Classification Method and Application of Carbonate Reservoir Based on Nuclear Magnetic Resonance Logging Data: Taking the Asmari Formation of the M Oilfield as an Example

Abstract

The strong heterogeneity of carbonate reservoirs poses significant technical challenges in reservoir classification and permeability evaluation. This study proposes a new method for reservoir classification based on nuclear magnetic resonance (NMR) logging data for the Asmari formation of the Middle East M Oilfield, a carbonate reservoir. By integrating NMR T₂ spectrum characteristic parameters (such as T₂ geometric mean, T_2R35/R50/R65, and pore volume fraction) with principal component analysis (PCA) for dimensionality reduction and an improved slope method, this study achieves fine reservoir type classification. The results are compared with core pressure curves and petrographic pore types. This study reveals that the Asmari reservoir can be divided into four categories (RT1 to RT4). RT1 reservoirs are characterized by large pore throats (maximum pore throat radius >3.8 μm), low displacement pressure (<0.2 MPa), and high permeability (average 22.16 mD), corresponding to a pore structure dominated by intergranular dissolution pores. RT4 reservoirs, on the other hand, exhibit small pore throats (<1 μm), high displacement pressure (>0.7 MPa), and low permeability (0.66 mD) and are primarily composed of dense dolostone or limestone. The classification results show good consistency with capillary pressure curves and petrographic pore types, and the pore–permeability relationships of each reservoir type have significantly higher fitting goodness (R² = 0.48~0.68) compared with the unclassified model (R² = 0.24). In the new well application, the root mean square error (RMSE) of permeability prediction decreased from 0.34 mD using traditional methods to 0.21 mD, demonstrating the method’s effectiveness. This approach does not rely on a large number of mercury injection experiments and can achieve reservoir classification solely through NMR logging. It provides a scalable technological paradigm for permeability prediction and development scheme optimization of highly heterogeneous carbonate reservoirs, offering valuable references for similar reservoirs worldwide.

1. Introduction

Carbonate reservoirs hold a significant position in global oil and gas resources, particularly those in the Middle East, as these reservoirs possess substantial potential for exploration and development, making them a focal point for global petroleum exploration and exploitation [1,2,3]. Approximately two-thirds of the world’s total oil production originates from the Middle East, with 80% of the oil-bearing reservoirs being carbonate reservoirs [4,5]. However, these reservoirs present numerous technical challenges for exploration and development due to the complexity of their depositional types, their strong heterogeneity, and poor reservoir permeability [6,7,8]. To conduct a more refined study of the flow capabilities in heterogeneous carbonate reservoirs, reservoir classification can be applied to the target oil reservoir. This process, carried out during the reservoir description phase, involves dividing the reservoir into several relatively homogeneous categories in the context of strong heterogeneity. The goal is to study the reservoir’s storage and permeability capabilities and predict the spatial distribution of physical properties, ultimately facilitating more efficient oil and gas reservoir development [9].

For reservoir classification, the ideal outcome is that each category of reservoir reflects similar depositional and diagenetic processes, exhibiting identical pore structures. Under conditions of consistent wettability, these reservoirs should display uniform porosity–permeability relationships, analogous capillary pressure curves, and similar relative permeability distributions [10]. However, in practice, there is no unified classification standard for reservoirs, and many scholars have conducted research in this area. A summary of previous studies on carbonate reservoirs revealed that the earliest differentiation method was based on geological sub-layers [11]. However, in practical application, it became evident that while this method is simple, it lacks specificity and fails to address the heterogeneity of the reservoirs [12]. Additionally, core coverage is often insufficient to cover all stratigraphic layers. Similarly, attempts to classify reservoirs based on lithology have been made, but these models fail to resolve the heterogeneity issue [13]. For example, in the case of the Mishrif formation in the Middle East, despite being a pure pore-type limestone reservoir, extensive research shows that its heterogeneity is extremely high [9,14]. Lithology-based classification methods are therefore not applicable. Based on subsequent research findings, commonly used methods can be categorized into three main types: geological, petrophysical, and production dynamic methods [10]. Geological methods typically combine depositional environment and diagenetic processes, classifying rocks based on geological factors such as carbonate composition or structural genesis [15]. Petrophysical methods, on the other hand, rely on core experimental data, such as physical parameters like porosity and permeability or capillary pressure curve parameters obtained from mercury injection experiments, to extract petrophysical characteristics as the basis for classification [16,17]. Production dynamic methods use production dynamic parameters such as oil and gas production development data as the classification basis. Regarding these methods, geological approaches involve numerous categories, making it difficult to establish corresponding log response characteristics, thus limiting direct application in actual development [18,19]. As for dynamic reservoir parameters, while they can identify macroscopic flow units, they fail to reveal microscopic features and cannot ensure that the extracted dynamic parameters are unaffected by engineering factors.

The prevailing methods in this field remain those based on rock physics, which can be broadly classified into two categories. The first category involves classification based on pore throat radius, where specific pore throat radii or combinations thereof corresponding to distinct features of the mercury injection capillary pressure (MICP) curves are used as classification parameters [20,21]. For instance, the Swanson parameter, derived from the inflection point of the capillary pressure curve in a double logarithmic plot, serves as a key parameter for classification [22]. Alternatively, the pore throat radius corresponding to specific cumulative saturations on the MICP curve, such as R₃₅ at a cumulative saturation of 35%, can also be used for classification [23]. Among these methods, the Winland R₃₅ has been particularly influential and is widely applied in the classification of carbonate reservoirs. The second category involves the use of the flow zone indicator (FZI) or rock quality index (RQI) as classification criteria to identify rock types with similar permeability–pore relationships [24,25]. This approach was first proposed by Amaefule in 1993 [26], and as one of the classical methods, it has been continuously refined through numerous subsequent studies [25,27,28]. Despite the theoretical innovations introduced in these updates, both method categories share a common challenge: difficulty in representing the model parameters using logging data, thereby limiting their widespread applicability. In practical applications, these methods perform well for reservoirs with similar capillary pressure curves, such as clastic rocks and relatively homogeneous carbonate reservoirs [29]. However, for carbonate reservoirs exhibiting strong heterogeneity and complex capillary pressure curves, which contain multiple pore types, including micropores and cavities, with multiple modes of pore throat radii, these methods are no longer applicable [30].

