The equilibrium phase behavior of the well-defined system tetraethyleneglycol decyl ether (C(10)E(4))/n-octane/water (SOW) at variable temperature (T) was revisited by careful analysis of the three bidimensional cuts, namely, the gamma (at constant water-oil ratio), chi (at constant surfactant concentration), and Delta (at constant temperature) plots. A straightforward methodology is reported to determine the frontiers of the triphasic (Winsor III) domain on any cut of the SOW-T phase prism. It comes from the systematic analysis of another cut, here gamma at different water-oil ratios and chi at different surfactant concentrations from the knowledge of Delta cuts at different temperatures. The method has been validated through comparison with experimental results. It enables one to show, for the first time, the evolution of a SOW system three-phase body contours with (i) water-oil ratio, (ii) surfactant concentration, and (iii) temperature. It exhibits a strong impact of the surfactant affinity for the pure oil and water phases on the shape of the phase diagrams. The systematic study of the effect of the surfactant concentration on the aspect of the chi plot sheds light on an unusual shape found at low surfactant concentration.
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