298 330 −18.70 −17.50.00659
353 395 −12.65
Table 7. Factors and levels used in the factorial design 23.
Factors Low level (−1) High level (+1)
X1(surfactant) SDS EOR ASP 5100
X2(concentration in ppm) 200 800
X3(temperature in ◦C) 25 80
Table 8. Experimental design matrix with the results of 23full factorial design.
Run X1X2X3Qe(mg/g) Qepredicted (mg/g)
1−1−1−12.3294 2.3289125
2 1 −1−12.7225 2.7229875
3−1 1 −14.1762 4.1766875
4 1 1 −17.0926 7.0921125
5−1−1 1 3.4734 3.4738875
6 1 −1 1 3.895 3.8945125
7−1 1 1 6.144 6.1435125
8 1 1 1 9.085 9.0854875
3.6 Thermodynamic parameters of adsorption phenomena
Table 6 shows the values of ΔH◦and ΔS◦obtained by plotting the ln(KL)versus (1/T ) using eq. (4).
The Gibbs free energy is negative (−18.70 kJ/mol)at25◦C which can demonstrate the spontaneity and the nature
of adsorption phenomena. Furthermore, it is remarkable that when temperature increases from 298 to 353 K, the
values of ΔG◦decrease, which can be explained by the weaker adsorption due to the spontaneity and feasibility
of the process. In the literature, physisorption and chemisorption could be within the range of the following values
[−20 kJ/mol; 0 kJ/mol] or [−400 kJ/mol; −80 kJ/mol]. For the low temperature, adsorption is very high [4,44].
It is worth mentioning that the negative adsorption standard free energy changes (ΔG◦) and positive standard
entropy changes (ΔS◦) at all temperatures showed the spontaneous happening of the adsorption reactions. A negative
value of enthalpy reveals that this process is exothermic [61,62]; however, the very low value of entropy shows the negli-
gible increase in a randomness of a system. The same tendency was observed recently by Ahmadi et al. when he studied
the thermodynamic analysis of adsorption of a naturally derived surfactant onto shale sandstone reservoirs [19,63].
3.7 Factorial design of experiments
The choice of surfactant “X1”, concentration “X2” and temperature “X3” are among the most important parameters
that affect the retention of surfactant on porous media, were used for the analysis of EOR ASP 5100 and SDS
adsorption on the Hassi Messaoud rock. The higher level is designated by +1 and the lower level by −1 as depicted in
table 7 for the parameters studied.
The response Ywas the experimental adsorption capacity equilibrium Qe(mg/g).
The run order of experiments carried out from right to left to correct the possible experimental errors [55] based
on the Yates’ algorithm, was applied in the case of all 2kfactorial experiments [64].
The design matrix of coded values for factors and response are shown in table 8 and the codified mathematical
model for the 23is given as
Y=a0+a1X1+a2X2+a3X3+a12X1X2+a13 X1X3+a23X2X3,
where Yis the experimental adsorption capacity at equilibrium Qe(mg/g) for SDS and EOR ASP 5100. While, the
a0,ai,aij represents the global mean. The regression coefficients assigned, respectively, to the principal factor effects
and interactions.
The student’s test “t” was used to confirm the validity of the regression coefficients of the studied parameters, when
t-value is higher than t-critic which is equal to 12.70, the regression is statistically significant [55]. After verification
of the results, R2was equal to 0.99 indicating the model to satisfy well the response [65].
Page 10 of 15 Eur. Phys. J. Plus (2019) 134: 436
Table 9. Estimated regression coefficients for adsorption capacity of SDS and EOR ASP 5100 on the Hassi Messaoud rock.
Parameter constant Estimate Standard error t-ratio p-value
4.8647625 0.000487 9979 <.0001∗
X10.8340125 0.000487 1710.8 0.0004(a)
X21.7596875 0.000487 3609.6 0.0002(a)
X30.7846875 0.000487 1609.4 0.0004(a)
X1∗X20.6303375 0.000487 1293 0.0005(a)
X1∗X30.0066375 0.000487 13.62 0.0467(a)
X2∗X30.2054625 0.000487 421.46 0.0015(a)
(a)p<0.05.
Fig. 6. The plot of predicted versus experimental adsorption capacity of ASP EOR 5100.
Table 10. ANOVA analysis of experimental adsorption capacity equilibrium Qe(mg/g).
Source Sum of squares DfMean square F-ratio p-value
Model 38.777910 6 6.46299 3399334 0.0004(a)
Residual 1.90125e-6 11.90e-6
C.Total 38.777912 7
(a)p<0.05.
