A Mathematical Model for the Scale-Inhibitor Squeeze Process

Abstract

Summary A mathematical model was developed to describe the scale-inhibitor-adsorption squeeze process. The objective of this study was to create a tool that will predict the duration of a squeeze treatment, given the operating parameters and the rock and inhibitor properties. Assuming that there is local equilibrium between the inhibitor in solution and on the rock, the mathematical model was solved analytically by the method of characteristics. Algebraic equations were derived to calculate the scale-inhibitor concentration in the produced water and the squeeze lifetime. The validity of the model is demonstrated by a comparison of its predictions with field and laboratory data. Sensitivity of the squeeze lifetime to variables associated with the process is presented. One important conclusion is that scale inhibitors should be screened on the basis of their adsorption characteristics and their effectiveness at low concentrations in preventing scale formation. Finally, the complete mathematical model, which allows for time-dependent adsorption/desorption of the inhibitor, is solved numerically. Accurate predictions of the squeeze process require incorporation of these kinetic effects when the residence time is short compared with the time required to reach equilibrium. As demonstrated here, this can be significant, especially in laboratory tests performed to measure squeeze lifetime. Scaling up laboratory results for the field should be done with caution because these kinetic effects tend to increase squeeze lifetime. The equilibrium model gives the most conservative prediction of squeeze lifetime.