Fractal Analysis of Donghetang Sandstones Using NMR Measurements

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Cite This: Energy Fuels XXXX, XXX, XXX−XXX

Fractal Analysis of Donghetang Sandstones Using NMR Measurements Ziyuan Wang,*,† Mao Pan,*,† Yongmin Shi,† Li Liu,‡ Fengyang Xiong,§ and Ziqiang Qin∥ †

School of Earth and Space Sciences, Peking University, Beijing 100871, China Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, 10100 Bureau Road, Building 130, Austin, Texas 78713-8924, United States § School of Earth Sciences, The Ohio State University, Columbus, Ohio 43210, United States ∥ Department of Petroleum Engineering, University of Wyoming, E Lewis Street, Engineering Building, Laramie, Wyoming 82071-2000, United States ‡

ABSTRACT: Routine core analysis, thin section epifluorescence and scanning electron microscopy (SEM) analyses were performed to delineate the reservoir qualities, pore systems, and pore network characteristics of the Devonian Donghetang sandstone samples. Nuclear magnetic resonance (NMR) measurements were used to gain insight into pore size distributions of these sandstones. Fractal analysis was performed on the NMR T2 spectrum measured at echo spacings of 0.6 and 1.2 ms. Then the relationships between NMR parameters and fractal dimension were investigated. The results show that the pore systems are dominated by primary intergranular pores with a combination of secondary dissolution pores, micropores, and microfractures. Samples with the highest reservoir quality are characterized by a coexistence of primary intergranular and secondary dissolution pores. The parameter T2gm (the geometric mean of the T2 distribution) is a sensitive one for characterizing the pore size distribution and microscopic pore structure since it shows good correlations with T2peak (value of T2 showing the highest frequency on T2 spectrum), permeability, and reservoir quality index (RQI). By using a short echo spacing, more smaller pores can be detected, resulting in a higher fractal dimension. The calculated fractal dimensions show strong positive relationships with the NMR T2peak and T2gm values. Fractal dimensions can be used here to represent the complexity degree and heterogeneity of pore structure, and the coexistence of dissolution pores and large intergranular pores contributes to a heterogeneous pore throat distribution and a high value of fractal dimension. The results are important for petroleum exploitation in the Donghetang sandstones and can provide insights into pore structure characterization in sandstones with similar geological settings. difficult.10,11 Pore throat systems in sandstones have been considered to have a fractal property,13,14 and the heterogeneity and complexity degree of pore structures can be quantitatively characterized by the fractal dimension.8,11,15−19 Fractals are those virtual, self-similar geometrical objects that appear independent of the scales.20,21 Since the concept of fractals was first proposed by Mandelbrot,22 fractal geometry has been widely used to evaluate the heterogeneity of reservoir rocks and build up the relationship between micromorphology and macro performance.10,17,19,23−29 The main goals of this study are to investigate the pore structure and fractal characteristics of the Donghetang marine sandstones in the Donghetang oilfield using a combination of thin section observations, SEM analysis and NMR T2 spectrum. The microscopic pore throat systems were first investigated and the macroscopic reservoir quality was analyzed by routine core analysis. Then the pore size distributions were determined from the NMR T2 spectrum measured at echo spacings of 1.2 and 0.6 ms, respectively, and the relationships between reservoir quality (permeability and reservoir quality index) and NMR parameters such as T2gm and T2peak values were investigated. Fractal analysis was performed on the NMR T2 spectrum, and

1. INTRODUCTION The Devonian Donghetang Formation is one of the most important extensive marine sandstone units for hydrocarbon exploration in the Hade and Halahatang oilfields of the Tarim Basin (Figure 1).1 It was deposited in wave-dominated shoreline and delta environments during the following sea level rise and transgression,1 and the lithology is predominately composed of clean quartzose sandstones.2,3 The clean quartzrich, landward-stepping Donghetang sandstones have been widely recognized as excellent and extensive reservoirs in the Hade and Halahatang oilfields.1 Since the highly productive Dh-1 well in 1990, abundant hydrocarbon has been produced from the Devonian Donghetang sandstones in recent years.1,4,5 However, little research has investigated the pore structure and the relationship between macroscopic reservoir quality and microscopic pore throat structures of Donghetang sandstones. The macroscopic petrophysical parameters, petroleum charging, migration, and accumulation in these sandstones are mainly controlled by the microscopic pore throat structures.6,7 In order to help with successful exploration and efficient development of hydrocarbon in these marine sandstones, quantitative relationships should be built up between the microscopic pore throat structures and macroscopic reservoir behaviors.8−12 However, the complexity and irregularity of the pore structure make the quantitative characterization of the pore structure using traditional Euclidean geometry methods © XXXX American Chemical Society

Received: November 9, 2017 Revised: February 1, 2018 Published: February 2, 2018 A

DOI: 10.1021/acs.energyfuels.7b03463 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. Map showing the location of the Donghetang oilfield within Tarim Bain in China (after Wang et al., 2015). The boundary of panel C is the study area. In panel C, the black points are wells without cores, and red points are wells with continuous cores sampled.

