2013_jsd_salager_eor_review_1_formulation.pdf

J Surfact Deterg (2013) 16:449–472 DOI 10.1007/s11743-013-1470-4

REVIEW ARTICLE

How to Attain Ultralow Interfacial Tension and Three-Phase Behavior with Surfactant Formulation for Enhanced Oil Recovery: A Review. Part 1. Optimum Formulation for Simple Surfactant–Oil–Water Ternary Systems Jean-Louis Salager • Ana M. Forgiarini Johnny Bullo´n

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Received: 18 January 2013 / Accepted: 22 March 2013 / Published online: 19 April 2013  AOCS 2013

Abstract Enhanced recovery of crude oil by surfactant flooding requires the attainment of an ultralow interfacial tension. Since Winsor’s work in the 1950s it has been known that a minimum interfacial tension and a concomitant three-phase behavior of a surfactant–oil–water system occurs when the interactions of the surfactant and the oil and water phases are exactly equal. It has been known since the 1970s that these conditions are attained when a linear correlation is satisfied between the formulation variables, which are characteristic parameters of the substances as well as the temperature. This first part of our review on how to attain ultralow interfacial tension for enhanced oil recovery shows how formulation scan techniques using these correlations are used to determine an optimum formulation and to characterize unknown surfactants and oils. The physicochemical significance of the original empirical correlation is reported as the surfactant affinity difference or hydrophilic–lipophilic deviation model. We report the range of accurate validity of, and how to test, this simple model with four variables. Keywords Enhanced oil recovery  Ultralow tension  Optimum formulation  Correlation accuracy

Introduction Enhanced oil recovery (EOR) has long been considered, but steady interest in EOR really began with the 1973 oil embargo and the sharp increase in price during subsequent J.-L. Salager  A. M. Forgiarini (&)  J. Bullo´n Laboratorio de Formulacio´n, Interfases, Reologı´a y Procesos (Lab FIRP), Universidad de Los Andes, Me´rida, Venezuela e-mail: [email protected]

years. At this time, serious research and development activity was triggered and sponsored by western nations in university, government and company research centers. Many different methods were suggested but, because of the basic trapping phenomena, those with the highest potential needed to generate an ultralow interfacial tension in the reservoir to eliminate capillary trapping. This was also the most difficult from a scientific point of view, and the most challenging to develop [1]. Five years of intensive work in the late 1970s, based on Winsor’s pioneering work [4], allowed the physicochemical conditions to be determined, and a more accurate way of handling the formulation to be found that was compatible with the precision required to attain ultralow tension. At the same time, some difficulties were identified because of the uncertainties of working down a 10,000-ft hole, and because of spontaneous (or difficult to control) phenomena taking place throughout the process, such as changes in formulation due to various effects like precipitation, adsorption–desorption or dilution of injected fluids. The first few pilots that were carried out by the end of the 1970s showed that the method was essentially feasible, but not yet economical, and diagnoses indicated that many problems still required substantial improvement. However, the crude oil price went down in the early 1980s and the motivation to develop EOR vanished, as well as most of the funding for research and development in this area. Only a few groups continued to follow related studies, and most researchers in the area switched to theoretical issues and to a better understanding of phase behavior and its consequences on different kinds of structures (microemulsions, liquid crystals, vesicles, liposomes etc.), and to other applications using physicochemical formulation concepts, particularly emulsions [2, 3]. In the mid-2000s,

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the energy crunch pushed the oil price up again and it seems that this time it is going to stay high because of the production deficit, and the lack of easy replacement of petroleum by renewable energy resources. On the other hand, and considering the global warming issue, governments are motivated to inhibit the production of carbon dioxide, and consequently enhanced recovery of the leftovers of light crudes is probably one of the best alternatives for producing energy in the next 20–30 years compared to heavy fossil fuels and coal. This is why surfactant/polymer EOR techniques are looking attractive in the near future. This is also why a serious continuation of the 1970s studies is required to try to solve the problems that are still pending. The first issue is how to achieve an ultralow tension in a given field. Studies carried out since 1975 have improved manipulation of formulation variables, in particular with mixtures, and today this is essentially a matter of practice. However, there are many degrees of freedom and the experimental work must be very well organized to find different alternatives for optimum formulation and to compare them. This first installment of this review is dedicated to presenting the state of the art in understanding how to handle the formulation aspects with the required numerical accuracy. After a short sum up of Winsor’s pioneering work back in the 1950s, and a basic description of phase behavior phenomena, the empirical correlations found in the 1970s are reported, as well as how they have been interpreted in terms of simple physical chemistry about 20 years later. The last section in this first part is a short discussion on the limits of accuracy of the simple correlation, and the need for a more complex approach to be injected in real systems. The second problem to be settled is how to improve the ultralow tension feature. Many studies have been carried out but are not really well organized, and claims about brand new formulation in symposia are sometimes not really justified. As a matter of fact, most of the know-how required to lower the interfacial tension has existed for some time, and will be analyzed in a systematic way in the second part of this review. A new way to present the evolution of the past 40 years will start from easy-tounderstand know-how derived from very simple ternary systems, before discriminating the complexities involved in modifying conventional surfactants and handling inter- and intra-molecular mixtures. Third, passing from formulation optimization in the laboratory to an actual field process requires taking different problems into account, not all of which are all solved, and requires both studies to gather data (precipitation, adsorption, formulation shifts), and experience to compensate spontaneous variations (formulation gradient, mixture insensitivity, wider optimum formulation zone). These criteria, not all of which fall within the scope of this review, might, however, be of importance for choosing between

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equivalent performance systems as far as ultralow tension is concerned. Consequently, the third part of this review will be dedicated only to issues dealing with formulation with non-linear mixing rules to be used in practice to improve performance, particularly by shifting limitations, and generating synergy effects through blending.

Winsor’s Pioneering R Ratio Model Winsor’s phase behavior studies in the early 1950s allowed a pedagogical presentation of the influence of the formulation [4] as an improvement on the hydrophilic–lipophilic balance (HLB) number, which was limited and considered as inaccurate even at that time. The R ratio of interactions of the adsorbed surfactant at the interface with the neighboring oil and water molecules was presented for the first time as a criterion to take into account along with the effects of all formulation variables found in a ternary surfactant–oil–water (SOW) system, i.e., the surfactant head and tail characteristics, the nature of the oil, the aqueous phase salinity, as well as temperature and pressure. A practical way to write the R ratio is with net interactions, i.e., interactions with respect to a reference state in which the three components are separated. This was stated by Winsor as follows in Eq. (1) [5], and in an even more pedagogical way in a later book reviewing the topic [6]. R¼

ðACO  AOO Þ ðACW  AWW Þ

ð1Þ

where ACO and ACW are the interaction of surfactant molecules per unit area at the interface with oil and water, respectively; AOO the interaction between two oil molecules; and AWW the interaction between two water molecules. Winsor’s three types of simple diagrams were called WI, WII, WIII, and are characterized by the nature of the polyphasic zone at low and moderate surfactant concentration. The WI (respectively, WII) diagram exhibits a characteristic two-phase behavior with water (respectively, oil) microemulsion in equilibrium with an oil (respectively, water) excess phase. For a SOW ternary system, Gibbs’ rule allows the separation of up to three phases—a phase behavior found in the WIII diagram with a bicontinuous microemulsion or liquid crystal containing most of the surfactant in equilibrium with both excess water and excess oil phases [6]. In all cases, the phase behavior in systems containing a large amount of surfactant is a single-phase microemulsion (WIV) or a liquid crystal (LC). Winsor did not use the word microemulsion in the WIII case. He proposed planar layer (neat phase G) when it was a liquid crystal and, when in liquid phase, it was called middle phase M, with cylindrical micelles and a continuous transition between anisotropic

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solutions with micelles S1 and S2 inverse micelles, i.e., a significant definition of what is today recognized as a bicontinuous structure microemulsion. A reading of Winsor’s review paper [5] is quite illustrative of the fair understanding that was available half a century ago. The presented diagrams and the corresponding phase behavior in the polyphasic zone at low surfactant concentration were linked by Winsor to the R ratio of interactions of surfactant with oil and water as defined in Eq. (1). R \ 1, R = 1 and R [ 1 correspond to WI, WIII, and WII diagrams, respectively. As a consequence, any formulation change that alters one of the interactions indicated in the ratio is able to increase or decrease R. When the formulation variation is properly selected to change R from R \ 1 to R [ 1 or vice versa, it changes the phase behavior from WI to WII or vice versa, with an intermediate WIII three-phase behavior at R = 1. Figure 1 indicates such a change in a so-called formulation scan that consists of a series of test tubes containing the same amounts of the SOW components and the same formulation with the exception of the scanned variable (here a salinity continuous variation). The figure shows the phase behavior in test tubes corresponding to a polyphasic system located at unit water-to-oil ratio (WOR = 1) with a low surfactant concentration (square dot in the associated Winsor SOW ternary diagrams). The shaded phase in the test tubes indicates the surfactant-rich phase; in general, a microemulsion. The arrows in the lower part indicate the direction of the R and phase behavior changes produced by the alteration of most common formulation variables. In the case of an increase in aqueous phase salinity (from left to right), the ACW interaction term between surfactant and water decreases, thus R increases. In the case of an increase in n-alkane length, generally called alkane carbon number (ACN), the numerator of the R ratio