To address this issue while considering the generalizability of reservoir classification methods, this study proposes a novel approach using nuclear magnetic resonance (NMR) logging phases for the classification of carbonate reservoir types. First, given that NMR logging data can finely describe the pore space characteristics of reservoirs, multiple parameters are extracted from the T₂ distribution of NMR data. A combination of principal component analysis and the improved rolling stone method is employed to classify new NMR logging phases as the basis for reservoir classification. Additionally, the rock physics and geological interpretations of these phases are provided based on core experimental data. The study also presents the porosity–permeability relationships for each reservoir type derived from the phase classification results. This method is applied to carbonate reservoirs in the Asmari formation in the Middle East, offering a novel, generalizable approach for classifying reservoir types and calculating permeability in the Asmari formation. The proposed method holds significant practical geological and engineering value for the study area.

2. Geological Survey and Core Data Analysis

2.1. Geological Survey of the Study Area

The study area is the M Oilfield in the Middle East, located across the southeastern part of Iraq and the southern side of the Iran–Iraq border. The reservoir core is composed of the Paleogene Asmari formation carbonate strata. From a structural background analysis, the oilfield is situated in the transitional zone between the northern Persian Gulf Basin’s Mesopotamian Basin and the Zagros Foreland Basin [31]. Its formation and evolution are directly controlled by the Zagros Orogeny, caused by the collision of the Eurasian plate and the African–Arabian plates. The structural morphology within the block is dominated by an asymmetric, narrow anticline trending northwest–southeast. The central region features a normal fault system aligned in the same northwest–southeast direction, while the western part is primarily characterized by a strike-slip fault system [32,33]. This study focuses on the reservoir of the Asmari formation in the M Oilfield.

2.2. Core Data Analysis

The analysis of core data from the Asmari formation in the M Oilfield shows several key findings, as depicted in Figure 1, which presents the porosity and permeability cross plot for the core samples. It should be noted that the porosity and permeability data from the core experiments were subjected to overburden correction. Figure 1 illustrates that the porosity distribution of the target layer ranges from 0.1% to 30%, with the majority of values concentrated between 3% and 20%. The average porosity is 12.87%. As for the permeability, it spans from 0.012 mD to 1000 mD, with the majority of values concentrated between 0.1 mD and 10 mD. The average permeability is 88.51 mD. Additionally, the Asmari formation reservoir exhibits strong heterogeneity, as evidenced by the fact that the permeability corresponding to a given porosity can vary by up to three orders of magnitude.

An analysis of the lithology and pore space characteristics of the target reservoir was conducted using core X-ray diffraction (XRD) experimental data and cast thin section data. Figure 2 shows the mineral composition and distribution obtained from the core XRD data. The core data reveal that the target formation is predominantly composed of siliceous clastic sediments and carbonate sediments, with lithologies primarily consisting of bioclastic limestone, mudstone–dolomite limestone, and dolomite. Locally, small amounts of gypsum and sandstone–mudstone are also present. Regarding the core cast thin section data, the types and quantities of pore structures were statistically analyzed. Figure 3 showcases representative images of core cast thin sections. Figure 3a displays intercrystalline pores in dolomite, Figure 3b illustrates the development of solution pores, Figure 3c shows the coexistence of intergranular and solution pores, and Figure 3d highlights the presence of intercrystalline pores, biocavity pores, and minor fractures.

Figure 4 shows a histogram of the statistical analysis of pore structure types. The data indicate that the Asmari formation in the study area is primarily characterized by intercrystalline pores in dolomite and solution pores, with a small number of fractures also developed. Combined with the actual stratigraphic distribution, it is observed that the lithology in Area A of the study region is predominantly dolomite, with the development of both primary and secondary pores as well as fractures. In contrast, Area B is composed of a mixture of dolomite, limestone, and sandstone, with fractures and microfractures developed within the dolomite and limestone. The presence of sandstone significantly enhances the porosity of the reservoir.

In summary, the Asmari formation in the M oil field exhibits complex lithology, primarily composed of carbonate rocks with a small amount of sandstone. The pore structure types are diverse, resulting in a complex relationship between core porosity and permeability. All core experimental data indicate strong heterogeneity within this reservoir section, necessitating a reasonable classification of reservoir types in order to evaluate key parameters such as permeability.

3. Methods

3.1. The Principle of Nuclear Magnetic Resonance Logging and T₂ Spectrum Parameter Extraction

NMR is a physical phenomenon where the magnetic moment of atomic nuclei, induced by their spin, interacts with an external magnetic field. Under the influence of an alternating magnetic field, nuclei absorb electromagnetic waves at specific frequencies, causing transitions from lower to higher energy levels. In NMR, relaxation is a key physical quantity, referring to the process by which the magnetization vector, after being excited by a radio frequency field, returns to its equilibrium state from a displaced state. In rock physics, the relaxation rate is influenced by the physical properties of the rock and the characteristics of the fluids. The transverse relaxation time (T₂) is commonly used to analyze the pore structure of rocks [34].

