Three—dimensional phase diagram of the brine-toluene-butanol-sodium dodecyl sulfate system

Three—dimensional phase diagram of the brine-toluene-butanol-sodium dodecyl sulfate system

Three-Dimensional Phase Diagram of the Brine-Toluene- Butanol- Sod ium Dodecyl Sulfate System ANNE-MARIE BELLOCQ, JACQUES BIAIS, BERNARD CLIN, ALAIN G...

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Three-Dimensional Phase Diagram of the Brine-Toluene- Butanol- Sod ium Dodecyl Sulfate System ANNE-MARIE BELLOCQ, JACQUES BIAIS, BERNARD CLIN, ALAIN GELOT, PIERRE LALANNE, AND BERNARD LEMANCEAU Centre de Recherches Paul Pascal, Domaine Universitaire, 33405 Talence, France

Received February 21, 1979; accepted July 30, 1979 A type of representation based upon variance for the quaternary system brine-oil-surfactant and cosurfactant is proposed in the three-dimensional space; it allows the topological properties of the multiphase regions of the diagram to be understood, in particular, those of the brine-toluenebutanol-sodium dodecyl sulfate system. The quaternary phase diagrams at two salinities are reported for this system in this work. Analysis of the phases in equilibrium shows very low variations of compositions for the aqueous and organic phases, while the water-oil and alcoholsurfactant ratios are strongly modified in the middle phase. These results indicate that the water-oil pair is then close to a critical state. INTRODUCTION

The purpose of this study is to investigate a system made of pure compounds--water, toluene, sodium dodecyl sulfate (SDS), and butanol--at different salinities and to examine its phase behavior in a quaternary representation. Structural and dynamic properties of this peculiar system have been investigated by several chemicophysical methods (8-12). In the first part of this work, the theoretical three-dimensional representation of the phase diagram of a four-component system is discussed. In the second part, the experimental quaternary phase diagrams and the compositions of the phases in equilibrium are presented. The possibility of a pseudoternary representation to describe the phase behavior of this system adequately will be discussed in the third part.

Projects on tertiary oil recovery by means of microemulsion have been mainly concerned with first, the ability of a microemulsion to dissolve oil and water simultaneously and second, the attainment of very low interfacial tensions (1). Consequently, phase behavior of these systems, which are composed of four components (water, oil, surfactant, and cosurfactant), is very important and has been the object of intensive studies (2-4). Previous research has shown that the phase behavior of these systems can be directly related to interfacial tensions (2). Frequently, the systems are characterized by three principal components, water, oil, and surfactant, and their phase behavior is represented in a Winsor ternary diagram. In practice the TOPOLOGY ELEMENTS OF THE PHASE actual number of compounds involved in the DIAGRAM OF A FOUR-COMPONENT system is much larger; therefore, in order SYSTEM to use the concept of a Winsor diagram, it is necessary to group several compounds The topology of the phase diagram of a at the same vertex and assume they behave quaternary system presented in this work as a single pure component (5-7). is based upon variance. However, only 311 Journal of Colloid and Interface Science, Vol.74, No. 2, April 1980

0021-9797/80/040311-11 $02.00/0 Copyright© 1980by AcademicPress, Inc. All rightsof reproductionin any formreserved.





Water x

FIG. l. Trirectangular representation of the quaternary system. C1 = demixing curve in the 17plane; hatched region is an element of demixing surface between the 17 plane such that k = 2 and k = ~.