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exhibits two modifications: the term ACO increases since it may be considered as roughly proportional to the length of the surfactant tail and to the length of the oil molecule, but the term AOO also increases, but this time proportionally to the length of each oil molecule in the interaction, i.e., as ACN2. Consequently, an increase in ACN generally is more effective on AOO, and decreases the R ratio, which results in a scan effect opposite to that shown in Fig. 1 by increasing salinity. Since any change in a formulation variable produces a variation of R one way or the other, it may be said that R qualitatively renders the effect of different formulation variables. A quantitative concept equivalent to R will be discussed later. The formation of a three-phase behavior, with a liquid crystal or microemulsion middle phase when the interactions are equal, i.e., R = 1, was a curiosity in the 1960s, that became extremely fashionable when it became clear in the 1970s that this condition exhibited a minimum tension in a formulation scan. This minimum tension was found to be often quite low, sometimes ultralow, e.g., 10-3–10-4 mN/m, so that the capillary number could become high enough for the crude oil trapped in a reservoir to be displaced by a surfactant flooding, often called microemulsion flooding. A formulation at R = 1 attaining a low minimum tension was called ‘‘optimum salinity’’ in the Fig. 1 scan, ‘‘optimum formulation’’ in general, and sometimes nmin or preferred alkane carbon number (PACN) when the scan variable was the n-alkane length, i.e., the ACN [7–11]. Extensive studies have dealt with systems at, or close to, an optimum formulation divulged different properties, among them the coincidence with a zero curvature at the oil–water interface. This involved either the plane geometry of a lamellar liquid crystal or a bicontinuous microemulsion structure with a non-flat surfactant layer with an average zero curvature as in a horse saddle, e.g., a parabolic hyperboloid [12, 13], which was rendered by Winsor as a combination of swollen micelles and swollen inversed micelles that had percolated [5]. The presence of liquid crystal must of course be avoided in EOR because of the associated viscosity. Bicontinuous microemulsions could be found instead of liquid crystals at optimum formulation not only through thermal disorganization by increasing temperature, but also by introducing some geometric disorder, which could be attained by branching the surfactant tail, by mixing different surfactants, or surfactants and co-surfactants like alcohols—the latter being the usual way when using linear alkyl tail sulfonates. This will be discussed in the second part of this review.

Three-Phase Behavior Zone Fig. 1 Ternary phase diagram, test tube phase behavior and R ratio variations along a one-dimensional formulation scan

As shown in Fig. 1, any change in a formulation variable produces a variation in R one way or the other.

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Consequently, it may be said that the R ratio concept qualitatively renders the effect of different formulation variables. It will be seen later that this gathering of the effects of different formulation variables can be provided in a quantitative way by another single criterion equivalent to R, but with a numerical and accurate value. For now it is important only to recognize that the phase behavior type could be associated with a single formulation variable, which includes the nature of any of the components as well as temperature and pressure. On the other hand, the minimum number of variables needed to alter the phase behavior of a SOW system is three, i.e., the amount of the three components, among them two independent variables that define the composition of the SOW system in a ternary diagram—in general, the surfactant concentration and the water-to-oil ratio (WOR). The actual phase behavior should thus be studied in a threedimensional prism as in Fig. 2, which shows several kinds of bidimensional cuts, one at constant formulation (Fig. 2 upper right) and another at constant WOR (Fig. 2 upper left). The volume in which three phases are in equilibrium close to the condition R = 1, which is called the three phase body, has a strange shape as illustrated in the lower left part of Fig. 2, and shown in various ways elsewhere [14–16], even in quaternary SOWA systems with an alcohol co-surfactant [17]. An outstanding analysis of the body volume of a three liquid phase equilibrium is available elsewhere [18], although the reported quaternary system does not contain any surfactant.

Fig. 2 Phase behavior in threedimensional space with axis as surfactant concentration, water/ oil ratio (WOR) and generalized formulation (the latter as R ratio qualitative variation)

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In the left side of Fig. 2, the bidimensional cut at constant WOR (here for instance WOR = 1) exhibits a threephase zone with the classical gamma shape or (hanging) fish aspect. In the series of cuts at constant formulation in the lower right part of Fig. 2, it is seen that the three-phase triangle collapses in a tie line, i.e., the three phase system becomes a two-phase system at the lower and upper limits of the three-phase behavior zone along the formulation scan. In the range between these limits, the system separates into three phases and consequently there are three different types of interfacial tensions, which will be discussed next. Outside this range, there are only two phases: an aqueous microemulsion, or O/W microemulsion, at equilibrium with an oil excess phase (on the R \ 1 side); and an oil microemulsion, or W/O microemulsion, at equilibrium with excess water on the R [ 1 side). As discussed later, the width of the formulation range in which three phases are in equilibrium varies from case to case, and has been shown to be linked directly with the performance of the system as far as low tension is concerned. As the lower and upper limits become closer, the composition of the three phases approach one another, the tension is lowered and finally a tri-critical point is attained [19, 20]. Although the theory dealing with tricritical points is not easy to follow for the non specialist, it is might be worth looking at its meaning to understand what is possible and what is not in the business of improving the interfacial tension for EOR [14, 21].

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Empirical Correlations to Attain Optimum Formulation Back in the mid-1970s, Winsor’s pioneer work was rediscovered, and attainment of the R = 1 condition was perfectly understandable as a concept. However, the problem was how to reach it from the selection of ingredients, i.e., surfactant, oil, brine, as well temperature and pressure, since some approximations in the relation between R factors and the actual system could be only guessed at [22]. The first thing to do was to define the characteristics of the components, both as independent from one another and as significantly representative parameters. For the oil phase it was relatively easy to take the n-alkane model since the liquid series from pentane to hexadecane seemed to mimic quite closely the physicochemical properties of most crudes [1]. The selected characteristic was the ACN. In some studies, refined characteristics like molar volume and aromaticity were selected [23]. For the water phase, a NaCl solution was taken as typically representative of brine, with the salt concentration as the characteristic parameter (referred to simply as salinity in the following). For the surfactant, the problem was that the parameter usually used, i.e., the HLB, was quite inaccurate, in particular with anionic surfactants, which were the most likely candidates in EOR for various reasons, particularly performance and cost. For the alkyl aryl sulfonates, the head group was fixed and the tail size (or molecular weight) was in general the adjustable parameter. If the head group was also likely to be chosen, then two parameters, one for the tail and one for the head, were to be selected as the surfactant characteristics—an easy choice for nonionic surfactants of the ethoxylated alkylphenol or alcohol type. Temperature was known to alter the hydrophilicity one way or the other depending on the surfactant type, and was thus a variable to be considered. Pressure was not very significant in liquid state systems and was thus initially neglected. Consequently, the basic formulation variables were: the brine salinity, the oil ACN, the surfactant characteristics (one or two parameters), temperature, and most of the time an additional effect for alcohol cosurfactant with anionics to avoid the formation of liquid crystals. Hence there were five to six independent variables that were likely to alter the R value. Most basic studies reported variation in the tension versus the formulation, i.e., along a scan as seen in Fig. 1 in which the formulation variable is the salinity as usual for anionics. For ethoxylated nonionics, the scanning variables used most are the temperature and the average ethylene oxide number (EON) in the head group. For any type of surfactant, the ACN has been also used as the scanning

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variable, although the actual liquid range (5–16) for n-alkanes is rather small as far as a physicochemical change is concerned. In effect, it will be shown later that the full experimental range of ACN for liquid n-alkanes (5–16) is, for ethoxylated nonionics, equivalent to a change in about 1.5 EO groups in the polyether head or 30 C in temperature variation, and for anionics to a change in salinity from 1 to 5 wt% NaCl. Consequently, the change in formulation due to scanning the ACN results in a relatively small variation range and is not much used in practical experiments, unless an appropriate prediction is available. The first step in correlating the relative effects of the variables on formulation is to carry out bidimensional scans. For instance, the unidimensional salinity scan indicated in Fig. 3a is repeated for different alkanes, i.e., with different ACN cases (Fig. 3b), but with the same surfactant, same alcohol, same temperature and same composition. The graph in Fig. 3a indicates how the phase behavior (also shown in Fig. 1) and interfacial tension (IFT) vary when the salinity changes. The tension plot versus salinity exhibits two lines in the three-phase behavior zone (3/), that correspond to the two interfaces. The minimum tension between oil and water (cOW ) is attained essentially where the two curves cross, and it is termed the optimum formulation, in the present case optimum salinity. More on this will be discussed later. The first characteristic to be noted in Fig. 3b where the tension variation versus salinity is shown for three oils (ACN = 6, 10 and 14), is that, as ACN increases, the tension variation plot shifts to a higher salinity, i.e., the optimum salinity becomes higher. In other words, the shift due to the increase in ACN is compensated by the increase in salinity. In Winsor’s R ratio, an increase in ACN from 6 to 14 diminishes the numerator, and the increase in salinity from 1.0 wt% NaCl to 3.5 wt% equally reduces the denominator, so that in both cases R = 1 and the optimum formulation condition is conserved. This equivalence is seen in the graph in Fig. 3c by projecting the minimum tension line (bold) on the S-ACN bottom plane, in which the W III three-phase zone is indicated by shading. Such a graph indicates the variation in S versus ACN, as a condition to maintain optimum formulation. It was found to be characteristic of the relationship between the two effects, which, with all other variables constant (i.e., same surfactant, cosurfactant, alcohol and temperature), could be expressed as follows for all tested ionic surfactants. Ln S ¼ KACN þ   

ð2Þ

where the slope K varies from 0.10 to 0.19 depending on the surfactant head group. The final dots in relationship (2) indicate contributions that depend on other variables, which are constant in the