In the water-saturated state of rock samples, the distribution of the T₂ spectrum can effectively reflect the heterogeneity of pore sizes: short relaxation times correspond to small pores, while long relaxation times are associated with larger pores. Through spectral analysis, the pore volume distribution can be quantitatively obtained, providing key insights for reservoir evaluation. The transverse relaxation time can be expressed as follows:

$${\displaystyle \frac{1}{T_2}}={\displaystyle \frac{1}{T_{2S}}}+{\displaystyle \frac{1}{T_{2B}}}+{\displaystyle \frac{1}{T_{2D}}}$$

(1)

In Equation (1), T_2s, T_2B, and T_2D correspond to the surface relaxation time, bulk relaxation time, and diffusion relaxation time of the rock, respectively, with units in milliseconds (ms).

In rock physics, for a uniform magnetic field with smaller echo signals, the rock’s bulk relaxation time and diffusion relaxation time can be neglected. Therefore, Equation (1) can be written as follows:

$${\displaystyle \frac{1}{T_2}}={\rho }_2\left({\displaystyle \frac{S}{V}}\right)=F_S{\displaystyle \frac{{\rho }_2}{R_{\mathrm{C}}}}$$

(2)

In Equation (2), ${\rho }_2$ represents the transverse surface relaxation intensity of the rock, with units in μm/ms; S is the pore surface area, with units in μm²; V is the pore volume, with units in μm³; $F_S$ is the geometric shape factor, which is dimensionless; and Rc corresponds to the pore radius, with units in μm.

Considering that NMR logging data are widely available in the study area, NMR logging, which detects reservoirs by applying an external magnetic field to the hydrogen nuclei in the formation, is almost unaffected by the rock framework. The NMR transverse relaxation spectrum obtained through multi-exponential inversion fitting of the echo series from the relaxation phenomena can accurately reflect the distribution of hydrogen-bearing fluids inside the rock. The normal probability curve can effectively characterize the pore throat size and distribution in the capillary pressure curve and the NMR T₂ spectrum. Therefore, the graphical features of the normal distribution can be used to analyze the NMR T₂ spectrum and the cumulative porosity. By quantifying the relaxation times and pore components in the NMR T₂ spectrum and extracting the graphical features from the T₂ NMR spectrum and the mathematical feature parameters from the normal probability distribution, it is possible to obtain a wealth of derived parameters that can quantitatively characterize the reservoir pore size, pore connectivity, and pore distribution. This can be used to quantify the rock pore throat size and distribution. Figure 5 shows a schematic diagram of the T₂ spectrum.

Various parameters are included in the schematic diagram of the T₂ spectrum in Figure 5, e.g., the geometric mean of T₂, BVI corresponding to bound fluid pores, FFV corresponding to movable fluid pores, and others. These parameters primarily reflect the microscopic pore structure characteristics of the rock. Related parameters such as T_2R35, T_2R50, and T_2R65 are extracted based on the pore component cumulative curve from the T₂ spectrum. These parameters can reflect the pore size, with the three values representing the transverse relaxation time when the cumulative nuclear magnetic pore component reaches 35%, 50%, and 65%, respectively. S₁, S₂, and S₃ are also shown in Figure 5, which in previous sandstone reservoirs represent clay-bound, capillary-bound, and movable fluids, respectively. The T₂ cutoff values are determined by two sets of T₂ cutoff values, but in carbonate reservoirs, the selection of T₂ cutoff values is not particularly standardized in the industry. Given the previous research literature [6,9] and considering that the actual results show that the T₂ cutoff values in carbonate rocks are highly variable, ranging from 30 ms to 100 ms, the cutoff values of 3 ms and 92 ms are set as the cutoff values for defining the T₂ cutoff values of S₁, S₂, and S₃, respectively. It should also be noted that the study used microporous, mesoporous, and macroporous to describe the parameters when defining them. S1 represents the proportion of small-sized pore components in the total nuclear magnetic porosity, referring to pores with relaxation times ranging from 0 to 3 ms. S₂ represents the percentage content of medium-sized pore components in the total porosity; it mainly represents capillary-bound water, typically referring to pores with relaxation times between 3 and 92 ms. S₃ represents the percentage content of large-sized pore components in the total porosity; it mainly represents the pore proportion of movable fluids with relaxation times greater than 92 ms. Certain quantification parameters for pore sorting features, such as sorting coefficient and coefficient of variation, derived from mathematical feature extraction based on the T₂ spectrum, cannot be incorporated into the diagram.

Table 1. Parameter extraction formulas based on nuclear magnetic resonance from the T2 spectrum.

Parameter Name	Calculation Formula
T2 Geometric mean	${({\displaystyle \prod _{i=1}^n{T}_{2i}\times {\varphi }_i})}^{{\displaystyle \frac{1}{{\varphi }_{nmr}}}}$
T2R35	${\displaystyle \frac{{\displaystyle \sum _{j=1}^i{\varphi }_j}}{{\varphi }_{nmr}}}=35\%,T_{2i}$
T2R50	${\displaystyle \frac{{\displaystyle \sum _{j=1}^i{\varphi }_j}}{{\varphi }_{nmr}}}=50\%,T_{2i}$
T2R65	${\displaystyle \frac{{\displaystyle \sum _{j=1}^i{\varphi }_j}}{{\varphi }_{nmr}}}=65\%,T_{2i}$
S2	${\displaystyle \frac{{\displaystyle {\int }_3^{92}{\varphi }_{T_2}d{T}_2}}{{\displaystyle {\int }_{T_{2\min }}^{T_{2\max }}{\varphi }_{T_2}d{T}_2}}}$
S3	${\displaystyle \frac{{\displaystyle {\int }_{92}^{T_{2\max }}{\varphi }_{T_2}d{T}_2}}{{\displaystyle {\int }_{T_{2\min }}^{T_{2\max }}{\varphi }_{T_2}d{T}_2}}}$
Sorting coefficient	${\sigma }_{T_2}=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\varphi }_i{(T_{2i}-\overline{T_2})}^2}}{{\varphi }_{nmr}}}}$
Coefficient of variation	$C={\displaystyle \raisebox{1ex}{${\sigma }_{T_2}$}\!\left/ \!\raisebox{-1ex}{$\overline{T_2}$}\right.}$

