**1. Introduction**

During drilling operations, drilling fluids are primarily used to ensure the smooth progress of drilling, and their importance is equivalent to the blood of the human body. The drilling fluid can carry out drilled cuttings, cool and lubricate the bits, balance and control the formation pressure, and maintain the stability of the wellbore [1]. To ensure the safety of drilling operation, the drilling fluid is usually circulated under a bottom hole pressure higher than the reservoir pressure, which is called overbalanced drilling [2]. Therefore, a fraction of the drilling fluid filtrate will penetrate the permeable formation under overbalanced pressure. Then, it will interact with the minerals and fluids in the formation rock, which will change the original petrophysical and geomechanical properties in the formation flushing zone [3]. The degree of invasion usually depends on two factors. The internal factors mainly include the quality control of reservoir formation, such as porosity, permeability, pore structure, original wettability of rock, and formation fluid properties. External factors are primarily controlled by drilling operation parameters, including drilling pressure, formation temperature, drilling time and drilling fluid properties [4]. On the walls of the wellbore, the solid particles in the mud are gradually deposited to form mud cakes. Because mud cakes are impermeable, when mud cakes are formed, they hinder

**Citation:** Sun, J.; Cai, J.; Feng, P.; Sun, F.; Li, J.; Lu, J.; Yan, W. Study on Nuclear Magnetic Resonance Logging *T*<sup>2</sup> Spectrum Shape Correction of Sandstone Reservoirs in Oil-Based Mud Wells. *Molecules* **2021**, *26*, 6082. https://doi.org/10.3390/ molecules26196082

Academic Editor: Robert Brinson

Received: 31 August 2021 Accepted: 2 October 2021 Published: 8 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the further invasion of mud filtrates [5]. As shown in Figure 1, this process will make the reservoir near the wellbore form several obvious annular areas: mud cake, invasion zone, undisturbed zone and impermeable zone.

**Figure 1.** Schematic diagram of mud invasion process.

Water-based mud (WBM) and oil-based mud (OBM) are considered the two types of drilling fluids that are most commonly used in the drilling process. Because shale oil reservoirs are rich in clay minerals and rock stability is poor, drilling with water-based mud will lead to water absorption and swelling in the rock, hydration expansion, borehole collapse, leakage, and so on [6,7]. Oil-based mud can effectively solve these problems, such as hydration expansion and wellbore instability of shale formations. Therefore, oil-based mud is most commonly used in the drilling process of shale oil reservoirs [8].

Nuclear magnetic resonance logging can directly measure the relaxation information of reservoir pore fluids and plays an extremely important role in the evaluation of petrophysical parameters, such as porosity, permeability, and saturation of various types of oil and gas reservoirs [9,10]. Based on the theory of NMR logging, the NMR transverse relaxation time (*T*2) is mainly affected by three relaxation mechanisms: bulk relaxation, surface relaxation, and diffusion relaxation, as shown in Equation (1):

$$\frac{1}{T\_2} = \frac{1}{T\_{2B}} + \rho\_2 \frac{S}{V} + \frac{D(\gamma G T\_E)^2}{12} \tag{1}$$

where *T*<sup>2</sup> is the transverse relaxation time, *T*2*<sup>B</sup>* is the bulk relaxation, *ρ*<sup>2</sup> is the surface relaxivity, *S/V* is the surface-to-volume ratio of the pore, *D* is the diffusion coefficient of the fluid, *γ* is the nuclear gyromagnetic ratio, *G* is the magnetic field gradient, and *TE* is the echo spacing of the measurement sequence.

However, due to the shallow detection depth of NMR logging, the *T*<sup>2</sup> spectrum is easily affected by mud invasion. Especially in the environment of oil-based drilling fluids in shale oil reservoirs, the displacement of fluid in the flushed zone by oil-based mud filtrate may seriously affect the overall shape of the *T*<sup>2</sup> spectrum and cannot accurately evaluate reservoir parameters [11].

The study area belongs to a typical low porosity and low permeability sandstone gas reservoir with water content (the original water saturation range is 23–85%) and strong hydrophilic characteristics [12]. In this context, the rock volume model of the gas reservoir and the corresponding ideal NMR *T*<sup>2</sup> spectrum were established, as shown in Figure 2. The model describes the ideal NMR *T*<sup>2</sup> spectrum of gas-bearing reservoirs in undisturbed formations of water-based mud wells and oil-based mud wells.

1. The undisturbed formation does not contain mud filtrate, and the natural gas is a fluid of nonwetting phase in the formation pores of the study area. Its NMR signal only includes diffusion relaxation and free relaxation, which is not affected by surface relaxation. Due to the fast diffusion rate of natural gas, it has a short *T*<sup>2</sup> time [13]. Figure 2a shows the rock volume model and ideal NMR *T*<sup>2</sup> spectrum of the undisturbed formation, and the red part represents natural gas.