some s y s t e m s will be considered; we will not deal with e v e r y possible case. A similar analysis for the w a t e r - b e n z e n e - e t h a n o l a m m o n i u m sulfate s y s t e m has b e e n carried out by Widom (13). Choice of representation. The compositions of the investigated quaternary s y s t e m - water, toluene, butanol, S D S - - a r e described by four concentration variables x, y, z, and u c o n n e c t e d b y the equation x + y + z + u = 1. T h r e e independent variables, e.g., x, y, and z, are needed to describe the s y s t e m completely. Composition can be r e p r e s e n t e d b y a point m a r k e d in relation to a trirectangular trihedron within the volume b o u n d e d by the 110, 011, 101, and 111 planes. L a t e r on in this p a p e r experimentally determined p s e u d o t e r n a r y representations are sections at constant butanol/ SDS ratio such as z/u = k. In the threedimensional space, the representative points of the composition are then in the II plane defined b y the e q u a t i o n x + y + z(k -1 + 1) = 1. This II plane is the preparing sample plane. Although, this trirectangular and not tetrahedral representation is not symmetrical, it Journal of Colloid and Interface Science, Vol. 74, No. 2, April 1980

provides a simple description of the multip h a s e equilibria (Fig. 1).

Variance of a quaternary system--onephase region. Since the variance of a s y s t e m is given b y vp,T = C - ~o (C = n u m b e r of independent c o m p o n e n t s , ~ = n u m b e r of phases) at fixed pressure and t e m p e r a t u r e , a f o u r - c o m p o n e n t s y s t e m can be constituted by one, two, three, or four phases in equilibrium. In this work, we deal with only the three first cases. The one-phase one is trivial; variance equals three: three composition variables represent the overall composition of the s y s t e m and represent also the composition of one phase in the single p h a s e region of the representation diagram. This region takes up a volume b o u n d e d by the tetrahedron faces and the t w o - p h a s e surfaces. Two-phase Equilibrium Demixing surface. F o r constant temperature and pressure the t w o - p h a s e s y s t e m s h a v e two degrees of freedom: Vp,T = C - ~o = 4 - 2 = 2. Only two composition variables


of one of the phases are required to determine all the others. If xa, y~, z~ and x2, Y2, z2 are the compositions of the two phases 1 and 2 in equilibrium, it is possible to find one range of variation for xl and ya for example, as the two phases are still in coexistence. Then, 21 -= Z l ( X l , Y l )


represents a surface element (Sa) and: X 2 = X2(Xl,Yl)

Y2 = y2(x,,y,) Z2 = 2 2 ( x l , y 1 )


Equations [1] and [2] establish a point-topoint correspondence between the phases in equilibrium and consequently the equations of the MaM2 binodal segments. Hence z2 = z2(x2,y2)


represents a surface element ($2). In the case where the preparing sample plane cuts the S~ surface along a C~ curve (i.e., boundary of demixing of a one-phase region) any M point on this curve represents a system which can be in equilibrium with a system of M2 composition. Conversely, if phase separation along a C1 curve has been observed on the II plane, this curve belongs to a phase separation surface element (Sx). The problem of continuity of the demixing surface, including then the (S~) and (S~) surface elements, is a specific problem of each type of system. The binodal lines or tie-lines. The MIM2 straight line segments are binodal segments. Any M point on one of these segments represents the overall composition of a system which has separated into two phases in equilibrium; the mass ratio of the phases characterized by M1 and M2 is equal to M M 2 / M M 1 ratio (the lever rule). According to the phase rule, two binodal lines can have a common end: the system is triphasic. This case will be discussed later. Moreover, two binodal lines cannot


