Dielectric logging is a valuable tool for locating and developing tight reservoirs, low contrast reservoirs, shale oil and gas reservoirs, and other unconventional oil and gas reservoirs. The processing of multi-frequency and multi-spacing dielectric logging measurements is based on a stable and efficient response computation algorithm. An equivalent computation model for the push-against-hole array dielectric logging tool is established in this paper, and an improved forward method based on the semi-analytical algorithm for dielectric logging response is devised. Thus the calculation speed of each measurement point's dielectric logging response is increased by more than 8 times. Dielectric logging response charts are also constructed, showing amplitude attenuation and phase shift as functions of formation resistivity and relative permittivity at various operating frequencies. The effects of mud cake, invasion, and anisotropy on the response signal are then simulated and evaluated. The findings reveal that: (1) as the high-frequency response changes significantly when the mud cake is thick, to correct the mud cake's influence, the mud cake parameters can be extracted using the high-frequency detection mode. (2) Invasion has a complicated effect on the high-frequency response, and higher resistivity or relative permittivity in the invasion zone can readily lead to an oscillatory nonlinear shift in the response as a function of invasion depth. This means that for high-resistivity and high-permittivity formations, the high-frequency response has a larger sensitivity and a deeper depth of investigation. (3) When the anisotropy coefficient is small, the high-frequency response is preferable for extracting anisotropy; however, as anisotropy increases, the low-frequency response becomes more sensitive to anisotropy than the high-frequency response.
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