Packed-bed chromatography is a cornerstone of bioseparation, yet its modeling landscape remains fragmented by numerous model variants, inconsistent terminology, and limited structural clarity. While prior work has categorized and contrasted individual variants, our approach shifts the focus to unification. We present a unified, modular, and composable framework that integrates diverse mechanistic packed-bed chromatography models into a coherent structure. Starting from a high-resolution three-dimensional model, the framework systematically derives a hierarchy of reduced-order models through formal model order reduction. It encompasses a broad range of bulk transport phenomena, intraparticle mass transfer processes, binding mechanisms, and chemical reactions. Formulated orthogonally, these modules are independently meaningful and can be systematically combined into mathematically consistent models tailored to specific applications. The framework recovers and generalizes existing models, establishes a consistent taxonomy, and enables novel model combinations and extensions, including alternative column and particle geometries, particle-size and particle-type distributions, component-specific pore accessibility, rapid-equilibrium binding and reaction formulations, and size-exclusion with simultaneous binding. The framework is accessible through CADET-Equations, an interactive web application for model assembly and automatic generation of governing equations in LaTeX, promoting standardization and transparency. Its design principles are increasingly reflected throughout the CADET ecosystem, whose modular architecture supports the majority of the proposed model family. The generality and composable design of the framework provide a foundation for extending chromatography modeling software toward integrated bioseparation processes and advanced computational biotechnology applications.

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