cross themselves in any point; indeed a system represented by a point of the plane defined by the two binodal lines should be a four-phase system in an indifferent state (14). The stack of tie-lines is cut by the 17 plane in the two-phase region. The ends of these tie-lines are generally on both sides of the II plane except those which abut the Ca curve (or C2 curve if the H plane cuts the $2 surface element). The two-phase space is bounded by the ($1) and ($2) surface elements and the binodal segments which abut the corresponding elements of the curves limiting ($1) and ($2). Consequently, the extent of the two-phase space depends upon these limits. We will see later on that it is also limited by the three-phase domain when this one exists. In the case where the ($I) and ($2) surfaces are bounded by a portion of common curve, this curve is its own corresponding curve; hence, it is the locus of the points where both phases of the two-phase space coalesce (locus of the plait points). Let us still notice that none of the tielines can abut one face of the tetrahedron since a tie-line which has one point on a face is a tie-line of the ternary system represented on this face. Dilution lines. In some cases, one system lying on the demixing boundary can be diluted by an oil-rich (or water-rich) ternary solution (15, 16) containing alcohol and water in a very well-defined concentration without leaving the demixing surface, within the experimental unreliability. This dilution process is represented in space by a segment termed the "dilution straight line." This property belongs to a set of limit systems represented, for example, by a part of the demixing curve in the II plane. At each system a dilution solution of determined composition corresponds. Each of the dilution lines being a limit line, the demixing surface is generated in this region by a set of segments located on straight lines which abut on one hand the curve element in the I I plane and on the other hand the corJournal of Colloid and Interface Science, Vol. 74, No. 2, April 1980


BELLOCQ ET A L . , These equations are compatible if the principle determinant equals zero. /I///





Y Ya Y2 Y3

/ FIG.2. Trinodaltriangleabutingto M,, Ms, M3 on the F~, F~, F3 curves lyingon the elements of demixing surfaces S~. responding curve element of the oil- alcoholwater ternary system representation plane. However, this property is not maintained in all cases up to an infinite dilution of the initial system by a convenient solution (Fig. 1). Three-Phase Equilibrium Three-phase demixing curves. The variance of a three-phase system for constant temperature and pressure equals one: Vp, T -- 4 - 3 = 1. One composition variable of one of the phases fixes all the other ones: then xl,

y1(xs) , zs(xO

in phase I



y2(xl) , z2(xs)

in phase II



y3(xs) , zz(xs)

in phase III


These equations define the Ms, M2, M3 corresponding points situated on elements of corresponding curves. Fs, F2, F3. These generally twisted curves, which lie on the boundary of the one-phase region, are singular lines of the demixing surface elements (Fig. 2). Trinodal t r i a n g l e s - - m a s s fractions o f the phases. Any M point within the M1, M2, M3 plane represents a system which equilibrates in the three phases Ms, M~, and M3. This results from the linear equation of the mass balance. Indeed, if a, /3, 3" are the mass fractions of the different phases: X ----- a X 1 3t- /3X 2 + 3'X 3


y -- ayl

+ ]~Y2 + TY3


Z = O/Z s "JC /3Z 2 -}- 3"7 3


ot +/3 +3" = 1.


Journal of Colloid and Interface Science, Vol. 74, No. 2, April 1980









= 0

This is the equation of the M, Ms M3 plane. Conversely if M is given in the M I M 2 M 3 plane, the mass fractions of the three phases can be calculated by: a M M , + /3MM2 + y M M 3 = 0

obtained from Eqs. [7], [8], and [9] by multiplying the left term of each of them by (a +/3 + 3"), then OL

X2 Y3 - X3 Y2



X3 Ys - X1 Y3

Xs Y2 - X2 Y1

with X~ = x - x~, Yi = Y - Y~, components of the MM~ vector projections on the x, y plane, or, a





Ira, Am~[

m~ being the MM~ vector projection on the x, y plane. A volume element in the three-phase region will, for example, be arbitrarily bounded by two trinodal planes and three surfaces generated by the edges of the triangles abuting the corresponding points of the three curves F,, F2, F3. The boundaries of the three-phase region are obviously r3 ~


q FIG. 3. Elementof volumeof the three-phase region bounded by two tie-triangles and by the surfaces generatedby the binodal lines.


315 hM

dependent upon the limits of the F~ curves (Fig. 3). The trinodal planes possess properties analogous to those of the tie-lines: in particular, two triangles cannot have any common point (neither c o m m o n intersection, nor edge, nor vertex). This implies that elementary shifts dM1, dM2, dM3 are obtained in the same way relatively to the triangle (same direction of their projections on the normal to the triangle M~M~Mz).

