Classifying Multiscale Pores and Investigating Their Relationship with

Aug 21, 2017 - Since tight sandstone usually contains pores of multiscales and various types, it is important to classify pores in scale and investiga...
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Classifying Multiscale Pores and Investigating Their Relationship with Porosity and Permeability in Tight Sandstone Gas Reservoirs Dianshi Xiao, Shuangfang Lu,* Jinxiu Yang, Luchuan Zhang, and Bo Li Research Institute of Unconventional Oil & Gas and Renewable Energy, China University of Petroleum (East China), Qingdao 266580, China ABSTRACT: Since tight sandstone usually contains pores of multiscales and various types, it is important to classify pores in scale and investigate their distinct contributions to porosity and permeability for better understanding of the storage and percolation mechanism of tight gas sandstone reservoirs. In this study, rate-controlled porosimetry (RCP) was performed to probe the pore connectivity and fractal structures and classify pores’ size, while low temperature N2 adsorption and nuclear magnetic resonance (NMR) were conducted to determine the specific surface area (SSA) and the relative content for different scales of pores, respectively. Based on the differences in pore connectivity and the contributions to storage and percolation, pores in tight sandstone are divided into nanopores (mainly < 0.5 μm), micropores (mainly 0.5−1.5 μm), and mesopores (mainly > 1.5 μm). Nanopores consist of the clay-associated pores and intraparticle dissolution pores, contributing to both percolation and storage, especially to the SSA; micropores comprise the narrow slits between grains and the quartz intercrystalline pores, mostly dominating the permeability, while mesopores, dominated by the interparticle-related pores, must be connected with micropores/nanopores and therefore mostly contribute to storage. The weak correlation between porosity and permeability is mainly attributed to the combination of diagenesis and compaction, because they damage the correlation of micropores content with porosity. For tight sandstones with the weak correlation between petrophysical properties, permeability established by producible porosity, Coates model, and Pittman method are better than that by the SDR (Schlumberger Doll Research) model. Tight sandstone reservoirs with different content of micropores and nanopores show a distinct gas storage and percolation mechanism; with decreasing microporosity, the contribution of nanopores becomes predominant, the adsorbed gas content becomes greater, and the decreasing rate in production with pressure decay becomes slow. micropores (1−62.5 μm), and mesopores (62.5 μm−4 mm), which is more suitable for tight sandstone,21 but the constant ranges employed in this classification are unsuitable for all types of tight sands that experience different processes of diagenesis (e.g., dissolution and clay cementation) and compaction which commonly result in a different decrease in pore size.10,22,23 The pore fractal structure and pore connectivity are usually employed to improve the reasonability of pore classification; for instance, Sakhaee-Pour and Bryant15 classified pores of tight sandstone into intergranular pores-dominated and intragranular pores-dominated based on mercury intrusion features; Zou et al.17 and Zhang et al.18 divided the coal and lacustrine shale pores into micropores, mesopores, and macropores based on the pore fractal structure using NMR and mercury porosimetry, respectively. However, these classifications were mainly for fine-grained rock (e.g., shale and carbonates) and rarely considered the distinct effects of different scales of pores on storage and percolation. The establishment of a new pore size classification for tight sandstone based on the differences in the contributions to storage and seepage will help to better understand the forming mechanism of the poor correlation between porosity and permeability and to guide the reasonable petrophysical interpretation and reservoirs evaluation.

