Low Interfacial Tensions Involving Mixtures of Surfactants
Authors: Wade W.H. , Morgan J.C. , Jacobson J.K. , Schechter R.S. 
Published: December 2007

Abstract
The interfacial tension of surfactant mixtures with hydrocarbons obeys a simple scaling rule. Many apparently inert surfactants give low tensions when in mixtures; the scaling rule still applies to these mixtures. The influence of surfactant structure and molecular weight on low-tension behavior is examined, and the application of these results to the optimization of surfactant flooding systems is discussed.

Introduction
It has been shown that the interfacial-tension behavior of a given crude oil with a surfactant solution of the sulfonate type may be modeled by replacing the crude oil with one particular alkane. The number of carbon atoms in the alkane is referred to as the equivalent alkane carbon number (EACN) of the crude oil, and this EACN is independent of the surfactant used (at fixed standard conditions). This equivalency of a crude oil and an alkane is a result of the simple averaging behavior of hydrocarbons when mixed. Any hydrocarbon may be assigned an EACN value. For instance, when homologous series of alkyl benzenes and alkanes are run against the petroleum sulfonate TRS 10-80 at 2 gm/liter of surfactant with 10 gm/liter NaCl present, heptyl benzene and heptane, respectively, give minimum interfacial tensions, a. The EACN of heptyl benzene is 7, since it is equivalent to heptane. A simple averaging rule will give the EACN of a hydrocarbon mixture :
(1)
where x is the mole fraction of the ith component. Thus, an equimolar mixture of undecane (EACN 11) and heptyl benzene (EACN 7) has an EACN of 9. If a surfactant gives a low (minimum) sigma against nonane (EACN 9), it will also give a low sigma against the above mixture. Eq. 1 implies that a crude oil, which is a multicomponent hydrocarbon mixture, may be assigned an EACN. This has been verified experimentally. For example, Big Muddy field crude oil has an EACN of 8.5. Therefore, any surfactant phase giving a minimum tension against an equimolar mixture of octane and nonane gives a low tension against Big Muddy crude. All crude oils rested to date have EACN's ranging from 6 to 9.
For a given surfactant, the alkane of minimum tension (min) may be affected by the electrolyte concentration or type, the temperature, the surfactant concentration, or the presence of a cosurfactant. These system variables may be adjusted until the nmin for a surfactant matches exactly the EACN of a crude oil. For any particular surfactant, many different combinations of variables will give the same n min value; therefore, there are many possible systems, each with n = EACN, available for crude oil recovery. In practice, however, the system variables may be manipulated to a limited extent only. The temperature of an oil field is fixed, and the surfactant concentration is limited by considerations of solubility and expense. The electrolyte concentration and type is partly determined by oilfield conditions and is limited by the effect on surfactant solubility. These limitations mean that many of the surfactants presently available on a large enough scale for use in low-tension flooding will not give minimum tensions in the range required (n of 6 to 9). This paper shows how minimal sigma's in the required range may be found for some of these "off-scale" surfactants when they are used in surfactant mixtures. The hypothesis tested here is that surfactant mixtures average in a manner analogous to the averaging of hydrocarbons in the oil phase. It will be shown that each surfactant component may be assigned an n value and that the alkane of minimum tension of a mixture of surfactants, (n), is then given by
(2)
where x is now the mole fraction of the ith component of the surfactant mixture. This greatly extends the number of surfactants that may be considered as candidates for use in low interfacial-tension flooding.
SPEJ
P. 122