A Mathematical Model for the Scale Inhibitor Squeeze Process

Abstract

Abstract 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 there is local equilibrium between the inhibitor in solution and on the rock, the mathematical model was solved analytically via 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 comparing 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 as well as 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 to 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. Introduction A common method of applying scale inhibitors to a producing well is the "squeeze technique". In this process, a small volume of scale inhibitor solution and overflush is injected into the formation. The inhibitor is retained in the porous matrix by adsorption onto the rock surfaces (adsorption squeeze) and/or by forming a sparingly soluble salt with calcium (precipitation squeeze). Another possible mechanism is the slow leaking off of inhibitor solution trapped in small fractures and vugs, which is not considered in this study. In this paper we consider only the adsorption squeeze technique. When normal production is resumed, the scale inhibitor slowly desorbs into the production water. Ideally, this places a low but effective concentration of inhibitor into the produced water for many months. Sometimes, however, the inhibitor concentration falls off very rapidly and another squeeze treatment is required in a matter of a few weeks. The design of the squeeze process for a given well has been based, up to now, on experience and intuition. When squeeze lifetime is short and premature retreatment is required, the reason for this poor result is · often unclear. The mathematical model presented in this paper is meant to help correct this problem. The objective here is to create a tool that will allow one to predict and optimize this process.