This paper presents a mathematical model for the scale inhibitor squeeze process. This particular model incorporates the Langmuir adsorption isotherm to describe retention/release of the inhibitor with the reservoir rock. This complements a previous, similar squeeze model based instead on the Freundlich adsorption isotherm. The analytical solution for a simplified version of both models requires only minimal computational effort.
Both models calculate the scale inhibitor concentration in the produced brine versus the cumulative produced water volume (and hence the squeeze lifetime). The Langmuir-based model appears to describe inhibitor return data and squeeze lifetime better for reservoirs containing a significant amount of clays and carbonate minerals. The Freundlich-based model better matches field data from cleaner formations such as are found in the North Sea.
Similar to the previous model, the Langmuir-based formulation illustrates the importance of the retention/release properties on squeeze lifetime. Parameter studies indicate the total amount of inhibitor injected is the most important design parameter controlling squeeze lifetime.