2. THEORIES AND METHODS

the fractal dimensions were derived from the fractal curves. The reasons why the small pore systems are not fractal were discussed, and the relationships between fractal dimensions and NMR parameters were investigated to determine the variation rules of fractal dimensions and the fractal characteristics of the pore throat structure. The work presented here helps improve our understanding of the pore structure characteristics and provides insights into pore structure classification and evaluation of the Donghetang sandstones and also helps extend the application of NMR measurements in fractal analysis for sandstones with similar geological settings worldwide.

2.1. Theory. The distribution of pore sizes in rocks can be described by a fractal model, in which the pore size distribution follows a fractal scaling and then the cumulative size-distribution of pores (N(r)), whose sizes are equal to or greater than the size follow the fractal scaling law as N(r) ∝ r−Df.10,19,30−33 In such a model, the cumulative pore volume Vp in the NMR measurements can be expressed as31,34

⎛ T ⎞3 ‐ D Vp = ⎜ 2 ⎟ ⎝ T2max ⎠

(1)

where Vp is the accumulative volume fraction when the transverse relaxation time is less than T2.35 T2max is the maximum T2 values, and B


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Energy & Fuels they correspond to the smallest and largest pore sizes present in the NMR measurements. T2 is the transverse relaxation time, and D is the calculated fractal dimension.31 The fractal dimensions calculated using NMR have been discussed in detail by Zhang,36 and the basic descriptions of fractal models based on NMR T2 spectrum are also discussed by Zhang and Weller, Zhou and Kang, and Zhao et al.35−37 The fractal model from NMR measurements is given in eq 2:

log Vp = (3 − D) log(T2) + (D − 3) log(T2max )

(2)

Equation 2 is treated as a representative mass fractal description of pore sizes, which is similar to models describing MICP measurements.31 It should be noted that the fractal dimension should be in the range from 2.0 to 3.0 for three-dimensional pore spaces, and 3.0 is commonly not included.12,17,24 The fractal dimension can therefore be deduced from the slope of the linear log−log plot of cumulative pore volume Vp against T2 value.38,39 2.2. Experimental Measurements. Routine core analysis, which includes porosity and air permeability measurements, was performed on the 725 core plug samples using an CMS-300 in the Core Laboratory at Yangtze University. A total of 90 thin sections, which were impregnated with blue epoxy samples to highlight porosity, were examined with a petrographic microscope under plane-polarized and cross-polarized light to determine the pore systems as well as amounts of detrital and diagenetic components. Freshly broken core plug samples, which were coated with carbon, were conducted at 15−20 kV acceleration voltage to take scanning electron microscope (SEM) images in order to identify the various types of clay minerals and detect the micropores associated with the clay minerals. Nuclear magnetic resonance (NMR) is the interaction between the nucleus and the magnetic field.40 A subset of 32 of core plug samples (1.5 in. in diameter and 1 in. in length) were sent to Core Laboratories in Yangtze University for NMR measurements to determine pore size distributions. In contrast with the longitudinal relaxation time (T1 is the time for the system returning to equilibrium), T2 refers to the characteristic time for the precessing secondary magnetic field to lose coherence in the direction perpendicular to the primary field.41 The NMR T2 distributions were measured at 20 °C using a 1 MHz CoreSpec-1000 instruments from Numar Company, U.S.A.. The experiment processes are introduced in the Chinese Standard “Specification for normalization measurement of core NMR parameter in laboratory” (SYT6490-2007).42 The waiting time of NMR apparatus is 6000 ms; the echo spacing (Te) is 0.6 and 1.2 ms, respectively; and 64 stacks were performed to obtain the relaxation curve. The signal/noise ratio for the laboratory NMR measurements was a minimum of 100:1. The samples were fully (100%) saturated with brine, and the NMR T2 distributions, which included the incremental and cumulative T2 relaxation time, were measured. In the NMR curves, the signal amplitude is proportional to the water content of the core sample. Consequently, the higher the signal amplitude, the higher the porosity will be.43 Short T2 components (T2s) indicate large surface-to volume ratio and therefore small pores, whereas long T2 components (T2l) indicate large pores but small surface-to-volume ratio.27,44 Therefore, the irreducible water produce very short T2 relaxation times due to the restriction of molecular motion in small pores, whereas the mobile water commonly exhibits long T2 values.40,42,43,45

Figure 2. Crossplot of core-measured permeability versus porosity for Donghetang sandstones.