Intersection of the three-phase region with the II plane (preparing sample plane at constant alcohol/SDS ratio). The intersection of a tie-triangle with the II plane is a straight line segment ab (Fig. 4). The a and b points lie on binodal lines, for example, M1M3 and M2M3; M3 in such a case would not be on the same side of the H plane as MaM2. An infinitely close trinodal triangle cuts the H plane along an a ' b ' segment infinitely close to the ab one. Two segments such as ab and a ' b ' cannot cut themselves. The a and b points describe two curved elements in the II plane when the M1, Ms, and M~ points move along the Fi, Fz, and F3 curves. Generally, these two curved elements join up in two points c and c', limits of the ab segment. The shift of the ab segment generates the three-phase region in the II plane. The ab segment can be reduced to one point c (or c') in two different ways:




6 % Na C[


FIG. 5. Effect of salinity on the pseudoternary diagram: toluene = T; active mixture = AM = butanol/ SDS = 2; water = W (the systems definedby a watertoluene ratio = 4 are marked--cf. Fig. 6). - - E i t h e r two vertices of the trinodal triangle, M1 and M2 for instance, coincide; in this case, the F1 and F2 curves have a c o m m o n point, this c o m m o n point being a coalescence point of the phases " 1 " and " 2 " (critical end point). - - O r one vertex of the triangle (M3 for example) goes in the II plane; this c point is the intercept of the F3 curve with the II plane; it is therefore located in the boundary of the single phase region. The three-phase region of the II plane then has as many c o m m o n points with the single phase region as there are intersection points of the II plane with the Fa, F2, F3 curves (for instance two connection points are shown in Fig. 4; the F3 curve crosses the II plane twice). This analysis explains the variety of outlines of the three-phase regions described in a pseudoternary representation (17). EXPERIMENTAL QUATERNARY PHASE BEHAVIOR OF THE BRINE-TOLUENESDS-BUTANOL SYSTEM

Pseudoternary Diagrams (Butanol/SDS = 2) at Different Salinities FIG. 4. Section of the three-phase volume with a H plane.

Winsor has shown that addition of electrolytes strongly affects the stability of microJournal of Colloid and Interface Science, Vol. 74, No. 2, April 1980


BELLOCQ ET AL. '% activemixture

alcohol _ 2 5135

As the salinity increases, the narrow single phase region which separates these 80 two two-phase regions of type I and II is 60 lowered and becomes more and more narrow. For the 2 wt% NaC1 brine system, this 40 one-phase region has disappeared and leads to a three liquid phase system: an upper 20 organic phase, a surfactant-rich middle 0 phase microemulsion, and a lower phase 2 4 6 8 ~'. Na CI predominantly composed of brine. This FIG.6. Phasebehavioras a functionof salinityof the system is of Winsor type III. The lower systemdefinedby water/toluene = 4 and butanol/SDS aqueous and upper organic phases are clear; = 2 (cf. Fig. 5) [for example for the 1.5% salinity, the middle phase strongly scatters light. we observe systemsmade of 2q5(type I) l~b,25 (type When the salinity is increased up to 6 wt% II) and lq~]. NaC1 brine, the corresponding pseudoternary diagram looks like the preceding one; howemulsion and has described three possible ever, we notice that the monophasic region types of two- and three-phase systems is very small and, on the contrary, the which can be observed when salinity is three-phase one is much more extended and it lies at a lower percentage of active varied (17). Before investigation of the quaternary mixture than for 2% NaC1. In both cases, phase behavior of the water-toluene- the three-phase region is entirely surrounded butanol-SDS system at two salinities, by two- and one-phase regions; it separates a salinity scan on the pseudoternary diagram two diphasic domains of Winsor type I and defined by butanol/SDS = 2 has been per- II and is connected to the monophasic region formed. The results are shown in Fig. 5. by two points. In the proximity of those For the 1 wt% NaC1 brine system, the connecting points the microemulsion region demixing boundary line is lowered with becomes very narrow and the observed respect to that of the unsalted system: this microemulsions very strongly scatter light. Data presented in Fig. 5 show that by means that the amount of active mixture required to make a microemulsion containing addition of salt a two-phase region of type II water and toluene in a given ratio is less appears inside the microemulsion region. with salted water. As the salinity goes up Transition between the two two-phase to 1.5 percent of NaC1 the oil-rich region is systems of type I and II can occur by means not changed, whereas the water-rich region butanol : 2 undergoes drastic modifications; the extent SDS of the monophasic region is entirely reduced due to the advent within the microemulsion domain of a two-phase region. Quantitative butanol_-i / ~ butanol. 4 analyses of the compositions of both of these two phases show that the system is of Winsor type II: it corresponds to an oil-rich upper phase microemulsion in equilibrium with an aqueous lower phase; the two-phase 15%NaCI T 1,5%NaC[i:~-"~~ T region lying under the demixing line is of Winsor type I, corresponding to an organic FIG. 7. Effectof active mixturecompositionon the upper phase in equilibrium with a water- phase diagram of the 1.5% NaC1 brine, toluene, butanol, SDS. rich lower microemulsion. -

