Abstract: The paper describes a new approach to reservoir simula-tion, the formulations in multi-component reservoir simulation model are firstly expressed as fully differential form on unknown variables, then are dispersed as numerical difference equations on these variables. The basic viewpoint is that all unknown variables’differences are regarded as new variables of singular
differences cells, and then all variables’differences can be expressed as the algebra sum of the cells.The differential variables of the variables are the differentially changing variables of the variables, which is derived from common solution of the variables. The iteration procedure of solving these difference equations will be improved on all unknown variables through using value of the cells step by step.

Key words: reservoir simulation, multi-component model, fully differential method, singular difference cells