1. INTRODUCTION Tight sandstone gas, an important and potential unconventional resource, is widespread in the major gas-bearing basins across the world, such as the San Juan Basin and Alberta Basin in North America,1,2 and the Ordos Basin and Songliao Basin in China.3−5 After experiencing strong compaction and various diagenesis,6,7 tight sandstone reservoirs commonly contain pores of various types and multiscales ranging from tens of nanometers to hundreds of micrometers in size,8−10 but only a portion of the pores play a major contribution to seepage11 which is different from that to storage. A tight sandstone reservoir is characterized by wide pore size distribution (PSD) and diverse pore−throat connectivity,12,13 which results in a weak correlation between petrophysical properties (i.e., porosity and permeability)11,14 and produces distinct reservoir performance.15 Therefore, effectively classifying multiscale pores and investigating the relationship between different scales of pores and petrophysical properties are the keys for better understanding the storage and seepage mechanism of tight sandstone and guiding reasonable petrophysical interpretation. There are many ongoing studies on pores size classification of tight reservoirs,16−18 among which those proposed by the International Union of Pure and Applied Chemistry (IUPAC)19 and Loucks et al.20 are generally accepted. According to IUPAC,19 pores are divided into micropores (50 nm), classification which is suitable for nanoscale pores-dominated reservoirs such as shale but not for tight sandstones with abundant micrometer-scale pores. Loucks et al.20 extended Choquette and Pray’s pore size classification for carbonates and grouped the pores into nanopores ( 0.45 for all samples (Figure 3), and these loops all belong to type H3 based on IUPAC.19 Type H3 is commonly related to the development of slit-shaped pores40 which were given rise to by the aggregation of platelike particles, such as clay minerals (e.g., chlorite and illite).28 The magnitudes C

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Figure 2. Comparisons of throat size distribution derived from RCP test and T2 spectra measured by NMR before (red line) and after centrifuging (blue dashed line). rinflect (left black dashed line) and rd (right black dashed line) represent the throat fractal inflection point and the throat radius corresponding to displacement pressure, respectively; based on these, pores are divided into nanopores, micropores, and mesopores from left to right.

or fall abruptly;26,27 according to this fluctuation, the size distribution of throats and pore bodies behind the throats can be separately revealed in RCP tests. The throat intrusion curve can be utilized to investigate throat fractal structure.43 For throats with a radius of rc accessible to mercury under the pressure of Pc, the total number of measured throats N(rc) and rc satisfy the following relation based on the fractal theory:44 N (rc) ∝ rc−D

(1)

where D is the fractal dimension. Assuming that there is a positive correlation between the cylindrical throat length, L, and radius, rc, with a scale coefficient of c, the volume Vi(rc) of a throat can be expressed as Vi(rc) = πrc 2l = cπrc 3

Figure 3. Adsorption and desorption branches measured by low temperature N2 adsorption for tight sandstone samples with different clay content.

(2)

Therefore, the total throat intrusion volume V(>rc) measured by RCP tests under the injection pressure of Pc can be expressed as

of loops, SSA, and the measured pore volume increase with increasing clay content (Figure 3 and Table 1), indicating that clay minerals play a significant contribution to the formation of small pores (mainly rc) = N (rc) Vi(rc) ∝ cπrc 3 − D

(3)

After the derivative with respect to rc, the following surface fractal equation can be obtained: −

dV ( >rc) ∝ cπ (3 − D)rc 2 − Ds drc

(4)

If throats are surface fractals in tight sandstone, −dV(>rc)/drc will show an obvious linear relation with rc in the double logarithmic coordinates, and the surface fractal dimension Ds = 2 − k, where k is the slope of the linear fitting. D

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Figure 4. Surface fractal features of throats using the throat intrusion data from RCP test for nine tight sands samples.

An obvious bilinear relation between −dV/dr and throat radius, r, can be found in all samples (Figure 4), and all fitting coefficients (i.e., R2) are higher than 0.6 with an average of 0.93, implying the general development of throats with bifractal structure in tight sandstone. The fractal inflection point (FIP), the intersection of two ranges with different Ds, varies from 0.768 to 0.306 μm in size (Figure 4), and the corresponding pressure can separate the total intrusion of RCP into two parts (Figure 5), characterized by an obvious increase and no change in the pore body intrusion increment with pressure, respectively, corresponding to different mercury intrusion features, pore connectivity, and pore type as follows. When pressure is lower than FIP, the total intrusion increment is contributed to by a large amount of pore bodies and relatively few throats (Figure 5), implying the connectivity of “larger pores with narrow throats”. The corresponding surface fractal dimension of measured throats, Ds1, varies from 3.76 to 6.19 (Figure 4), which is larger than the upper limit of the surface fractal (i.e., 3) mainly due to the presence of many types of throats and microcracks.10 Ds1 can reflect the connectivity of larger pores since it shows a better correlation with the average pore to throat ratio derived from RCP (Figure 6A); that is, the larger Ds1 is, the more irregular the surface of the throats and the worse the pore connection are. Therefore, throats in this range mainly correspond to narrow necks connecting two adjacent pore voids (e.g., the interparticle pores) and play the major role in seepage, and these throats mainly consist of the narrow slits between grains and quartz intercrystalline pores (Figure 7A−C). Once the pressure is higher than FIP, the total intrusion increment is mainly contributed to by throats (Figure 5); no obvious intrusion of pore bodies following that of throats means no obvious distinction between throats and pore bodies, implying the connectivity of a “treelike pores network”,15 which indicates that throats in this range contribute to both seepage and storage.

