1 INTRODUCTION

The south slope of Dongying Sag is the most typical and largest low-lying gentle slope structure belt in Jiyang Sag. The beach bar sandstone is a kind of important oil and gas reservoir in the south slope, which was deposited by shore-shallow lacustrine beach bar in Es₄ period (Tian et al., 2004). Because of the complex depositional environment, reservoir-forming mechanism, tectonism and lithogenesis reasons (Liu J H et al. 2003) in Es₄, the core porosity distribution is 1.9% to 19.6%, and the permeability distribution is 0.02 to 69.40 mD. It is a typical complex pore structure of low permeability sandstone reservoir, which is often difficult to effectively identify. It is found that the pore throat distribution information of nuclear magnetic resonance (NMR) logging T₂ spectrum can effectively identify the effective reservoir (Si et al., 2013). The key point lies in the establishment of accurate conversion relationship between pore throat size distribution and nuclear magnetic T₂ spectrum of different pore structure. At present, the relation between pseudo capillary pressure curve and nuclear magnetic T₂ spectrum is being widely studied in China and abroad. For example, Volokitin puts forward the relationship between transverse relaxation time and capillary pressure. In addition, the pseudo capillary pressure curve transformed from the nuclear magnetic resonance (NMR) and the capillary pressure curve measured by mercury injection are compared (Volokitin et al., 2001; Hofman et al., 2001; Yun et al., 2002). Liu T Y et al. uses maximum likelihood principle to determine the pseudo capillary pressure curve (Liu T Y et al. 2003). He Y D et al. uses power function to built the pseudo capillary pressure curve on large and small pore scales (He Y D et al. 2005a). Liu et al.(2004) classifies the pores into spherical pore and capillary pore and find the proportion of them to unfold the spectrum to get the T₂ distribution which characterizes the pore structure. Besides, Nakashima puts forward using the NMR logging to evaluate the fracture pore (Nakashima and Kikuchi, 2007). Lu (2015) builds an one-dimensional model to construct the T₂ spectrum which could reflect the fracture pore and evaluate the space distribution of the pores (Lu and Heidari, 2015). But all of them partly ignore the membrane bound water influence on the NMR signals among the small pores. He Y D uses free fluid spectrum to eliminate the membrane bound water influence (He et al., 2005b). Gao (2015) determines the mobile fluid parameters (mobile fluid percentage and porosity) by NMR data to analyze and evaluate the characteristics of the pore structures in the low-permeability and tight sandstone (Gao and Li, 2015), but the method is aimed at the rock core instead of the continuous computation of the NMR logging along the stratigraphic section. The authors consider the membrane bound water effect, and compare the free fluid spectrum with mercury intrusion pore throat size distribution in different pore structures. Next, we establish the conversion method on different pore size scales, then, quantitatively invert for pore size distribution from NML logging data after pore structure identification along borehole profile, which can save the work of pseudo capillary curve building. Simultaneously it not only provides a direct basis for evaluation of the effectiveness of low permeability sandstone reservoir, but is also beneficial to the exploration in the field of reservoir microscopic pore structure quantitative inversion by well logging information.

2 THE RELATIONSHIP BETWEEN NUCLEAR MAGNETIC T₂ SPECTRUM AND CAPIL- LARY PRESSURE CURVES 2.1 Theory

Because the rock has various pores with different nuclear magnetic resonance (NMR) relaxation, the spinning echoes of NMR logging satisfy the multi-exponential decay:

(1)

The M (t)is the echo amplitude of time t, M_i(0) is the echo amplitude of zero time in the ith relaxation component; T_2i is the transversal relaxation time of the ith relaxation component.

Making the multi-exponential fit of the echoes data from the experiment by Eq.(1) could get the Mi (0) of every T_2i which make up the T₂ distribution.

