Non-Uniqueness of Adsorption Isotherm History Matching in Squeeze Treatments

After squeezing the well with scale inhibitor, field samples are normally collected from the produced brine to monitor the squeeze treatment lifetime, resulting in a return concentration profile. This profile is typically used to derive a field-representative isotherm by history matching the return concentration data. This field isotherm is then used to predict the lifetime and to optimize the subsequent treatments in the well. However, isotherm history matching is an inverse problem, and its solution might be non-unique. Hence, multiple isotherms may be identified that satisfy the data-match criteria reasonably well, causing prediction uncertainty for the next squeeze treatments. Ignoring this feature and selecting just one single isotherm out of a whole range of the plausible solutions may result in a poor-quality lifetime prediction based on the model. The main objective in this work is to evaluate the non-uniqueness of the isotherm history matching and to illustrate its effect on designing the subsequent treatments. Four synthetic cases were considered, and the SI concentration return profile was produced for each case to demonstrate the non-uniqueness nature of the problem. Moreover, to represent the field conditions more closely, randomly generated synthetic noise was also added to the profiles. In practice, the noise may come from the errors in sampling/analyzing or from the reservoir heterogeneity. A real field case was also considered with the field data available for two subsequent squeeze treatments. A sensitivity study was conducted to show the degree of uncertainty in the lifetime prediction for a variety range of squeeze designs, using several isotherms matching the return profile. The systematic method proposed in this manuscript assists in the isotherm history matching, leading to a more accurate squeeze lifetime prediction.