3. Multivariable Scans and Generalized HLD Expression for Optimum Formulation
Figure 3 displays the phase behavior transitions in the two-dimensional S-ACN space when all other variables are constant. In the left plot, numerical values are indicated in the ordinate for salinity and in abscissa for ACN. The gray area indicates the three-phase zone (WIII). A vertical variation of salinity at the ACN constant corresponds to Figure 2 salinity scan, while a horizontal variation of ACN at constant salinity is an ACN scan. The line at the center of the three-phase zone is the optimum formulation line in a bidimensional scan; it corresponds to the optimum ACN* at constant salinity and to the optimum S* at constant ACN. Hence, an increase in salinity results in the transition WI > WIII > WII, while an increase in ACN does the opposite. Figure 3 corresponds to a typical system for EOR, containing 1 wt% of a commercial alkylbenzene sulfonate with 3 vol% of 2-butanol co-surfactant at a fixed temperature and pressure. It can be seen in Figure 3 (right plot) that the optimum formulation line at the center of the three-phase zone becomes exactly a straight line if the LnS scale is used in the ordinate.
Figure 3. Bidimensional (water salinity and oil ACN) formulation scan
[5]. S* is the salinity at optimum ormulation.
Consequently, the equation of the optimum formulation line in this LnS-ACN space may be written as LnS = KA ACN + CST, where the constant term (CST) depends on the other variables that do not change, i.e., the surfactant and cosurfactant, the temperature and the pressure. Such a bidimensional variation of both oil ACN and water salinity (for instance, between the two square dots located on the optimum line) may be expressed as ΔHLD = ΔLnS − KA ΔACN = 0 at all other constant variables.
Numerous studies from various laboratories in the past 40 years
[24][47][52][53][54][55][56] indicated that this linear relationship is essentially valid (at least over some range of ACN of about 10 units for all ionic surfactants). However, the ACN coefficient K
A value was found to depend on the surfactant, particularly its head group. It is 0.16 for alkylbenzene sulfonate, 0.10 for
n-alkyl sulfate or carboxylate, 0.17 for the dihexylsulfosuccinate, and 0.20 for alkyl trimethyl ammonium salts. For extended surfactants with several blocks, such as the alkyl polypropoxy ethoxy sulfates or carboxylates, this K
A coefficient is particularly low, i.e., 0.05 to 0.10, and depends on the exact structure—in particular, the alkoxylated central block size
[2].
A slight departure from linearity with LnS has been found for complex head groups, mainly when there is an internal or external mixture of ionic and nonionic parts
[6][14][57]. A linear relation between S (instead of LnS) and ACN generally better matches ethoxylated nonionic surfactant
[47][58]. However, the effect is much weaker than for ionic species and a partitioning inconvenience occurs with commercial surfactants, affecting the numerical data accuracy.
This double scan technique with an exact compensation of two opposite effects was introduced by the University of Texas group in 1977 and was later applied to many different pairs of variables susceptible to altering the interactions of the surfactant with both oil and water. The equations summarized in Table 2 indicate numerical results from a double scan change involving two variables, i.e., ΔHLD = 0, from our data and other publications cited in the two previous paragraphs.
Table 2. Different cases of equations indicating the changes of two formulation variables to deviate from optimum formulation and to return to it (ΔHLD = 0) with coefficients found in experimental data.
HLD Equation–Surfactant Type |
ΔHLD1 = ΔLnS − 0.16 ΔACN = 0 for alkylbenzene sulfonates ΔHLD2 = ΔLnS − 0.19 ΔACN = 0 for alkyltrimethyl ammonium chlorides ΔHLD3 = ΔLnS − 0.07 ΔACN = 0 for alkyl hexapropyleneoxide diethylenoxide sulfates ΔHLD4 = 0.33 ΔSAT − ΔEON = 0 for ethoxylated n-alcohol with EON~5 and T~25 °C ΔHLD5 = 0.13 ΔS − ΔEON = 0 for ethoxylated n-alcohol with EON~5 and T~25 °C ΔHLD6 = 2.25 ΔSAT − ΔACN = 0 for ethoxylated n-alcohol with EON~5 ΔHLD7 = − 0.24 ΔACN − ΔEON = 0 for ethoxylated n-alcohol with EON~5 ΔHLD8 = − ΔT − 20 ΔACN = 0 for n-alkyl sulfates ΔHLD9 = − ΔT − 14.3 ΔACN = 0 for alkylbenzene sulfonates ΔHLD10 = ΔT − 4 ΔACN = 0 for ethoxylated nonionic (EON~5–6 & T~20–30 °C) ΔHLD11 = ΔT − 1.4 ΔACN = 0 for ethoxylated nonionic (EON~8–9 & T~70 °C) ΔHLD12 = ΔT − 0.90 ΔACN = 0 for ethoxylated nonionic (EON~10–11 & T~80–90 °C) ΔHLD13 = − ΔGN − 0.12 ΔACN = 0 for polyglyceryl monolaurate (GN~5–6) ΔHLD14 = ΔLnS − 0.14 ΔPON = 0 for alkyl polypropyleneoxide diethylenoxide sulfates |
where S is the salinity in wt% NaCl, EON is the exact or average number of ethylene oxide groups, SAT is the surfactant n-alkyl tail length in carbon atom number, T is the temperature in °C, and GN is the number of glyceryl group in polyglyceryl monolaurate oligomers.