There is a big difference between total fluid nuclear magnetic resonance (NMR) relaxation property and free fluid NMR relaxation property. For that, not only the free relaxation and diffuse relaxation but also surface relaxation caused by solid-liquid interface have effects on rock pore fluid. These three parts make the relaxation rate increase and relaxation time shortened. Based on NMR theory (Xiao, 1998), the transverse relaxation time T₂ is:

(2)

where T_2B is the bulk relaxation time of the fluid in ms; D is the diffusion coefficient in µm2·ms^-1; G is the magnetic field gradient in G·cm^-1; T_E is the echo spacing in ms; S is the pore surface area in cm²; V is the pore volume in cm^3; ρ₂ is the transverse surface relaxation time of the fluid in µm·ms^-1; γ is the gyromagnetic ratio.

While in the practical application, T_2B is much larger than T₂, G(when the magnetic field is uniform distribution) and TE are quite small. Therefore, the first term and the third term can be ignored. Hence, the Eq.(1) reduces to

(3)

where F_S is the shape geometrical factor. T₂ is proportional to the pore size and pore size distribution from the Eq.(2).

2.2 Comparison Between T₂ spectrum and Pore Throat Distribution

In general, the pore-surface is hydrophilic, and contains a layer of bound water/irreducible water. In the mercury injection method, the non-wetting phase (mercury) is used to displace gas from a dry sample under the condition of vacuum (Shen, 1995). Mercury injection curves reflect the free-water porosity which ruled out the influence of membrane bound water pore. While the NMR T₂ distribution contains the contributions from the free fluid porosity and the bound water (He, 2005b). He Y D figures out that the free fluid T₂ spectrum (the spectrum reflects the pore of the free fluid) has a good corresponding relation to capillary pressure curve. The way to get a free fluid T₂ spectrum is to deduct the centrifuged T₂ spectrum from the saturated T₂ spectrum (He et al., 2005b).

Considering the characteristics of the samples of Es₄, the test machine is AniMR-150 Full Diameter Core Nuclear Magnetic Resonance Imaging System which sets 32 times of the cumulative frequency, 0.1 ms of the echo spacing, 6 s of the waiting time to do the saturated water and centrifuged NMR test and get the saturated and centrifuged T₂ spectrums by the multi-exponential fit method (Xiao, 1998). And the free fluid T₂ spectrum of every sample is obtained by the corresponding method. For example, the free fluid nuclear magnetic T₂ spectrum of sample 3 from the area of well A (3115.45 m), of which the Cpor (the core porosity) is 11.46%, the CP erm (the core permeability) is 0.3627 mD and the SBVI (bound water saturation) is 58.2%, shows a good corresponding relation to the mercury intrusion pore throat distribution (Fig. 1). So, the relationship between mercury intrusion pore throat distribution and free fluid T₂ spectrum is better than the saturated spectrum. As the contribution of membrane bound water of saturated spectrum and centrifugal spectrum is in a same way in the small spectrum scale. Thus, the influence of membrane bound water can be eliminated by calculating the free fluid spectrum (Fig. 2). In conclusion, the free fluid spectrum can be used to evaluate the rock pore size and distribution.

2.3 The Relationship Between Free Fluid T₂ Spectrum and Pore Throat Distribution

Nuclear magnetic T₂ spectrum response contains 2 kinds of information simultaneously. One is pore size information, and the other is the volume fraction of different pore size in total porosity (Yang, 2013). The previous research in the longitudinal conversion coefficient of T₂ spectrum and capillary pressure curve, found that the coefficient is different for large and small pores in the one sample (He, 2005b). We found the same phenomenon by directly comparing T₂ spectrum and capillary pressure curve (Fig. 3). This phenomenon is caused by the impact of the membrane bound water. And the influence degree is not the same on different pore size scales. Therefore, the relation between T₂ spec- trum and pore throat distribution is different on dif- ferent scales. In addition, this relation is a kind of a multi-scale power function relationship, but not the linear relationship on small pore size scale. Scholars divided pore size into two ranges. One is big hole scale (50 microns or higher), and the other is under 50 mi-crons (Xiao, 1998). Another kind of ranges is large scale (10 microns or higher) and small scale (under 10 microns)(He, 2005b). However, this dividing method is no longer applicable for low permeability sandstone. As the pore size of low permeability sandstone is quite small, generally under 3 microns. Based on the analysis of actual data, we classified the pore size into three scales: ≥ 1 µm, 0.1∼1 µm, <0.1 µm, then establish the corresponding relation between nuclear magnetic free fluid T₂ spectrum and capillary pore throat distribution on these three scales (Fig. 3).

