High-temperature supercritical CO2 Brayton cycles are promising possibilities for future stationary power generation and hybrid electric propulsion applications. Heat exchangers are critical components in supercritical CO2 thermal cycles and require accurate correlations and comprehensive performance modeling under extreme temperatures and pressures. In this paper (Part I), new Colburn and friction factor correlations are developed to quantify shell-side heat transfer and friction characteristics of flow within heat exchangers in the shell-and-tube configuration. Using experimental and computational fluid dynamics (CFD) data sets from existing literature, multivariate regression analysis is conducted to achieve correlations that capture the effect of multiple critical geometric parameters. These correlations offer superior accuracy and versatility as compared to previous studies and predict the thermohydraulic performance of about 90% of the existing experimental and CFD data within 15%. Supplementary thermohydraulic performance data are acquired from CFD simulations with supercritical CO2 as working fluid to validate the developed correlations and demonstrate its capability to be applied to supercrtical CO2 heat exchangers.