3.1. The Normalized Hydrophilic Lipophilic Deviation (HLDN) Equation
The previous data comes from many different experiments. It should be noted that the numerical values of the equivalence of the change between two variables are arbitrarily written as K1 ΔV1 − K2 ΔV2 = 0, which could be systematically written as ΔV1 = K21 ΔV2 with the coefficient K21 = K2/K1, as the linear equivalence in the ΔHLD double change.
The proper variable to make a comparison between different cases is to have the same change, which has been recently taken as a unit change in ACN, which is the same in all the cases
[9][11]. Consequently, the previous list of equations on ΔHLD = 0 will be divided by the coefficient before ACN, so that in the “normalized” expression, it would become −1 as in
Table 3 ΔHLD
Ni Equations (1)–(3). The minus sign is explained by the fact that an increase in ACN tends to decrease the numerator of R, thus reducing the HLD.
Table 3. Various cases of equations indicating the changes of two formulation variables to deviate from optimum formulation and return to it (ΔHLD = 0) with the same −1 coefficient in front of the ΔACN so that all the equations have the same scale.
HLDN Equation−Surfactant Type |
ΔHLDN1 = 6.25 ΔLnS − ΔACN = 0 for alkylbenzene sulfonates ΔHLDN2 = 5.26 ΔLnS − ΔACN = 0 for alkyltrimethyl ammonium chlorides ΔHLDN3 = 14.3 ΔLnS − ΔACN = 0 for alkyl hexapropyleneoxide diethylenoxide sulf. ΔHLDN4 = 1.4 ΔSAT − 4.2 ΔEON = 0 for ethoxylated n-alcohol (EON~5 & T~25 °C) ΔHLDN5 = 0.55 ΔS − 4.2 ΔEON = 0 for ethoxylated n-alcohol (EON~5 & T~25 °C) ΔHLDN6 = 2.25 ΔSAT − ΔACN = 0 for ethoxylated n-alcohol with EON~5 ΔHLDN7 = − 4.2 ΔEON − ΔACN = 0 for ethoxylated n-alcohol with EON~5 ΔHLDN8 = − 0.05 ΔT − ΔACN = 0 for n-alkyl sulfates ΔHLDN9 = − 0.07 ΔT − ΔACN = 0 for alkylbenzene sulfonates ΔHLDN10 = 0.25 ΔT − ΔACN = 0 for ethoxylated nonionic (EON~5–6 & T~20–30 °C) ΔHLDN11 = 0.70 ΔT − ΔACN = 0 for ethoxylated nonionic (EON~8–9 & T~70 °C) ΔHLDN12 = 1.1 ΔT − ΔACN = 0 for ethoxylated nonionic (EON~11 & T~80–90 °C) ΔHLDN13 = − 8.3 ΔGN − ΔACN = 0 for polyglyceryl monolaurate (GN~5–6) ΔHLDN14 = 1.2 ΔPON − ΔACN = 0 for alkyl polypropyleneoxide PON sulfates |
Thus, all the previous equations will be written as follows with the properly evaluated or calculated Ki coefficient before any Vi variable. The normalized equation implies ACN and at least one Vi variable to produce the double scan compensation but can include 3, 4, 5, etc.
If the double change does not include a unit variation of ΔACN, it should include variations of (at least) two other variables that are equivalent to ΔACN = ±1, as in the ΔHLDNi equations numbers 4, 5, in the previous list, which indicate the proper coefficient Ki before all formulation variables.
The data displayed in Table 3 deserve some specific comments. When a − ΔACN term appears in one of the equations, a positive effect of another term indicates that the corresponding variable change increases the HLD. It means that it is increasing the interaction of the surfactant with oil or diminishing its interaction with water by an amount equivalent to a negative unit of ACN. Therefore, from the previous Table 3 data, diminishing the ACN by one unit has the same effect as adding 0.44 carbon atoms in the surfactant n-alkyl tail (SAT) or adding 0.83 propylene oxide group (PON) in the intermediate part of an alkyl polypropoxy extended surfactant, or removing 0.24 ethylene oxide group from the head (EON) of an ethoxylated alcohol.