Journal of Colloid and Interface Science, Vol. 74, No. 2, April 1980



of either a one-phase region or a three-phase one. Figure 6 shows the limits of the monoand polyphasic regions (expressed in concentration in active mixture) versus salinity when the ratio butanol/SDS equals 2 and the ratio water/toluene equals 4. A discontinuity of the minimal concentration in the active mixture needed to make a microemulsion is observed as the three-phase region appears. The corresponding salinity is a function of the water-oil ratio and of the active mixture composition.

Quaternary Representation of the Phase Diagram In order to determine the detailed shape of the liquid three-phase region in the composition tetrahedron, quaternary phase diagrams of the studied system have been investigated at low (1.5% NaC1) and high (6% NaC1) salinities. They have been constructed by examination of several planes for which the active mixture has a constant composition; the corresponding pseudoternary diagrams are shown in Figs. 7 through 9. As the alcohol-to-surfactant ratio is inbutanol : 0,9



6% Nael

T 6% NaCl T 1 6% NaCI :


)2 bu~nol


FIG. 8. Effect of active mixture c o m p o s i t i o n on the p h a s e diagram of the 6% NaC1 brine, toluene, butanol, SDS.

w /


5o /











\,0 T








FIG. 9. Three-phase region in the planes defined by the following alcohol/SDS ratios (salinity = 6% NaCI): a= 0.9;b = 0.95;c = 1;d = 2;e = 4;f= 9;gisthe locus of the projections of the points connecting the

one- and three-phases regions (F3 curve) on the water-toluene-butanol plane. creased, one two-phase region appears inside the microemulsion one; it is more expanded as the alcohol content is higher. The narrow monophasic region which separates both two-phase areas opens for a given value of the alcohol surfactant ratio and it is replaced by a three-phase system. Furthermore it is worthwhile to note that addition of sodium chloride causes the destabilization of a large gel region observed in the 1/1 alcohol-SDS plane in the absence of salt (unpublished results). The evolution of the diagrams presented in Figs. 7-9 is quite similar to that observed for low salinity. The results clearly show that the three-phase systems are lying in the alcohol-rich planes. For a given value of the alcohol-surfactant ratio, the plane under consideration cuts the three-phase region. The latter abuts the one-phase region by two points. Both points move increasingly away from one another as the active mixture is richer in alcohol and go toward the water-alcohol and toluene-alcohol edges Journal of Colloid and Interface Science,

Vol. 74, No. 2, April 1980


B E L L O C Q ET A L. TABLE I C o m p o s i t i o n s of Phases in E q u i l i b r i u m Overall compositions

