PETROPHYSICS

Keywords:
Gas shale,Nuclear magnetic resonance(NMR),T2 distribution,Kerogen,Gas saturation,Petrophysical interpretation method

abstract:

Nuclear magnetic resonance (NMR) characteristics provide critical information to study the storage of organic shale. Based on NMR petrophysical experiment of Haynesville Shale, the response characteristics of transverse relaxation time (T2) are analyzed. According to the shape and amplitude of T2 distribution of shale, Haynesville Shale can be categorized into two types: continuous and discontinuous T2 spectrums. Compared with routine density porosity, NMR porosity is generally underestimated for organic shale. Therefore, the controlling factors are investigated in detail. Through constructing the correlations of NMR porosity and clay volume, total organic carbon (TOC) content, kerogen content and pyrite volumetric concentration, the pyrite and kerogen are ﬁnally regarded as dominant factors. Subsequently, a new NMR porosity correction model is proposed. Moreover, the permeability model based on NMR bin porosity is built, and water, gas and oil saturation models are also established through building some correlations between gas saturation and NMR bin porosity. NMR experiment indicates that the kerogen and adsorbed gas are located in bound ﬂuid part of NMR T2 distribution, and the gas storage is dominant as absorbed gas rather than free gas. The study provides a novel petrophysical interpretation method for gas-bearing shale.

1. Introduction:

Gas-bearing shale is one of the most valuable unconventional reservoirs. Comparing with conventional sandstone resourses, the mineralogy of shale gas reservoir is extremely complex, and its pore space mostly includes both sub-micron and nano-scale ma-trix pore, sometimes, relatively large aperture fractures are de-veloped (Curtis, 2002; Rick, 2004; Glorioso and Rattia, 2012; Sondergeld et al., 2012). In gas-bearing shale, occurrence of gas is complex, gas is partly free in matrix and kerogen, and partly ab-sorbed on the surface of pores and in kerogen. A small portion of gas is dissolved in ﬂuids of shale (Sondergeld et al., 2012). So, or-ganic shale is a typical “self-generating and self-storage” system (Curtis et al., 2012).
Routine petrophysical experiment is the most effective method to study the properties of organic shale, which can measure re-sistivity, porosity, permeability, saturation, and is also an indispensable bridge between logs response and logs interpreta-tion (Luffel et al., 1992; Guidry et al., 1990; Ross and Bustin, 2007, 2008; Xu and Torres-Verdín, 2013; Yang and Torres-Verdín, 2013). In recent years, Nuclear magnetic resonance (NMR) is only sensi-tive to hydrogen ﬂuids in pores of saturated rocks, and has been widely used in petrophysical experiments and geophysical logging (Coats et al., 1999; Dunn et al., 2002). NMR instrument can not only measure the total porosity, movable ﬂuid volume, and bound ﬂuid volume, it can even calculate the permeability based on NMR bin porosity. Furthermore, NMR experimental results of core plugs can be used to calibrate NMR logging. In last two decades, core NMR experiment and NMR logging were extensively applied to sandstone and carbonate reservoirs, some experimental results of core plugs can provide the guidance for logs interpretation and help to construct the petrophysical models (Rick, 2004; Luffel et al., 1992; Decker et al., 1990; Arvie et al., 2005; Passey et al., 1990; Akkurt et al., 1996), which indicates that NMR applications in conventional reservoirs were successful. Unfortunately, NMR core measurement and NMR logging were not fully utilized in gas shales.
So far, NMR logging technique for natural gas was mainly on the bulk and unrestricted gas (Akkurt et al., 1996; Daniels, 2004;Hook et al., 2011). Recently, Sigal and Odusina (2011) published NMR laboratory work on methane-saturated cores from Barnett Shale. The limitation remains with overlapping T2 signals between water and gas/oil in the complex pore systems, which makes it difﬁcult to separate different ﬂuids from the T2 distribution. Ry-lander et al. (2010) studied the NMR T2 distribution in the Eagle Forward Shale, and analyzed the NMR characteristics of bound oil and free oil, and compared the difference of lower and upper Eagle ford Shale.
In this study, based on NMR core experiment of Haynesville Shale, we analyzed the NMR T2 response characteristics. Then, we compared NMR porosity with routine density porosity, analyzed the inﬂuence factors, and investigated contributions of free gas, kerogen, adsorbed gas to T2 distribution. Finally, we established NMR petrophysical interpretation models including corrected NMR porosity model, permeability model, and saturation models. Moreover, the speciﬁc area and throat radius are estimated from NMR T2 distribution. Therefore, this NMR experiment of shale core plugs provides an important alternate for log interpretations of gas-bearing shale.