Ds2, the surface fractal dimension of measured throats, varies from 2.19 to 4.22 with the mean value of 2.96 (Figure 4) and shows an obvious correlation with the calculated BET SSA from LTNA tests except sample S6 (Figure 6B), indicating that Ds2 can reflect the SSA of tight samples. Due to the significant contribution of clay minerals to the SSA as mentioned above, it can be concluded that throats in this range are dominated by clay-associated pores. The intraparticle dissolution pores with better interconnection are another contributor to throats in this range (Figure 7E,F), which leads to an obvious increase in Ds2 such as for sample S6 (Figure 6B). Therefore, there are obvious differences in types and pore connectivity between throats with different Ds. Using the fractal inflection point of throats, pore space can be divided into the interparticle-related pores with “large pores with narrow throats” structure and the intraparticle-related pores with “treelike pores” structure (Figure 5). 3.2.2. Classifying Pores in Tight Sandstone. Displacement pressure (Pd) is the minimum pressure required for mercury to overcome the capillary force to enter the rock,30 once the pressure is greater than Pd, mercury starts to fill pore voids through narrow throats; therefore the maximum throat radius, rd (corresponding to Pd), can further divide the interparticle-related pores into two parts mainly acting as pore bodies and throats, respectively. Therefore, with rd and rinflect (i.e., the radius of FIP), pores can be divided into nanopores, micropores, and mesopores (Figure 2). The rd of all samples varies from 0.5 to 2.91 μm, with an average value of about 1.5 μm (Table 2), while rinflect is in the range of 0.306−0.768 μm with an average value of 0.5 μm (Table 2), meaning that mesopores are commonly larger than 1.5 μm and nanopores are usually smaller than 0.5 μm for tight sandstone samples. There is an obviously positive correlation between rd and rinflect (Figure 2 and Table 2); with decreasing E

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Figure 5. Mercury intrusion curves of total, throat, and pore body with pressure for typical tight sandstone samples. The throat inflection point is used to divide pores into the interparticle-related pores with “larger pores connected with throats” structure and the intraparticle-related pores with “treelike pores” structure, corresponding to an obvious increase and no change in pore body intrusion increment, respectively; the displacement pressure is used to further divide the interparticle-related pores into two parts mainly acting as pore bodies and throats, respectively.

Figure 6. (A) Relationship between Ds1 (surface fractal dimension of throats at lower pressure) and average pore to throat ratio derived from RCP test. (B) Relationship between Ds2 (surface fractal dimension of throats at higher pressure) and BET SSA from LTNA tests.

permeability from samples D18 to S18, rd becomes smaller and closer to rinflect (Figure 2), implying that the constant range employed in pore size classification is not suitable for tight sandstones with different permeabilities. SEM images were used to identify the pore types (Figure 7) and to further investigate the differences in pore connectivity of different scales of pores in tight sandstones. Pores were classified into the interparticle pores, dissolution pores (including interparticle and intraparticle), clay-associated pores, quartz intercrystalline pores, and a few microcracks (Figure 7) according to the classification of Zhao et al.21 Based on the relationship between pore types and pore size distribution from sample D5 (Figure 8), the interparticle pores and interparticle dissolution pores are larger and account for 90% of pores with radius larger than 1.0 μm, meaning that these pores constitute the majority of mesopores, but they are scattered and should be connected with narrow throats for the entrance of fluid (Figure 7B,C); therefore