From the data given in table 8, replacing the values coded by the estimates, the model can be written in the form
Qe(mg/g) = 4.8647625 + 0.8340125X1+1.7596875X2+0.7846875X3
+0.6303375X1∗X2+0.0066375X1∗X3+0.2054625X2∗X3.
All coefficients values have a positive sign in the polynomial model, indicating their positive influences on SDS and
EOR ASP 5100 adsorption.
Table 9 and fig. 6 show the predicted values versus the experimental values of the adsorption capacity in equilibrium,
the high value of R2=99.58% and R2
adjusted =99.28% indicate that the model was successful in correlating the response
to the studied parameters [65].
It appears from the table that the linear effects of surfactant, concentration, and temperature are significant. The
same trend was observed for the interactions effects between these factors, which confirms that the model is highly
significant with the p-value of 0.0004 <0.05 [50,66, 67] and F-value of 3399334 cited in ANOVA analysis in table 10.
By analyzing the data obtained and shown in table 10, it can be noted that the concentration (X2) is the most
important parameter for the overall adsorption process with a high (t-ratio = 3609.6), so the concentration exerts
a stronger influence on adsorption. After that, the surfactant type can be the second important parameter that
influenced this phenomenon with a (t-ratio = 1710.8). Temperature was the least significant parameter among the
main parameters with a (t-ratio=1609.4).
The interactions of (X1and X2) (with a high t-ratio=1293) was the most significant compared to the other
combinations (X2and X3) and (X1and X3). The latter was the least significant (with a t-ratio = 13.62).
Eur. Phys. J. Plus (2019) 134: 436 Page 11 of 15
Fig. 7. InteractioneffectplotsoftheQefunction of the studied parameters.
Fig. 8. Prediction profiler of Qe(mg/g) function for SDS surfactant.
3.7.1 Interactions plots
Figure 7 illustrates the differences between the interactions of two parameters on the adsorption capacity of surf ASP
EOR 5100 and SDS surfactants. The non-parallel lines indicate the presence of interaction that can be estimated
between surfactant “X1” and concentration “X2” equal to 0.6303375, which means that the higher surfactant ASP
EOR 5100 affects the adsorption capacity when concentration is low and equal to 200 ppm.
In addition, the effects of interactions, such as surfactant “X1” and temperature “X3”, concentration “X2”and
temperature “X3”, are negligible due to parallel lines that indicate the temperature is the least significant or non-
significant in the presence of other parameters simultaneously. These results confirm the previous finding obtained
from table 9, related to each parameter of influence on the adsorption process.
3.7.2 Optimal design conditions using the desirability method
One of the important reasons for this work was to find the optimal conditions at which the adsorption capacity (Qe)
will be minimized. For this, the desirability function was used by Derringer and Suich in 1980 to solve the problems
related to the optimization of multiple responses related to industry [68,69], applied by Derringer and Suichin in many
studies [38,70].
From fig. 8, which shows the prediction profiler function of the studied parameter, it can be concluded that the
optimized conditions were the surfactant SDS concentration equal to 200 ppm and temperature 25 ◦C for a predicted
response Qeequal to 2.3289 mg/g with a desirability value of 0.942118.
Page 12 of 15 Eur. Phys. J. Plus (2019) 134: 436
Fig. 9. Prediction profiler of Qe(mg/g) function for ASP EOR 5100 surfactant.
Fig. 10. Iso-response for Qe(mg/g) of the Hassi Messaoud rock on surfactant EOR 5100.
Likewise, the optimal conditions are obtained for EOR ASP 5100 (fig. 9) at a low concentration equal to 200 ppm
for 0.750683 of desirability, which gives the adsorption capacity equilibrium Qeequal to 3.894513 mg/g, corresponding
to a temperature of reservoir of 80 ◦C. This result can be used in the industrial field.
The results obtained in figs. 8 and 9 show that the proposed mathematical model satisfactorily represents the
experimental results in the studied domain, in terms of desirability and adsorbed quantity illustrated in the previous
sections.
3.7.3 Iso-response of Qefunction
In order to evaluate the influence of concentration and temperature on the response Qe(mg/g) fixed at their optimum
(Qe=3.8945125 mg/g) with surf EOR 5100. The iso-response is shown in fig. 10.
In our case, the minimized adsorption is desired in the range of experimental study, which must be between 200 ppm
and 353 ppm for concentration and temperature scale between (25–80 ◦C).
