Compression equations in pharmaceutical tableting: from classical compaction models to data-driven and mechanistic approaches.

Abstract

Powder compaction remains the key step in pharmaceutical tablet manufacturing, but its multiscale and path-dependent nature makes accurate prediction of tablet properties difficult. Compression equations have long been used to relate applied pressure to densification, porosity, and mechanical strength, providing descriptors for material comparison and formulation design. Classical models such as Heckel, Kawakita-Lüdde, and Cooper-Eaton remain widely used, although they are limited by pressure-range dependence, sensitivity to in-die versus out-of-die measurements, and restricted mechanistic interpretation. Recent developments have expanded compression modeling to include extended in-die formulations incorporating solid compressibility, continuum constitutive laws for finite-element simulations, particle-scale discrete-element approaches, and data-driven process analytical technology (PAT) frameworks. These approaches are critically evaluated alongside classical equations with respect to constitutive validity, calibration transferability, contact-law realism, computational cost, data governance, model drift, and regulatory acceptability. Together, they form a hierarchical modeling framework spanning empirical screening, mechanistic prediction, and real-time process control. This review integrates classical and emerging compaction models and discusses their relevance to critical quality attributes, scale-up, and digital-twin-enabled pharmaceutical manufacturing.