Radial inversion method of oil saturation using combined nuclear magnetic resonance and resistivity logging for application to low-resistivity-contrast reservoirs

Abstract

Estimation of oil saturation in low-resistivity-contrast reservoirs using resistivity-log analysis is an inherently challenging process. However, nuclear magnetic resonance (NMR) logging is less sensitive to formation-water salinity and rock matrix variations when predicting fluid properties. Integrating a greater volume of well logging data to effectively address the issue of reservoir parameter calculation represents the trend of big data development. This feature allows NMR logging to have significant advantages over conventional resistivity-based methods in evaluating low-resistivity-contrast reservoirs. The proposed method of estimating oil saturation integrates both NMR and resistivity logging data through two key steps. First, the oil saturation of the invaded zone is estimated using an NMR-based oil saturation model, which has been validated through experimental NMR data obtained from oil-bearing rock samples. Second, the oil saturation of the uninvaded zone is derived by inverting a resistivity-based oil saturation model. Based on analyses of the experimental data and thin sections, the primary reason for low resistivity-contrast in the study area is attributed to the presence of montmorillonite and illite–montmorillonite mixed-layer minerals. The application results demonstrate that the oil saturation calculated using this new method aligns well with both experimental measurements and production test data. Compared to the Archie model that is normally applied in resistivity-contrast reservoirs, the proposed method shows improved accuracy, indicating its effectiveness for such reservoir evaluations.

1 Introduction

Given the developments in exploration and technology, low-resistivity-contrast reservoirs (where the resistivity ratio of the oil reservoir to water reservoir is less than 1 (Ω·m/Ω·m)) have been extensively explored in many petroliferous basins (Iqbal et al., 2019). The depositional features and hydrocarbon accumulation mechanisms of low-resistivity-contrast reservoirs have been studied in recent works (Jianmin and San, 2018; Changxi et al., 2010). Many scholars have proposed that the resistivity values of low-resistivity-contrast reservoirs are significantly affected by clay minerals, low oil saturation, formation water, and complex pore geometry structures (Pratama et al., 2017; Chen et al., 2009; Mashaba and Altermann, 2015).

As the effects of fluids on resistivity-log responses are minimal (Zhang et al., 2013; Feng et al., 2017), oil saturation estimates of low-resistivity-contrast reservoirs using resistivity-based methods may be difficult or even impossible (Qin et al., 2013; Liu et al., 2013). Many methods, including theoretical electrical conductivity models like the Archie model (Archie, 1942), W-S model, dual water model (Waxman and Thomas, 1974; Clavier et al., 1984), and equivalent rock element model (Shang et al., 2004), as well as data analysis methods like forward modeling and big data technology (Xu et al., 2019; Yan et al., 2018) have been explored for the evaluation of oil saturation. However, the accuracies of oil saturation calculated using these resistivity-based methods are insufficient for reservoir evaluation and oil reserve estimation, which are the main topics of research in petroleum geology, reservoir development, and enhanced oil recovery (Mannhardt and Svorstøl, 1999; Liu et al., 2020; Gong et al., 2020).

It is challenging to quantify oil saturation accurately in low-resistivity-contrast reservoirs (Arbab et al., 2017; Lubis et al., 2016; Song et al., 2008). Nuclear magnetic resonance (NMR) logging measurements respond to the presence of hydrogen protons that occur primarily in pore fluids and are less influenced by formation-water salinity or rock matrix properties (Freedman, 2006; Heaton et al., 2004). This feature is a distinct advantage of NMR logging over conventional resistivity analysis methods in low-resistivity-contrast reservoir evaluations (Rima et al., 2012; Hodgkins and Howard, 1999; Liang et al., 2017). However, owing to the shallow detection capabilities of NMR logging, it is necessary to combine NMR with other logging techniques to estimate oil saturation in medium or high-porosity and high-permeability reservoirs. The present work proposes an oil saturation calculation method for low-resistivity-contrast reservoirs by combining NMR logging with resistivity logging and includes two steps. First, the oil saturation of the invaded zones is obtained using the NMR T2 geometric mean time and oil saturation relationship model derived from nuclear magnetic relaxation principles related to pore fluids in water-wet rocks that have been verified by experimental data from NMR tests on oil-bearing rock samples. Second, the oil saturation of the uninvaded zone is inverted in accordance with a rock conductivity model along with variations based on radial distribution patterns. The proposed method was then validated within Nanpu sag by comparing the application results between conventional and low-resistance-contrast reservoirs owing to the higher montmorillonite content along with illite/smectite (I/S) mixed layers. The results indicate that the proposed combined approach significantly enhances accuracy when evaluating these challenging reservoir types.

