Injection of sea water is the most common practice to displace oil in porous media in subsurface formations. In numerous studies, conventional surfactants at concentrations in a range of one weight percent have been proposed to be added to the injected water to improve oil recovery. Surfactants accumulate at the oil-water interface and may reduce the interfacial tension by three orders of magnitude or more, resulting in higher oil recovery. Recently, we have proposed the addition of ultralow concentration of a non-ionic surfactant to the injected water to increase interface viscoelasticity as a new process. The increase in interface viscoelasticity increases oil recovery from porous media. This alternative approach requires only a concentration of 100 ppm (two orders less than the conventional improved oil recovery) and therefore is potentially a much more efficient process. In this work, we present a comprehensive report of the process in an intermediate-wet carbonate rock. There is very little adsorption of the functional molecules to the rock surface. Because the critical micelle concentration is low (around 30 ppm), most of the molecules move to the fluid-fluid interface to form molecular structures, which give rise to an increase in interface elasticity. We also demonstrate that interface elasticity has a non-monotonic behavior with the salt concentration of injected brine, and an optimum salinity exists for maximum oil recovery.