柱状成层地层中仪器偏心对阵列感应测井响应的影响

Effect of tool eccentricity on responses of array induction logging tools in cylindrical multilayered formations

采用柱状成层介质的并矢Green函数高效计算井眼中偏心发射源产生的电磁波,并利用该算法模拟了阵列感应测井仪器在井眼中偏心时的响应.在模拟时既考虑到了金属心轴的存在也考虑到了线圈系所处绝缘层的存在,并重点分析了绝缘层的影响.数值模拟结果表明,对相对低泥浆电导率情况而言,无论线圈距长短,线圈系所处绝缘层对仪器响应的影响均较小,可忽略不计.而对于相对高泥浆电导率情况,线圈系所处绝缘层对仪器响应的影响明显,不可忽略,且线圈距越短影响越大,仪器偏心距越大影响越大.另由数值模拟结果可以看出,在相同泥浆电导率情况下,仪器线圈距越短偏心对线圈系响应的影响越大.

The effect of eccentricity on the responses of electromagnetic well-logging tools in a borehole is of great value for precisely interpreting the measured data. For real electromagnetic well-logging tools such as array induction-logging tools, usually both a metal mandrel and an insulating protection layer are included in the tools. Only the existence of the metal mandrel was considered for simulating and analyzing the effect of tool eccentricity in conventional analytical methods, and the influence of the insulating protection layer has been neglected. Since the insulating protection layer has occupied part of the space of the drilling fluid, its influence on the responses should also be considered whether the tool is centric or eccentric in a borehole. An analytical algorithm was developed that can simulate the responses of centric or eccentric electromagnetic well-logging tools with both a metal mandrel and an insulating protection layer in a borehole.The algorithm was based on the dyadic Green＇s functions of cylindrical multilayered medium, in which the coils are supposed to be positioned in the 0-th layer, i.e. the insulating protection layer. The borehole is taken as the 1-th layer in the algorithm, which was used to be taken as the 0-th layer where the coils are supposed to be positioned in conventional analytical methods. Thus the new model adopted is more suitable for describing real electromagnetic well-logging tools, whose responses can not be directly simulated by conventional analytical methods. In the new developed analytical algorithm, the continuity condition of the tangential electromagnetic fields across the boundary between the insulating protection layer and the borehole fluid was used, thus the fields in the borehole can be expressed by the fields in the insulating layer. The relationship between the electromagnetic fields under the cylindrical coordinates relative to the borehole and to the tool was then used and finally the new algorithm was developed.The responses of centric and eccentric array induction logging tools in a borehole were simulated by the algorithm, and the difference between the responses of the tool with or without an insulating protection layer was compared. The observations include：（1） Given the borehole diameter and the conductivity of the drilling fluid and formation, the relationship between the receiver coil＇s response and the eccentric distance was obtained for different arrays. The results showed that the effect of the insulating layer on the tool＇s response is small and can be neglected when the fluid＇s conductivity is relatively low, whether the transmitter-receiver spacing is long or short. The effect is big for the condition of relatively high fluid＇s conductivity, and the shorter the transmitter-receiver spacing the bigger the effect, the bigger the eccentric distance the bigger the effect. （2） Given the conductivity of the drilling fluid and formation, the relationship among the coil＇s geometric factor and the borehole＇s diameter was obtained for different arrays with the tool being in the borehole center. Since the tool was positioned in the borehole center, the effect of the insulating layer was relatively small. （3） Given the conductivity of the drilling fluid and formation, the relationship among the coil＇s geometric factor, borehole＇s diameter and eccentricity ratio for different arrays was obtained. The results can be used to analyze the radial detection depth with different borehole diameter and eccentricity ratio.From all the results we can conclude that it is better to consider all the specific constructions of the tool and coils when simulating the responses of electromagnetic well-logging tools in a borehole, and it is better to adopt a model as much as closer to real tools, thus the simulated results will be much more precise.