Reactive batch distillation (RBD) is a preferred process intensification technology to carry out equilibrium-limited reactions. It is a multicomponent, multiphase system. Appropriate process description requires dynamic modeling of coupled thermodynamics and transport phenomena including the chemical reactions. Such models are barely applicable to online model based operation technology such as model predictive control, real-time optimization and online process monitoring. Therefore, in this paper, the rigorous dynamic model of an RBD is transformed into a set of decoupled ordinary differential equations using linear transformation matrices, called extent transformation, that preserve the physical meaning of the transformed variables. The resulting model has a state space representation with a diagonal state matrix. This representation is suitable for control purposes and can be considered as a linear parameter varying system. Based on the final structure of the model, controllability conditions are stated, and model reduction scenarios are proposed. Finally, the model based on extent transformations is compared with the rigorous nonlinear model via the simulation of a polyesterification process.