Determination of the equilibrated calcium carbonate (calcite) scaling in aqueous phase using a reliable approach

• Support vector machine algorithm is used to model deposition in calcium carbonate aqueous phase.
• The coupled simulated annealing optimization tool obtains the optimal model parameters.
• The model has been developed and validated using 200 series of the data.
• Statistical and graphical error analyses are presented to show accuracy of the model.

The deposition of mineral scale, in particular calcium carbonate (CaCO3) deposits, is a persistent and expensive problem in industries ranging from oil and gas to desalination. This communication presents a reliable and predictive model namely, the least square support vector machine (LSSVM) optimized with a simulated annealing (SA) optimization strategy to estimate the potential deposition from an equilibrated calcium carbonate aqueous phase. This model has been developed and tested using 200 series of literature-reported data of correction factor (K) as a function of temperature and total ionic strength. Moreover, statistical and graphical error analyses have been performed to establish the adequacy and accuracy of the model. The results indicate that the model developed provides estimations which are in good agreement with literature data. Moreover, it is illustrated that the model is capable of interpolation and even extrapolation in a wide range of ionic strengths and temperatures. Performance of the model in estimation of calcium carbonate deposition demonstrates that it can be reliable for other types of scale deposition. Finally, to check whether the model developed is statistically correct and valid, leverage approach, in which the statistical hat matrix, Williams plot, and the residuals of the model results lead to identification of the probable outliers, is applied. It is found that all of the collected calcium carbonate deposition literature data used in this study seems to be reliable.