3 LOW PERMEABLE SANDSTONE PORE STRUCTURE CLASSIFICATION AND QUAN- TITATIVE EVALUATION OF PORE DISTRIBUTION 3.1 Pore Structure Classification

Characteristics of pore structure reflect the reserving capability and the percolation ability. And it is an important basis for reservoir evaluation and reservoir classification. On the whole, the mercury injection curve of the Es₄ in the south slope of Dongying sag (Fig. 4) is very messy. The reason for this is that the difference in pore structure of the samples is great. The maximum mercury saturation (SHgmax) and mercury injection pressure (P_d) is dispersed. And the other characterization parameters which could also reflect the pore structure is of low value and wider distribution range, like permeability, porosity and the average pore throat radius. The above description clearly illustrates the complexity and low permeability of the beach bar sandstone pore structure in this filed.

In view of the complex diversity of low permeability sandstone pore structure types, and to facilitate the classification research, the authors make further statistic analysis of the capillary pressure curve shapes and characteristic parameters of Es₄, analyze the corresponding relation between various pore structure parameters with conventional physical and nuclear magnetic resonance (NMR) data, and so on. We classify low permeability sandstone pore structures into three major types, and 5 minor classes (Table 1). And the mercury injection and nuclear magnetic characteristics of each type are as follows (Table 2):

Type Ⅰ₁ pore structure (Table 2, Ⅰ₁ ) has good connectivity, the low expulsion pressure value (P_d) is generally under 0.2 MPa; nuclear magnetic free fluid T₂ spectrum mainly between 10∼300 ms; the pore throat distribution within the scope from 0.73 to 1.495 microns. The characteristic of property level is medium porosity and low permeability. That means good physical property. And the reservoir space is mainly original intergranular pore and solution pore.

Type Ⅰ₂ pore structure (Table 2, Ⅰ₂ ) has relatively good connectivity, the expulsion pressure value (P_d) is lower than type Ⅱ₁ , but higher than type Ⅰ₁ ; nuclear magnetic free fluid T₂ spectrum mainly between 10∼300 ms, but its pore content is below type Ⅰ₁ ; the pore throat distribution within the scope from 0.1374 to 0.3721 microns. The characteristic of porosity level is medium porosity and super-low permeability.

Type Ⅱ₁ pore structure (Table 2, Ⅱ₁ ) has relatively poor connectivity, of which the Pd is higher than type Ⅰ₂ ; nuclear magnetic free fluid T₂ spectrum mainly between 5∼300 ms; the pore throat distribution within the scope from 0.1497 to 0.3801 microns, but its pore content lower than type Ⅰ₂ . The characteristics of property level is low porous and extreme low permeability.

Type Ⅱ₂ pore structure (Table 2, Ⅱ₂ ) has poor connectivity, of which the Pd is higher than 1.5169 MPa; nuclear magnetic free fluid T₂ distribution is wide; the pore throat distribution within the scope of 0.0936 to 0.1477 microns, but its pore content is low. The characteristic of property level is extremely low porosity and ultra-low permeability.

Type Ⅲ pore structure (Table 2, Ⅲ) has the worst connectivity and the highest Pd value which is more than 1.6 MPa, and the difference between centrifugal T₂ spectrum and the saturated T₂ spectrum is not big. Saturated spectrum is generally distributed between 0.3∼20 ms, meanwhile the pore throat is mainly microporous (<0.0248 microns). The characteristic of property level is ultra-low porosity and non-penetration which is a typical kind of non-reservoir.