2. NMR T2 relaxation mechanism
2.1. Petrophysical model of organic shale

Organic shale has complex pore types, and the pore morphol-ogy is also diverse. According to different types of shales, the re-servoir space can be divided into two types including matrix pore and fracture, and the former includes intergranular pore, in-tragranular pores, and voids within the organic plasmids (Fig. 1), which is mostly nano-level. The connectivity between these voids is so poor (Fig. 1a, Curtis et al., 2010). In gas-bearing shale, oc-currence of gas is various, gas is partly free in matrix and kerogen, and some are absorbed on the surface of pores and in kerogen (Fig. 1b). A small portion of gas is dissolved in ﬂuids of shale (Kausic et al., 2011).
Organic shale is rock matrix and ﬂuids. The rock matrix usually consists of dry clay, quartz, feldspar, plagioclase, calcite, pyrite and kerogen. For Haynesville Shale, X-ray diffraction (XRD) results of shale are shown as below (Fig. 2a), which demonstrates that the clay content is dominating. So, the petrophysical model is set as Fig. 2(b).

2.2. NMR T2 relaxation mechanism

As we all know, NMR is the interaction between the hydrogen nucleus and the magnetic ﬁeld. Total NMR relaxation includes surface relaxation, bulk relaxation of ﬂuid precession, and diffu-sion relaxation caused by gradient ﬁeld. Therefore, total NMR re-laxation in porous media can be described by the following mathematical formula:

where ρ2 is the surface relaxivity, μs/m; D is the free diffusion coefﬁcient for the ﬂuid, μs/cm2; γ is the gyromagnetic ratio; TE is the echo spacing of the measurement sequence, ms; and S/V is the surface area to volume ratio (speciﬁc surface area) of the pores,μs-1; G is the magnetic ﬁeld gradient, which includes the external and interior magnetic ﬁeld gradient, Gauss/cm; B0 is the applied magnetic ﬁeld strength, Gauss/cm; r refers to the distance from the magnetic ﬁeld changes, m; Δχ is the susceptibility difference between rock matrix particles and pore ﬂuid, 10?6 SI.
From Eq. (1), total T2 relaxation time is related to speciﬁc sur-face area, ﬂuids in rocks as well as diffusion coefﬁcient and echo spacing. Usually, the measurement of NMR experiment is under uniform magnetic ﬁeld, and the diffusion relaxation term could be ignored, so the speciﬁc surface area can reﬂect the pore size dis-tribution in the sandstone and carbonate formations. But, for or-ganic shale, the total clay content is so high, and small pores or throats may induce an internal magnetic gradient in terms of Eq.(1) even though in homogenous magnetic ﬁeld. So, it will also decrease the T2 relaxation time and make T2 spectrum shift leftward.
The pattern and amplitude of NMR T2 distribution reﬂect the characteristics of different reservoirs. Generally, the higher am-plitude of T2 distribution at short relaxation time indicates larger bound ﬂuid volume, whereas, the higher amplitude of T2 distribution at long relaxation demonstrates larger movable ﬂuid volume.

Fig. 1. All kinds of pores in organic shale (a) and gas occurrences in different pores (b).