Considering the character analysis of nuclear magnetic resonance logging data in oilbased mud wells, many researchers have conducted related research [14–17]. Chen [14,15] believed that surfactants in oil-based drilling fluids would change the wettability of reservoir rocks, and thus using the default 33 ms as the *T*2*cut-off* value for interpretation is no longer applicable; Marschall and Coats [16] believe that the macropores reflected by the *T*<sup>2</sup> spectrum are greatly affected by the oil-based mud filtrate, while the small pores are not sensitive to the intrusion of the oil-based mud filtrate. However, the method of morphological correction of the *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging in oil-based mud wells is not well studied. Ighodalo [17] proposed a fluid substitution method to correct the nuclear magnetic *T*<sup>2</sup> spectrum in oil-based mud wells, yet this method needs to accurately obtain the total water saturation in the invasion zone. Therefore, a method to quickly and accurately correct the shape of the NMR *T*<sup>2</sup> spectrum after the invasion of oil-based mud filtrate in shale oil reservoirs is needed. However, due to the complex pore structure of shale oil reservoirs and the complex response mechanism of NMR logging, correction work is difficult. In this regard, this study proposed a new approach to correct the unreal NMR logging responses due to oil-based mud invasion in gas sandstone formations. By establishing the multivariate linear function relationship between the nuclear magnetic *T*<sup>2</sup> spectrum of water-based mud wells and oil-based mud wells, the shape correction of the NMR logging *T*<sup>2</sup> spectrum after the invasion of oil-based mud filtrates are realized, which improved the accuracy of NMR logging evaluation of reservoir parameters, and laid a foundation for the shape correction of the nuclear magnetic resonance logging *T*<sup>2</sup> spectrum after the invasion of oil-based mud filtrates in shale oil reservoirs.

**Figure 2.** Gas reservoir volume model and theoretical NMR *T*<sup>2</sup> spectrum diagram. (**a**) Volume model of gas-bearing reservoirs in undisturbed formations and theoretical distribution of the nuclear magnetic *T*<sup>2</sup> spectrum. (**b**) Volume model of gas-bearing reservoirs in water-based mud wells and theoretical distribution of the nuclear magnetic *T*<sup>2</sup> spectrum. (**c**) Volume model of gas-bearing reservoirs in oil-based mud wells and theoretical distribution of the nuclear magnetic *T*<sup>2</sup> spectrum.

## **2. Results and Discussion**

## *2.1. Comparison of NMR Logging Responses in Different Mud Environments*

As shown in Figure 2, under the condition of drilling differential pressure, the original formation fluid was displaced by mud filtrate, and the properties of the formation fluid have changed. Moreover, the wettability of the formation determines the different distribution positions of oil-based mud filtrate and water-based mud filtrate in pores, resulting in the difference in the *T*<sup>2</sup> spectrum morphology of NMR logging under different drilling fluid environments.

In this study, the *T*<sup>2</sup> spectrum characteristics of water-based mud well A and adjacent oil-based mud well B were compared and analyzed. Figure 3a is a comprehensive logging diagram of well A measured in a water-based mud environment. The sandstone interval is a gas reservoir, and its NMR *T*<sup>2</sup> spectrum is distributed in a single peak. The *T*<sup>2</sup> value of the main peak is less than 300 ms, and the maximum *T*<sup>2</sup> value is less than 1000 ms. According to the volume model of gas-bearing reservoirs in water-based mud wells and the theoretical distribution of the nuclear magnetic *T*<sup>2</sup> spectrum in Figure 2b, the distribution form of the nuclear magnetic *T*<sup>2</sup> spectrum in water-based mud wells is basically not affected by the water-based mud filtrate and can be used for the calculation of reservoir petrophysical parameters and the evaluation of pore structure. A long relaxation time represents large pores, and a short relaxation time represents small pores [18].

**Figure 3.** NMR logging response in different mud environments: (**a**) Water-based mud well A; (**b**) Oil-based mud well B.

Figure 3b is a comprehensive logging diagram of well B measured in the oil-based mud environment. The sandstone unit at interval 4039.0–4062.0 m is also a gas reservoir, but there is an obvious difference in NMR response characteristics from adjacent well A. Due to the influence of oil-based mud filtrate, there is a serious "tailing" phenomenon in the nuclear magnetic resonance *T*<sup>2</sup> spectrum of this horizon. The *T*<sup>2</sup> spectrum demonstrated a bimodal distribution. The *T*<sup>2</sup> value of the second main peak is approximately 1000 ms, and the maximum *T*<sup>2</sup> value is greater than 3000 ms. According to Figure 2c, the volume model of gas-bearing reservoirs in oil-based mud wells and the theoretical distribution of the nuclear magnetic *T*<sup>2</sup> spectrum, the distribution form of the nuclear magnetic *T*<sup>2</sup> spectrum in oil-based mud wells are obviously affected by the oil-based mud filtrate, so it is impossible to directly calculate reservoir petrophysical parameters.

