The feasibility of three component distillation columns containing kinetically controlled chemical reactions and side streams is addressed through the use of difference points. We decompose complex columns into sections and identify feasible regions in composition space where each section operates. These regions enclose sectional profiles for the full range of operating parameters and are bounded by profiles constructed under extreme conditions. We efficiently determine the bounding profiles without computing interior compositions. We also develop a graphical feasibility test to connect sections and construct full columns using feasible regions. Finally, we present a technique to characterize the feasible regions and quantify how much reaction or side stream may be placed on any stage of a column section. The first three papers in this series [Hauan et al., 2000. Difference points in extractive and reactive cascades. I-Basic properties and analysis. Chemical Engineering Science 55 (16) 3145-3159; Lee et al., 2000. Difference points in extractive and reactive cascades. II-Generating design alternatives by the lever rule for reacting systems. Chemical Engineering Science 55 (16) 3161-3174; Hoffmaster and Hauan, 2004. Difference points in extractive and reactive cascades. Ill-Properties of column section profiles with arbitrary reaction distribution. Chemical Engineering Science 59 (17) 3671-3693] derive the fundamental properties of difference points, develop a lever rule to facilitate full column design, and analyze the properties of sectional profiles in reactive cascades. This fourth paper develops the necessary feasibility analysis tools for systematic identification of reactive distillation design alternatives. (c) 2005 Elsevier Ltd. All rights reserved.