Organic phase

Middle phase

Aqueous phase

Water + NaCI Tolu ene Butanol SDS NaCl/water

46.49 46.47 4.69 2.35 6

0.15 94.10 5.75 ---

38.1 47.6 6 4.64 5.95

98.15 -1.85 -6.20

W ater + NaCI Toluene Butanol SDS NaC1/water

46.95 47.05 4.00 2.00 6

-0.10 94.80 5.10 ---

52.5 33.5 4.55 4.80 5.6

98.35 -1.65 -6.13

W ater + NaC1 Toluene Butanol SDS NaC1/water

36.79 57.13 4.06 2.02 6

-0.1 95.4 4.5

60.7 25.5 3.7 6.36 6.35

98.35 -1.65 -5.3

of the tetrahedron. Figure 8 allows us to estimate what the thickness of the observed three-phase region is when the water-oil ratio equals one.

Compositions of Phases in Equilibrium in the Two- and Three-Phase Regions In order to test the results of the assumption of a thermodynamic equilibrium, compositions of several multiphase systems have been analyzed by gas chromatography, atomic absorption, and chemical titration of the chloride ions. The investigated systems correspond to the 6 wt% NaC1 salinity and are located in the plane defined by a butanol-SDS ratio of 2. The compositions of the phases in equilibrium for a few systems are given in Table I. All the components partition into every phase, except the surfactant which is concentrated in the middle phase microemulsion and salt which partitions into the aqueous and microemulsion phases. The SDS content of the aqueous phase is very low--less than the CMC which is known to be lowered by addition of ions (18). Light scattering Journal of Colloid and Interface Science, Vol. 74, No. 2, April 1980

experiments have been performed on the aqueous phase; they do not reveal the presence of micelles. Furthermore, analysis of sodium chloride indicates that water relative to salt content is almost the same in the aqueous and microemulsion phases. Hence, we consider in a first approximation that brine behaves as a single component and we maintain a quaternary representation although the system contains five components. The compositions of the organic and aqueous phases of the three-phase systems exhibit a very small variation when the overall composition of the initial system is changed (Fig. 10). Examination of one sample located in the plane defined by the alcohol-SDS ratio equal to 0.95 leads to the same compositions for these excess oil and excess water phases. In Figs. 11 and 12, the water and toluene compositions of the microemulsions in the type I, II, or III systems are plotted either as a function of the active mixture content for the water-oil ratio of one or as a function of this ratio at constant active mixture amount. Abrupt variations of compositions are observed as the I ~ II --~ III transition occurs and also very large variations of water and toluene contents of the

%waterl 11oo

1 ,0 I- .....

% toluene


i ~d 30



% toluene

~oo~ 9° t ,




50 60 % toluene



_._.,._.~_-,00 , 6

, , 190 8 10 % activemixture

FIG. 10. W a t e r and t ol ue ne c o n t e n t s of the a q u e o u s and organic pha s e s as a function of t ol ue ne p e r c e n t a g e at c o n s t a n t active mixture (butanol/SDS = 2) c o n t e n t = 6% a nd as a function of a c t i ve mixture (butanol/ SDS = 2) c ont e nt at c o n s t a n t w a t e r - o i l ratio = 1.



toluene or water

" "~ 1%.]]I 7\I--II

-butanol - 2

II •


5DS water ': l





e' %



FIG. 11. Water and toluene contents of the microemulsion phase in the type I, III, and II systems. middle phase when the initial overall composition is varied. We have indicated that the three-phase volume is defined by a stack of trinodal triangles; the vertices of each one give the compositions of the three liquid phases that coexist. These vertices move on the F1, F2, and F3 lines. In the case under study, there is great discrepancy among their dimensions. The lengths of the F1 and F2 lines relative to the organic and aqueous phases are very short while the F3 line which is the one for the middle phase is by far the largest (Fig. 9g). The result is that the figure of the three-phase volume is very much lengthened along the w a t e r - o i l edge and is very narrow in the s u r f a c t a n t - a l c o h o l direction. Analysis of the phases show that points c and c' of the coupling of the one- and three-phase regions belong to the same F3 fine. Indeed, we never observed three phases in equilibrium in which the compositions of two o f them could be represented by two points on this curve. Finally, we check that in the plane investigated in this work (butanol/SDS = 2) there exists straight fines of constant compositions inside the three-phase region. These straight lines result from the intersection of the trinodal planes with the studied plane; they are the ab segments previously discussed (Fig. 13).