${\varphi }_i$ represents the pore fraction at the NMR measurement point i, in percentage; T_2i denotes the relaxation time at NMR point i, in milliseconds (ms); ${\varphi }_{nmr}$ refers to the total NMR porosity, in percentage; n represents the total number of NMR measurement points; T_2min and T_2max correspond to the minimum and maximum relaxation times, in milliseconds, respectively. In some of the calculation methods, the use of a comma indicates a “constraint condition, under which the corresponding value is applied”.

presents the corresponding calculation formulas for the parameters extracted from the T₂ spectrum.

3.2. Reservoir Type Division Method and Principle

The pore structure of a reservoir significantly influences its storage space and the flow channels for fluids. Under consistent conditions, a better pore structure generally correlates with improved production capacity. NMR logging, through the multi-exponential inversion fitting of echo trains based on relaxation phenomena, provides a T₂ spectrum that effectively reflects the distribution of hydrogen-containing fluids within the rock. The parameters in Table 1 represent physically meaningful parameters derived from the T₂ spectrum, which can effectively characterize the reservoir’s pore structure. The geometric mean of T₂ is used to describe the average growth rate of pore fractions in the T₂ spectrum; the sorting coefficient measures the dispersion of T₂ spectrum pore fractions, with smaller values indicating more concentrated pore distributions; the coefficient of variation is a comprehensive parameter for evaluating both the distribution and the mean position of the pores. In the same formation, it can be used to assess the quality of the pore structure, with higher values indicating a poorer pore structure. However, it is important to note that there is a correlation between the various extracted feature parameters from the T₂ spectrum, and the excessive use of parameters in reservoir classification can reduce the applicability of the method. Therefore, dimensionality reduction methods are applied to reduce feature dimensions while retaining as much original information as possible.

3.2.1. Principal Component Analysis

Quantitative parameters that can characterize the pore space features are extracted from the T₂ spectrum of NMR. Principal component analysis (PCA) is then applied to reduce feature dimensionality. PCA is a reliable and widely used dimensionality reduction method. This technique reduces high-dimensional data to lower dimensions, transforming multiple indicators into fewer composite indicators with minimal information loss [35]. These composite indicators are called principal components, with each principal component being a linear combination of the original variables. Moreover, the principal components are uncorrelated, making them superior to the original variables in certain aspects.

The main process of performing PCA on the sample set from the study area is as follows:

(1)

The collected sample set is standardized using the Z-score standardization method to eliminate the dimensional influences between the different extracted parameters;

(2)

A correlation coefficient matrix is established between the different variables, and the eigenvalues and eigenvectors of the correlation coefficient matrix are computed;

(3)

The number of principal components is determined based on the variance contribution rate of the selected parameters;

(4)

Finally, the standardized sample set is transformed using the eigenvalues and component matrix of the correlation coefficient matrix, and the principal components are calculated to obtain the final evaluation indicators.

3.2.2. Reservoir Classification Method Based on the Improved Slope Method

Al-Qenae proposed a rock physics reservoir classification method based on the mathematical approach of Winland R₃₅ [36]. His specific approach arranges the R₃₅ parameter in ascending order and plots it on a semi-logarithmic scale, where the x-axis represents the R₃₅ value (logarithmic scale), and the y-axis represents the sequence number (linear scale). Different slopes represent different pore structures, which are then used to classify various reservoir types. Based on this idea, this study replaces the R₃₅ parameter with the derived parameters from the T₂ spectrum, which are the evaluation indicators obtained after performing principal component analysis. Additionally, considering the strong heterogeneity of actual reservoirs and the complexity of the pore structures, it becomes difficult to effectively identify inflection points.

To address the aforementioned issue, this study improves upon the original method. The x-axis of the original slope method is replaced with the reciprocal of the difference between the later and earlier terms of the evaluation indicator. This has mathematical significance when performing differentiation on the indicator (Figure 6). At the same time, considering the large number of evaluation indicators and the excessively sharp variations in the computed curves, an interpolation method is applied to preserve the shape of the ascending curve. The curve is interpolated, and the derivative of the interpolated curve sequence is calculated. The computed curve is then subjected to filtering interpolation to prevent excessively abrupt changes. A cubic spline interpolation function is used for filtering interpolation, which, compared with other interpolation functions, has the advantage of ensuring the smoothness of the curve (Figure 7) and eliminating large-scale curvature mutations. Finally, different reservoir types are determined based on the change interval of the filtered curve.

In summary, the new reservoir classification involves deriving new evaluation indicators from the T₂ spectrum after performing principal component dimensionality reduction. These indicators are then arranged in ascending order, and interpolation is used to reduce the number of original sample points while preserving the shape of the original curve. The reciprocal of the difference between the later and earlier terms is calculated to obtain a new curve. After applying cubic spline interpolation to the new curve, points where the slope changes are selected as the markers for reservoir type classification. In this study, the criterion for selecting slope mutation points to divide the reservoir types is based on the n standard points with the largest slopes. This allows the reservoir to be classified into n + 1 types. In theory, each inflection point of the slope can be considered a change node for reservoir types. However, using all inflection points would result in an excessively large number of reservoir types. Therefore, in this study, the reservoirs in the target area are divided into four classes by selecting the first three points with the most significant slope changes.