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Fig. 3 Variation in interfacial tension (IFT) versus water salinity and oil alkane carbon number (ACN) in two representations. a, b Series of IFT versus S plots at different ACNs. c 3D representation of IFT versus S and ACN

case shown in Fig. 3, i.e., surfactant type, alcohol type and concentration, as well as temperature. This procedure, a so-called bidimensional scan, was repeated, selecting any set of two formulation variables, measuring the shift of the scanned variable required to compensate the shift of the changed variable, so that an optimum formulation is retained. Thousands of experiments returned a high degree correlation for the attainment of an optimum formulation with independent contribution of all variables. Figure 4 indicates typical bidimensional scans. It was shown 25 years later that the same correlation could have been estimated with much less experimentation by using data analysis techniques [24] provided artifacts had not been present, i.e., with relatively pure ternary systems, particularly as far as the surfactant is concerned. The correlations were expressed as linear rules in which the characteristics of the three basic components

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(surfactant/oil/water), as well as temperature, contribute in independent terms. The alcohol effect was also introduced as an assumed independent term that included both its nature and concentration. For ionic surfactants [25, 26] ln S  KACN þ r þ af ðAÞ  aT ðT  25Þ ¼ 0

ð3Þ

For ethoxylated nonionic surfactants [27] b þ bS  KACN þ a/ðAÞ þ cT ðT  25Þ ¼ a  EON þ bS  KACN þ a/ðAÞ þ cT ðT  25Þ ¼ 0 ð4Þ where S is the aqueous phase salinity expressed as wt% NaCl, ACN is the alkane carbon number, r and b are the characteristic parameters of the surfactant. b decreases linearly with the number of ethylene oxide groups EON in the head group (b = a - EON), where a is the

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Fig. 4 Three-phase behavior zone and optimum formulation in bidimensional scans

Table 1 Coefficient values in Eqs. (3) and (4)

Values of parameter a Alcohol 1 or 2 propanol 1 Butanol 2-Butanol Isopentanol 1 Pentanol 1 Hexanol

Parameters values valid for low alcohol percentage (<3%). Due to the phenomenon of fractionation (changes with surfactant concentration and WOR).

ionic surfactants

nonionic surfactants

0 + 0.3 to 0.6 + 0.05 + 1.0 + 1.1 +4

– 0.2 + 0.35 – 0.05 + 0.6 + 0.7 + 1.1

aT or cT value (ºC) -1

Surfactant Anionics sulfate, sufonate or carbonate Cationics C12-16 trimethylammonium, chloride Nonionics Iso-C n alcohol ethoxylated

- 0.01 - 0.02 0.06

Values for parameter b, characteristic accoding to type of Salt (nonionic surfactants) NaCl 0.13

hydrophobic contribution, which increases with surfactant tail length. [11, 27] f(A) and /(A) are the alcohol co-surfactant effects, expressed essentially as mA CA, where mA is a constant that depends on the alcohol type and CA is the alcohol concentration. T is the temperature in C. Symbols b, K, aT and cT are positive constants depending on the system type. As a consequence, the sign in front of each variable contribution indicates the actual direction of change of the left expression when this variable increases. When the sign is positive, an increase in the variable increases the lipophilic tendency and the expected phase behavior transition at optimum is in direction WI ? WIII ? WII and vice versa. It is worth noting that the sign corresponding to the temperature effect is negative (positive) for ionic (nonionic, particularly polyethoxylated) surfactant systems. More information concerning the temperature effect is available elsewhere [13, 28–32].

CaCl2 0.10

KCl 0.09

Some values of the parameters can be found in Table 1, and more data on the effect of the mentioned variables have been published elsewhere [6, 34, 35], as well as data on other variables like branching [36, 37], which will be discussed in detail in the second part of this review because it considerably alters performance. Salt effects are reported in most publications concerning the phase behavior of SOW systems, particularly ionic surfactants, for which the effect of anions has been studied in detail [38, 39]. The effect of divalent cations with anionic surfactant systems does not match the ionic strength concept [30, 40] and has to be handled with some effective salinity concept [41, 42]. It has been shown recently to be quite a complex issue [43]. Moreover, the electrolyte concentration has been found to be slightly different in the microemulsion and excess phases, because of the partitioning of salts [44–46], though this is usually neglected for the sake of simplicity. Fortunately, the effect

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of different salts on nonionic surfactants is relatively simple, as indicated elsewhere [27, 47]. Alcohol effects have been reported [8, 25, 27, 37, 48, 49] and the principle is quite simple as a contribution of amphiphile characteristic at the interface, i.e., as an alteration of the surfactant effect r or b, by an extra contribution. The alcohol formulation effect is essentially zero for short alcohols, i.e., water-soluble species like n or iso-propanol, as well as neutral species like sec-butanol or ter-pentanol. With n-butanol, n- or iso-pentanol and longer alcohols, the contribution at the interface is lipophilic, i.e., the f(A) and /(A) in Eqs. (3) and (4) have been suggested to vary linearly with the alcohol concentration in the system, i.e., f(A) or /(A) = mA CA, where mA is a constant depending on the alcohol, and CA is the concentration of the alcohol [25, 27]. For alcohols exhibiting a formulation effect, like n-butanol, n-pentanol or other lipophilic alcohols proposed for use in EOR applications, the constant mA is positive and increases with alcohol chain length. Although some values are available in the literature, the data on alcohol contribution are quite inaccurate for several reasons. First of all, alcohol molecules in a SOW system can migrate to different places, i.e., water, oil and middle phase microemulsion, and what is likely to change the formulation is only the amount of alcohol that is adsorbed at the interface (i.e., a cosurfactant in the microemulsion). Since partitioning of alcohol between phases and the interface depends not only on the natures of the alcohol, oil, brine and temperature, but also on the overall concentration [48], as well as the WOR. In summary, the alcohol effect is obviously not independent from the other formulation variables. It was thus inaccurate to introduce it as a separate contribution in the formulation expression. Discrepancies were not obvious at first because the few systems studied in the 1970s were similar. Comparison with other scarce data indicates large deviations [7, 49–51]. Furthermore, lipophilic alcohols like n-pentanol or n-hexanol are likely to migrate to the oil phase when their contribution to the interface is filled, thus they participate in the oil phase as a polar species. Since the most polar species tend to accumulate at the interface in oil phase mixtures [52], the actual polarity of the oil phase interacting with the interfacially adsorbed surfactant is altered by the migration of alcohol. This means that the alcohol concentration increase tends to produce an effect on another variable, i.e., ACN, which tends to decrease. If the ACN is taken to be independent from the alcohol effect, then the f(A) function, which will be calculated from the experimental evidence, loses linearity as the alcohol concentration in the oil phase increases. This has been reported to happen as soon as the f(A) effect exceeds 0.5–1.0 units in Eqs. (3–4) [25]. The notion that alcohol made some independent contribution, which motivated its introduction into the

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empirical correlations back in the 1970s, was wrong. With the current understanding of what happens at the interface, it is obvious that introducing alcohol in a SOW ternary is just like adding another surfactant-like species, which results in a mixture of amphiphiles at the interface. Since alcohols and surfactants are obviously quite different, at least in size and behavior, such a mixture is not likely to be ideal. Consequently, the introduction of alcohol corresponds to a complex situation, which will be discussed through non-ideal mixing in part 3 of this review. For the sake of simplicity, in what follows, most systems will be assumed to contain a real SOW ternary and, if there is some alcohol, it will be one with no formulation effect, i.e., an alcohol with f(A) = 0, or at worst without alcohol variation in comparison, i.e., at constant f(A). Other relationships to express the optimum formulation from the physicochemical point of view—similar, though less general than Eqs. (3–4)—are available for specific systems [8, 11, 23, 53–57]. The pressure effect is not significant, unless the conditions are far from atmospheric [58]. Nevertheless, it may be useful to predict some variations down the hole, in particular if the live crude contains a large amount of dissolved gas likely to change the oil characteristics. Relations (3–4) were found to be quite general and accurate for systems containing relatively pure SOW components, and were used to estimate the parameters for different surfactants, as well as the characteristics of oils different from alkane, and of brine different from sodium chloride solutions. The techniques used to characterize a surfactant, i.e., to estimate the r or b parameter, were based on the attainment of the optimum formulation in one or several one-dimensional scans. For instance, if, at a given temperature, for instance 25 C, an optimum formulation is attained at a certain salinity S , for a given alkane ACN in the absence of alcohol, then relationship (3) results in r = -ln S ? K ACN. Of course, it is not necessarily easy to determine the optimum formulation with any kind of surfactant, i.e., to select the ACN and the temperature, so that the S* value will fall within the usual experimental scan range, i.e., 0.5– 20 wt% NaCl. In some cases, such as for very hydrophilic surfactants (with a highly negative value of r), it might be necessary to add some lipophilic alcohol to add a significant -f(A) contribution to satisfy the relationship written as r = -ln S ? K ACN - f(A). This, however, contributes to inaccuracy because f(A) is not necessarily independent of the system and thus should be avoided whenever possible. To classify an unknown surfactant (parameter r2) with respect to another (reference parameter r1), and to carry out an experiment with great probability of success to

