Abstract: In this paper, we take account of the factors of anisotropic formation damage, perfo-rated hole state and various boundary conditios, and establish the reservoir model and transient flow mathematical model. By using the direct solution of borndary element math-ematical model and regional cut technique, we also obtain the rule of the transient flow of the reservoir near the perforations varying with perforations and formation damage and the
characteristics of roduction performance and transient pressure changes. It is of guiding significance to the distribution of well network, the optimization of perforating parame-ters, the design of production increasing measures and the improvement of well testion lo-cation and other production problems. It is certain that boundary element algorithm will be widely used in the realm of reservoir digital simulation.

Key words: Perforated completion, Formation damage, Boundary element migra-tion, Unsteady state flow, Oil well performance, Pressure behaviour, Mathematical mod-el