Abstract: Because of the co-effect of formation heterogeneity and mud invasion, there exits varied radius of filtrate-invaded zone with depth. In this paper, the analytical model of mid-induction log in 2D axis symmetrical heterogeneous media is developed. Based on the skin effect geometrical factor theory and formation resistivity log method, the theory of the forward modeling of gradual change of filtrateinvaded zone front are discussed. The main features of induction log response in different angles of inclination area are described and the effect of environmental factors such as well bore, filtrate-invaded zone and layer thickness on inductologs is estimated. The results show that the deep-and mid-induction logs have similar shape but different amplitudes in the same stratum condition. The mid-induction log is more influenced by the filtrate-invaded zone. Few influences on the logging response occur in only change of well bore size, mud resistivity, filtrate-invaded zone resistivity along with its invaded depth or the layer thickness, except for changing shape of the invaded zone. The results not only provide a general explanation for the invaded environment, but also make a reasonable interpretation on some anomaly in induction log. This consideration will be helpful to get proper well log interpretation.

Key words: filtrate-invaded zone, skin effect, geometrical factor theory, induction log, forward modeling