In Quantitative Structure-Property Relationship (QSPR) models, graph-theoretical techniques are employed to explore the connections between the physicochemical properties of chemical compounds and their molecular structure properties. Topological indices serve as valuable tools for predicting the properties of chemical compounds and are used to develop QSPR studies. Titania nanotubes play a crucial role in materials science, finding practical applications in catalytic materials, gas sensors, biomedical devices, and solar cells. In this paper, we compute Sombor-type topological indices of an infinite class of titania nanotubes using the edge-partition strategy in graph theory modeling. The results of this study showed that among Sombor-type topological indices, the modified Sombor index and the elliptic Sombor index have the lowest and highest values, respectively, for the molecular graph of titania nanotubes. Also, among the multiplicative Sombor indices in the structure of titania nanotubes, the lowest and the highest values are related to the multiplicative modified Sombor index and the multiplicative increased Sombor index, respectively. Furthermore, using QSPR modeling, the predictive power of Smbor-type indices for the physico-chemical properties of benzoic hydrocarbons was investigated using a linear regression model. The results of this study showed that the inverse Sombor index is the best index for predicting boiling point, Enthalpy of vaporization, flash point and molar volume, while the increased Sombor index is the best predictor for the molar refractivity and polarizability of benzoic hydrocarbon molecules. The results of this paper, offer valuable insights into the structural characteristics of titania nanotubes and contribute to advancing topological indices for predicting the behavior of other chemical compounds.