Transforming expression (2) to a differential equation level and taking into account that the first partial derivatives are constant (over some range)
[10][11]
Including an integration constant which is zero when all the variables are at a reference in which there is an optimum formulation.
Using only four variables to describe a simple system, i.e., surfactant, oil, water and temperature, the equation HLD
N = 0 at optimum formulation can be written as follows for ionic and nonionic surfactants
[9]:
In the past few years and with or without clear explanations, the references have been taken as follows. S
ref = 1, because ionic surfactants are salts that thus provide a minimum salinity or equivalent salinity in wt% NaCl, which is in general much smaller than 1 wt%
[59]. What is favorable is that, consequently, LnS
ref becomes zero in the ionic surfactant equation. A Sref = 0 often provides the reference for nonionic surfactants, but it is unfortunately different from the ionic case. Thus, it might be more logical to use S
ref = 1 in all the cases, the term K
S S
ref being almost negligible in most cases. ACN
ref = 0 also simplifies the equations, even if it is not a very logical choice, since it corresponds to no carbon atom in the
n-alkane, i.e., something which does not exist. However, an equivalent EACN = 0 was found to be some approximation for benzene
[60]. The temperature reference is often taken as 25 °C, but also at T = 0 °C, which simplifies the equation. This occurs even though it often corresponds to a solid-state of oil. In this simplified equation, there is no particular term for the pressure effect nor for a co-surfactant, initially called f(A)
[52]; however, if this is so, the references would be the atmospheric pressure and the absence of co-surfactant.
3.2. The Normalized Surfactant Characteristic Parameter (SCPN)
The SCP
N abbreviation means the normalized surfactant contribution term
[9][11], also called σ/K
A for ionic and β/K
A for nonionics in the literature
[5][52][61], including a very comprehensive recent review
[48]. To avoid confusion, the SCP
ref term is always taken as zero. However, it could be a misleading value when it is related to a characteristic surfactant curvature since it depends on many aspects other than the surfactant
[10][62]. The term SCP
N changes with the surfactant, i.e., it increases by 2.26 when a carbon atom is added to its
n-alkyl tail, and it decreases by 6.67 when an EON group is added to its polyethoxylated head). Then, its value depends on the references for all the variables, which is the reason why it is not a surfactant characteristic.
HLDN = 0 equation makes it possible to numerically express the conditions for an optimum formulation in the same scale (ΔACN unit change). It thus allows to make comparisons between the corresponding SCPN values for various surfactants, and it also makes it possible to calculate the values of mixtures according to
With X indicating the molar fraction at the interface, which is often approximated as the weight fraction in the system, although such linearity could be erroneous in the presence of partitioning of the different species, as in many commercial surfactants.
[63][60][64][65].
4. Lipophilic and Hydrophilic Linkers, and Extended Surfactants
4.1. The Lipophilic Linker
Since the main difficulty was to increase the interaction on the oil side, a special C1 highly lipophilic amphiphile was used to replace the C1 surfactant, as indicated in
Figure 4b, while the C2 surfactant was only slightly hydrophilic, and thus was likely to mainly go to the interface. This C1 species was typically a
n-decanol or dodecanol that was not really a surfactant adsorbed at interface but rather a polar oil segregated in the oil phase close to the interface because of the affinity of the OH end group with water
[66].
This kind of substance was called a lipophilic linker
[67][68][69][70][71] because it was not a co-surfactant (since it was not adsorbed at the interface) but was a species of the oil phase staying close to the interface, as shown in
Figure 4b. As a consequence of its location, the lipophilic linker was more or less sticking to the surfactant tail and somehow extending it further in the oil phase. Therefore, it was increasing the interaction on the oil side, and thus improving the performance.
Figure 4. Interfacial arrangements (a) with two ordinary surfactants C1 and C1, (b) with a surfactant and a lipophilic linker, (c) with an ordinary surfactant and a polar oil, and (d) with an extended surfactant and a polar oil.
4.2. The Hydrophilic Linker
It was suggested that a similar intermediate be placed on the other side of the interface between the surfactant head and the water and was called a hydrophilic linker
[72][73]. Its benefit was, however, much less significant, mainly because it was not producing a much higher penetration of the surfactant head group into water.
Moreover, it was known that the solubilization of a polar oil with an ordinary surfactant having a head group and an alkyl tail, as indicated in Figure 4c, was not very good because of a lack of perfect matching of the hydrocarbon tail with the polar oil. This is why adding a lipophilic linker in the oil phase close to the interface produced an improvement of the interaction with polar oil.