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Fig. 5 Phase behavior along a formulation scan (here salinity increase from left to right) with different surfactants 1 (left) and 2 (right) but the same oil, alcohol and temperature

attain an optimum formulation, the usual technique is to start from a typical optimum formulation known from a surfactant relatively close to the unidentified one. For instance, assume that the reference ionic surfactant 1 has a characteristic parameter r1, and that an optimum formulation is attained at salinity S1 with an alkane ACN, with a certain amount of alcohol that results in an effect f(A) at temperature T. Hence ln S1  KACN þ r1 þ f ðAÞ  aT ðT  25Þ ¼ 0 ð5Þ If another salinity scan is carried out with the same ACN, same alcohol and same temperature, but with the new unidentified surfactant 2, it results in the optimum salinity becoming S2 , (see Fig. 5), then ð6Þ ln S2  K ACN þ r2 þ f ðAÞ  aT ðT  25Þ ¼ 0 and if the value of K is the same for the two surfactants, subtraction between the two previous equations results in   r2 ¼ r1 þ ln S1 =S2 ð7Þ If the new surfactant, 2, is relatively close to the reference one, 1, then the difference in S2 and S1 is not large and there is a good probability of achieving an optimum formulation in the second scan at S2 . If S2 is slightly higher than S1 , then the new surfactant, 2, is slightly more hydrophilic than surfactant 1, and vice versa. It has been found that if surfactants 1 and 2 are sulfonates, an increase in 1 unit in r would correspond to an increase in approximately 2.5 carbons atoms in the tail, or 35 daltons in molecular weight. The optimum salinity shift in such a case will be an increase of one unit in ln S , i.e., salinity increased by a factor 2.7, for instance from S1 = 3 wt% NaCl to S2 = 8. If the K values for the two types of surfactants are different, then the subtraction between Eqs. (5) and (6) should include the fact that K1 and K2 are different and the result will be slightly more complex [59] and involve oil ACN as follows:

  r2 ¼ r1 þ ln S1 =S2  ðK1  K2 ÞACN

ð8Þ

It is worth noting that values of K are well known with accuracy for most of the head groups (K = 0.16 for sulfonates and carboxylates, 0.10 for sulfates, 0.15 for alkyl or phenyl ethoxylated, 0.17 for alkyl ammonium salts, 0.19 for alkyltrimethyl ammonium salts). For some new complex surfactants, such as alkyl propoxysulfates, there is some inaccuracy due to the lack of data, but on average they are close to the values for the alkyl sulfates (0.10), hence following the nature of the head group. However, if the available surfactant information is not guaranteed correct, it is just a matter of determining the variation of S with ACN, i.e., to carry out a salinity scan with hexane (ACN = 6) and another one with dodecane or hexadecane (ACN = 12 or 16) and for ionic surfactant to apply the equation ln S = K ACN ? … to both oil cases to estimate K. Similar experiments can be carried out with Eq. (4) and a bidimensional scan EON-ACN to estimate K for nonionic systems. The above technique has allowed classification of many surfactants with a characteristic parameter defined as r or b, or better as r/K or b/K, which are the parameters expressed in ACN units with exactly the same meaning in both types of correlations (3) and (4). For all types of surfactants, the parameter (r/K or b/K) was found to increase 2.4 units per additional carbon atom in a linear alkyl tail—a proof of proper parameter selection for comparison purposes and a very useful relation in practice [33]. It will be discussed later that the configuration structure of the hydrophobic part, particularly branching or ramification, also alters the surfactant parameter value. The above experimental data allows us to estimate the characteristic parameters of any surfactant and thus to obtain some approximate value, even if the exact structure is not known. For relatively pure surfactants, the estimated parameter value is essentially independent of the experimental conditions (oil, brine, temperature, and possibly alcohol if the contribution is small), i.e., it is a

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characteristic of the surfactant. The technique may of course be used with any surfactant mixture and will determine a value. However, this value often changes with the experimental conditions (oil, brine, temperature, alcohol) for partitioning phenomena discussed elsewhere [60– 62], and consequently will not be a precise characteristic of the mixture. Similar scan techniques may be applied to characterize an oil that is not an alkane. For instance, a salinity scan is carried out with a given alkane (for instance ACN1 = 7), under constant conditions of ionic surfactant, alcohol and temperature, resulting in a S1 optimum salinity. Hence ln S1  KACN1 þ r þ f ðAÞ  aT ðT  25Þ ¼ 0

ð9Þ

The salinity scan is repeated with the same surfactant, alcohol and temperature, after changing the oil phase for a new one, whose characteristic is called ACN2, which results in a shift of the optimum salinity to S*2. Hence ln S2  KACN2 þ r þ f ðAÞ  aT ðT  25Þ ¼ 0 ð10Þ 

 

By subtraction ACN2 ¼ ACN1 þ 1=K ln S2 =S1

ð11Þ

When the new oil is not an alkane but behaves exactly as if it were an n-alkane with an ACN2 number of carbon atoms, this value is called the equivalent alkane carbon number (EACN) [63]. Experiments have shown that the EACN may be deduced from the oil molecular structure. For instance, squalane, a triterpene with 6-branched methyl group exhibits an EACN of 24 [64], which is the exact difference between the number of carbon atoms (30) and the number of lateral methyl groups. Hence, its EACN is equivalent to the number of carbon atoms in the backbone. This is not the case for short iso-alkanes; the exact effect of branching has not been studied accurately, though it can be said that branching tends to decrease the EACN. Cyclization also produces a significant decrease in the EACN with respect to linear alkanes. Cyclohexane has an EACN of about 3–4 units, and for alkyl cyclohexanes, the alkyl group determines the number of carbon atoms. Hence, butyl cyclohexane has an EACN of 7.5; the benzene cycle essentially counts for nothing in short alkylbenzenes, and even makes a negative contribution for long alkyl counterparts. Accepted EACN values are 3 for isopropyl benzene, and 4–5 for n-octyl benzene [63]. However, benzene derivative data has been found to depend on the surfactant used due tothe strong solvent characteristics of these oil species, which tend to produce a high fractionation of the surfactant(s) in the oil phase, as discussed elsewhere [62]. Previous data indicate that EACN is essentially a measurement of oil polarity, being lower with more polar oils. A recent paper comparing the EACN of different terpenes with ten carbons atoms [65] shows that the EACN can vary

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from 10, for non-cyclic low branching varieties, to 6 for saturated cycle species, 3 when there is a single double bond in the cycle, and down to 0 when there is a benzene ring. Oil may be polar because of the presence of a heteroatom like oxygen in ether [66] or ester as in synthetic triglycerides [67] or natural oils [68]. For instance, dibutyl ether has an EACN of 4, ethyl oleate an EACN of 6–7, and soya oil an EACN of 18. This indicates that an ester group is significantly polar as its presence tends to decrease the EACN by about 10–12 carbon atoms in the accounting. Heteroatoms like chloride are even more polar than oxygen and are able to decrease the EACN considerably to negative values, such as -14 for chloroform [35, 69–71]. Low viscosity (3 cP) silicon oil of the polydimethylsilicone type with a molecular weight about 400 has been reported with an EACN of around 15 [72]. As for surfactants, the blending of different oil species can produce non-ideal mixing rules close to the interface, where the most polar species tend to accumulate [52], thus resulting in a low estimate of EACN. For heavy crude oil products, intuition might suggest that the higher molecular weight would result in a higher EACN as with alkanes, but this is not generally the case because the bigger molecules are generally polyaromatic ones; hence, more polar and thus with lower EACN contribution and higher segregation at the interface. The evaluation of bituminous oil has recently returned an EACN of 2–3 units [73], probably because of the very large proportion of (polar) asphaltenic species accumulating close to the interface. This is why the actual contribution of an oil mixture in Eqs. (3–4) does not necessarily follow the linear mixing rule proposed for n-alkanes in the 1970s [9]. In complex mixtures of different polarity oils, the EACN contribution in Eqs. (3–4) has to be analyzed with a proper mixing rule. The equivalent salinity with electrolytes other than NaCl has been determined with certainty for nonionic surfactants through the value of the ‘‘b’’ coefficient in the corresponding correlation [27]. However, the data are not very accurate because the salinity effect is small for these surfactants, i.e., decreasing the ethylene oxide number by 1 unit in b, is equivalent to increasing the salinity from 0 to 7wt% NaCl or from 0 to 5 wt% CaCl2. For ionic surfactant systems the situation is more complex. Di- and tri-valent cations like Ca??, Mg??, Al??? are able to precipitate typical anionic surfactants and thus produce effects that cannot be treated simply with an equivalence factor [30, 39, 42, 46]. The effect of the electrolyte anion in sodium salt electrolytes has been studied in detail, and an equivalent salinity has been found to depend on the anion valence [38]; for instance, a sodium phosphate (Na3PO4) electrolyte solution is two times less salty than a monovalent NaCl or NaF solution with the same molar concentration. It may be said that by the late 1990s many practical studies had demonstrated that the correlations for optimum

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formulation proposed 20 years previously were quite general and worked well for systems containing relatively pure surfactants at relatively high concentration, i.e., 2 wt% or more. In such cases, the actual system containing mixtures of surfactants, mixtures of oil species and mixtures of electrolytes could be handled similarly, as in the case of a ternary of pure substances, through use of the concept of pseudo-components. However, with typical commercial mixtures, particularly mixtures containing widely different surfactants or surfactants and co-surfactants, and widely different oils, it was clear that the three pseudo-components approximation could not be used accurately and satisfactorily, in particular at low surfactant concentration. Some appropriate nonlinear mixing rules [74] had to be considered to calculate the equivalent surfactant parameter, the EACN, and equivalent salinity. This situation prompted two types of studies. First, a physical-chemistry approach to explain why such a simple equation was so general, and to query the actual meaning of the correlation. Secondly, researchers asked why this approach was working very well with pure products and but not for mixtures. In other words, how could the pseudocomponent equivalent to a mixture be calculated from the characteristics of the different contributing species, in order to be able to use the correlation for optimum formulation with a real system. Since in practice in EOR the crude oil and the connate brine are essentially fixed by the oil field conditions, mixture selection and management were focused on the amphiphilic pseudo-components containing different surfactants and cosurfactants such as alcohols.