DISCUSSION The presented data clearly show that in the two- and three-phase regions of the phase diagram, the surfactant-cosurfactant ratio is different in the different phases in equilibrium. Considering the three-phase region results from a stack of nonparallel tie-triangles, it is impossible to define pseudocomponents (surfactant + alcohol) able to represent the system in polyphasic regions correctly. In all strictness, the same is true for the w a t e r - s a l t pair; however, the analysis has shown that for this system the w a t e r - s a l t ratio is nearly the same in the low and middle phases. In a first approximation, we I ~'o toluene

o 9 % AM : 11 v 6% A M : I l l • 4% b , M : l


% water 100




~ o . - . - -







W o




W T water L01uene

FIG. 12. Water and toluene contents of the microemulsion phase in the type i, III, and II systems as a function of the water-toluene ratio for different active mixture contents. Journal of Colloid and Interface Science, Vol. 74, No. 2, April 1980



;o/ v 20







\ 70L e



"° D

FIG. 13. Straight lines of constant composition within the three-phase region of the pseudoternary diagram 6% NaCI brine-toluene-butanol/SDS.

can consider this couple has a pseudocomponent. There is a curve representing the middle phase composition, which is extended in a very large range of variation of the watertoluene ratio (30 to 1/4 in the range that we have investigated) and of the cosurfactant/surfactant ratio (0.95-9). It is worthwhile to point out that the aqueous and organic phases in equilibrium with the middle phase have compositions almost constant. One is very rich in water, the other is very rich in oil, although the water-oil ratio varies greatly in the middle phase. This means that the chemical potentials of water and oil are almost constant in the middle phase and maintain a high value. The water-oil pair in the middle phase is close to a state analogous to a critical one. This result should certainly be related to the very low interfacial tensions usually observed for three-phase systems (2, 3). SUMMARY AND CONCLUDING REMARKS

A type of representation based upon variance for the quaternary system wateroil-surfactant and cosurfactant is proposed in the three-dimensional space; it allows the topological properties of the multiphase regions of the diagram to be understood. The total composition of the system is depicted in an orthogonal frame of reference. In this frame the two-phase equilibriums (variance Vp,T = 2) are depicted by two sets of related points, lying on two parts of related demixing areas. While the system is a three-phase one (variance vp,T = 1) the phase compositions are depicted by three Journal of Colloid and Interface Science,

Vol. 74, No. 2, April 1980

sets of points, describing in the coordinate system of reference three curves respectively lying on the elements of demixing areas of the single-phase regions. Three related three-phase points define a trinodal triangle, the sides of which are limit tie-lines. Just as two tie-lines cannot cross themselves, so two trinodal triangles cannot have any common point. The volume of the threephase region is generated by moving such triangles, the vertices of which describe the three-phase curves. The intersection of this volume with a plane, corresponding to a given ratio (cosurfactant/surfactant) defines the three-phase region of this peculiar plane. Such behavior has been observed for the brine-toluene-butanol-sodium dodecyl sulfate system. Quaternary phase diagrams for two salinities (15 g/liter and 60 g/liter NaC1) have been constructed by examination of several planes for which the active mixture has a constant composition. Two- and threephase regions are observed by varying either salinity or the alcohol-SDS ratio. The three-phase region lies in alcohol-rich planes. Its shape is very lengthened along the wateroil edge of the tetrahedron and is quite narrow in the surfactant-alcohol direction. Moreover, the analysis of the different phases in equilibrium shows that the tielines cannot lie in the studied plane, defined by a constant ratio (cosurfactant/surfactant) and that a three-phase region in such a plane is restricted to a lenticular zone, supported by two points of the demixing limit of the plane. Once this region is described in some limits, very low variations of the compositions can be observed for the


very water-rich aqueous phase and for the very oil-rich organic phase, while the water/ oil ratio is strongly modified in the middle phase which is a microemulsion. The wateroil pair is then close to a critical state. EXPERIMENTAL