mesopores mainly contribute to storage and have no significant effects on permeability although mesopores may be also necessary for the formation of seepage paths (Figure 7B); the clayassociated pores and intraparticle dissolution pores commonly coexist (Figure 7E) and are continuous, multiscaled,41 and wellinterconnected (Figure 7A,D), accounting for more than 70% of pores with radius smaller than 0.5 μm (Figure 8). Therefore, they dominate the nanopores and lead to the contribution of nanopores to both percolation and storage, especially to the SSA of tight samples. Micropores mainly consist of the quartz intercrystalline pores; narrow slits between grains and microcracks, these pores serve as the necessary flow paths connecting mesopores (Figure 7B) and therefore play the major contribution to percolation. Therefore, this new classification takes into account the differences in pore types and the contributions to percolation and storage capability (including adsorption capacity) between different scales of pores. F

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Figure 7. Pore types, morphology, and connectivities found in SEM images (A−E) and thin section analysis (F). Panel A shows the interparticle pores, interparticle/intraparticle dissolution pores, clay-associated pores, narrow slits between grains, and quartz intercrystalline pores in sample D5. Panel B illustrates the distribution and connectivities of nanopores (mainly including clay-associated pores and intraparticle dissolution pores), micropores (including quartz intercrystalline pores and narrow slits), and mesopores (including the interparticle pores and interparticle dissolution pores). Panel C shows that the residual interparticle pores are connected with narrow slits and quartz intercrystalline pores in sample D18. Panel D shows the clayassociated pores are honeycombed and with well interconnection in sample S33. Panel E shows the coexistences of the clay-associated pores and intraparticle dissolution pores of feldspar. Panel F shows the interparticle dissolution pores and intraparticle dissolution pores in sample S6.

3.3. Relationship of Different Scales of Pores with Porosity. Due to the limitation of the maximum intrusion pressure of RCP (i.e., 6.22 MPa), the measured porosity by RCP is obviously lower than helium porosity or NMR porosity (Table 1), which indicates that pores accounting for 50% of total porosity cannot be revealed by RCP. Therefore, NMR-derived PSD should be applied to determine the content of different scales of pores and then further investigate their relations with porosity and permeability. 3.3.1. Content of Different Scales of Pores. T2 distribution measured by NMR can be converted into the PSD by calibrating with other experimental data, such as mercury porosimetry.10,30 RCP-derived PSD consists of a right peak and a left semipeak (Figure 9), corresponding to the distribution of pore bodies and throats, respectively. The size of a pore body is calculated as the radius of an equivalent sphere with the same pore volume;13,21 however, pore bodies in tight samples are

actually irregular and have a rough surface due to chlorite coating and quartz cementation (Figure 7); therefore RCP will yield inappropriate pore body size (mainly ranging from 100 to 200 μm) (Figure 9). In contrast, throat distribution is calculated from the throat intrusion using the Washburn equation with the assumption of cylindrical pores being more reliable,10 and the better correlation between RCP-derived throat distribution and the shorter population of T2 spectra is commonly observed in tight samples (Figure 9 and Figure 2). Therefore, based on this correlation, the surface relaxivity and NMR-derived PSD of tight samples can be determined (Table 2 and Figure 2). The surface relaxivity of all samples varies from 7 to 30 μm/s (Table 2), which is mainly affected by the content and distribution of iron-bearing minerals (e.g., pyrite, chlorite, and illite).45 The content and percentage of different scales of pores (Table 2 and Figure 10) are determined by calculating the cumulative pore volume and frequency distribution with NMR-derived PSD, G

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Table 2. Lists of Dividing Radii, Porosity, and Producible Porosity of Different Scales of Pores (Including Meso-, Micro-, and Nanopores)a mesopores

micropores

nanopores

sample

rd (μm)

rinflect (μm)

surface relaxivity (μm/s)

porosity (%)

producible porosity (%)

porosity (%)

producible porosity (%)

porosity (%)

producible porosity (%)

