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Surfactants are responsible for foam generation and stability in foam-assisted enhanced oil recovery and carbon subsurface storage operations. Predicting possible surfactant loss due to adsorption on the rock surface is necessary to obtain an optimal foam performance and to ensure viability of the implementation. This work aimed to develop a three-step adsorption model to enhance surfactant adsorption prediction on porous media, by incorporating hemimicelle desorption induced by micelles into the classical mechanisms. Cocamidopropyl betaine and brine were used to prepare foaming formulations. Two types of rocks were used as adsorbents, namely, sandstone and carbonate. Sufactant adsorption was quantified by an optimized chromatographic (HPLC) method, and the adsorption isotherms were normalized using specific surface area of the rock powder. The results were adjusted by a new three-step model with parameters obtained in MATLAB with non-linear squares fitting. The perfomance of this model was compared with a classical two-step isotherm model from the literature. Adsorption mechanisms for the zwitterionic surfactant were infered based on the model parameters, the rock-brine interface species, and the zeta potential, as obtained from surface complexation models. The effect of micelles on adsorption was more pronounced on the sandstone due to the negative charged surface sites. The developed model was able to describe surfactant adsorption near and above the critical micelle concentration, and is reduced to the classical model when the aggregation effects are suppressed. Classical model would led to the wrong conclusion that hemimicelle adsorption is more favorable on carbonate surface compared to sandstone. Positive charges on carbonate surface correlates with lower effect of micelles on desorption. Both the isotherm model and each step adsorption rate can be coupled with transport equations to predict dynamic adsorption.
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