The difference of capillary pressure curves of these five kinds of pore structures is obvious, the better pore structure has a more gentle capillary pressure curve platform with a coarser crooked degree, a smaller displacement pressure, a greater maximum mercury saturation, and a larger area of nuclear magnetic free fluid T₂ spectrum (Table 2). There is a good corresponding relationship between free fluid T₂ spectrum and mercury intrusion pore throat distribution. We found that, if the porosity and permeability is lower, the free fluid T₂ spectrum moves to left, the free pore content is lower and the mercury intrusion pore throat distribution moves to micro pore throat radius.

3.2 Establish the Calculation Formula of Pore Throat Distribution for Different Pore Structures

Nuclear magnetic T₂ spectrum measures the relaxation time of hydrogen atoms from unbalance to balance. For different pore structures, and the same other conditions (pore fluid and rock grain size, etc.), the T₂ spectrum is greatly influenced by the pore structure (Zou and Yu, 2008). From Table 4, it is clear that the worse the pore structure is, the more the T₂ spectrum moves to left. In fact, nuclear magnetic free fluid T₂ spectrum responds to the connected pore space. While mercury injection experiment data can identify the effective pore space, when the pore throat is greater than or equal to 0.0248 µm. However, if the pore throat size is less than 0.0248 µm, including connected and non-connected pore space, it is hard to be accurately identified. In order to eliminate the differences caused by non-connected pore space, we compare the part of the pore throat distribution curve (≥ 0.0248 µm) and the nuclear magnetic free fluid spectrum, finally on the basis of dividing pore structure types, establish the corresponding relationship between free fluid T₂ spectrum and mercury intrusion pore throat distribution (≥ 0.0248 µm) of these five kinds (Table 2). We also establish the relationship between saturated T₂ spectrum and mercury intrusion pore throat distribution (Table 3), and compare Table 3 to Table 2.

However, the nuclear magnetic free fluid T₂ spectrum cannot be directly obtained by nuclear magnetic resonance (NMR) logging. Therefore, based on the five pore structures, we build corresponding relationship between nuclear magnetic saturation spectrum and nuclear magnetic free fluid (Table 4). Then, along wellbore section, using nuclear magnetic resonance (NMR) logging T₂ spectrum, the free fluid pore throat distribution can be continuously calculated. According to the transformation formula of Table 2 and Table 3, the nuclear magnetic free fluid T₂ spectrum of different pore structure samples is converted to nuclear magnetic free fluid pore throat distribution, and the nuclear magnetic saturation T₂ spectrum to nuclear magnetic pore throat distribution (Table 5). Comparing the nuclear pore throat distribution and mercury intrusion pore throat size distribution, it is obvious that the nuclear pore throat distribution of types Ⅰ₁ , Ⅰ₂ , and Ⅱ₁ is similar to mercury intrusion pore throat distribution. But the nuclear pore throat of types Ⅱ₂ and Ⅲ has some differences in the small-scale part of pore throat distribution, where the proportion of nuclear pore throat is higher.

Then we compare the nuclear free fluid pore throat distribution and mercury intrusion pore throat size distribution (Table 5). There is a good consistency relation between nuclear free fluid pore throat distribution and mercury intrusion pore throat distribution (≥ 0.0248 µm). It demonstrates that this method is effective, which converts nuclear magnetic free fluid pore throat distribution by directly extracting corresponding relation of nuclear magnetic free fluid T₂ spectrum and mercury intrusion pore throat distribution.