D18 D24 D20 D5 D7 S46 S6 S33 S18

2.82 2.68 2.91 1.03 0.94 0.77 0.91 0.63 0.49

0.62 0.77 0.73 0.49 0.47 0.35 0.36 0.39 0.31

30 30 15 17 22.5 17 15 7 9

2.5 2.19 1.63 2.93 1.28 2.71 2.18 1.56 0.56

2.28 1.67 1.333 2.545 1.07 1.22 0.94 0.93 0.31

2.93 2.57 1.67 1.03 1.1 1.32 1.03 0.57 0.2

2.71 2.07 1.35 0.7 0.96 0.68 0.69 0.28 0.01

4.43 2.26 2.28 4.67 4.67 3.87 7.28 6.67 6.64

1.67 0.91 0.48 1.69 1.69 1.6 2.46 0.69 1.13

a

Notes: rd and rinflect, throat radius corresponding to displacement pressure and throat fractal inflection point, respectively. Surface relaxivity is calculated by calibrating T2 distribution with NMR-derived throat size distribution.

Figure 8. Proportion distribution of different types of pores in different pore size ranges for sample D5.

respectively. It is indicated that nanopores are predominant in tight samples (Figure 10), accounting for 32.2%−89.7% of porosity, followed by mesopores, varying from 7.6% to 34.3% in percentage, and micropores are the fewest, with an average value of 17.7%. The percentage of nanopores shows an obviously positive correlation with the content of illite and chlorite (Figure 10), which confirms that nanopores are dominated by the clay-associated pores. 3.3.2. Effects of Diagenesis on Different Scales of Pores. Helium porosity is the sum of different scales of pores content, and the relations of porosity with the content of different scales of pores are affected by the combination of diagenesis and compaction besides the original sediments (e.g., grain size, sorting, and so on). For instance, the dissolution of unstable minerals (e.g., feldspar and rock fragments) gives rise to a large number of intraparticle/interparticle dissolution pores (Figure 7A,F),46 and therefore results in an increase in the total porosity and the content of all scales of pores; the claydominated cementation fills the interparticle pores and blocks throats (Figure 7A,C−E),7,47 and results in a decrease in the content of mesopores and micropores but leads to an obvious increase in that of nanopores. The compaction will lead to an obvious reduction in the content of all types of pores and total porosity;22 however, the early quartz overgrowth (Figure 7A,C) can prevent the residual interparticle pores (i.e., mesopores) from the impact of later compaction.47 Total porosity of all samples shows a certain positive correlation with the content of mesopores but no obvious relationship with that of nanopores or micropores (Figure 10), suggesting that tight sandstone

Figure 9. Comparisons of PSDs derived from RCP and NMR for tight samples D5 and S6.

samples had experienced various types of diagenesis and stronger compaction. The relationships of microporosity (i.e., the content of micropores) with mesoporosity and nanoporosity (i.e., the content of nanopores) are shown in Figure 11. The following observations can be found: (1) For samples with low clay content and weak compaction (e.g., D18, D24, and D20), mesoporosity and nanoporosity both increase with increasing the microporosity, meaning that the content of all scales of pores shows a positive correlation with each other. (2) With increasing clay cementation (i.e., the color of circles in Figure 11 varies from yellow to blue), the microporosity decreases and nanoporosity increases constantly, while the mesoporosity keeps stable in the beginning (e.g., D5 and D7) and then decreases significantly (e.g., S33 and S18), confirming that clay plays an important role in the formation of nanopores in tight sandstone. With increasing clay content, the occurrences of clay vary from pore-lining (Figure 7D) to pore-filling (Figure 7E),23 and its impacts on mesopores become greater, leading to a faster decrease in mesoporosity. (3) Compared to other samples with low clay content (e.g., D24, D18, and D20), sample S46 with the deeper burial depth has similar mesoporosity and nanoporosity, but lower microporosity (Figure 11), indicating that the intense H

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Figure 10. Comparisons of the fraction porosity and proportion of different scales of pores and the content of illite and chlorite for nine tight sandstone samples.