Fig. 2. Mineral compositions and petrophysical model in different pores.

3. NMR characteristics and interpretation method in shale
3.1. NMR experiments of core plugs

In our experiment, 11 core plugs of Haynesville Shale were selected from the drilling cores and stored for laboratory mea-surement. The size of all core samples is about 1.0 in. diameter, and the bulk volume ranges from 13.53 cm3 to 33.02 cm3, which is listed in Table 1. The measurement pressure is about 800 psi, and the temperature is about 28 °C. The equipment used is MARAN-DRX, which is a low-ﬁeld NMR instrument with uniform magni-tude ﬁeld. The number of echoes is 1024 and the echo spacing is 0.2 ms. The number of scanning and stacking is 128. Because little fractures were observed in these shale cores, the waiting time of NMR experiments was set as 5.0 s through comparison of testing.
In addition, some routine experimental measurements such as density porosity and permeability, are carried out, and total or-ganic carbon content (TOC) and kerogen volume were measured in core plugs. The porosity and matrix permeability were calculated from measured pressure-decay data using a fresh crushed (20/35 mesh size) sample including all interconnected pore space. Gas saturations were determined by Dean-Stark technique using a crushed sample and dried at 110°, and oil saturation was com-puted using an ambient oil density of 0.80 g/cm3; water saturation was computed using a brine concentration of 30,000 ppm with an ambient density of 1.018 g/cm3. The clay minerals content was from X-ray diffraction (XRD) analysis.

Table 1 shows NMR and routine experimental results of 11 shale core plugs, including NMR porosity, clay bound water vo-lume, effective porosity, density porosity, air permeability, and TOC content. T2 geometric mean value was calculated. The NMR porosity of 11 cores averages about 4.35% and the routine density porosity is about 5.70%, so, the former is lower than the latter. The measured air permeability is in the range of (0.07–816) * 10 3nd, with an average of 268.7 ? 103nd. The TOC content ranges from 0.45 wt% to 2.69 wt%.

3.2. NMR T2 distribution of gas shale
T2 distribution of water-saturated conventional rocks such as sandstone and carbonate usually describes pore sizes distribution. The more developed the large pores in reservoir rock are, the stronger the NMR T2 spectrum signal at the long relaxation time will be; instead, if the small pores in the rock are poorly developed, the NMR T2 spectrum at short relaxation time is dominated. Thus, according to the characteristics of T2 spectrum, we can analyze quantitatively the storage and ﬂow properties of ﬂuids in shale.
Fig. 3 shows the NMR T2 distributions of 11 shale core samples. In terms of the characteristic of T2 spectrum and morphology, NMR T2 distributions of shale cores are categorized into two types: con-tinuous bimodal T2 spectrum (Type I) and discontinuous bimodal T2 spectrum (Type II). Fig. 3(a) shows that NMR T2 distribution (H6) has a signiﬁcant unimodal, and the left peak of T2 spectral is much more signiﬁcant than the right one, whose corresponding relaxa-tion time is about 1 ms. Moreover, the right part of T2 spectrum has much lower amplitude with the relaxation time ranging from about 8 ms to 80 ms. Generally, the whole T2 distribution is discontinuous with logarithmic mean of about 0.3 ms. In this NMR experiment, three of the 11 cores are classiﬁed as Type I.
Different from NMR T2 spectrum of Type I, NMR T2 spectrum of Type II (H12) is continuous, and the amplitude difference between left and right peaks is much smaller than that of Type I shale (Fig. 3b). The relaxation time of left peak ranges from about 0.8 ms to 2.0 ms; in contrast, the relaxation time of right peak ranges from about 2.0 ms to 200 ms with wider distribution. It reﬂects that the latter has a relatively wider pore size than the former, which indicates that some relatively large pores, fractures, and small caves can be well developed. Furthermore, from Table 1, the permeability of Type II shale is also much higher than Type I shale.