4. Reservoir Type Division Results and Rock Physical Significance

4.1. Reservoir Type Classification Results

Based on the method’s principles, PCA dimensionality reduction is first applied to the T₂ spectrum-derived parameters. Figure 8 shows the corresponding scree plot. Combining it with the principal component analysis table (

Table 2. Principal component analysis table.

Component	Grand Total	Variance Proportion	Accumulation, %
1	5.348	67.969	67.969
2	1.410	17.630	85.598

) shows that the first two principal components after dimensionality reduction account for 85.598% of the total information in the original data. This variance contribution rate indicates that the majority of the valid information from the selected sample set in the study area can be retained through principal components Y1 and Y2.

Table 3. Table of the proportion coefficients of the original parameters in each principal component of the two groups of principal components.

Parameter Name	Coefficient (Component 1)	Coefficient (Component 2)
T2 Geometric mean	0.969	0.075
$T_{2R_{50}}$	0.954	0.042
$T_{2R_{35}}$	0.937	−0.005
$T_{2R_{65}}$	0.934	0.082
S3, %	0.901	−0.104
S2, %	−0.872	0.093
Sorting coefficient	0.360	0.829
Coefficient of variation	−0.372	0.830

presents the component matrix from the principal component analysis, which details the specific composition of the two principal components. Analysis of Table 3 shows that principal component Y1 primarily consists of the first six parameters, excluding the sorting coefficient and variation coefficient. These parameters mainly reflect the pore size and the proportion of pore intervals in reservoir rocks, meaning that principal component Y1 mainly characterizes the pore structure of the reservoir rock. On the other hand, principal component Y2 has significantly lower values for the first six coefficients that represent pore size and pore interval proportion, and is mainly composed of the sorting coefficient and variation coefficient, which reflect the sorting characteristics of the pores. Thus, the principal component Y2 primarily characterizes the morphological features of the NMR relaxation spectrum.

By using the principal component analysis matrix and the variance contribution rate table, the specific calculation formulas for principal component 1 (Y1) and principal component 2 (Y2) are derived as follows:

$$\begin{array}{l}{Y}_1=\\ {\displaystyle \frac{0.969}{\sqrt{5.348}}}\times T_{2GM}+{\displaystyle \frac{0.954}{\sqrt{5.348}}}\times T_{2R_{50}}+{\displaystyle \frac{0.937}{\sqrt{5.348}}}\times T_{2R_{35}}+{\displaystyle \frac{0.934}{\sqrt{5.348}}}\times T_{2R_{65}}+\\ {\displaystyle \frac{0.901}{\sqrt{5.348}}}\times S_3-{\displaystyle \frac{0.872}{\sqrt{5.348}}}\times S_2+{\displaystyle \frac{0.360}{\sqrt{5.348}}}\times {\sigma }_{T_2}-{\displaystyle \frac{0.372}{\sqrt{5.348}}}\times C\end{array}$$

(3)

$$\begin{array}{l}{Y}_2=\\ {\displaystyle \frac{0.075}{\sqrt{1.410}}}\times T_{2GM}+{\displaystyle \frac{0.042}{\sqrt{1.410}}}\times T_{2R_{50}}-{\displaystyle \frac{0.005}{\sqrt{1.410}}}\times T_{2R_{35}}+{\displaystyle \frac{0.082}{\sqrt{1.410}}}\times T_{2R_{65}}-\\ {\displaystyle \frac{0.104}{\sqrt{1.410}}}\times S_3+{\displaystyle \frac{0.093}{\sqrt{1.410}}}\times S_2+{\displaystyle \frac{0.829}{\sqrt{1.410}}}\times {\sigma }_{T_2}+{\displaystyle \frac{0.830}{\sqrt{1.410}}}\times C\end{array}$$

(4)

After determining the expressions for the two principal components, the comprehensive evaluation index can be written based on the variance percentages as follows:

$$Y=0.67969Y_1+0.17630Y_2$$

(5)

Equation (5) serves as the evaluation criterion in this study. Based on this new metric, a classification method is employed to categorize reservoir types. Given that the focus of this research is carbonate reservoirs, data from the sandstone sections were excluded. The new metric derived from the carbonate data was then ordered and interpolated (Figure 9a). The reciprocal difference between subsequent and preceding values was calculated (Figure 9b), and the curve was smoothed through cubic interpolation to identify the inflection points. It is important to note that, due to the complex and diverse pore structures of the reservoirs, if each inflection point were to be used as a basis for classification, an excessive number of reservoir types would result. Therefore, three points with the most significant changes in slope were selected as inflection points (Figure 9c). Consequently, the carbonate reservoirs were divided into four categories: Reservoir Type 1 (RT1), Reservoir Type 2 (RT2), Reservoir Type 3 (RT3), and Reservoir Type 4 (RT4).

Table 4. The range of the reservoir type division index of this method.

Reservoir Type	Index Range (Y)
RT1	Y > 9.7
RT2	1.24 < Y ≤ 9.7
RT3	0.28 < Y ≤ 1.24
RT4	Y ≤ 0.28

presents the boundary values of the indicators for each reservoir type.