Surfactant Affinity Difference/Hydrophilic–Lipophilic Deviation Concepts (at Interface) as the Basis for SOW Ternary Behavior So general an equation could not be a coincidence, and some theoretical work was thus dedicated to explain this as something that has to do with chemical potential.

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In SOW systems, the equilibrium of surfactant molecules between the water and oil phases may be rendered by the equality of chemical potentials. l W ¼ lO W

O

W

i:e: l þ RT ln aW ¼ l þ RT ln aO or l þ RT ln aW C W O

¼ l þ RT ln aO C O

ð12Þ

where the l are the standard chemical potentials at some reference, ‘‘a’’ represents activities, and a the activity coefficients. The optimum formulation corresponds to a system in which the activity of the surfactant is the same in both oil and water phases—a definition equivalent to R = 1 in the Winsor approach. In other words, optimum formulation occurs when the standard potentials of a surfactant in oil and water are W O equal, i.e., when l ¼ l . In three-phase systems close to optimum formulation, most surfactant species are generally in the microemulsion middle phase, and the oil and water excess phases exhibit a low concentration, usually close to the CMC [75]; consequently, the activity coefficient in these phases is likely to be close to unity. The same happens outside the three-phase region at very low surfactant concentrations, e.g., at or below the CMC. With such an assumption, then W

O

l þ RT ln C W ¼ l þ RT ln C O

ð13Þ

at optimum formulation and thus CO = CW, as can be seen in Fig. 6 which indicates the partitioning coefficient PC = CO/CW of the surfactant in the case of anionic surfactant systems from very pure alkylbenzene sulfonate (Fig. 6a) to a commercial petroleum sulfonate mixture (Fig. 6b) along different scans [75–82]. In the petroleum sulfonate plot (Fig. 6b), PC is reported for two final concentrations of all surfactant species. The partition coefficient is essentially unity in both cases, but it can be seen that the optimum formulation for three-phase systems (black dots) is shifted to the right in the scanned ACN scale (Fig. 6b) when the concentration of the petroleum

Fig. 6 Surfactant partition coefficient Pc = CO/CW variation along a formulation scan. a Very pure alkylbenzene sulfonate; b technical grade alkylbenzene sulfonate system. Data from [77]

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sulfonate decreases. This means that the surfactant mixture at the interface becomes more lipophilic as the total concentration decreases. This does not happen for the pure surfactant system [76]. W O The difference DlO!W ¼ l  l was called the surfactant affinity difference (SAD), following the definition of affinity as the negative of the standard chemical potential [83]. SAD measures the standard chemical potential change during the transfer of a surfactant molecule from the oil to the water phase, and is thus dependent on the nature of the components and on temperature. Its measurement provides essential information on the formulation influence [84]. W

O

SAD ¼ l  l ¼ DlO!W ¼ RTln PC ¼ RT ln

CO CW ð14Þ

The standard chemical potentials of the surfactant are altered along formulation scans as shown in previous figures; W for instance, in the salinity scan shown in Fig. 7a, l O increases with S, whereas l remains constant since the salinity has no effect on the oil phase. SAD = 0 at the intersection (in S1) of the two lines, indicating the variation of W O l and l , for a system containing an oil phase with ACN1. Figure 7b indicates the same effect of salinity on the standard chemical potential but this time for another value ACN2, O higher than ACN1 and thus with a higher l , resulting in a higher optimum salinity at S = S2. In both cases, the remaining formulation characteristics, i.e., surfactant type, alcohol contribution and temperature, are unchanged. The change in SAD between the two optimum formulation cases, assumed to be small enough to be a differential variation, may be written as follows, since the only variables that changed in this map are the ACN and the salinity S (expressed as a log scale to obtain a linear variation of the potential). oSAD oSAD d ln S þ dACN oln S oACN   W  O W O o l l o l  l d ln S þ dACN ¼ o ln S oACN

dSAD ¼

ð15Þ Fig. 7 Variation of the chemical potential of the surfactant in the oil and water phases along a salinity scan for two n-alkane oil phases, a lower ACN1 (a) and a higher ACN2 (b)

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this may be simplified as  W  O o l o l dlnS  dACN dSAD ¼ olnS oACN

ð16Þ

When the double formulation change S-ACN is from an optimum state (S1/ACN1) to another (S2/ACN2), then dSAD = 0, and the relationship for the attainment of an optimum formulation in the lnS/ACN bidimensional space is  W  O o l o l dlnS ¼ dACN ð17Þ olnS oACN It has been shown experimentally [25, 27] that such a change takes place along a straight line, i.e., the ratio of the two partial derivatives in Eq. (17) is constant for a given surfactant head group, and this constant has been called K in correlation (3). The same double change to pass from one optimum formulation to another may be expressed with any pair of formulation variables, and the experimental evidence for a constant ratio of the partial derivatives for all pairs indicates that all partial derivatives with respect to formulation variables are constants. Hence, SAD is a linear relationship of the formulation variables, just like the correlations for optimum formulation. X oSAD dSAD ¼ dXi and oXi i X oSAD SAD ¼ ð18Þ Xi þ integration constant oXi i Since it is a measurement of variations, the integration constant may be arbitrarily taken as zero. Since the salinity, ACN, f(A) and DT terms have a physical meaning, the zero constant is included with the surfactant term, referred to as r or b in what follows. Consequently the surfactant term may possibly be defined with a non zero constant if needed for simplicity. If a dimensionless SAD/RT expression is preferred, the expression becomes X oHLD SAD=RT ¼ HLD ¼ ð19Þ Xi oXi i

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461

where HLD indicates the hydrophilic–lipophilic deviation from optimum formulation, i.e., the driving force chemical potential for the surfactant to move from one phase to the other. HLD is thus a measure of the imbalance of the surfactant between the phases. The present review deals with optimum formulations, i.e., situations in which HLD = 0. In other instances, in particular with emulsions, this HLD value has been found to be linked to the system properties and is thus very useful for the practitioner. This is out of scope of this review and is discussed elsewhere [85]. A striking result is that the expression attained for the variation of HLD as a function of the formulation variables is identical to the correlation for optimum formulation, for ionic (Eq. 3) and for ethoxylated nonionic (Eq. 4) surfactants in the absence of alcohol. Note that it would be essentially the same with a neutral alcohol like sec-butanol for which f(A) or /(A) = 0, i.e., with no formulation effect, whose role is to avoid the formation of liquid crystals with some surfactants. HLD ¼ SAD=RT ¼ ln S  KACN þ r  aT ðT  25Þ ¼ 0 ð20Þ HLD ¼ SAD=RT ¼ bS  KACN þ b þ cT ðT  25Þ ¼ 0 ð21Þ For simple systems containing pure surfactant, pure oil and a simple (NaCl) brine, these equations are found to be accurate with parameters r or b (a-EON) and ACN (or EACN for non-alkane oils), which are characteristics of the surfactant and the oil phase. The salinity should appear as a log scale because of the logical relation between the chemical potential and a concentration, but it is kept as a linear variation with nonionic surfactants because the variation is very small and thus approximately linear. Moreover, such a non-logarithmic scale allows for zero salinity to occur, as is possible with nonionics. On the

contrary, with ionic surfactants, a zero salinity does not actually occur in the absence of salt, since the presence of the surfactant contributes to some electrolyte concentration. This contribution to salinity of the ionic surfactant has to be taken into account in S as an equivalent NaCl concentration corresponding to the same Na? concentration than that coming from the surfactant. This correction is required when the NaCl salinity is lower than 0.5–1.0 wt% to keep the linearity with a log scale salinity in the negative part. The effect of temperature is not strictly linear as suggested in early publications [27], particularly with ethoxylated nonionics. This is probably because the temperature essentially influences both l terms, and also because it is known that the division by RT to write the relationship as dimensionless introduces a temperature effect as follows [84] oðSAD=RT Þ oðDl =RT Þ oðDh =RT  Ds =RÞ ¼ ¼ oT oT oT  Dh ¼  2 ¼ cT RT

ð22Þ

This cT coefficient in the HLD expression for polyethoxylated nonionics has been shown [84] to depend not only on temperature, but also on the ethoxylation degree through Dh . However, the two effects are opposite and thus the coefficient does not vary very much with temperature, particularly for pure surfactants. For instance, Fig. 8a shows that the slope of the optimum formulation line in the EON versus T map for a pure surfactant system is not far from constant over a large range of formulation change. The nonlinearity is worse for commercial mixtures as seen in Fig. 8b, although the accuracy of determining the optimum formulation at the center of the three-phase region is not very good when the range is quite wide. However, it may be said in this second case that most of the slope change is probably due to another effect, i.e., the partitioning of

Fig. 8 Ethylene oxide number (EON) versus temperature phase behavior and optimum formulation. a Data from [14], b data from [86]

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oligomers as discussed elsewhere [62]. In practice, the evidence shows [87] that cT does not vary very much even for commercial ethoxylates and, in most cases, an appropriate constant value can be taken over the temperature (20 C) and EON (2 units) variations used in practice. It is worth noting that the wider three-phase range for kerosene (EACN = 9–10) than for tetradecane (ACN = 14), which is opposite to the usual trend, may be related to the fact that Fig. 8b systems contain wide range mixtures of surfactants and oil. However, it is probably mainly due to the effect of alcohol on performance, as will be discussed in part 2 of this review. Surfactants with both an anionic and a nonionic part in the head group, such as alkyl ethoxy carboxylate [88] or alkyl propoxy sulfate [32], exhibit an intermediate behavior with respect to temperature. Tributyl phenol ethoxy(4) sulfonate [29] was reported to behave as an anionic (nonionic) at high (low) temperature. This non-constant temperature coefficient is equally likely to occur for ionic surfactants from the theoretical point of view, but the effect is much less and the accuracy insufficient to find significant variation experimentally. Hence, aT is thought to be constant quite appropriately [25, 26] though some difference have been reported for sulfate and sulfonates [30]. A change in pressure [29, 58] has been found to produce a change in formulation, but the effect is extremely small, within the inaccuracy of the other variations, and it is not considered in practice.

