Industrial Heat Exchanger Networks (HENs) are working ill conditions of process streams temperature and flow-rate variations, different kinds of disturbances and changing operating conditions as foulings, catalyst deactivation, etc. Unfortunately, recent state of the art does not give a comprehensive procedure for operability analysis of heat exchanger systems, working in conditions of process streams parameters variations. The objective of the recent work is to present an approach to operability analysis of existing industrial HENs, designed for conditions that differ from the recent ones. This approach can also be used as a module in a complex procedure for design of new HENs. The study presents the first step of the analysis of HENs for flexibility and resilience. It performs mainly feasibility study that can answer the question: "Does the: available network fulfil all the requirements, remaining feasible?". Given approach covers so called convex and non-convex cases. A special attention is paid to the problems when the stream parameters change cause Pinch Jumps.