Figure 11. Relations of microporosity with mesoporosity (A) and nanoporosity (B). The burial depth and clay (illite and chlorite) content of all samples are represented by the size and color of circles, respectively, which reflect the strength of compaction and clay cementation experienced by the samples, respectively.

compaction greatly damages micropores in tight sandstone, while it has limited damage to mesopores likely due to the effect of early quartz overgrowth. Interestingly, S6 is the tuffaceous sandstone, in which the volcanic ash filled the interparticle pores and was subsequently dissolved by organic acid (Figure 7F); therefore, this sample corresponds to the higher nanoporostiy and mesoporosity but similar microporosity (Figure 11) due to the stronger compaction compared to other samples with the similar clay content (e.g., D5 and D7). Therefore, the combination of various diagenesis and compaction play the major role in controlling the relative content of different scales of pores, resulting in the poor correlation of total porosity with microporosity and nanoporosity (Figure 10). 3.4. Relationship of Pores with Permeability and Evaluating Permeability. 3.4.1. Relationship of Pores with Permeability. The producible porosity is determined by combining T2 distributions measured by NMR before and after centrifuging (Figure 2). It is indicated that permeability shows a better positive correlation with the producible porosity than with total porosity for all scales of pores (Figure 12), meaning that the producible pores by centrifuging play the major contribution to permeability; the content of producible micropores has the best correlation with permeability (Figure 12B), followed by that of mesopores (Figure 12A) and nanopores (Figure 12C), implying

the producible micropores dominate the percolation of tight sandstone; although the producible mesopores show good correlation with permeability mainly due to the obvious relationship between producible mesoporosity and microporosity in tight samples (Figure 2 and Figure 12A), these pores have limited contribution to permeability since they must be connected by micropores (Figure 7B) as discussed above. However, the e-exponential fittings of permeability and producible microporosity do not pass the origin (Figure 12B); i.e., the evaluated permeability will be larger than 0.03 mD even if producible microporosity closes to zero, theoretically implying that other pores also contribute to permeability. The producible nanopores show the weakest correlation with permeability for all samples but show an obviously positive correlation with decreasing permeability, further confirming that producible nanopores play the important role in controlling the percolation of lower permeability in tight samples (e.g., sample S18, S33, S46, and S6). Therefore, permeability is mainly controlled by the producible micropores and producible nanopores in tight sands, while the total porosity shows no clear correlation with the contents of micropores and nanopores (Figure 10) due to the combination of compaction and diagenesis, which leads to the poor correlation between porosity and permeability for tight sandstones experiencing a different process of diagenesis. I

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Figure 12. Relationships of permeability with the porosity and producible porosity of mesopores (A), micropores (B), and nanopores (C) for tight sandstone samples.

Table 3. Empirical Equations of Coates Model, SDR Model, ri (i Increasing from 10 to 25) Method and the New Model Proposed in This Work with or without Porosity Developed from Regression Analysisa with porosity

without porosity

function expression

R2

function expression

R2

Coates

⎛ FFI ⎞ ⎟ log(k) = 0.668 + 1.12 log(ϕ) + +1.54 log⎜ ⎝ BVI ⎠

0.82

⎛ FFI ⎞ ⎟ log(k) = − 0.578 + + 1.58 log⎜ ⎝ BVI ⎠

0.82

SDR

log(k) = − 3.54 − 0.34 log(ϕ) + 1.758 log(T2gm)

0.59

log(k) = − 0.578 + 1.58 log(T2gm)

0.62

r25

log(k) = − 0.207 + 1.458 log(r25)

0.65

r20

log(k) = − 0.427 + 1.423 log(r20)

0.78

log(k) = − 0.533 + 1.465 log(r15)

0.81

log(k) = − 0.726 + 1.562 log(r10)

0.80

prediction model

r15

log(k) = − 0.388 + 0.828 log(ϕ) + 1.43 log(r15)

0.8

r10 new model a

k = 3486ϕ1f

2.1

+ 0.702ϕ2f

0.557

0.92

Notes: ϕ1f, producible microporosity, %; ϕ2f, producible nanoporosity, %.

predicted by the Coates model considering the fluid mobility and r15 model considering the throat distribution is much better than that by SDR model considering the pore distribution (Table 3 and Figure 13), which is mainly due to throats’ size dominating