Additional Effects Known to Complement the Simple SAD Relationship with Accurate Details of Surfactant Characteristics Effect of Tail Length The double scan technique mentioned in a previous section was used experimentally to estimate the surfactant characteristic parameter defined for many species as r/K (ionics) or b/K (nonionics) in ACN units. The data in Table 2 indicate the surfactant parameter values for different surfactants with a C12 linear alkyl tail (at 25 C). These values can be completed by a standard increase of about 2.4 units per additional carbon atom in a linear alkyl tail, which allows the parameter value for any other chain length species to be estimated. r=K ¼ r0 =K þ 2:4ð0:2Þ TACN(ionics) and b=K ¼ ða  EONÞ=K ¼ a0 =K þ 2:4ð0:2ÞTACN  EON=KðnonionicsÞ

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ð23Þ

Table 2 Characteristic parameters for some pure surfactants and commercial mixtures Surfactant

r/K or b/K

K

C12 linear benzene sulfonate LAS

-3

0.16

C12 orthoxylene sulfonate, AOXS

?3

0.16

C12 sulfate

-26

0.10

C12 carboxylate

-5

0.16

nC12EO4 pure oligomer

?12.5

0.15

nC12EO5 pure oligomer

?5.6

0.15

nC12EO6 pure oligomer isoC9/EO6.0 commercial mixture

-1.0 ?2.2

0.15 0.15

isoC12/EO6.3 commercial mixture

?8

0.15

isoC9/EO5.1 commercial mixture

?8

0.15

tC8/EO5.3 commercial mixture

?8

0.15

This relationship is fairly well corroborated for sulfonates and ethoxylates, where TACN is the tail ACN, i.e., the number of carbon atoms in the (more or less) linear alkyl tail of the surfactant. TACN has been also referred to as surfactant alkyl carbon number (SACN) in the literature. Iso-alkyl chains arising from the polymerization of propylene seem to exhibit a slightly lower coefficient in Eq. (23) (2.25 instead of 2.4), but this is not certain because the structure of the tested commercial product is not known with accuracy. The two methyl groups on the benzene ring in the alkyl orthoxylene sulfonate (AOXS) are worth about 6 units in the accounting, hence about 3 units per methyl group, not far from the standard 2.4 unit increase per carbon atom in a linear alkyl tail. The three last alkyl phenol ethoxylates in Table 2 (commercial products) have a b/K equal to 8, i.e., they are found to exhibit exactly the same contribution in the HLD general formulation at a 0.02 M concentration. Because the tail length TACN and EON length both have to vary in the same direction to keep the same b = 8 according to equation (23), then the C8 alkyl tail (TACN = 8, i.e., lower than 9) would be expected to be compensated by an EON lower than 5.1, which is the value corresponding to C9 alkyl in Table 2. This is not the case, since EON is reported in Table 2 to be 5.3 for the C8 alkyl tail ethoxylate. It may be because the ter-alkyl tail is more branched than the iso-nonyl, thus more hydrophobic as will be seen next, or because the fractionation of the mixture is not necessarily the same, due to the different distribution of head and tail groups. Effect of Ramification As noted in the previous paragraph, the branching of the tail has a significant influence on the surfactant characteristic parameter. A few comparisons between linear and

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non-linear chain in the surfactant tail have shown a systematic variation in the parameter with branching or ramification [89]. A polypropylene tail, with the branching of a methyl group every two carbon atoms, decreases the tail length and, according to the characteristic parameter estimation, tends to decrease the surfactant characteristic parameter r/K by about 1–2 units per methyl group [90]. A recent study with different positions for a single branch in a nonionic surfactant tail indicates very significant variation, qualitatively consistent with Israelashvili’s critical packing parameter [91]. In the double tail ramification feature attained by placing the hydrophilic group at a different location along the linear alkyl chain, as in the linear alkyl benzene sulfonates (LAS) used in detergents, the hydrophobe doubling tends to increase hydrophobicity. On shifting the benzene from the extreme of the nC16 alkyl to its middle (i.e., on the 8th carbon atom), the r/K value has been found to increase by about 10 units, i.e., a hydrophobe increase equivalent to adding four carbons atoms in a single linear chain with benzene at the extreme [89]. A similar effect takes place with so-called internal olefin sulfonates species [92]. In all cases, tail doubling results in an increase in hydrophobicity together with an increase in water solubility [92]—in practice, a fancy concomitance to improve surfactant performance with no precipitation penalty, as will be discussed in part 2 of this review. Complex structures using dual or multi-branches, such as in the so-called Guerbet hydrophobes [93], have been proposed for surfactants [94–96] with the same double benefit. These results indicate clearly that the hydrophobic contribution of the surfactant tail is not only related to the number of carbon atoms, as sometimes assumed, but depends significantly on its structure. Knowing the precise relationship between the structure and the parameter might be important from a knowledge point of view but is probably not so important for commercial products, which are always a mixture with unknown exact structure distribution in most cases, and for which the actual parameter value will have to be measured anyway.

463

[98]. Double bonds are also known to reduce the probability of the surfactant to form a liquid crystal—a convenient feature that allows any requirement for an alcohol co-surfactant to be disregarded. Alkyl Propoxylated (Extended) Surfactants The increase in the number of propylene oxide groups at the root of the tail of an alkyl propoxy sulfate (so-called extended) surfactant results in a decrease in optimum salinity, and thus exhibits an increase in surfactant hydrophobicity [99]. The variation is quite linear in term of lnS, and may be rendered by a r/K increase of 1.3 unit per added propylene oxide group. The experimental value of K for these extended surfactants has been reported to range from 0.08 to 0.12 [32, 68, 90, 91, 94, 100, 101]. This is a rather wide range and, as a consequence, the above results, which depend on K, might be inaccurate. Nevertheless, the addition of propyleneoxide definitively increases the lipophilicity, and it may be said that the polypropyleneoxide extension forms part of the tail of the surfactant. However, it is unlike a typical hydrophobe, since the contribution of an additional propylene oxide (1.3 unit in r/K) may be said to be weakly hydrophobic when compared to the 2.3 unit increase produced by an additional carbon atom in the alkyl tail. In other words, a simple comparison shows that the contribution of propylene oxide group hydrophobicity is equivalent to about half that of a methylene group. This is a small but expected result when both the branching and polar ether features are considered. The use of two propyleneoxide groups instead of one methylene will produce a similar formulation change, with a completely different size variation in the tail—an important feature for performance issues. Moreover, the 2–3 first propylene oxide units next to the head group in the chain have been shown to stay close to the interface. In other words, the polypropyleneoxide chain is bent [102], resulting in the inhibition of the formation of liquid crystals in the absence of cosurfactant. Finally, the extended surfactants with a sulfate head group have been found to exhibit a temperature effect like that of polyethoxylated nonionics, though with an absolute cT value of about four times lower [32].

Effect of Double Bonds A recent review [97] has reported the effect of double bonds in an ethoxylated alcohol tail. It was found that two double bonds in the tail considerably reduce the b/k characteristic parameter, i.e., they turn the surfactant much less hydrophobic, as if half of the 8 carbons of the tested surfactant tail had disappeared, according to the data from compounds of the same length but with a saturated tail [14]. Similar trends were found with cationic surfactants

SAD/HLD in Practice SAD as a Generalized Expression to Characterize Formulation SAD is a physicochemical concept basis that allows us to understand why a single formulation expression is able to take care of the effects of many variables. It is a numerical