The products used in determining the quaternary diagrams were pure grade. All the diagrams and compositions presented in this work are expressed in weight percent. Upon equilibration of the samples, the temperature was maintained constant at 20°C. Some samples took a few days to reach equilibrium. The equilibrated phases were separated and chemical analyses were performed on them. Gas chromatography was used in order to determine the water, toluene, and butanol contents of the various phases. Sodium chloride and surfactant concentrations were measured by atomic absorption of the sodium ion and volumetric titration of the chloride ion. REFERENCES I. Shah, D. O., and Schechter, R. S., "Improved Oil Recovery by Surfactant and Polymer Flooding." Academic Press, New York, 1977. 2. Healy, R. N., Reed, R. L., and Stenmark, D. G., Soc. Pet. Eng. J. 16, 147 (1976). 3. Salager, J. L., Morgan, J. C., Schechter, R. S., Wade, W. H., and Vasquez, E., Soc. Pet. Eng. J., Paper No. 7054, p. 181 (1978).


4. Robbins, M. L. ,' 'Micellization, Solubilization and Microemulsion" (K. L. Mittal, Ed.). Vol. 2, p. 713. Plenum Press, New York, 1977. 5. Vinatiefi, J., and Fleming, P. D., Soc. Pet. Eng. J., paper No. 7057, p. 215 (1978). 6. Fleming, P. D., and Vinatieri, J., J. Chem. Phys. 66, 3147 (1977). 7. Salter, S. J., Soc. Pet. Eng. J., paper No. 7056, p. 199 (1978). 8. Bellocq, A. M., Biais, J., Clin, B., Lalanne, P., and Lemanceau, B., J. Colloid Interface Sci., 70, 524 (1979). 9. Biais, J., Clin, B., Lalanne, P., and Lemanceau, B., J. Chim. Phys. 74, 1197 (1977). 10. Biais, J., Mercier, M., Lalanne, P., Clin, B., Bellocq, A. M., and Lemanceau, B., C.R. Acad. Sci. 285C, 213 (1977). 11. Lalanne, P., Biais, J., Clin, B., Bellocq, A. M., and Lemanceau, B., C.R. Acad. Sci. 286C, 55 (1978). 12. Lalanne, P., Biais, J., Clin, B., Bellocq, A. M, and Lemanceau, B., J. Chim. Phys. 75, 236 (1978). 13. Widom, B., J. Chem. Phys. 77, 2196 (1973). 14. Prigogine, I., and Defay, R., "Thermodynamique Chimique," chap. XXIX. Liege, 1950. 15. Gracia, A., Lachaise, J., Martinez, A., Bourrel, M., and Chambu, C., C.R. Acad. Sci. 282B, 547 (1976). 16. Garciaa, A., Lachaise, J., Martinez, A., and Rousset, A., C.R. Acad. Sci. 285B, 295 (1977). 17. Bellocq, A. M., Biais, J., Bourbon, D., Clin, B., Lalanne, P., and Lemanceau, B., C.R. Acad. Sci. 288C, 169 (1979). 18. Winsor, P. A., "Solvent Properties of Amphiphilic Compounds." Butterworths, London, 1954. 19. Mukerjee, P., Mysels, J., and Dulin, C., J. Phys. Chem. 62, 1390 (1958).

Journal of Colloid and Interface Science, Vol. 74, No. 2, April 1980