3.4.2. Comparison of Tight Sandstone Permeability Prediction Models. There are many oncoming research works on the permeability estimation using NMR or mercury porosimetry; popular models include the Coates model29 based on the content of free fluid and irreducible water, the mean T2 model which was also called the SDR (Schlumberger Doll Research) Model,48 and the ri method introduced by Pittman,49 and these models can be expressed by the following formula: log(k) = A + B log(ϕ) + C log(f )

(5)

where k is permeability, mD; ϕ is porosity, fraction; f is variable and takes FFI/BVI (the ratio of free fluid index to irreducible bulk volume, fraction); T2gm is the geometric mean of T2 distribution, ms; and ri is the throat radius corresponding to the total mercury saturation of i%, μm or the Coates model, SDR model, and Pittman method, respectively. The parameters A, B, and C can be obtained using multiparameter regression with the measured permeability and experimental results from NMR or RCP. The fitting empirical equations of the three permeability models are listed in Table 3. Each model includes two cases: with porosity and without porosity. The following findings can be reached: (1) the employment of helium porosity in the permeability estimation model has limited improvement in the accuracy of permeability prediction likely due to the poor correlation between porosity and permeability in tight sandstone. (2) For the ri method, the best model is yielded when i = 15, which is significantly smaller than that in the conventional sandstones (i = 35),49 and is consistent with that in the Western Australian tight gas sands (i = 10),12 indicating that the required mercury saturation for initial forming of the connected flow path in tight sandstone is obviously lower. (3) The permeability

Figure 13. Comparisons of the power function fitting and e-exponential fitting of producible microporosity and permeability in log−log plot.

the fluid mobility and permeability for tight sandstone samples and is poorly correlated with pore size distribution (Figure 2). For instance, samples S46 and D5 have similar PSD and helium porosity (Figure 2, Table 1), but D5 has a significantly larger throat size distribution (Figure 2) and therefore corresponds to a higher permeability than S46. 3.4.3. New Permeability Evaluation Model. Producible pores provide the predominant percolation channels for rocks; therefore the content and size of these producible pores both control permeability. If the producible porosity is close to zero, permeability will be theoretically close to zero; therefore the power exponential relation between permeability and porosity as J

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Energy & Fuels shown in eq 5 is widely accepted.29,48 The power exponential correlation between permeability and producible microporosity is suitable for tight samples with high permeability, but it will underestimate permeability for tight samples with lower permeability (e.g., samples S18 and S33) (Figure 13), which implies that the effects of producible nanopores must be taken into account for establishing a more practical permeability model. Zou et al.17 established a permeability prediction model for coal based on the producible porosity of different scales of pores. With some appropriate adjustments, a new permeability estimation model for tight sandstone with few microcracks can be established with the content of producible micropores (ϕ1f) and producible nanopores (ϕ2f) which dominate the permeability as discussed above.

k = aϕ1f b + cϕ2f d

an increase in the micropores content from 3.3% (sample S18) to 37.2% (sample D24) (Figure 10), their contribution to permeability widely varies from 0.1% to 96.1% (Table 4) and air permeability increases from 0.0352 to 2.35 mD (Table 1). When permeability is less than 0.06 mD (e.g., samples S33 and S18), the contributions of nanopores to permeability and that to porosity are higher than 75% and 95% (Figure 10 and Table 4), respectively, meaning that nanopores instead of micropores and mesopores dominate the percolation and storage for lower permeability tight sandstones. 3.5. Implications for Percolation and Production of Tight Gas. There are distinct transportation mechanism and accumulation states of gas in different scales of pores,28,50,51 leading to those tight sandstone reservoirs with different relative contents of mesopores, micropores, and nanopores exhibiting various percolation features and production performances. Both free gas and adsorbed gas can be found in tight reservoirs;51 mesopores and micropores, dominated by interparticle-related pores with lower SSA, mainly accommodate free gas, while the predominant clay-associated pores with higher SSA in nanopores and the strong adsorption of methane (CH4) to clay minerals (e.g., illite and smectite)52,53 lead to a great amount of gas being adsorbed on the pore walls and others being free in the center of the nanopores. The gas transportation through mesopores and micropores (mainly >0.5 μm) is predominantly darcy flow,54 and the percolation capability is related to pore structure, e.g., proportional to the square of pore radius and to the content of micropores,55 while in nanopores (mainly