3.3. Analysis on NMR porosity
Theoretical studies of NMR suggest that, for hydrogen-con-taining ﬂuid saturated rock, NMR measures the relaxation signal from the ﬂuid rather than matrix, so NMR measurement can provide accurate porosity estimation independent of mineralogy (Coats et al., 1999). Experimental study from a large number of scholars conﬁrmed that NMR porosity is accurate in sandstone and carbonate reservoirs, and the absolute error between NMR por-osity and density porosity is generally less than l.0% (Dunn et al., 2002). So, the measured NMR porosity is usually the same as routine density porosity.

Fig. 3. NMR response characteristics of shale. Shale is classiﬁed into two types: Type I (a) and Type II (b).

Fig. 4. Comparison of NMR porosity and routine density porosity of shale. NMR porosity of some cores is worse underestimated.

Fig. 4 shows comparison of NMR porosity and routine density porosity of shale, which indicates that NMR porosity of some cores with medium porosity is underestimated. To investigate the in-ﬂuence factors, we built some crossplots (Fig. 5). Fig. 5(a) shows the correlation of NMR porosity and clay minerals content, which indicates that the ﬁne clay pore in shale increases porosity rather than decreasing porosity even though the internal magnetic ﬁeld gradient is induced by micro-pore in the clay. Therefore, the clay mineral's content is not the main reason causing NMR porosity reduction. To investigate this problem, we calculated the porosity difference between the density porosity and NMR porosity. Fig. 5 (b) and (c) shows the correlations of the porosity difference and clay content, and gas saturation, which indicates neither the clay nor ﬂuid in gas shale is one of the impact factors. Fig. 5(d) shows that, for these cores whose NMR porosity is lower than density porosity, NMR porosity decreases with increasing clay content, but the porosity difference increases (Fig. 5e). Moreover, Fig. 5 (f) illustrates that TOC content also increases with the pyrite content rising, which indicates NMR porosity is related to pyrite, and that is, NMR porosity decreases with the increasing pyrite. Furthermore, Fig. 5(g) and (h) also illustrates that the kerogen volume is related to the pyrite content, which further veriﬁes that the pyrite is associated with the kerogen. As we all know, pyrite is rich in iron (Fe) and has high relaxavity, which will accelerate NMR echo decaying, so, it is difﬁcult to capture the ﬂuid signal in NMR experiments of shale cores, and the measured porosity is sure to be lower. Therefore, the pyrite or other ferromagnetic minerals contained in organic shale mainly contributed to the decreasing porosity. To correct the NMR porosity, it is possible to build the correc-tion,

Fig. 5. Crossplots for analysis on impact factors of NMR porosity. NMR porosity increases with the clay content rising (a); porosity difference is not related to clay content (b) and gas saturation (c); NMR porosity decreases with TOC content rising when TOC larger than 1.0 wt% (d), and porosity difference increases with TOC content rising (e). In addition, TOC content is proportional to pyrite volume (f) and kerogen volume (g), and kerogen is negative related to pyrite volume (h).

Fig. 6. Relationships between permeability and NMR component porosities. The permeability is worse related to NMR porosity (a) and routine density porosity (b), but it is positively related to NMR effective porosity (c) and negatively related to clay water volume (d).