4.2. Reservoir Characteristics and Petrophysical Significance

After categorizing the reservoir types using the method outlined in this study, the characteristics and petrophysical significance of each reservoir type were determined. From the perspective of the indicator itself, a higher value indicates a larger T₂ geometric mean, a higher proportion of macropores, and better sorting. In other words, as the evaluation indicator decreases, the pore throat sizes of the reservoirs become smaller, and their permeability deteriorates. This conclusion was validated using core experimental data.

For the RT1 reservoir, the capillary pressure curve is located at the bottom of the graph (Figure 10a). This type of sample represents the reservoir with the best pore structure, exhibiting excellent petrophysical properties, with an average porosity of 15.1% and an average permeability of 22.16 mD. In terms of pore structure parameters, the maximum throat radius is greater than 3.8 μm, with an average of 11.79 μm. The displacement pressure is less than 0.2 MPa, with an average value of 0.10 MPa, which is smaller than other reservoir types. The pore throat distribution frequency shows a multimodal pattern, with 3–4 peak values, and the coarsest throat typically falls within the 3–8 μm range (Figure 10b). The pore types in this sample are relatively simple (Figure 10c), primarily consisting of intergranular solution pores.

For the RT2 reservoir, the capillary pressure curve exhibits a relatively steep plateau section (Figure 10d). The average porosity of the reservoir is 9.53%, with an average permeability of 6.61 mD. The maximum throat radius ranges from 1.5 to 3.8 μm, with an average of 3.06 μm. The displacement pressure ranges from 0.2 to 0.45 MPa, with an average of 0.29 MPa. The pore throat distribution frequency shows a bimodal pattern, with the primary focus on the region corresponding to the smaller throats in the post-peak value range. The first peak occurs at values greater than 1 μm, while the second peak is located at 0.7 μm (Figure 10e). The pore types in this sample are diverse, including dolomite intergranular pores, intergranular solution pores, biogenic cavity pores, and microfractures (Figure 10f).

For the RT3 reservoir, compared with RT2, the capillary pressure curve exhibits a much flatter plateau section (Figure 10g). The average porosity of the reservoir is 14.52%, with an average permeability of 1.31 mD. The maximum throat radius ranges from 1 to 1.5 μm, with an average of 1.17 μm. The displacement pressure ranges from 0.45 to 0.7 MPa, with an average of 0.64 MPa (Figure 10h). This reservoir type, compared with RT2, has a higher porosity but a significantly lower permeability, increased displacement pressure, and decreased maximum throat radius, sorting coefficient, and variation coefficient. Its pore structure is poorer than that of RT2. The pore throat distribution frequency follows a unimodal pattern, with the majority concentrated at around 0.7 μm. The primary pore types are dolomite intergranular pores and a small amount of intergranular solution pores (Figure 10i).

For the RT4 reservoir, the capillary pressure curve is positioned at the uppermost part of the figure (Figure 10j), with an average porosity of 8.40% and an average permeability of 0.66 mD. The maximum pore throat radius is less than 1 μm, with a mean value of 0.75 μm. The displacement pressure exceeds 0.7 MPa, with a mean of 1.29 MPa (Figure 10k). This reservoir type is characterized by poor physical properties, a small maximum pore throat radius, and high displacement pressure. The pore throat distribution frequency exhibits a unimodal pattern, with a peak frequency lower than that of RT3 and a wider peak distribution interval compared with RT3. In comparison to RT3, the pore throat radius is finer, distributed between 0.2 and 0.7 μm. Pores are poorly developed in such samples, with occasional intercrystalline pores in dolomite and minor microfractures (Figure 10l).

The comparative analysis presented above indicates that as the evaluation parameters decrease, the permeability of the reservoir diminishes correspondingly. This is reflected in both the morphology and distribution of the capillary pressure curves as well as the radius dimensions of the maximum pore throat system. Specifically, from RT1 to RT4 reservoirs, the mercury injection pressure progressively increases, the capillary pressure uplift becomes increasingly gradual, and the maximum pore throat radius steadily diminishes. This typically suggests a continual decline in the reservoir’s permeability. Existing thin section data reveal that RT1 reservoirs are primarily composed of dolomite and arenaceous limestone, RT2 reservoirs are predominantly characterized by magnesian dolomite with some dolomitic limestone, RT3 reservoirs consist mainly of limestone, while RT4 reservoirs are more complex in lithology, exhibiting poor pore development and limited connectivity, and they are characterized by relatively dense dolomite or limestone. It should also be noted that the limited thin-section samples from the Asmari formation in the study area do not provide a definitive representation of the pore space types.

