A Theoretical Study of the Structure and Elemental Abundances of HD 20794

HD~20794 is a nearby, bright, metal-poor G-type dwarf hosting a compact planetary system, including a super-Earth near the habitable zone. Its low stellar activity and the availability of precise radial-velocity and photometric data make it an excellent benchmark for studying stellar structure and chemical abundances in low-metallicity planet-hosting stars. We present, to our knowledge, the first grid-based stellar evolution analysis of HD~20794 using \texttt{MESA}, focusing on its main-sequence and late main-sequence evolution. A set of 252 stellar models was computed for initial masses between $0.78$ and $0.80\,M_{\odot}$, varying convective efficiency, numerical resolution, and atmospheric boundary conditions. Models were selected through $\chi^2$ minimization using observed constraints on effective temperature, surface gravity, luminosity, radius, and age. The best-fit models favor a mass of $0.80\,M_{\odot}$ and an age of about $9$~Gyr, reproducing all observed stellar properties within uncertainties. They also successfully recover the observed surface abundance pattern over a wide range of elements, including light elements, $\alpha$-elements, and the odd-$Z$ species phosphorus and chlorine. Comparison with nucleosynthesis yields from massive stars suggests that the measured phosphorus and chlorine abundances are compatible with enrichment from core-collapse supernovae and have remained preserved during stellar evolution. Our results support standard stellar evolution theory, indicating that low-mass, metal-poor G dwarfs such as HD~20794 can retain their natal chemical signatures over Gyr timescales. This highlights their importance as probes of stellar evolution, Galactic chemical enrichment, and the chemical environments associated with long-lived planetary systems.