#### *2.2. Classification of Pore Structure Types of Reservoir Rocks*

For the low-porosity and low-permeability reservoirs in the East China Sea, there is significant heterogeneity in the pore structure and lithology, and rocks with different lithologies and pore structures are affected by the invasion of oil-based mud filtrate. Therefore, the shape correction of the nuclear magnetic *T*<sup>2</sup> spectrum under the condition of oil-base mud needs to be based on the difference in the pore structure of the rock, and the morphology correction should be conducted separately for different reservoir rock pore structure types.

Through the observation and analysis of cast thin sections in this area, the pore structure of gas-bearing reservoir rocks can be divided into four categories according to the degree of pore development and connectivity. Figure 4a–d are the cast thin sections of typical plunger cores of reservoir rocks with four types of pore structures (hereinafter referred to as type I–IV rocks). The total porosity and permeability are the physical property test results of plunger cores. Type I rock clastic particles are well sorted, dominated by medium sand, rock pores are relatively developed, and pore connectivity is good. The clastic particles of type II rock are well sorted, dominated by medium sand, and the rock pores are relatively developed, but the connectivity is general. The clastic particles of type III rock are moderately sorted, slightly dominated by medium sand, and the rock pores are poorly developed and unevenly distributed. Type IV rock clastic particles are moderately sorted, slightly dominated by fine sand, poor rock pore development, and poor connectivity.

**Figure 4.** Casting sheet images of four types of rocks: (**a**) Type I (Φ = 13.9%, K = 269 mD); (**b**) Type II (Φ = 10.6%, K = 17.1 mD); (**c**) Type III (Φ = 10.4%, K = 4.9 mD); (**d**) Type IV (Φ = 9.7%, K = 0.45 mD).

Although the total porosity of cores decreases with the deterioration of pore connectivity, it is difficult to distinguish the types of reservoirs by porosity because the total porosity of cores of reservoirs with different pore structure types has little difference. Permeability reflects the seepage capacity of reservoir rocks and is a comprehensive characterization of porosity and pore structure [19]. Especially for reservoir rocks with low porosity and permeability, the permeability is primarily controlled by the pore structure in the rock, and the primary factor affecting the seepage capacity is the pores of different sizes and their matching relationship with the throat [20]. Figure 4 also shows that there are orders of magnitude differences in the permeability of reservoir cores with different pore structure types. Therefore, permeability can be used as the basis for classifying pore structure types. To facilitate the follow-up treatment, the pore structure types were divided according to the order of permeability: the permeability of type I rock is *K* > 100 mD, the permeability of type II rock is 10 mD ≤ *K* < 100 mD, the permeability of type III rock is 1 mD ≤ *K* < 10 mD, and the permeability of type IV rock is *K* < 1 mD. The results of the pore throat radius distribution calculated by the high-pressure mercury injection experiment can verify the feasibility of the pore structure classification standard. Figure 5 shows the pore throat radius distribution of 36 sandstones of four types of rocks divided according to the order of permeability, with obvious differences in pore throat dimensions. The main peak mean values of pore throat radius of type I–IV rocks are 16.13 μm, 4.74 μm, 1.35 μm and 0.55 μm, respectively. Although the main peak and mean values of the pore throat radius of a few cores are quite different, the overall pore throat radius distribution corresponds well with the four types of rocks. In addition, the pore throat radius distribution calculated by

the high-pressure mercury injection experiment also explains the difference between the apparent porosity and total porosity of cast thin sections. For type IV rocks, micropores are relatively developed.

**Figure 5.** Pore-throat size distributions of four types of rocks.

The permeability affects the depth of oil-based mud filtrate invading the formation [21], and the pore fluid of rocks in different permeability formations has their own unique distribution characteristics [22]. Therefore, the *T*<sup>2</sup> spectrum of NMR logging will be significantly different for reservoir rocks with different types of pore structures under the condition of oil-based mud. To compare the difference in *T*<sup>2</sup> spectrum characteristic parameters between oil-based mud wells and water-based mud wells under similar formation physical parameters, this study selected the typical *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging of four types of rocks (Figure 6), and the analysis of characteristic parameters is shown in Table 1. For the *T*<sup>2</sup> spectrum of water-based mud wells, the proportion of spectral area greater than 600 ms is very low. Therefore, the invasion degree of the oil-based mud filtrate can be reflected by counting the proportion of porosity with transverse relaxation times greater than 600 ms. The *T*<sup>2</sup> spectrum of nuclear magnetic resonance logging of type I rocks under different mud conditions had the greatest difference, indicating that for cores with good pore connectivity, the mud filtrate had the strongest change to the original formation fluid. Under the conditions of oil-based mud and water-based mud, the difference in *T*<sup>2</sup> spectrum of type II–IV rocks gradually decreased, indicating that with the deterioration of pore structure, the influence of mud filtrate on the fluid of the original formation gradually decreases, yet the shape of the *T*<sup>2</sup> spectrum still needed to be corrected.

**Figure 6.** Comparisons of *T*<sup>2</sup> spectrum of four types of rocks in different mud environments: (**a**) Type I; (**b**) Type II; (**c**) Type III; (**d**) Type IV.

**Table 1.** *T*<sup>2</sup> spectrum characteristic parameters of four types of rocks in different mud environments.

