There is a growing interest in developing Inter-Plant Heat Integration (IPHI) methods for reducing energy consumptions and emissions beyond that of independent plants. However, practical IPHI problems present complexities as boundaries for simultaneous intra- and inter-plant heat integration are considered. Pinch Analysis (PA) can mitigate these complexities by elucidating design insights before developing more detailed inter-plant Heat Exchanger Networks (HENS). In this paper, a novel screening algorithm based on PA and the theoretical maximum inter-plant heat recovery potential Q(rec)(max) is proposed for practical IPHI problems. By using this screening algorithm, a large-scale IPHI problem including multiple plants is divided into several smaller sections with each section including two or three plants. Utilizing this algorithm allows for easier calculation and improved total heat recovery potentials approaching to Q(rec)(max). The final inter-plant HEN configuration(s) for the segregated IPHI scheme(s) are easily developed separately using PA or Mathematical Programming (MP). Before these two steps, the selection of participating streams for IPHI from individual plants is also recommended. Finally, a mathematical model is used to determine the inter-plant HEN configuration(s) in the companion paper of this study. (C) 2017 Elsevier Ltd. All rights reserved.