2 Estimation of oil saturation by combined NMR and resistivity logging for low-resistivity-contrast reservoir

2.1 Oil saturation of invaded zone obtained using the oil-saturation-to-T2-geometric-mean-time relationship model

Water present in the pores of water-wet rocks includes irreducible water in the micropores and free water in the macropores. As the oil enters the pores, it preferentially moves into the macropores and displaces free water. The T2 spectrum of the oil-bearing rock is the superposition of the oil and water spectra. Figure 1 shows the T2 distributions of the oil-bearing and water-saturated rocks.

FIGURE 1

As the NMR T2 spectrum has typical logarithmic distribution characteristics (George et al., 2007; Xu and Torres-Verdín, 2013; Li et al., 2019), the T2 geometric mean time can be used to characterize this spectrum (Fordham et al., 1999; Rios et al., 2014; Christensen et al., 2015). As seen in Figure 1, the T2 value (x-axis) is divided into n parts; since the T2 value is directly proportional to the pore size, the T2 value intervals from 1 to n correspond to pore components from 1 to n.

Assuming that the water and oil spectra are distributed from pore components 1 to n, as shown in Figure 1, the T2 geometric mean time of the oil-bearing rock can be expressed as

where is the irreducible water porosity of pore component i, is the oil porosity of pore component i, is the free water porosity of pore component i, is the total porosity, and is the T2 value of pore component i.

For water-saturated rock, the T2 geometric mean time can be expressed as

where is the free water porosity of pore component i in water-saturated rock.

The ratio of Equation 1 to Equation 2 is then obtained as

According to the definition of the T2 geometric mean time, the corresponding value for the oil spectrum can be defined as

where is the pore volume of oil, and is the T2 geometric mean time of the oil spectrum.

Similarly, the T2 geometric mean times of the irreducible water and free water spectra can be defined as

where is the T2 geometric mean time of the free water spectrum in oil-bearing rock, is the T2 geometric mean time of the free water spectrum in water-saturated rock, and is the T2 geometric mean time of the irreducible water spectrum.

The T2 distribution characteristics observed in the NMR measurements are closely related to the pore structures of the rocks. In high-porosity and high-permeability rocks, the pore structure tends to be relatively simple, and the NMR T2 spectrum of water-saturated rock shows a bimodal structure. Assuming water-wet conditions, the pore fluid components in fully water-saturated rocks can be categorized into bound water and free water, and the peaks in the T2 spectra corresponding to these components satisfy a normal distribution with a single peak. The geometric mean position coincides with both the peak position and arithmetic mean, as dictated by the properties of a normal distribution, as shown in Figure 2.

FIGURE 2

When oil molecules enter the pore space, they primarily displace the free water, thereby reducing its volume without affecting the bound water, as shown in Figure 2. Consequently, the T2 spectral component associated with bound water remains unchanged in both fully water-saturated and oil-bearing rocks. The reduction in free water volume is predominantly reflected by the decreased amplitude of the corresponding T2 spectral peak, with minimal influence on its position. Therefore, the geometric mean values of the T2 spectra for both bound water and free water pores can be approximated as constants, leading to the following relationship: .

