Geometric design methods for the conceptual design of azeotropic distillation processes are fast and efficient tools for the economic screening of different process alternatives. This two-part series presents a fully automated conceptual design method for finding an optimal recycle policy for the separation of mixtures with distillation boundaries. It does not require visualization and graphical inspection of residue curve or pinch maps and is, hence, not limited to ternary mixtures. The first part introduces a fully computational geometric split feasibility test based on bifurcation analysis. This bifurcation-based feasibility test can be used as a valuable stand-alone tool for the assessment of different separation options. It is also one of the core elements of the recycle optimization discussed in the second part of this series. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 1526-1539, 2011