3.4. Permeability model from NMR bin porosity
The permeability is an important parameter for deliverability evaluation of gas-bearing shale. Typically, the permeability of shale is so small, and it is difﬁcult to predict accurately. NMR measurements can provide some component porosities, such as effective porosity, clay bound water volume, and free ﬂuid volume, which is the advantage of NMR measurement over the routine laboratory measurement. Therefore, constructing the relationship between permeability and NMR component porosities may pro-vide a good alternative way for the permeability prediction of shale.
Fig. 6 shows the crossplots of permeability and routine density porosity, and NMR porosity. These correlations are both poor, which indicates that the permeability does not tend to increase with both porosities increasing (Fig. 6a and b). On the right-bot-tom of Fig. 6(a), three cores with large porosity have extremely low permeability, which indicates that this type of pores has no contribution to permeability of organic shale even though they have high porosity. For these ﬁne pores, they could be isolated in kerogen or among mineral particles, and not connected with the outside, which hinders the penetration of the ﬂuid, so they cannot elevate the permeability of shale. These three cores are veriﬁed as H6, H7 and H9 shown in Table 1, and they belong to Type I shale. Their bound ﬂuid volumes are extremely high; their movable ﬂuid volumes are extremely small, and TOC content is so low. It in-dicates that the water in pores among ﬁne clay particles in such shale is absolutely irreducible and affects the permeability. For this, we build the correlations of permeability and NMR effective porosity, and clay bound water volume, which are illustrated in Fig. 6(c) and (d), respectively. The absolute permeability is pro-portional to NMR effective porosity and it decreases with the bound ﬂuid volume increasing. Therefore, in terms of Fig. 6(c) and (d), we built the following formula to calculate the absolute per-meability of shale by data ﬁtting method:

3.5. Saturation model from NMR bin porosity
Except for NMR, TOC, kerogen, and others measurements, gas saturation was measured for 11 core plugs of Haynesville Shale, and the relationship between gas saturation and various NMR bin porosities is established, which can be used to study the mode of occurrence of shale gas.
First, we built crossplots of gas saturation and NMR porosity, and total porosity, but the correlations are both so poor. However, the correlations of gas saturation and NMR effective porosity, TOC con-tent, and kerogen volume are so excellent (Fig. 7). Fig. 7(a) indicates that the gas saturation increases with NMR effective porosity rising. Moreover, Fig. 7(b) and (c) indicates gas saturation has positive cor-relations with TOC content and kerogen volume, which means that natural gas of organic shale is related to kerogen. As we know, free gas, and adsorbed gas or dissolved gas all contribute to total gas saturation, but what are the response characteristics of these gas components above in NMR measurement?

Fig. 7. Relationships between gas saturation and NMR porosity, TOC content, and kerogen volume. Gas saturation is positively related to NMR porosity (a), TOC content (b) and kerogen volume (c).

In order to study the contribution of NMR effective porosity to gas saturation, we construct an index ( Seff ,NMR), namely, NMR ef-fective porosity index, which indicates the proportion of NMR ef-fective porosity volume throughout the pore space .

where ϕNMR is the NMR porosity, % and ϕE is the NMR effective porosity, %. Fig. 7(d) shows the relationship between gas saturation and NMR effective porosity index, which indicates that the measured gas saturation is higher than NMR effective porosity index. This clearly shows that NMR effective porosity only includes a little amount of free gas with long relaxation time, and most of gas is from “clay bound water” part of T2 distribution with fast relaxa-tion. To further analyze the relationship between gas saturation and NMR bin porosity, we construct another parameter, Sgasdiff , which is named as gas saturation difference between really mea-sured gas saturation and NMR effective porosity index

where ϕNMR is the NMR porosity, % and Seff ,NMR is the NMR effective porosity index, %.

If Sgasdiff value is relatively small, it suggests that the con-tribution to gas saturation is mainly from the effective pores of NMR T2 distribution. On the contrary, if Sgasdiff value is relatively large, it shows that the adsorbed gas in small pores or kerogen dominantly contributes to gas saturation. In this study, Sgasdiff ranges from 8% to 82%, most are more than 70%, which indicates that a larger proportion of gas is absorbed in pores of kerogen or dissolved in small pores. To further illustrate this problem, we construct two crossplots of gas saturation difference and clay bound water volume, kerogen volume shown in Fig. 7(e) and (f). Fig. 7(e) indicates that gas saturation difference decreases with the increasing clay bound volume, which suggests that NMR “clay water volume” is related to true clay water volume, and the gas saturation difference is little associated to the dissolve gas content. Fig. 7(f) shows that gas saturation difference increases with the kerogen volume rising and the linear relationship is very good. So, it is the kerogen volume that dominantly causes the saturation difference. Therefore, it is further pointed out that it is the ad-sorbed gas in the kerogen that contributes to this gas saturation rather than dissolved gas, and of course, the contribution of the adsorbed gas to gas saturation is greater than that of free gas.
According to the basic principles of NMR and the mode of gas occurrence in organic shale, the water in organic shale is in bound status, and NMR T2 relaxation of kerogen and adsorbed gas are both very short (Sigal and Odusina, 2011). In order to analyze if T2 distributions of kerogen and adsorbed gas overlap together with clay bound water, we built an index