4 BOREHOLE PROFILE PORE STRUCTURE TYPE RECOGNITION AND PORE THROAT DISTRIBUTION INVERSION

On the basis of pore structure classification, combine the logging information and statistics of the logging response information of each pore structures. Then, establish two kinds of pore structure recognition charts: Radar map “AC-GR-HRID”(Fig. 5) and Bubble chart “AC-GR-HRID”(Fig. 6). In addition, if the pore struc- ture is better, the AC, HRID value is higher, and the GR value is lower. According to this feature, pore structure types of reservoir can be qualitative identified along wellbore section with these three kinds of well logging response.

Take well FX (Fig. 7) as an example, Exclude three non-reservoir intervals: 3238.125∼3241.2 m, 3244.8∼3246.13 m and 3248.7∼3249.625 m. Then, the bubble chart is used to recognize pore structure types of well FX. The pore structure of No.87 layer (3241.25∼3243.2 m) and No.89 layer (3246.13∼3248.7 m) is of type Ⅱ₁ , No.88 layer (3243.2∼3244.8 m) is of type Ⅱ₂ , and No.90 layer (3243.2∼3244.8 m) is of type Ⅰ₂ (Fig. 7).

After pore structure type recognition, inverse nuclear magnetic free fluid pore throat distribution and saturation pore throat distribution with formula in Table 2 and Table 4. It is clear that the pore throat distribution of three type Ⅲ layers (3238.125∼3241.2 m, 3244.8∼3246.13 m, and 3248.7∼3249.625 m) is located in the left side. It means that pore size of these three layers is minimum, and the pore structure is worst. And the characteristics of type Ⅱ₁ layers (3241.25∼3243.2 m and 3246.13∼3248.7 m) is wide pore distribution, clear bimodal distribution and obvious nuclear magnetic free fluid pore throat distribution. Finally, these two layers are explained as dry oil layers. And the reservoir stratum of 3241.25∼3243.2 m has an output of about 1.7 t every day, the reservoir stratum of 3246.13∼3248.7 m has an output of about 2.3 t every day. The reservoir stratum of 3243.2∼3244.8 m (sample 88) has a unimodal pore distribution which is typical Ⅱ₂ type and is interpreted as dry formation (like oil layer). The reservoir stratum of 3249.63∼3251.8 m (sample 90) of Ⅰ₂ has a wide pore distribution which is mostly in the high range of nuclear magnetic free fluid pore throat distribution and is interpreted as oil layer with an output of about 7.8 t every day. All the explanations are consistent with the testing results. This phenomenon shows that, on the basis of pore structure classification, with nuclear magnetic logging T₂ data to inverse pore throat distribution is good to improve the accuracy of low permeability sandstone reservoir recognition.

5 CONCLUSION

The low permeability sandstone reservoir has low physical property, strong heterogeneity and complex pore structure. To solve this problem, we analyzed low permeability sandstone pore structure of Es₄ in Dongying sag which is classified into three major categories considering the Clastic Rock Reservoir Physical Property of Oil and Gas Division Standard (SY/T 6285-2011). Nuclear magnetic free fluid T₂ spectrum could reflect the three types of pore structure.

Nuclear magnetic T₂ spectrum and capillary pressure curve both reflect the pore throat distribution in a certain extent. But there is a large residual between mercury intrusion pore throat distribution and nuclear magnetic saturation pore throat distribution in conventional method. Finally, we established the corresponding relation between mercury intrusion pore throat distribution and nuclear magnetic free fluid T₂ spectrum on different pore throat scales and in different pore structure types (large scale: linear; small scale: piecewise power function).

Based on the logging response characteristics, pore structure types can be identified along the shaft section. Then set up pore throat calculation formulas of different types. In addition, calculate the inverse nuclear magnetic free fluid pore throat distribution with nuclear magnetic resonance logging (NML) data. By this method, it not only saves the step of building pseudo capillary curves, but also provides direct evidence for low permeability sandstone reservoir effectiveness evaluation. And it is a beneficial exploring work in the field of reservoir microscopic pore structure information quantitative inversion.

Acknowledge

This work was supported by the National Natural Science Foundation of China (41202110).