Analytical identification of process design spaces using R-functions

A process design space (DS) is defined as the combination of process design and operational conditions that guarantees the assurance of product quality. This principle ensures that, as long as a process operates within its DS, it consistently yields a product that meets specifications. A novel DS identification method called the R-DS identifier has been developed in this work. It makes no assumptions about the underlying model - the only requirement is that each model constraint (e.g., defining product Critical Quality Attributes or process Key Performance Indicators) should be approximated by a closed-form function, e.g., a multivariate polynomial model. The method utilizes the methodology of V.L. Rvachev's R-functions and allows for explicit analytical representation of the DS with only a limited number of model runs. R-functions provide a framework for representing complex geometric shapes and performing operations on them through implicit functions and inequalities defining the regions. The theory of R-functions enables the solution of geometric problem such as identification of DS through algebraic manipulation. It is more practical than traditional sampling or optimization-based methods. The method is illustrated using a batch reactor model.