Then, the oil saturation can be derived from Equations 3, 4, 5 and Equation 4

When the rock is wetted by water, the oil molecules are at the center of the pores, and the T2 transverse relaxation time of the oil is mainly affected by the bulk relaxation that is related only to the oil viscosity (George et al., 2007) such that is a constant related to oil quality. The rock–oil signal satisfies a normal distribution with a single peak. According to the characteristics of the normal distribution, its geometric mean position is equal to the peak and equal to the arithmetic mean position. Thus, is a constant value, and Equation 6 can be written as

Here, Equation 7 is the T2 geometric mean time relationship model for oil saturation that is similar to the conclusions of previous studies (Wang et al., 2019; Ge et al., 2023), where is the T2 geometric mean time of oil-bearing rock, is the T2 geometric mean time of water-saturated rock, and the regional factor is a constant value.

The T2 spectrum of water-saturated rock is the superposition of the irreducible and free water spectra (Figure 1). The ratio of to can be obtained

According to the definition of the T2 geometric mean time Equation 8, the free water saturation can be obtained

where is the free water saturation, is the T2 geometric mean time of the irreducible water spectrum, and is the T2 geometric mean time of the free water spectrum. Let and be the regional factors.

In water-saturated rock, . Thus, the T2 geometric mean time of the water-saturated rock spectrum Equation 9 can be expressed as

Equation 10 shows that is a function of the irreducible water saturation.

2.2 Resistivity-based inversion method for oil saturation determination in the uninvaded zone

NMR logging often has a shallow depth of investigation and provides results only for the invaded zone, so that the oil saturation of the uninvaded zone needs to be inverted from the resistivity-log analysis.

The pore fluids of the water-saturated rock include clay-bound water, capillary irreducible water, and movable fluids. The formation factors of free water (), capillary irreducible water (), and clay-bound water () are given as (Kurniwan, 2005; Bashiri et al., 2017)

Based on the Archie model and Equation 11, three different water conductive models are derived (Hu et al., 2024; Chen et al., 2025):

where is the measured conductivity of the uninvaded zone; is the volume ratio of movable water in movable fluids; is the porosity of movable fluids; is the porosity of capillary irreducible water; is the porosity of the clay irreducible water; is the saturation factor; , , and are the cementation factors of movable water, capillary irreducible water, and clay irreducible water, respectively; , , and are the conductivities of movable water, capillary irreducible water, and clay irreducible water, respectively.

In Equation 12, can be calculated as

where is the total water saturation and is the total irreducible water saturation.

The differential equation of Equation 12 is given by

We define

such that is the derivative of and is the derivative of in Equation 15.

Figure 3 shows the radial variance of oil saturation simulated using the second-order step response model (Boaca and Boaca, 2018; Gunawan et al., 2011). In Equation 13, is the difference between deep and shallow conductivities (, where is the deep conductivity and is the shallow conductivity; both and can be obtained from resistivity logging), while is the conductivity difference between formation water and mud filtrate (, where is the conductivity of movable water and is the conductivity of mud filtrate).

FIGURE 3

Then, Equation 14 reduces to in the invaded zone can be expressed as

In Equations 16, 17, is the oil saturation of the invaded zone and we have

According to Equation 13 and Equation 18, the oil saturation can be expressed as

where is the oil saturation in the uninvaded zone.

From Equations 7, 15, and 19, the oil saturation of the uninvaded zone can be calculated. Here, and can be obtained from resistivity logging, while , , and can be obtained from NMR logging analysis. The other parameters n, , , , , , , and are regional constants and can be determined from petrophysical experiments. Typically, .

3 Validation and application

The study area is located in the first member of the Dongying Formation (Ed1) within the Nanpu Sag, which is situated in the northeastern Huanghua Depression of the Bohai Bay Basin (Lai et al., 2019). The reservoir primarily consists of fine-to-medium sandstone, with minor amounts of siltstone, coarse sandstone, and pebbly unequal-grain sandstone as well as a carbonate content of less than 4%. The clay volume ranges from 2% to 30%, and the clay minerals are dominated by montmorillonite and I/S mixed layer that account for nearly 62% of the total clay fraction (illite: 13%; kaolinite: 20%).