where ϕCBW is the NMR “clay bound water” volume, %; and Swirr is the NMR “clay bound water” or irreducible water saturation, %.Fig. 8(a) is the crossplot of the measured water saturation, Swater , and Swirr . As can be seen, Swater is far lower than Swirr , which shows that NMR “clay bound water” volume also includes other ﬂuids besides true clay water. To this end, we construct a para-meter, Swaterdiff , named as ﬂuid saturation difference, which de-scribes the difference between Swirr and Swater ,

where Swaterdiff is the water saturation difference, %

Fig. 8(b) and (c) are crossplots of Swaterdiff and TOC content, and kerogen volume, respectively. The water saturation difference in-creases with TOC content and kerogen volume rising, and espe-cially, it has an excellent linear relationship with kerogen volume. This proves the kerogen or adsorbed gas in kerogen is located in short relaxation part of T2 distribution, and their NMR T2 dis-tributions overlap together with that of NMR “clay bound water” volume. Therefore, NMR “clay bound water” in T2 distribution includes the contributions of both kerogen and its absorbed gas.
Therefore, based on the above analysis, NMR response in or-ganic shale includes movable ﬂuid, that is, free gas, true clay bound water, kerogen, and its absorbed gas. Therefore, we built a gas saturation model based on NMR bin porosity.

where Vkero is the kerogen volume, %.
Since there is no movable water in organic shale, and the water comes from bound ﬂuid part of T2 distribution with fast relaxation time. Therefore, we constructed a water saturation formula as follows:

Fig. 8. Relationship between water saturation and NMR bin porosity. It indicates taht NMR bound water saturation includes true bound water as well as other ﬂuids. Water saturation difference is proportional to both TOC content (a) and kerogen volume (b).

Otherwise, water saturation may be attained from correlation listed in Fig. 9,

So, the ﬂuid saturations evaluation of organic shale is com-pleted by using some formulae above.

4. Pore structure of gas shale

From the above Eq. (1), the ﬂuid has long bulk relaxation time, and it contributes little to total T2 relaxation time. Moreover, in the low ﬁeld NMR experiment, the magnetic ﬁeld applied into the NMR instrument is uniform, so there is no diffusion relaxation (Xu and Torres-Verdín, 2013). If the pyrite volume of organic shale is little such as core H7 and H48, which could not induce internal magnetic ﬁeld gratitude, the diffusion relaxation time may be ig-nored. Furthermore, the porous medium generally has large spe-ciﬁc surface area with strong interactions between hydrogen-containing ﬂuids (such as water, kerogen, and so on) and grains, and the surface relaxation is dominated in total T2 relaxation. So, the NMR porosity for such shale like H6 and H48 would approx-imate the real porosity. Therefore, Eq. (1) can be simpliﬁed as

From Eq. (1), T2 relaxation time is related to the surface relaxivity (ρ2) and the surface area to volume ratio (S/V). The surface relaxavity reﬂects transverse relaxation of protons, which is mainly related to minerals of the rock, and it is larger in classic carbonate than in classic rocks. Therefore, the echo decays quickly in classic rock, whereas it decays slowly in carbonate rocks. Fer-romagnetic minerals such as chlorite and hematite have high magnetic susceptibility, which greatly accelerates the echo decaying.
The size of pores also plays an important role in the T2 re-laxation. Large pore has smaller S/V, less chance of collisions among the particles, and the T2 relaxation time is relatively longer; in contrast, small pore has larger S/V value, and the T2 relaxation time is much shorter. Therefore, NMR T2 relaxation of water-sa-turated rocks reﬂects substantial interaction between the ﬂuid and surface of pores.