Nevertheless, the lipophilic linker was actually an oil phase component; a significant amount of it was lost in the oil bulk far from the interface, and thus partitioning was even worse with a polar oil. It was thus necessary to find a means to cumulate the favorable effects and avoid the unwanted ones.
4.3. The Extended Surfactant with an Intramolecular PO Extension
The idea developed in the 1990s
[13][15][53][74] was to fasten together the rather hydrophilic surfactant and the lipophilic linker, producing the same effect as the mixture without losing a part of the lipophilic linker deviating from the interface. Since the lipophilic linker was an amphiphile with a small hydrophilic part located close to the interface, the single structure shown in
Figure 4d to imitate the mixture situation is a so-called “extended” surfactant. It contains a polar head located in water, then an intermediate slightly polar zone in the oil phase close to the interface, and finally, the surfactant classical hydrocarbon tail.
Figure 4d shows that the slightly polar intermediate extension is bent and interacts with the water molecules, producing more A
CW interaction.
The central extension was selected to be a polypropylene oxide (PO) because it was neatly lipophilic and was thus located on the oil side of the interface with good interaction with polar oil molecules. It also perfectly plays its main role of displacing the alkyl part of the tail further away from the interface, as shown in
Figure 4d, without the usual precipitation problem at increasing the tail size. It is worth noting that our original extended surfactants, e.g., C
12PO
NEO
2SO
4-Na
+, had a much longer intermediate (N up 14) than the alkoxylated surfactants available at this time, which had very few units only. It should be noted that a 10-unit PO chain is about three times longer than a C12
n-alkyl group, so that the actual tail extension is considerable, even if it is not completely perpendicular to the interface
[20][75].
The PO chain is in the zone where the polar oil molecules are segregated, while the alkyl hydrocarbon part of the tail could be far away from the interface where most of the oil could be the non-polar one. This was an extra matching situation between the surfactant tail and the oil phase containing polar molecules. Sometimes, a very short ethoxylation (2 groups) is placed at the end of the PO chain, not really as a hydrophilic linker part, but rather because it makes an easier addition of the sulfate or other hydrophilic group
[17][18][19][21][22].
The improving performance with polar oil was reported first by Miñana
[13][53], particularly in mixtures of extended surfactants with ordinary species that were not solubilizing at all like triglyceride vegetable oils. Most research carried out in the following years used different anionic and nonionic heads sometimes connected by two EO groups to the propoxylated extension
[76].
4.4. The Increased Performance of Extended Surfactant Systems with Polar Oils and Crude Oils
The general results obtained in the last 20 years have been extensively reviewed very recently
[2] and should be examined in detail because of the large amount of available data. The main aspects can be summarized as follows. First of all, the PO chain is significantly lipophilic, and only sightly hydrophilic, i.e., much less than a polyethylene oxide chain. The PO unit is three times longer than a (CH
2) methylene group in a surfactant typical
n-alkyl tail; it thus considerably extends the surfactant penetration in oil and increases the interaction, particularly with polar oil segregated close to the interface. The first 2–4 PO groups stay close to the water phase, so the molecule is twisted in this zone, and is not really straight and perpendicular to the interface, as can be seen in
Figure 4d
[26][77]. In some cases, the accumulation of the PO groups outside the water can be considerable, in particular at the air surface where they are said to form rugby balls
[78][79]. This arbitrary gathering of the first PO group in a short and twisted hydrated chain close to the water phase produces some disorder that helps avoiding the surfactant’s rigidity and precipitation. A branched structure, such as the Guerbet double tail, was found to improve the extended surfactant interaction with oil phases, in particular with di/triglycerides
[14][80]. An increasing number of PO groups from five to 15 definitively increases the performance, which practically stays constant at higher PON. A PON term may be introduced in the HLD correlation but not as a linear term since it is also dealing with the surfactant hydrophobe part length (SAT)
[2][27]. A more continuous change from hydrophilic to lipophilic parts, including an intermediate with an additional butylene oxide block between the alkyl tail and the propylene oxide block, improves, even more, the performance
[28]. This is probably because it results in a very wide zone with a smooth variation of hydrophilicity, which is particularly appropriate to interact with crude oils containing many polar species containing functional groups bearing nitrogen, sulfur and oxygen atoms, such as asphaltenes, naphthenic acids, etc.
[81][50][51][82][83].
The last benefit found in an extended surfactant is that being an intramolecular mixture between ionic and nonionic parts, a proper adjustment of the different blocks could present new opportunities such as insensitivity to temperature
[84][85] or insensitivity to surfactant concentration
[25] and robustness to electrolyte concentration and mixture variations, including new applications with complex biobased polar oils
[29][86][87].