3.1 Verification of the oil-saturation-to-T2-geometric-mean-time relationship model

In this work, 49 sandstone samples collected from five boreholes were selected from the sandstone reservoir of the Dongying Formation in Nanpu Sag. The sandstone samples showed high porosity (porosity range: 0.04–0.31 v/v; average porosity: 0.17 v/v) and high permeability (permeability range: 0.01–1819 mD; average permeability: 141 mD), as shown in Table 1. The tests included two procedures, where all samples were first tested and analyzed for physical properties, followed by NMR experiments under water-saturated and partially water-saturated conditions. All samples were shaped into cylinders of diameter 2.5 cm and length 4.9 (±0.2) cm; then, they were washed with dichloromethane and distilled water before being dried. The sample porosity was determined using the Porerm-200 instrument through helium injection, and the permeability was measured by the STY-2 gas permeability tester using helium as the carrier gas. The irreducible water saturation (S_irr) was determined using a centrifuge with 150 psi of pressure. The T2 spectra were measured using the MARAN-II equipment operated at 35°C with a resonance frequency of 2 MHz, waiting time of 6,000 ms, echo spacing of 0.2 ms, and number equal to 128. The T_2cutoff value was determined by comparing the T2 spectra obtained from fully and partially water-saturated core samples. The T_2LM value is the geometric mean of the relaxation spectrum, as shown in Table 1.

Next, 18 sandstone samples collected from two boreholes were selected from the sandstone reservoir of the Dongying Formation in Nanpu Sag. Among these, six samples were selected from the water layer under the water-saturated state, and the remaining 12 samples were selected from the oil layer under the oil-bearing state. All 18 rock samples underwent NMR experiments, where the tests included three procedures: first, all samples were tested and analyzed for their physical properties; second, all rock samples underwent NMR experiments; third, the oil-phase T2 spectra signals were obtained by submerging the samples in MnCl₂ solution. Since Mn²⁺ is insoluble in oil but soluble in water and acts as a paramagnetic relaxation agent, this process selectively eliminates water signals and allows isolation of the oil spectra. Table 2 summarizes the experimental data for all 18 samples. Figure 4A displays the NMR T2 spectra of the water-saturated rock samples, and Figure 4B shows the corresponding spectra for the oil-bearing rock samples. In Figure 4B, the solid lines represent the T2 spectra of the 12 oil-bearing rocks, and the dotted lines indicate the corresponding oil-phase NMR signals.

FIGURE 4

To verify the relationship between and irreducible water saturation (Equation 10), as shown in Figure 5, the expression used was

FIGURE 5

Figure 5 shows the relationship model Equation 20, for which the goodness of fit is 0.88878.

The NMR experimental data from the 18 sealed sandstone samples were used to validate the oil saturation versus T2 geometric mean time relationship model (Equation 7). Using Equation 7 and Equation 10, the relationship between the experimental oil saturation and is determined, as shown in Figure 6. The corresponding relationship model is

FIGURE 6

The goodness of fit for this model Equation 21 is R = 0.92014, and the results show that the coefficient k is approximately 1.2038 in the study area.

3.2 Case analyses in high- and low-resistivity-contrast reservoirs

To validate the oil saturation estimation method integrating NMR and resistivity logging data, we conducted comparative analyses wells NPX49 (high-resistivity-contrast reservoir) and XX16 (low-resistivity-contrast reservoir) of the Dongying Formation in Nanpu Sag. The corresponding results are presented in Figures 7, 8, and the detailed acquisition parameters are provided in Table 3. Both wells were configured for the D9TWE3 NMR logging mode as follows: Group A: TW_l = 12.988 s, TE_s = 0.9 ms, and 500 echoes; Group B: TW_s = 1 s, TE_s = 0.9 ms, and 500 echoes; Group C: TW_c = 0.02 s, TE_c = 0.6 ms, and 20 echoes; Group D: TW_l = 12.988 s, TE_l = 3.6 ms, and 125 echoes; Group E: TW_s = 1 s, TE_l = 3.6 ms, and 125 echoes.

