*2.4. Case Studies*

According to the morphological correction method of the *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging under the condition of oil-based mud, the *T*<sup>2</sup> spectrum data of nuclear magnetic resonance logging under the condition of oil-based mud and water-based mud extracted by the multi-dimensional matrix method were used to calibrate four types of rocks, and the coefficients and constants of multivariate linear function corresponding to each type of rock were obtained. The executable program was compiled based on the FORTRAN language to correct the *T*<sup>2</sup> spectrum of NMR logging of oil-based mud wells (well B and well C) in the East China Sea. The results are shown in Figures 7 and 8.

According to the core porosity and permeability results, Figure 7 shows that the pore structure type of the well B reservoir in the study area is type III, belonging to a low permeability reservoir. It can be seen from the fifth track that the measured *T*<sup>2</sup> spectrum (Initial T2 spectrum) shows a continuous bimodal shape, representing that the maximum relaxation time of the second peak of the oil-based mud filtrate signal reaches 3000 ms, showing the characteristics of the macropore structure, which is seriously inconsistent with the core analysis results. Compared with the nuclear magnetic resonance *T*<sup>2</sup> spectrum before correction, the macropore part of the corrected nuclear magnetic *T*<sup>2</sup> spectrum (Corrected T2 spectrum) moves to the left, showing a continuous single peak shape, and the "tailing" phenomenon disappears, eliminating the fake long transverse relaxation time signal caused by the invasion of the oil-based mud filtrate. In addition, under the condition

of oil-based mud, the permeability calculated by the *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging before correction (Initial SDR permeability) is obviously larger than that of core analysis (Core-permeability), and the permeability calculated by *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging after correction (Corrected SDR permeability) is smaller, which is in good agreement with the permeability results of core analysis.

**Figure 7.** A field example of correcting the invasion of oil-based mud to field NMR logging in well B. In the first track, the displayed curves are gamma-ray (GR), borehole diameter (CAL), and bit diameter (BIT). The second track is the depth. The third is resistivity curve. The acoustic transit time log (AC), the density log (DEN), compensated neutron log (CNL) are shown in the fourth track. The fifth track is the initial measured *T*<sup>2</sup> spectrum of NMR logging before correction (Initial *T*<sup>2</sup> spectrum). The *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging (Corrected *T*<sup>2</sup> spectrum) under the condition of water-based mud corrected by the method proposed in this study is displayed in the sixth track. The NMR calculated porosity (NMR-por) and core analysis porosity (Core-por) are shown in the seventh track and have good consistency. The Corrected SDR permeability is calculated permeability from the corrected *T*<sup>2</sup> spectrum by using Schlumberger-doll-Research (SDR) model, and the Initial SDR permeability is estimated permeability from the Initial *T*<sup>2</sup> spectrum by using the SDR model, the Core-permeability is derived permeability from core analysis. The ninth track is the permeability calculated by using the traditional porosity-permeability relationship (Fitted permeability). Good consistency of estimated permeability from the Corrected *T*<sup>2</sup> spectrum with core derived permeability illustrates the reliability of the proposed method.

**Figure 8.** A field example of correcting the invasion of oil-based mud to field NMR logging in well C. In the first track, the displayed curves are gamma ray (GR), borehole diameter (CAL), and bit diameter (BIT). The second track is the depth. The third is resistivity curve. The acoustic transit time log (AC), the density log (DEN), compensated neutron log (CNL) are shown in the fourth track. The fifth track is the initial measured *T*<sup>2</sup> spectrum of NMR logging before correction (Initial *T*<sup>2</sup> spectrum). The *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging (Corrected *T*<sup>2</sup> spectrum) under the condition of water-based mud corrected by the method proposed in this study is displayed in the sixth track. The NMR calculated porosity (NMR-por) and core analysis porosity (Core-por) are shown in the seventh track and have good consistency. The Corrected SDR permeability is calculated permeability from the corrected *T*<sup>2</sup> spectrum by using Schlumberger-doll-Research (SDR) model, and the Initial SDR permeability is estimated permeability from the Initial *T*<sup>2</sup> spectrum by using SDR model, the Core-permeability is derived permeability from core analysis. The ninth track is the permeability calculated by using the traditional porosity-permeability relationship (Fitted permeability). Good consistency of estimated permeability from Corrected *T*<sup>2</sup> spectrum with core derived permeability illustrates the reliability of the proposed method.

According to the core analysis results, Figure 8 shows that the pore structure of well C is better than that of adjacent well B, and the pore structure is type II. It can be seen from the results of the fifth track that due to the improvement of pore structure and the increase of the number of macropores, the phenomenon of oil-based mud filtrate invading the formation pores is more serious. The nuclear magnetic *T*<sup>2</sup> spectrum shows a double peak or three peak shape, and the last two peaks even produce fractures and empty white belts. Compared with the nuclear magnetic resonance *T*<sup>2</sup> spectrum before correction, the macropore part of the corrected nuclear magnetic *T*<sup>2</sup> spectrum moves to the left, which not only eliminates the macropore illusion caused by the invasion of oil-based mud filtrate but also eliminates the phenomenon of the blank zone in the middle, making the nuclear magnetic *T*<sup>2</sup> spectrum continuous. In addition, under the condition of oil-based mud, the permeability calculated by the *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging after correction also decreases, which is in good agreement with the permeability results of core analysis.

To further illustrate the reliability of the *T*<sup>2</sup> spectrum morphology correction results, the permeability results calculated by the *T*<sup>2</sup> spectrum of NMR logging before and after correction were compared with the permeability of core samples in wells B and C (Figure 9). The permeability calculated by the uncorrected *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging obviously deviates from the 45◦ line, and the error with the core analysis result is approximately one order of magnitude (relative error 779.37%). The permeability calculated by the *T*<sup>2</sup> spectrum of corrected NMR logging is more consistent with that of core samples (relative error 34.32%), which is better distributed on both sides of the 45◦ line. Compared with the permeability calculated by core porosity and permeability fitting (relative error 82.98%), the overall accuracy of permeability calculated by the corrected nuclear magnetic *T*<sup>2</sup> spectrum improved by 48.66%. The results show that the morphological correction method of the *T*<sup>2</sup> spectrum of NMR logging under the condition of oil-based mud is reliable, and the influence of oil-based mud invasion on the *T*<sup>2</sup> spectrum of NMR logging has been eliminated. The corrected NMR *T*<sup>2</sup> spectrum can be used as the NMR *T*<sup>2</sup> spectrum measured under the condition of water-based mud, which lays a foundation for subsequent processing and interpretation.

**Figure 9.** Comparison of permeability calculated by various methods and core analysis results.