To further elucidate the differences in NMR characteristics across various reservoir types, a more in-depth analysis was conducted by combining the classification results with the T₂ NMR spectrum features. The classification indicator (Y) is derived from two principal components, Y1 and Y2, which are computed based on the T₂ spectrum-derived parameters. Figure 11 presents box plots that illustrate the distribution of four parameters indicative of pore throat characteristics across different reservoir types. Panel 11a shows the variation in the proportion of medium-sized pores. Given the difficulty in accurately determining the T₂ cutoff value for carbonate reservoirs, the assumed cutoff values in this study are 3 ms and 92 ms. This metric can be interpreted as the proportion of capillary-bound fluids. Panel 11b illustrates the variation in the proportion of large pores, representing the pore space where the transverse relaxation time exceeds 92 ms. This can be interpreted as the proportion of movable fluids. In theory, a T₂ spectrum with a greater rightward shift typically reveals a larger pore space and a higher proportion of large pores. Upon examining the box plots of these two indicators, it is evident that, from RT1 to RT4 reservoirs, the proportion of medium-sized pores increases while the proportion of large pores decreases. This trend suggests that, as the flow capacity of the reservoir decreases, the proportion of bound fluids increases, while the proportion of movable fluids decreases. These findings are consistent with core analysis results. For example, the mercury injection data for RT1 reservoirs indicate that this reservoir type has the largest pore throat radii, with the NMR T₂ spectrum predominantly representing large pore components and the highest proportion of movable fluids compared with other reservoir types. Similarly, the proportion of bound fluids in RT1 reservoirs is lower than that of the other reservoir types. Panel 11c illustrates the response of T_2R65 across various reservoir types. T_2R65 corresponds to the transverse relaxation time at which the pore volume in the T₂ spectrum reaches 65%, and it reflects the pore throat size. A larger T_2R65 value indicates that the peak of the corresponding NMR T₂ spectrum shifts toward a longer relaxation time, signifying a larger pore space in the reservoir. Panel 11d shows the T₂ geometric mean, which is the logarithmic average of the T2 relaxation times. A higher T₂ geometric mean typically corresponds to a larger pore throat radius. Figure 11c,d demonstrate that RT1 reservoirs exhibit the largest values for both T_2R65 and the T₂ geometric mean compared with other reservoir types, indicating that RT1 reservoirs have the largest pore spaces. As the permeability of the reservoir decreases, both T_2R65 and the T₂ geometric mean gradually decrease from RT1 to RT4 reservoirs, signifying a reduction in pore space and a gradual decrease in pore throat size.

This section provides an explanation of the core experiments and the classification results of reservoir types based on the NMR T₂ spectra. The study shows that there are significant differences in the permeability of the four reservoir types classified within the Asmari formation carbonate rock in the research area. Moreover, indicator Y used for classification retains most of the information from the NMR T₂ spectra, effectively reflecting the pore structure characteristics and pore throat sizes of the reservoirs.

4.3. Reservoir Permeability Evaluation

Based on the four classified reservoir types, further characterization is conducted by combining core porosity–permeability data. Figure 12 shows the cross-plot of core porosity and core permeability for the study area, illustrating the relationship between porosity and permeability for the four core types.

Table 5. The fitting formulas for core porosity and core permeability under different conditions.

Reservoir-Type	Calculation Formula of Permeability	R2
RT1	$K=4.42\times {\varphi }^{1.01}$	0.48
RT2	$K=31.64\times {\varphi }^{1.19}$	0.62
RT3	$K=367.37\times {\varphi }^{1.59}$	0.57
RT4	$K=8670.2\times {\varphi }^{2.33}$	0.68
Not classified	$K=608.55\times {\varphi }^{2.37}$	0.24

provides the permeability fitting formulas for each reservoir type. It should also be noted that some cores belonging to RT1 or RT2 reservoir types contain fractures. Although the porosity of these cores does not exceed 10%, their permeability is relatively high, and these samples were excluded from the permeability fitting. Analysis of the fitting results reveals that the RT4 reservoir type has the lowest goodness of fit for permeability calculation, with a value of 0.48. As the reservoir permeability increases, the formula coefficients and exponents increase. For the RT1 reservoir type, the goodness of fit for permeability calculation reaches 0.68. When no reservoir classification is applied and porosity–permeability fitting performed directly, the goodness of fit for the permeability formula is only 0.24. In contrast, after classification, the fitting accuracy of permeability is significantly improved.

5. Discussion

This study proposes a reservoir classification method based on nuclear magnetic resonance logging data and discusses three aspects with regard to this method.

5.1. Advantages of the New Method

The reservoir classification method proposed in this study is based on nuclear magnetic resonance logging data. The evaluation index can finely characterize pore throat size and pore space. Compared with the Winland R₃₅ method, the method in this study does not require a large amount of mercury injection test data. In the study area, the number of core experiments is limited, and the number of mercury injection test samples is small, making it difficult to establish a relationship between the logging curve and reservoir types. Therefore, the Winland R₃₅ method is not applicable in this block. Additionally, the Winland R₃₅ method considers relatively few factors, whereas the new method makes full use of the information in the nuclear magnetic resonance T₂ spectrum, providing a higher information coverage rate than the Winland R₃₅ method.

In previous studies, Zhu et al. [37] considered using the T₂ spectrum to construct pseudo-capillary curves. In practical applications, especially when dealing with carbonate reservoirs with strong heterogeneity, the difficulty and accuracy of constructing pseudo-capillary curves need to be considered. In the method proposed in this study, the construction significance of the T_2R35 and T_2R65 parameters is similar to that of R₃₅ and R₆₅ in the capillary curves, and no further conversion is required, thus avoiding the introduction of iterative errors.

The FZI method relies on a large amount of core porosity and permeability data. Although the classification results obtained using the FZI method show a good pore–permeability relationship for each type of reservoir, its interpretability is poor, and its correlation with logging data is weak, limiting its generalizability. There are few core samples in the study area, making the use of the FZI method difficult; additionally, the delineated types are not necessarily representative, which is a technical challenge in this study area; however, future research can develop this idea further, and the boundaries of reservoir type delineation can be combined with the FZI method when core data are sufficiently large to further supplement the correlation with flow units. The new method proposed in this study is based on nuclear magnetic resonance logging data, significantly improving its generalizability; moreover, the core experimental data verify that the correlation of core porosity–permeability relationships is significant for each type of reservoir classified using this method.