FIGURE 7

FIGURE 8

In Figures 7, 8, the tracks 1–12 include conventional well logs, dual-TE T2 spectra, NMR-logging-based clay-bound water saturation, NMR-logging-based capillary-bound water saturation, NMR-logging-based movable water saturation, NMR-logging-based permeability, T2 geometric mean time, calculated oil saturation of the invaded zone from NMR logging, calculated irreducible water saturation from NMR logging, calculated oil saturation of the uninvaded zone by the proposed method, and calculated water saturation of the uninvaded zone by the Archie equation and layer number.

Figure 7 presents the application results for well NPX49 (layers 1–4). The distributions of both long-TE and short-TE T2 spectra narrow progressively from layers 1 to 4. Both the resistivity logging and NMR T2 spectra indicate gradual decrease in oil saturation from layers 1 to 4. In layer 1, the clay content (0.04 v/v) has negligible influence on the measured resistivity. The calculated errors are less than 2% between the results of the experimental oil saturation and proposed methods as well as the experimental oil saturation method and Archie model. This demonstrates that both the proposed method and Archie model can accurately determine oil saturation in conventional reservoirs. Layer 1 exhibits a daily oil production of 14 m³ with no water production.

Figure 8 shows the application results for well XX16 (layers 1–3). The drilling mud resistivity was 0.15 Ω·m at 18°C, and the regional parameters were n = 1.78, = 1.66, , , , and , as well as that was calculated based on the mud resistivity, reservoir depth, and geothermal gradient. It is seen that the distributions of the long-TE and short-TE T2 spectra of layer 1 have wide ranges, indicating the presence of oil; the corresponding distributions for layer 2 have narrow ranges, indicating the absence of oil. The calculated oil saturation values of layers 1 and 2 based on the new method are in good agreement with the experimental oil saturation values (errors less than 3%). Figure 9 shows a thin-section micrograph of layer 1 in well XX16 depicting that the I/S mixed layer has filled intergranular pores. As the high cation exchange capacity (Qv) caused by the high content of the I/S mixed layer cannot be accurately characterized by the Archie model, the oil saturation value calculated using the Archie model is contrary to the reservoir oiliness. The daily oil production of layer 1 is 8 m³ without water.

FIGURE 9

In Figures 7, 8, the tracks from left to right are as follows: tracks 1–4: natural gamma-ray logging (GR: GAPI)/spontaneous potential logging (SP:MV), depth (m), apparent resistivity logs (RLLD/RLLS: Ω·m), acoustic wave slowness logs (AC: µs/m)/bulk density (DEN: g/cm³)/neutron porosity (CNL: %); track 5: NMR logging T2 spectra measured with parameters TE = 0.9 ms and TW = 12,988 ms (NMR.TA: ms); track 6: NMR logging T2 spectra measured with parameters TE = 3.6 ms and TW = 12,988 ms (NMR.TB: ms); track 7: clay-bound water saturation computed from NMR logging (PWC: v/v)/capillary-bound water saturation computed from NMR logging (PWI: v/v)/movable water saturation (POR: v/v) computed from NMR logging/experimental porosity of the rock samples (CORE.POR: v/v); track 8: permeability calculated from NMR logging (NMR.PERM: mD)/experimental permeability of the rock samples (CORE.PERM: mD); track 9: T2 geometric mean time of NMR.TA (T_2LM: ms)/T2 geometric mean time of the water-saturated rock (T_2LM,sw: ms); track 10: oil saturation of the invaded zone computed by NMR (SOH: v/v)/irreducible water saturation of the invaded zone computed by NMR (SWIR: v/v)/experimental irreducible water saturation of the rock samples (CORE.SWIR: v/v); track 11: Archie-model-based water saturation of the uninvaded zone (ARCHIE.SW: v/v)/experimental oil saturation of the rock samples (CORE.SO: v/v); track 12: oil saturation of the uninvaded zone calculated using the new method (NEW.SO: v/v)/experimental oil saturation of the rock samples (CORE.SO: v/v); track 13: layer number.

