| The mud filtrate permeating into permeatrable formations affect the precision of evaluation of logs. In order to get true formation resistivity, further to provide credible result for oil and gas estimation, it's necessary to study the effect of mud filtrate permeating into the formation on logging result. Because the formation is non-homogeneous, also and permeate the formation is affected by the liquid property, the depth of invasion zone is at the same formation usually. Different log method have different radial resolution, at this status, we can't distinguish the vertical and gradient invasion zone front, so in the simple model, the invasion zone front is seen as the vertical front actually. But this model can't satisfy the real logging circumstance, therefore this thesis give a model of gradient invasion zone.Base on the geological condition and the demand of task, I choose induction log to calculate. The induction log study the conductivity of formation base on the electromagnetic induction theory. It can work in the non-electrical well, such as oil-base well or well is full of air. In the generic water-base well, induction log behaves a series of advantages too, for example, induction log is influenced by surround rock weakly, but it is sensitive to low resistivity layer, so it play a important part to differentiate low resistivity oil and water layer. Certainly induction must be exit some disadvantage, the equipment's linear range is not larger enough, the mud have a large influence on measure result, based on these reason, this paper used three coils, 6ILD-0.8米, and 1503 dual induction log who have different radial and longitudinal properties to calculate respectively, the combination of equipment response is benefit to know complex invasive zone deeply.The geometrical factor is used to describe every part of formation contribution to measure signal. The geometrical factor theory regard spacial medium as infinite small section and unit conductive loop which is coaxial with coil, the second inductive electromotive force of receive coil is seem as the summation of second inductive electromotive force which is produced by unit conductive loop. In this way, the total signal provided by axis-symmetry divisional homosphere can be calculated by making addition of every part signal. So a complex boundary problem can be expressed by a simple algebraic expression.In the paper, I study the properties of Doll, Moran, Gianzero and Born geometrical factor which have different physical foundation and applied area. I choose Born geometrical factor to make forward calculation.The geological model this paper considered is like that: the horizontal layer whose thickness is H perpendicular to borehole whose diameter is d, formation is invaded by mud, the resistivity of mud, invasive zone, formation and surround rock is Rm,R i,R t and Rs respectively, coil record point move along with axis. The invasive zone depth is variable in this paper, this is strongly differ from the former common geological model. Combining with instrumental characteristic, we give two basic model in the paper: resistive invasion and conductive invasion model. The parameter of conductive invasion model: the mud resistivity Rm =1.0Ωm, invasive zone resistivity Ri =40Ωm, formation resistivity Rt =100Ωm , surround resistivity Rs =20Ωm , the thickness of layer H=3m , the diameter of well d=0.2 m , the diameter of invasive zone Di =0.6 m . The parameter of resistive invasion model: the mud resistivity Rm =1.0Ωm , invasive zone resistivity Ri =50Ωm , formation resistivity Rt =10Ωm, surround resistivity Rs =20Ωm , the thickness of layer H=3 m , the diameter of well d=0.2m , the diameter of invasive zone Di =0.6 m . The main features of induction logging response in different angles of inclination invasion will be described according to the analysis of the computed logs with different environmental factors(include well size, invasive zone, the thickness of layer).In this paper, in the axis symmetrical two-dimension heterogeneous media, through the analytical model of induction logging, based on the skin effect Born geometrical factor theory, use the vc program, we simulate and solve the problem of gradient invasive zone forward calculation.After prove the forward result is right, the paper study the influence of environmental factors (include well size, invasive zone, the thickness of layer) on log response. Through the simple analysis to forward result, we get several conclusions about induction log of gradient invasive. The well size has a great effect on three coils, the log response become closer to formation response as the well size decrease. When the mud resistivity change from 0.1Ωm to 10.0 Ωm , each log response have unconspicuous change. The form and amplitude of logs depend on the resistivity contrast between the invaded zone and the uninvaded formation and adjacent layers, especially for the three coils whose detect depth is small comparatively. When the invaded depth become larger, the ILM response is more closer to invaded zone than ILD. The formation logs become smoother and higher when the thickness of layer increase. The shape of invaded zone has a obvious influence on logs, the bigger of the angle between invaded zone front and axis, the stronger influence of the apparent resistivity is deserved, even when the angle reach to a large degree, in the bottom of formation, the log response close to the invaded zone response, also the larger of the angle, the closer of the response. In the same parameter condition, three coils, 6ILD-0.8米, and 1503 dual induction log have similar logs and different amplitudes which is decide by different detect properties. The radial and the longitudinal property of three coils are not good, the radial property of ILD and the longitudinal of ILM is better, moreover, the detect property of 6ILD-0.8米is intervenient.The discussion of this paper provide the theoretical proof in complex invaded environment, it will help people to consider the environment influence correctly in the interpretation.
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