Fig. 10. NMR-based speciﬁc surface area and pore size distribution of shale. The speciﬁc surface area of shale is mainly in the range of 62.5–1960 μm?1 with an average value of about 9.8 μm?1 (a), and the pore radius averages is around 0.05 μm (b). These pores in such shale belong to micro-pores.

According to Eq. (13), NMR T2 spectrum in water-saturated rock mainly reﬂects the characteristics of the speciﬁc surface area (surface area to volume ratio) of the porous medium. The more developed ﬁne pores in the rock, the larger the speciﬁc surface area, and the relaxation time will be shorter. Thus, according to NMR T2 experiments, the speciﬁc surface area from T2 distribution of shale can be a derived from Eq. (13), the speciﬁc surface area is

If the pore is spherical, SV/=3r/; If the pore is ideal cylinder, SV/= 2r/, where rc is the radius of pore. From the microscopic part of organic shale shown in Fig. 1, the pore geometric of shale can be regarded as cylinder. Therefore, Eq. (14) can be rewritten as

According to the results from Sondergeld et al. (2012), the transverse surface relaxivity ( ρ2) of shale is constant and about 0.051 μs/m. Therefore, the speciﬁc surface area distribution of H42 core was calculated from Eq. (13), which is shown in Fig. 10. The speciﬁc surface area of shale is mainly in the range of 62.5–1960 μm?1 with an average value of about 9.8 μm?1 (Fig. 10a), and the pore radius distribution is also calculated (Fig. 10b) with an average pore radius of around 0.05 μm. So, it seems that these pores in such shale belong to micro-pores, which agrees well with the descriptions from Sondergeld et al. (2012).
Therefore, compared to other experimental methods, NMR experiment has higher efﬁciency and more explicit physical mechanism.

5. Case study

The target formation of a case well is Haynesville Shale. In this well, Geophysical logs include: natural gamma ray (GR), sponta-neous potential (SP), array induction logs (AIT), compensated acoustic log (DT), litho-density log (RHOBþPE), compensated neutron log (NPHI), natural gamma ray spectrometry logs includ-ing Uranium (U), Thorium (TH), and potassium (K), and CMR logs. At the same time, 49 cores samples were plugged in the target organic shale, and the TOC measurement of core samples is made in the laboratory.
To correct the NMR porosity, ﬁrstly, TOC content was predicted, which can be calculated from well logs by using Δ log R (Passey et al., 1990), experimental formula, or radial base function (RBF) method (Tan et al., 2013a, 2013b). Because the corrections of TOC and logs are all so poor, we used RBF method to calculate TOC content, named as TOCR, which is illustrated in Tack 5 of Fig. 11 and is better than that from experimental formula. Then, the kerogen volume was calculated by using the equation showed in Fig. 9(g), and the corrected NMR porosity was subsequently gained from Eqs. (2) and (3), named as TCMR. Next, the absolute per-meability and water saturation are estimated from Eq. (4) and Eq.(10), respectively. All results are illustrated in Fig. 11.
For verifying the interpretation results, another 3 core plugs at different positions were chosen for gas saturation measurement and Langmuir adsorption isotherm test. However, it is so regret that gas saturation of three cores were not measured successfully, and the gas storage capacity was obtained under formation pres-sure. Fig. 12 illustrates the relationship between gas storage ca-pacity and the calculated gas saturation from NMR bin porosity. As is known to all, three states of gas in shale contribute to the gas storage capacity. The calculated gas saturation is mainly relative to free gas and desorb gas, and the higher the gas saturation, the larger the corresponding gas storage capacity, so both match well with echo other. From Fig. 12, the calculated gas saturation in three cores trend to the corresponding gas storage capacity, and this veriﬁes the saturation calculation method is correct. Of course, it is not a strict proof but an auxiliary veriﬁcation, and the laboratory measurement of gas saturation will be a strict proof for the sa-turation calculation model.