5.2. Improvement of Permeability Accuracy

The accuracy of permeability evaluation serves as a critical benchmark for assessing reservoir classification methods. In this study, a newly drilled well in the research area was selected for analysis, and reservoir classification was performed using NMR data. Permeability was then determined using the formula provided in Table 5. For comparison, permeability was also determined using the conventional method of geological layer subdivision. Figure 13a presents a cross-plot of permeability values obtained via the traditional method versus core permeability, while Figure 13b displays a cross-plot of permeability derived from the new model, based on the reservoir classification method proposed in this study. The results in Figure 13 indicate that the permeability model developed using the new classification method exhibits higher accuracy when applied to the new well. Of the 78 sample sets, only two displayed errors greater than 1, whereas the conventional geological layer-based permeability evaluation method demonstrated relatively lower accuracy. This disparity arises from the challenges in capturing the strong heterogeneity of the reservoir using traditional methods. The root mean square error (RMSE) was reduced from 0.34 mD to 0.21 mD, and the magnitude of permeability error decreased from 0.58 to 0.40. These results further substantiate the efficacy and broader applicability of the proposed reservoir classification method.

5.3. Limitations of the Method

This method has certain limitations, which are discussed in three aspects:

• Generalizability: While the proposed method improves upon the traditional approach in terms of generalizability, it faces challenges when applied to wells lacking NMR logging data. In such cases, one possible solution is to develop a data-driven model that maps conventional logging curves to reservoir-type labels using data from wells with NMR data. However, this approach is not without its drawbacks, as it inevitably introduces errors that may affect the subsequent calculation of reservoir parameters;
• Number of Reservoir Types: The number of reservoir types can be controlled to some extent. If the coverage of NMR logging data is extensive in the study area, it is possible to increase the number of reservoir types to enhance the accuracy of reservoir characterization and parameter evaluation. However, this requires more core data to support the classification. In practical scenarios, many development wells lack NMR logging data, which limits the number of reservoir types that can be defined. An excessive number of types would lead to increased errors in generalization, thereby reducing the reliability of parameter evaluation. In this study, four reservoir types were classified (with three inflection points), considering both the quantity of core data and its coverage. Additionally, while this method addresses the classification of pore-type reservoirs, it is not applicable to fracture-type reservoirs, as NMR data cannot effectively characterize fractured reservoirs;
• Stability of NMR Data: The detection range of NMR logging data is limited, and data distortion can occur in enlarged borehole sections. Therefore, when applying the method proposed in this study, it is essential to carefully check the quality of the NMR logging data;
• Improvable forms of reservoir typing methods: In this study, the improved slope method is applied to classify reservoir types, though other mathematical methods, such as cluster analysis, can also be used for classification. Figure 14 shows the results of clustering based on the principal components Y1 and Y2, using the K-means clustering method to categorize the reservoirs into four types. However, it is challenging to interpret the geological significance of these four reservoir types after classification, particularly because the significance represented by the two principal components differs greatly. Furthermore, future research could explore automated algorithms and testing approaches to reduce the influence of human factors. It is important to note that the method used to classify reservoir types should be based on the richness of actual data and information in the study area, especially when determining the number of reservoir types.

In summary, this method offers a classification approach for carbonate reservoirs in the Asmari formation of the M oil field. When dealing with carbonate reservoirs in different geological contexts, it is crucial to integrate actual data and reservoir types with the proposed method for classification. Additionally, if imaging or array acoustic data are available to characterize fractured sections, they can be further combined with other specialized logging data to refine the classification of reservoir types.

6. Conclusions

This study addresses the challenge of strong heterogeneity in the carbonate reservoirs of the Asmari formation in the M oil field, located in the Middle East. A new reservoir classification method based on NMR logging facies is proposed. By integrating multi-dimensional pore structure characterization with mathematical dimensionality reduction techniques, the method effectively divides complex reservoir types. The main conclusions are as follows:

(1)

A reservoir classification method suitable for highly heterogeneous carbonate reservoirs is established based on pore structure parameters extracted from the NMR T₂ distribution (e.g., T₂ geometric mean, T_2R35/R50/R65, and pore component ratios), combined with PCA for dimensionality reduction and an improved slope method. This method uses a comprehensive evaluation index (Y) that reflects pore throat size, connectivity, and distribution characteristics to classify the Asmari formation carbonate reservoirs into four types (RT1 to RT4). The classification results show good consistency with capillary pressure curves and cast thin-section pore types, validating the reliability of the method;

(2)

The various reservoir types exhibit significantly different porosity–permeability relationships: the R² of permeability of the RT1 to RT4 reservoirs are 0.68, 0.62, 0.57, and 0.48, respectively, all of which are notably higher than the global goodness-of-fit (0.24) when not classified. The new method, by precisely characterizing pore structure differences, addresses the issue of multiple solutions in traditional permeability prediction using only porosity. In the application to new wells, the RMSE of permeability calculations decreased from 0.34 mD with traditional layering methods to 0.21 mD, and the magnitude error was reduced from 0.58 to 0.40, confirming its superiority in permeability prediction;

(3)

Compared with traditional rock physics methods (such as Winland R₃₅, FZI), this method does not need to rely on a large number of mercury injection experiments or core physical property data, and only nuclear magnetic resonance logging can achieve reservoir classification, which is significantly enhanced. However, its limitation is that it relies on the coverage of nuclear magnetic resonance data, and its applicability to fractured reservoirs is insufficient. It is also greatly affected by the quality of logging data (such as borehole enlargement). In the future, it can be combined with imaging logging or machine learning models to further expand its application scenarios in complex reservoirs.

This study provides a new approach for the detailed evaluation of highly heterogeneous carbonate reservoirs. The established reservoir classification system can directly serve in permeability prediction, flow unit division, and development plan optimization. It holds significant reference value for the exploration and development of carbonate reservoirs with similar geological backgrounds in the Middle East and globally.