A project was carried out at The National Institute of Standards and Technology (NIST) to study the feasibility of developing a new-generation, multi-room, compartment fire model computer code, called the Consolidated Compartment Fire Model (CCFM) computer code. The idea was that such a code would consolidate past progress in zone-type compartment fire modeling, and allow readily for integration of future advances with the greatest possible flexibility. The project lead to the development of a prototype multi-room CCFM product called CCFM.VENTS. This is Part I of a four-part report which documents the above effort. Introductory remarks discuss the generic features of the CCFM and the specific features of CCFM.VENTS. The main objective of this Part I document is to present a comprehensive description of the governing equations of CCFM.VENTS and their technical basis. The other three parts of this report are: Part II: Software Reference Guide; Part III: Catalog of Algorithms and Subroutines; and Part IV: User Reference Guide.