Fig. 11. NMR logs interpretation results of a case study including TOC content, NMR porosity, NMR permeability, and NMR saturation. They are in good agreement with the laboratory measurements of core plugs.

Fig. 12. Relationship between the calculated gas saturation and gas storage capa-city. It veriﬁes the saturation calculation is correct.

6. Discussions

NMR technology can provide rich bin porosity information of rock, so it improves petrophysical interpretation models including porosity, permeability, and saturation evaluation. The case study also illustrates it is advantageous in the formation evaluation of shale. Furthermore, mud ﬁltrate does not invade the organic shale, which is different from sandstone, and NMR depth of investigation is in the range of undisturbed shale. So, the NMR-based gas sa-turation method in organic shale is more applicable and more accurate than in other permeable formations.
However, the T2 distribution of organic shale is still effected by kerogen and pyrite volumetric concentrations, and NMR porosity may be underestimated. Moreover, the T2 signals of absorbed gas and kerogen overlap together with clay bound water, and it is difﬁcult to discriminate one from another. Therefore, two-dimen-sional NMR technology should be developed and applied into or-ganic shale, which can not only observe T2 relaxation, but also measure the contribution of diffusion (Tan et al., 2013a, 2013b; Cao Minh et al., 2012; Chalmers and Bustin, 2008; Kausik et al., 2011), so it can greatly improve the ﬂuid typing through integrated analysis of T2 relaxation and diffusion coefﬁcient among oil, gas, and water.

7. Conclusions

Based on NMR measurements of shale core plugs, NMR re-sponse characteristics of shale were investigated in detail, and the differences between NMR and conventional porosity in shale were explained, and the corrected NMR porosity model is proposed after some inﬂuencing factors were analyzed. A speciﬁc perme-ability model based on NMR bin porosity was also built, and some saturation models of shale were also established. Some conclu-sions were drawn as follows:

(1) NMR T2 distributions of shale can be divided into two types: left peaks dominated discontinuous T2 distribution type (Type
I) and continuous bimodal T2 distribution (Type II). The am-plitude difference between the left and right peaks in Type I shale is more dominated than Type I shale. The T2 geometric mean of Type II is also larger, which indicates that different sizes of pores in Type II are developed and distribute relatively broadly. Moreover, the permeability of Type II is higher than that of Type I because of larger movable ﬂuid volume.
(2) NMR porosity of shale is usually lower than density porosity, and the porosity difference increases with TOC content rising. So, we deduce that the pyrite and kerogen leads to lower NMR porosity.
(3) The permeability of shale is related to NMR effective porosity and NMR clay bound ﬂuid volume rather than total porosity. The permeability model based on NMR effective porosity and clay bound water volume clearly reﬂects the penetration mechanism of ﬂuids.
(4) For the shale with a little pyrite, the measured NMR T2 dis-tribution dominantly reﬂects the pore geometry. So, speciﬁc surface area can be calculated from NMR T2 distribution. For Haynesville Shale, speciﬁc surface area ranges mainly from 80.0 μm?1 to 1000 μm?1, and the pore radius averages about 0.05 μm. So, the pores of Haynesville Shale are classiﬁed as micro-pores.
(5) Total gas contained in organic shale not only includes free gas in NMR movable ﬂuid volume, but also the adsorbed gas in kerogen or pores among clays. NMR experiment indicates that the kerogen and adsorbed gas are located in clay bound water part of NMR T2 distribution, and they overlap together with clay bound water. Moreover, the adsorption gas contributes to total gas saturation more than free gas for Haynesville Shale.