4 Conclusions
A detailed research on the adsorption of EOR ASP 5100 surfactant onto an Algerian rock reservoir was established.
The XRD and BET characterizations hepled in determing the mineralogy and the specific surface area of the Hassi
Messaoud rock. The adsorption parameters for the Langmuir, Freundlich and Temkin isotherms were determined, and
Eur. Phys. J. Plus (2019) 134: 436 Page 13 of 15
the adsorption kinetics of this new surfactant has been evaluated using two of the well-known models. The influence
of parameters, such as surfactant type, temperature, and surfactant concentration on adsorption capacity, has been
studied to improve oil recovery. These important parameters were evaluated using a statistical mathematical model
namely the 23full factorial design methodology. The following important conclusions can be drawn based on the
results obtained:
1) The main constituent element of the Hassi Messaoud rock (with a specific area equal to 5.71 m2/g) are quartz with
84.64%.
2) The kinetics and adsorption models were adequately modeled by Langmuir and pseudo-second order, respectively,
for all concentration and temperature variations, suggesting that the rate-limiting step may be the chemical ad-
sorption.
3) Higher surfactant concentrations and applied temperatures lead to a greater surface adsorption on the Algerian
rock until reaching a steady state which refers to the point of saturation.
4) From this study, a full factorial design of experiment can be an efficient method for the predicted val-
ues of surfactant adsorption which is reported for the newly statistical model with R2=0.99, F-ratio =
3399334 and p-value = 0.0004; Qe(mg/g) = 4.8647625 + 0.8340125 ∗surfactant + 1.7596875 ∗concentration +
0.7846875∗temperature + 0.6303375 (surfactant∗concentration) + 0.0066375 (surfactant ∗temperature)+0.2054625
(concentration ∗temperature).
5) All factors and interactions considered in the experimental design were statistically significant at the 95% confidence
level.
6) The adsorption capacity values minimized for the SDS surfactant were Qe=2.3291 mg/g for SDS surfactant,
concentration = 200ppm and temperature 25 ◦C. Likewise, minimized adsorption capacity values for EOR ASP
5100 was Qe=3.894513 mg/g for concentration 200 ppm and temperature of reservoir 80 ◦C.
Nomenclature
EOR: Enhanced Oil Recovery X2: Second factor: concentration of
IFT: Interfacial Tension surfactant (ppm)
SDS: Sodium Dodecyl Sulfate X3: Third factor: Temperature (◦C)
P: Probability ANOVA: Analysis of variance
R2: Coefficient correlation a0: Intercept
R2
adjusted: Coefficient correlation adjusted ai: Regression coefficients attributed
t: student value to the principal factor effects
Y: Response aij : Regression coefficients attributed
C◦: Initial concentration of surfactant in solution to interactions effects
Ce: Equilibrium concentration of adsorbate RL: Separation factor
in solution DF: Degree of freedom
KT: Temkin isotherm constant 2: Number of levels
BT: Constant in Temkin adsorption isotherm k: Number of factors
KF: Freundlich isotherm constant q: adsorption of surfactant
K1: Rate constant of pseudo-first order kinetic model ASP: Alkaline Surfactant Polymer
K2: Rate constant of the second-order kinetic model t-ratio: The estimate to its standard error
n: Exponent in Freundlich isotherm F-ratio: The ratio of the mean square
Qe: Amount of the adsorption at equilibrium for the effect divided by the mean
qt: Amount of the adsorption at any time tsquare for error
RSM: Response Surface Methodology CTAB: CetylTrimethyl Ammonium Bromide
SEM: Scanning Electron Microscopy GO: Graphene oxide
XRD: X-Ray Diffraction ΔG◦: Change in Gibbs energy (kJ/mol)
XRF: X-Ray Fluorescence ΔH◦: change in enthalpy (kJ/mol)
BET: Brunauer, Emmett et Teller ΔS◦: change in entropy (kJ/mol)
PPM: Part per million R: gas constant
X1: First factor, surfactant T: Temperature
Page 14 of 15 Eur. Phys. J. Plus (2019) 134: 436
This work is part of a project supported by the petroleum company, SONATRACH - Algeria, that we gratefully acknowledge
for its contribution in providing additives and reservoirs rocks as well as the SOLVAY Company is gratefully acknowledged.
Our gratitude goes to Dr. Mohammed Abdelfetah Ghriga and Dr. Azzeddine Mazouzi for their help during the redaction of the
manuscript.
Publisher’s Note The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional
affiliations.
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