Iron acquisition is essential for microbial survival, biofilm formation, and pathogenicity. Many bacteria use siderophores, such as pyoverdines produced by fluorescent pseudomonads, to chelate iron under limiting conditions, and studies show that siderophore production and cross-feeding confer a fitness advantage over species that lack these abilities. This phenomenon has been experimentally studied in species such as rhizosphere bacterium Pseudomonas protegens Pf-5 and Pseudomonas aeruginosa PAO1 using chemostat and batch culture systems. However, most previous studies do not account for spatial heterogeneity. In contrast to well-mixed, homogeneous environments, bacterial populations typically grow in spatially structured communities such as colonies. In this study, we address this gap by extending a previously developed ordinary differential equation model of iron chelation and cross-feeding into a reaction-diffusion model for two related species in two-dimensional space. This approach leads to a highly non-linear system of partial differential equations. To solve it numerically, we use a finite difference method with semi-implicit discretization in both space and time. Our findings indicate that siderophore production and cross-feeding confers a significant growth advantage even in spatially structured environments. This modeling approach provides a quantitative framework for understanding complex microbial interactions in heterogeneous environments.