In recent years, Al alloys have drawn considerable interest due to their excellent strength-to-weight ratio, qualifying them as cutting-edge candidates for aerospace applications. Precipitation hardening is responsible for improved mechanical properties in these alloys by constraining the dislocation motion. The θ' phase is the crucial strengthening phase existing as precipitates with plate-shaped morphology in Al-Cu alloy. The anisotropy in the precipitate shape can be attributed to the direction-dependent coherent and semi-coherent interfaces [1]. Phase-field method is an effective tool for studying the precipitate evolution as it can replicate the system thermodynamics and kinetics through its framework. In the present work, the chemical free energy is incorporated from the CALPHAD database, and the parameters required for determining the elastic free energy are computed via Density Functional Theory. A coupled system of Cahn-Hilliard [2] and Allen-Cahn equations is numerically discretized through a finite-difference approach and solved for obtaining the temporal evolution of microstructure in the Al-Cu system. An appropriate combination of various energies captures the precipitate shape. In addition to the equilibrium shape of a single precipitate, it is essential to study the evolution of multiple precipitates and validate them with the experimental results. Therefore, the work also includes a multi-particle system study, where the growth and coarsening dynamics during the entire microstructure evolution are investigated, and a correlation with the precipitate aspect ratio is established.