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expression, which is much more useful in practice than Winsor’s R because it delivers a value or at least a numerical estimate on how far is the optimum formulation and which variables(s) may be changed to reach it. However, the features influencing the characteristic parameter of a surfactant seen in the previous paragraphs are so many that the numerical value is somewhat inaccurate, even for pure surfactants. This inaccuracy becomes even worse with real systems containing mixtures of surfactants, oils, and salts. The right approach seems to be to extend the use of the concept with pseudo-components, and to use current knowledge to estimate the pseudo-component characteristic values at the interface from the actual total composition of the system. Many studies have been carried out and, in spite of complex relationships, a fairly sophisticated knowhow is available as will be shown in part 3 of this review. The handling of pseudo-component systems implies in most cases the use of mixing rules, i.e., relationships between the single species characteristics and the combined pseudo-component one. Since SAD is an energy term, the contributions are likely to add up, at least in the simplest cases. Consequently, the contributions must be expressed in the same units. It was shown that when the surfactants have a different head (sulfate, sulfonate, ethoxylate etc.), the K term that deals with the compensation between salinity and ACN differ, though not very much. The HLD = SAD/RT correlations contain terms that are not equivalent as far as the effects are concerned, with the exception of the ACN contribution, which has absolutely the same meaning in both correlations. This is related with the fact that it depends on the interaction between the surfactant tail and the oil phase, which is independent of the head group, and thus is likely to be exactly the same for the two equations. Consequently, writing all expressions of HLD by dividing SAD by KRT instead of RT, would produce a numerical term with the same value variation independently of the K characteristic. This dimensionless expression will be called HLDu, with ‘‘u’’ for unity or unique. HLDu ¼ 1=KðSAD=RTÞ ¼ PACNref  ACN þ 1=Kðsalt effect þ alcohol effect þ temp effectÞ ð24Þ The terms will be the same as in HLD, with a unique definition of the surfactant characteristic parameter PACNref as the preferred ACN at zero salt effect (S = 1 in all cases), no alcohol (f(A) or /(A) = 0) and reference temperature (DT = 0). The S = 1 wt% NaCl for ethoxylated nonionic systems is not absolutely accurate, but the difference with a reference at no salt is extremely small, equivalent to a unit error in PACNref of just 0.6, or

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equivalent to 0.25 carbon atoms less in the surfactant tail— a difference that is negligible within the actual accuracy in practice. Under these conditions, the characteristic parameter of each surfactant pseudo-component will have to be calculated and the combination of the contributions in the mixture will be handled by the corresponding mixing rule to be determined in each case. It is worth remarking here that the linear mixing rule expressed as X PACNref ðmixtureÞ ¼ Xi PACNref ðeach species iÞ all species

ð25Þ is not the general case but rather an exception, because the collective behavior is not the rule in most systems, especially at the interface, and particularly for the intermolecular association and fractionation with surfactants and cosurfactants to be discussed in part 3 of this review. The splitting up of the contribution into the PACN of each component of the mixture, i.e., its tail characteristics (length branching, double bonds and rings), head (ethylene oxide units, ionic groups) and intermediate alkoxide (propylene oxide) can lead to some overall linear expression [103] that may be useful as a guideline but would be quite approximate in practice because it assumes linearity. The previous remark deals with surfactant mixtures. The same kind of non-collective behavior complexity will have to be handled similarly with segregation phenomena for oil mixtures [104], and for electrolyte mixtures effects [38]. Physical Meaning of SAD and the Surfactant Parameter PACNref The situation SAD = 0 is a balanced state of interactions, which has been defined as a standard chemical potential equality from thermodynamics argumentation. It corresponds to some physical meaning related to a zero interfacial curvature associated with equal tension interactions on both sides of the interface. This curvature concept was first introduced by Bancroft [105, 106], and was then illustrated by Langmuir’s recently revisited wedge theory [107], then partially quantified by the Winsor R ratio and compared [108] with Israelashvili’s [109] critical packing parameter. The wedge has to do with the shape of an arrangement of a surfactant molecule associated with oil and water at interface, which can exhibit a more bulky side because the surfactant exhibits more interactions with oil or with water, thus resulting in curvature toward one of the phases. The surfactant molecule at interface has an inherent or natural curvature generally called preferred curvature, whose effect is combined with the steric effects due to the

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association with oil/water, to result in the average interfacial curvature, which is represented by different models, such as the classical average between the principal curvatures [20, 110] or the net average curvature, which is the difference between the curvatures of the water and oil domains [111–113]. All these concepts are related, as pointed out recently [108]. What is described by all models is that, at optimum formulation, the average curvature is zero, and the water and oil domains in the bicontinuous microemulsion [12] exhibit a maximum size, though not infinite, which has to do with the allowable perturbation and is thus related to the minimum interfacial tension [114, 115]. This increase in phase domain size as formulation approaches an optimum is visible on both sides in Fig. 5, as an increased opacity of the microemulsion phase in WI and WII systems. The curvature, i.e., the inverse of the domain typical length, has been linked with HLD with fair accuracy for different kinds of surfactants [91, 111, 116]. This has been studied in a fairly sophisticated manner for systems containing the most simple ternary SOW systems, as will be seen in part 2 of this review. However, the extension to real systems with complex mixtures is not yet advanced enough to make exact predictions with mixtures. The SAD equation is still valid at interface as a concept, but the parameter describing the surfactant mixture pseudocomponent is no longer characteristic of the involved mixture in itself, but depends on the way the composition of the mixture changes according to phase partitioning and intermolecular association [62]. The current state of the art on how to estimate mixture behavior as a pseudo-component will be discussed in part 3 of this review.

Accuracy and Validity Limit of HLD Simple Equations for a Real System Approach A SAD equation including three terms representing the nature of surfactant, oil and water, in the absence of alcohol (or with an alcohol like sec-butanol that does not exhibit a significant formulation influence) is a linear relationship of lnS or bS, K ACN or EACN, r or b, as well as temperature as aT or cT DT. The point is that, in a pure components system, each component of a SOW has a characteristic parameter that is independent of the conditions of the system. For an ionic surfactant system, in the 3D space lnS/ACN/T, SAD = 0 is the equation of a plane shown in Fig. 9. This optimum formulation plane cuts the ACN axis (lnS = 0 and T = 25 = Tref) at r/K, which is the characteristic surfactant parameter, called the extrapolated preferred ACN at a reference salinity effect (S = 1) and no alcohol, i.e., EPACNUS [25] or PACNref as previously defined. This

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Fig. 9 3D representation of the optimum formulation relationship (no alcohol anionic system). Hydrophilic–lipophilic deviation (HLD) = ln S - KACN ? r - aT (T - 25) = 0. After [77]

term has also been called the characteristic curvature (Cc) to emphasize its meaning as the surfactant contribution to the net curvature model [117]. If the S/ACN/T conditions of an actual brine/crude system do not correspond to the optimum formulation for the tested surfactant at field temperature T, a change in surfactant would produce a displacement of the plane parallel to itself (along arrow 4) until it matches the conditions for optimum formulation [118]. In the SAD = 0 plane in Fig. 9, all the points are at optimum formulation, and some displacement from one place to the other in the plane (along arrows 1, 2 or 3 or any combination) would exhibit variations in performance, i.e., higher or lower minimum tension. Such displacements along paths 1–3 correspond to the experimental trials to be carried out to search for a better optimum formulation performance in practice. Although experimentally determined iso-IFT contours in this plane are not freely available, some trends in the minimum tension variation are known, as will be discussed in part 2 of this review. This is extremely interesting in practice as a guideline with which to determine proper formulation in EOR. However, most practical situations imply the use of mixtures of substances, particularly mixtures of surfactants, for different reasons like availability, cost and of course performance. When mixtures are used, the number of relevant variables increases far above three components plus temperature. Hence, the use of the previous 3D approach might not be sufficient, or the optimum surface will no longer be a plane in 3D space. The use of pseudo-components might resolve the dimension problem, but then the characteristic parameters of the pseudo-components are no longer necessarily the same everywhere, particularly for the surfactant mixture. In other words, the characteristic parameter will not be characteristic but will change with the other

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variables. This is because the different species in a pseudocomponent do not necessarily behave in a collective way, and the formulation at interface could be different from the global formulation in the system, as will be discussed in part 3 of this review. In practice, a critical issue is to know whether a real system, particularly with surfactant mixtures found in the market or selected for exhibiting better performance, is likely to follow or to strongly deviate from the simple HLD linear equation. This is relatively simple to diagnose by carrying out a simple experiment that detects whether a mixture behaves as if it were composed of an ideal pseudocomponent or not. The deviation from ideality is found easily by plotting a scanned variable at optimum, e.g., ln S for ionics and EON for nonionics, versus mixture composition and looking at the linearity [59, 76, 78, 80]. However, this is not the most sensitive test to predict the accurate validity of the HLD linear equation, in particular for commercial systems in which the mixture already exists with unknown proportions of components. The shift in optimum formulation with the variation of surfactant concentration over at least one order of magnitude, particularly in the low concentration range around 0.01 wt%, is very significant as reported a long time ago with petroleum sulfonates [76]. Examination of the shape of the gamma/ fish phase behavior map seen in Fig. 2 (as a cut at constant WOR) also allows a very simple diagnostic of whether the HLD equation with the global formulation is valid or not at interface when any kind of pseudo-components are used. Figure 10 shows the phase behavior of a SOW(A) system versus formulation and surfactant concentration. The formulation variable may be the nature of any of the four components or temperature; here, the typical ones, e.g. salinity for anionic systems and temperature for nonionic ones, respectively, are shown in Fig. 10 plots numbered 1 (left) and 2 (right). The three-phase region has two limits in these plots, i.e. Cm at low surfactant concentration, below which there is not enough surfactant to produce a microemulsion, and CX at high surfactant concentration, above which a single phase system is produced at optimum formulation. The center of the three-phase range along the scanned formulation variable is essentially the optimum formulation at which the tension is minimum, and is indicated as a bold line. In Fig. 10a1 and a2, the bold optimum formulation line is essentially a straight line at a constant value when the surfactant concentration changes from Cm to CX. This means that, in such a case, the optimum formulation at which the minimum tension takes place does not vary when changing surfactant concentration. Consequently, the HLD equation is valid at any surfactant concentration with the same surfactant characteristic parameter, which can be calculated from the formulation variable value at optimum.

