An enterprise information system distinguishes itself from other types of software as it is developed to facilitate the operation of an organization hence its requirement reflects its strategies, plans, organizations, processes, marketing etc. We believe that the requirements in the form of domain knowledge acquired in the early stage of system development can be organized and modeled in an Enterprise Architecture. Zachman Framework is one of the most widely used Enterprise Architectures. However, in the original version of the Zachman Framework, there is neither a rigorous meta-model nor a well-defined sequence in which to instantiate the cells, which prevents it from being used practically during the requirement engineering phase of an enterprise information system project. To improve such a situation we develop a conceptual meta-model for the Zachman Framework by adapting and integrating the Bunge-Wand-Weber ontology and the Enterprise Ontology. Based on this meta-model, various requirement acquisition processes can be formulated by specifying a sequence to traverse the meta-model graph and instantiate its nodes and edges. In this paper we present such a process, suitable for an enterprise system development project of a particular situation.