*3.1. Workflow of T2 Spectrum Shape Correction Method*

Since there are reliable technical means to evaluate reservoir parameters using nuclear magnetic resonance *T*<sup>2</sup> spectrum measured under water-based mud conditions, this study establishes the correlation between the *T*<sup>2</sup> spectrum of oil-based mud wells and the *T*<sup>2</sup> spectrum of water-based mud wells. The *T*<sup>2</sup> spectrum morphology of oil-based mud wells was corrected to the *T*<sup>2</sup> spectrum morphology of water-based mud wells. The realization method is shown in Figure 10. First, according to the difference in pore structure, the reservoir rocks were divided into four types. Second, the multidimensional matrix technology was used to construct the NMR *T*<sup>2</sup> spectrum sample library in the study area. Core saturation and centrifugal NMR experiments were used to determine the optimal *T*<sup>2</sup> cutoff value in the study area and then divide the large and small pores. Finally, under the condition of a similar pore structure, the multivariate linear function relationship of the *T*<sup>2</sup> spectrum of rock macropores in water-based mud wells and oil-based mud wells was established, and the correction of the rock *T*<sup>2</sup> spectrum morphology of oil-based mud wells was realized.

**Figure 10.** Workflow of the *T*<sup>2</sup> spectrum shape correction method for NMR logging under oil-based mud conditions.

*3.2. Extraction of T2 Spectrum from NMR Logging by the Multidimensional Matrix Method*

To correct the morphology of the *T*<sup>2</sup> spectrum of formation nuclear magnetic resonance logging in an oil-based mud environment, it is necessary to determine the *T*<sup>2</sup> spectrum

of nuclear magnetic resonance logging in a water-based mud environment, to establish the correlation between the *T*<sup>2</sup> spectrum of oil-based mud wells and the *T*<sup>2</sup> spectrum characteristics of water-based mud wells. However, for a well, nuclear magnetic resonance *T*<sup>2</sup> spectrum measurements in water-based mud and oil-based mud environments cannot be conducted at the same time. Additionally, due to the relatively small number of cores drilled during offshore operation, a large number of different types of mud invasion and nuclear magnetic resonance joint measurement experiments cannot be conducted. To obtain the nuclear magnetic *T*<sup>2</sup> spectrum in water-based mud and oil-based mud with similar pore structures, this study proposes the use of a multi-dimensional matrix method to construct a nuclear magnetic *T*<sup>2</sup> spectrum sample library in the study area to obtain *T*<sup>2</sup> spectrum data of NMR logging of reservoir rocks under the conditions of water-based mud and oil-based mud with similar curve values, such as porosity, permeability, natural gamma ray (GR), acoustic transit time log (AC), compensated neutron log (CNL), and density log (DEN). For the wells with two types of drilling fluid, the formation porosity is calculated by NMR logging. For water-based mud wells, because the *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging can accurately calculate the permeability, the permeability calculated by the *T*<sup>2</sup> spectrum is used as the permeability of water-based mud wells; for oil-based mud wells, the permeability calculated by the *T*<sup>2</sup> spectrum is quite different from the core analysis results, but the difference between the permeability calculated by the porosity and permeability fitting method and the core analysis results is relatively small. Therefore, the permeability calculated by the porosity and permeability fitting method was used as the permeability of oil-based mud wells. The formula of the multidimensional matrix method is as follows:

$$A = \left[ M(\phi, \textit{K}, \textit{GR}, \textit{AC}, \textit{CNL}, \textit{DEN}), \textit{N}(\phi, \textit{K}, \textit{GR}, \textit{AC}, \textit{CNL}, \textit{DEN}) \right] \tag{2}$$

where, *A* is the total data matrix, including nuclear magnetic *T*<sup>2</sup> spectrum data in oil-based mud and water-based mud environments. *M* is the NMR *T*<sup>2</sup> spectrum sample library in an oil-based mud environment, and *N* is the NMR *T*<sup>2</sup> spectrum sample library in a water-based mud environment.

According to the different logging curve values of typical reservoirs in the study area, the nuclear magnetic *T*<sup>2</sup> spectrum data under the conditions of oil-based mud and water-based mud were classified into the corresponding sample library point by point, and the *T*<sup>2</sup> spectrum sample libraries under the conditions of water-based mud and oil-based mud are established. Therefore, for a certain depth point in the formation of oil-based mud wells, the *T*<sup>2</sup> spectrum of similar pore structure of adjacent water-based mud wells can be obtained, and then the characteristics of *T*<sup>2</sup> spectrum under different mud types can be compared to establish the correlation between them. This method avoids the problems of limited core NMR experimental data, poor representativeness, and a long experimental cycle, and is convenient for the subsequent calibration of the *T*<sup>2</sup> spectrum morphology correction model.
