Resistivity Logging Through Casing Response of Inclined Fractured Formation

The calculation of resistivity logging response (RLR) of the microfracture has always been a challenge in formation evaluation in different scales. The transmission line equation (TLE) has been proven to be effective in solving the apparent resistivity of formation in the resistivity logging through casing. However, the existing algorithms are not suitable to calculate the RLR of fractured formation through casing. A new method is proposed to calculate the transverse resistance in the inclined fractured formation by using the TLE and current flux tube model. In the case when inclined fractures are not intersected with the casing, an analytic expression of the transverse resistance is derived. However, in the case where inclined fractures intersect with the casing, the transverse resistance of intersection can be calculated numerically through simplifying from the double integral to single integral. The validity tests show that the transverse resistance and apparent resistivity calculated with this proposed method have excellent match with the analytical solutions in the case of homogenous infinite formation. In addition, the apparent resistivity of formation increases with the decrease of fracture dipping angle. The existence of inclined fracture with highly resistant fluid affects the RLR significantly.