4 Discussion and future work

4.1 Factor analysis causing low-resistivity-contrast reservoir

Figure 7 shows a resistivity ratio of 3.7 (Ω·m/Ω·m) between layers 1 (oil layer) and 4 (water layer), indicating a high-resistivity-contrast reservoir, with the clay volume of layer 1 in Figure 7 being 0.02 v/v. Figure 8 demonstrates a resistivity ratio of 0.75 (Ω·m/Ω·m) between layers 1 (oil layer) and 2 (water layer), characteristic of a low-resistivity-contrast reservoir, with the clay volume of layer 1 in Figure 8 being 0.12 v/v.

Due Owing to the extremely high Qv of the montmorillonite and I/S mixed layer, as documented in Table 4, the rock resistivity is lower than those observed in conventional reservoirs with equivalent oil saturation. Figure 10A illustrates the experimental relationship between Qv and resistance increase rate. Figure 10B demonstrates the correlation between Qv and clay content. Figure 10C quantifies the relationship between Qv and the combined content of the montmorillonite and I/S mixed layer. Collectively, Figure 10 reveals (1) an inverse proportionality between the resistance increase rate and Qv as well as (2) a direct proportionality between the clay content and Qv, particularly for the montmorillonite and I/S mixed layer. This indicates that the low resistivity-contrast in the study area is a result of the high contents of montmorillonite and the I/S mixed layer minerals (Saidian et al., 2016).

FIGURE 10

4.2 Factor analysis causing the calculation errors

The application results reveal that the oil saturation values calculated by the new method show good agreement with those from the Archie model in conventional reservoirs; furthermore, the new method provides more accurate oil saturation calculations than the Archie model in low-resistivity-contrast reservoirs. This difference is attributable to two key factors. First, compared with conventional reservoirs, low-resistivity-contrast reservoirs exhibit wider variation ranges for both formation factor and resistivity index under the Archie model (Al Gathe, 2009); in the proposed model, the value of the formation factor m has been eliminated, thereby eliminating its influence on the oil saturation calculation caused by the wide range of formation factors in low-resistivity-contrast oil layers. Second, the complex pore structures and mineral compositions in low-resistivity-contrast reservoirs reduce the sensitivity of the resistivity-log responses to pore fluids, consequently decreasing the calculation accuracy of the Archie model. Although a larger number of parameters are required by the proposed method than the Archie model, in addition to its greater complexity in practical applications, the new method effectively overcomes the problem of calculation errors in low-contrast reservoirs caused by the Archie model.

In Figure 7, at the middle depth of layers 1–4, the oil saturation calculated by the new method is consistent with that obtained with the Archie model. However, at the upper and lower edge depths of the reservoir, the curve-shaped results produced by the new method and Archie model are quite different; the depth distribution range of oil saturation calculated using the new method is wider, while that of the Archie model is narrower. This is attributable to the fact that when a sandstone reservoir approaches the upper and lower surrounding rocks (shale), the clay volume usually increases and eventually graduates into shale. An increase in clay volume usually leads to a decrease in the value of the formation factor m; in the Archie model, the formation factor m has a fixed value, which results in a rapid decrease in the calculated oil saturation and a narrow depth distribution range of the result. However, the proposed method eliminates the influence of the formation factor m such that the calculation result is more reasonable.

The sources of calculation errors in the proposed method may be as follows: ① Errors from the regional parameters determined using the experimental data, such as n, , , and k. ② Environmental effects on the log data. ③ Errors from invaded oil saturation calculated via NMR logging. ④ Errors caused by the step response model when simulating actual mud invasion.

4.3 Further research

5 Conclusion

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