Modeling the density of chlorinated brines with nonlinear multivariate regressions

Abstract

There is still no conclusive or definitive model for calculating brine density. The soft computing models that have been published are black boxes that do not allow us to observe the relationships of attributes or generalize results in new brine. Nevertheless, some techniques enable modeling "interpretable" regressions for multivariate and nonlinear data. These include Symbolic Regression, M5P trees, and the MARS method. In this paper, a generic regression is developed for each technique, using published density data for NaCl, KI, KCl, MgCl₂, SrCl₂, and CaCl₂ brines. The results show that all obtained models have a %AAD lower than 0.72 % in test data. Although this result is less accurate than published ones, it is offset by the automatic generation, the models' simplicity, and their ability to be used in new untrained brine, such as Na₂SO₄, NaHCO₃, and AlCl₃. The residual of the generated regressions is studied, concluding that the models still must incorporate new attributes. The regression models confirm a nonlinear relationship between the data attributes. An intercept is observed in them, which is similar between the models. A temperature variable shows a relationship with a significant tendency towards linearity and inverse with respect to density, which differs from that indicated in several publications. Similarly, pressure shows a linear and positive behavior with a small influence in magnitude. Finally, the salt molar weight attribute interacts strongly with the molality and temperature attributes, presenting the most complex expressions. A comparison with a physicochemical model (Laliberté) was made. Despite the latter showing better performance, advantages are observed in the new regressions. It is concluded that it is possible to generate nonlinear multivariate density regressions for single-component brines and to deduce the behavior of the variables from these models. This model could be illustrative and useful as a basis for future rigorous formulations of single-component brine.