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This situation happens with a pure surfactant or with a mixture in which the species behave in a collective way as a perfect pseudo-component, which is a very rare occurrence in practice [14, 64, 119–121]. In Fig. 10b1 and b2, the optimum formulation changes when the surfactant concentration changes, and the bold optimum formulation line is slanted, i.e., the gamma or fish shape centerline is not a straight line at constant formulation, but is slanted and twisted [49, 55, 71, 122, 123]. In this case, the surfactant parameter in the HLD equation changes with surfactant concentration. In other words, the HLD equation with a single surfactant parameter is not valid, because the surfactant parameter varies with surfactant concentration. This variation with surfactant concentration has long been reported [25, 76, 77, 124], and a similar shift effect has been found when the water-to-oil ratio changes [77, 125, 126], as in most cases of phase

Fig. 10 Phase behavior of a surfactant-oil–water (SOW) system in a formulation versus surfactant concentration map, typically for an anionic (left) and a nonionic (right) surfactant. a–c Typical cases of a pure surfactant, a commercial mixture, and an usual shape, respectively

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behavior studies in formulation-composition plots that exhibit slanted three-phase zones [74]. This variation of the characteristic parameter occurs with surfactant mixtures in which each species has an individual behavior, which is what happens in most practical cases, especially with widerange polyethoxylates [56, 62, 71, 123, 127, 128]. Most of the time, the variation in the surfactant parameter is as shown in Fig. 10c1 and c2, i.e., the formulation is almost constant (part following arrow) at high surfactant concentration close to CX, but it varies greatly at low concentrations close to Cm. In other words, the gamma or fish is twisted close to the head, and is straight at constant formulation close to the tail [55, 129]. This means that the surfactant mixture characteristic parameter is altered when the concentration becomes low [25, 27, 130], which is unfortunately the case in the conditions in which EOR processes are trying to work. Notwithstanding, this problem can be fixed with a proper trick using a mixture of surfactants with opposite shifts [131], as will be discussed in part 3 of this review. A More Sophisticated Description of the Interfacial Situation is Required The basic Winsor model includes a surfactant adsorbed at interface with interactions with oil and water molecules, and it is thus logical to describe the situation in terms of what might influence these interactions, i.e., the nature of the three components and temperature. The introduction of alcohol complicates things because the role of the alcohol is not simple [49]. Alcohol might alter the water hydrophilic character for C1/C2/C3OH, or it can migrate to adsorb at the interface as a cosurfactant, in particularly large amounts in the case of alcohols that are not very hydrophilic nor lipophilic, like sec-butanol or terpentanol. These alcohols might occupy a large proportion of the surface area at the interface and thus elbow the surfactant away, avoiding the formation of liquid crystals but also reducing the surfactant adsorption and thus impairing the tension lowering. Clearly lipophilic alcohols like n-C4/n-C5/n-C6OH participate as cosurfactants at the interface, i.e., they will contribute to making the adsorbed amphiphile layer more lipophilic. With systems containing alcohol, the parameter r, i.e., the surfactant contribution in SAD, is replaced by r ? f(A), in which f(A) is larger for longer alcohols and higher alcohol concentration. This is not obviously a nice mixing rule between the effects of the surfactant and co-surfactant. Moreover, this kind of (lipophilic) alcohol tends to partition into the oil, where it tends to accumulate close to the interface as a polar oil species [52]. These alcohols will actually change the composition of the oil phase interacting with the interfacial amphiphile and, as a consequence, will decrease the actual EACN. Any

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variable susceptible to altering the alcohol partitioning will change the role of alcohol as cosurfactant and as oil. Long chain alcohols like dodecanol that do not adsorb at interface have been found to produce the so-called lipophilic linker effect [50, 51], which is intermediate between the surfactant at interface and the bulk oil molecules. Lipophilic linkers are not at the interface since their presence does not alter the interaction balance between the surfactant and the oil and water, hence they do not change the formulation, but exert their effect through a change in oil EACN. Substances like asphaltenes in crude oils are polar oils that could be considered as lipophilic linkers that reduce the oil EACN [73] even more than the value expected from the aromatic composition; however, there are some species that tend to behave as surfactants, and this is why their effect is countered by demulsifiers, which are also surfactants that mix with asphaltenes. The question to analyze is whether asphaltenes should be considered as lipophilic surfactants or as polar oils [132, 133]. It is not really straightforward to define the limit between the surfactant and the polar oil. This perplexity indicates that the simple SOW case in the Winsor model is not really valid, and that the simple HLD linear equation with four variables cannot be valid either. Since a more complex model would require many new variables, including some that describe the location and the role of the species, the inclusion of score of variables in the HLD equation does not seem to be the right solution in practice, because it is known that the suggested linearity [103], which is the logical way to expand the formula, is probably wrong. It is certainly more efficient to use the simple HLD model, with an appropriate estimate of the corresponding parameters for the pseudo-components through corrections or deviations coming from studies on mixture optimization for synergy attainment to improve performance. The improvement trends will be presented in part 2 of this review and the accommodation of mixture effects in amphiphilic structure into the pseudo-components characteristics entering the HLD equation will be discussed in part 3.

Conclusions The SAD/HLD relationship that includes a linear expression with (at least) a term for the nature of each component as well as temperature, is followed well by relatively pure systems, and is an excellent guide for predictions. In the simple case in which there is no alcohol in the system, the phase behavior and optimum formulation can be manipulated with only four independent variables: brine salinity,

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oil ACN, surfactant parameter and temperature. For this case, systematic studies have been carried out on the effect of the different variables on the performance of the formulation for EOR, and very clear trends have emerged to lower the tension or to increase the solubilization in microemulsion. There are three important independent guidelines for this process that can be combined to give a synergistic boost. The current physicochemical understanding and the published empirical results agree quite well, so that a fairly elaborate know-how can be organized, which will be presented in part 2 of this review. The improvement in performance has been shown to compel the use of mixtures of amphiphilic substances, i.e., various surfactants and eventually co-surfactants to find a compromising optimum balance between advantages and inconveniences [134]. Application to EOR also implies mixtures of oils and of electrolytes. Consequently, a proper extension of the SAD/HLD equation with 3 components and temperature implies the use of up to 10 or 15 variables in an actual case. This number is obviously impossible to handle, and use of pseudo-components is mandatory to keep the number of variables to 4 (and in some very specific cases to 5 or even 6). The problem in handling a relationship of the SAD/HLD type is to estimate the actual value of each pseudo-component parameter, in particular the surfactant parameter, which is the essential selection in the formulation. This could be easy in some cases in which the molecular interactions and resulting pseudo-component parameter values may be estimated with a linear mixing rule, for instance in the case of alkyl benzene sulfonates in which the length of the tail is variated [59]. If the length distribution is relatively narrow, say a difference of no more than 6 carbon atoms, the average length will provide a good approximation for the mixture effect, at least if the concentration is not too low. If one head group is hydrophilic and the other lipophilic, a proper mixture would be intermediate and the attainment of an optimum formulation could be predicted with accuracy. For dodecyl alcohol ethoxylates, the same will occur for the head group mixture if the polyether length variation is not too large. However, above a difference of 3–4 ethylene oxide units between oligomers, fractionation would take place and result in a non-linear mixing rule [62]. Discrepancies from linearity also happen if the mixture contains different head groups, e.g., a sulfonate and an ethoxylated group. In such a mixed pseudo-component, the occurrence of wrapping of the nonionic polyethylene glycol around the anionic sulfonate would result in a considerable reduction in the interaction with water, i.e., the mixed head will be notably more hydrophobic than expected [74]. These are just examples of very common situations in which a close look at what happens when a mixture of various species is absolutely necessary, most of the time with a qualitative guess of what

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could happen and a required experimental evaluation of the actual effect. This will be discussed in part 3 of this review. The extension of the simple SAD/HLD method to real cases does not maintain such accuracy, but helps the formulation practitioner to considerably reduce the number of trials by building up screening techniques consisting of a progression towards the optimum, in which the required experimental data is much less that in the usual trial and error essays. These techniques are useful not only for EOR studies in which HLD = 0 is the sought formulation, but also in many applications of micro-, macro-, mini- or nanoemulsions, for which the generalized formulation has to be set with some accuracy to attain the required property [85].

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Author Biographies Jean-Louis Salager earned a BS in Chemistry and a BS in Chemical Engineering from the University of Nancy (France) and a PhD from the University of Texas at Austin (US). For the past 40 years he has

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J Surfact Deterg (2013) 16:449–472 been involved in teaching and research at the University of the Andes (Me´rida-Venezuela) where he is the founder and former director of the FIRP laboratory. He is currently Emeritus Professor and Consultant in Surfactant Science and Technology, petroleum production, health care, hygiene and detergent products. Ana M. Forgiarini earned a BS in Chemical Engineering from the Technological Institute in Barquisimeto (Venezuela) and a MS in Chemical Engineering from University of the Andes (Me´ridaVenezuela). She received her PhD from the University of Barcelona (Spain) and spent a year as a postdoctoral fellow at North Carolina State University (US). Over the past 25 years she has been involved in teaching and research at the University of the Andes, where she is currently Professor and Deputy Director of the FIRP laboratory, and head of the micro/nanoemulsions research and development group, particularly with applications involving petroleum production. Johnny Bullo´n earned a BS in Chemical Engineering from the University of the Andes (Merida-Venezuela) and a PhD from the European Membrane Science and Technology Institute at the University of Montpellier 2 (France). He has been involved in teaching, research and development with the University of the Andes for the past 20 years. He is currently Professor and Director of the FIRP laboratory, with research interests in membrane and separation processes related to surfactant science and emulsions, particularly with applications in the wood industry.