R2 of 0.40, implying that the permeability is unrelated to the total porosity but rather controlled by pore structures and possibly the presence of microfractures (Figure 2). There are a few samples characterized by high permeability but relatively low porosity, and they are suggested to contain microfractures (Figure 2). In contrast, samples which have high porosity but low permeability commonly contain poorly connected pore systems. Thin section observation and SEM analysis reveal that the primary pores dominate the pore systems of Donghetang sandstones (Figure 3A,B). The grain contacts are dominated by

Figure 3. Photomicrographs showing the pore and throat systems of Donghetang sandstones. Legend: Q, quartz; F, feldspar; L, Lithic fragment; K, Kaolinite; red arrows, quartz cement. A. Abundant primary pores, Donghe 1-6-7, 293. B. Primary pores dominate the pore systems, Donghe 1-6-7, 26, C. Intragranular pores associated with feldspar dissolution, Donghe 1-6-7, 333. D. Coexistence of primary pores with secondary intragranular dissolution pores, Donghe 1-6-7, 559, PPL. E. Moldic pores, Donghe 1-6-7, 593, PPL. F. Microfracture, Donghe 1-6-7, 134, PPL. G. Micropores associated with the authigenic clay minerals, SEM. H. Authigenic clay minerals which are abundant with micropores, SEM. I. Laminated pore throats, Donghe 1-6-7, 847, PPL. J. Bending laminated pore throats, Donghe 1-6-7, 738, PPL. K. Curved lamellar pore throats in geometry, SEM. L. Control shape pore throats, SEM.

3. RESULTS 3.1. Porosity, Permeability, and Pore Systems. The Donghetang sandstones in Donghetang oilfield generally have moderate reservoir quality, and most of the samples have a porosity greater than 10% and permeability larger than 10 mD (Figure 2). The average helium porosity is 15.9% (range, 4.1%−25.3%), while the porosity ranges from 0.06 to 2520 mD with an average of 157.6 mD (Figure 2). There is a general trend of higher permeability with increasing porosity. However, the correlation between porosity and permeability is low, with C


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Energy & Fuels point, and long grain contacts are rarely observed. Abundant primary pores can be detected by thin sections (Figure 3A,B), which indicates that the Donghetang sandstones had underwent low to moderate degree of mechanical compaction. Secondary intragranular pores, which are mainly derived from the dissolution of feldspars and rock fragments, can also be detected in many samples (Figure 3C,D). These secondary dissolution pores are commonly observed to coexist with the primary pores (Figure 3C,D), and actually the primary intergranular pores are the predominant pore types (Figure 3A−D). Additionally, some moldic pores, which are formed from the complete dissolution of framework grains such as feldspar, can occasionally be observed (Figure 3E). Samples with the highest reservoir quality are characterized by a combination of primary intergranular and secondary dissolution (moldic) pores (Figure 3A−E). Microfractures, which have apertures less than 0.1 mm, are also important reservoir space in the Donghetang sandstones (Figure 3F). Besides the porosity detected by the thin section analysis, there are also abundant micropores, which can be observed by the SEM analysis. The micropores, which tend to have a pore radius less than 10 μm, are mainly associated with the authigenic clay minerals such as Illite and mixed Illite/smectite and kaolinite (Figure 3G, 3H). The pore throats are dominantly of laminated and curved lamellar types (Figure 3I−K). The control shape pore throats are mainly associated with the samples containing abundant authigenic clay minerals (Figure 3L). 3.2. Pore Size Distributions. The NMR T2 transversal relaxation time distribution provides important information on interactions between pore fluids and grain surfaces and therefore the pore structure.43 Pores with large pore throats have longer NMR T2 transverse relaxation time, in contrast, NMR T2 relaxation times of small pores are short.40,43,44,46 In addition, the higher the signal amplitude at certain T2 values, the more the fluid there will be.40 Therefore, the pore size distributions can be differentiated from the NMR T2 spectrum, and additionally the fluid content of certain pore sizes can be calculated.40 Besides NMR porosity, many NMR parameters such as T2gm (amplitude weighted mean on a logarithmic scale), bulk volume of Immovable fluid (BVI), free fluid index (FFI), as well as permeability can be calculated or estimated from NMR data.40,47 In this subsection, we present the pore size distribution characteristics of Donghetang sandstones, and the NMR T2 spectrum are then used for fractal analysis to quantitatively characterize the complexity of the pore structures of the Donghetang sandstones. Figure 4 shows the unimodal behaviors of the NMR incremental T2 distribution, and the cumulative porosity distributions as a function of the relaxation time are also presented (Figure 4). Only one modal is presented in samples with unimodal T2 behaviors, possibly indicating a continuous range of pore size (good sorting of the pore systems; Figure 4).27 Most of the analyzed samples are characterized by a unimodal T2 spectrum, and this is in accordance with the thin section observation and SEM analysis since the dominant pore systems are large intergranular pores, whereas the secondary intragranular pores and micropores are only occasionally observed (Figure 4). Previous studies have confirmed that the bimodal NMR incremental T2 distribution is mainly attributed to the coexistence of large intergranular pores and secondary intragranular pores.27,43 The occasionally observed bimodal NMR incremental T2 distribution is presented in Figure 5, in which both long T2

Figure 4. NMR T2 incremental and cumulative spectra for echo spacing of 1.2 and 0.6 ms, respectively. Note that the T2 incremental spectrum shows bimodal behaviors.

Figure 5. NMR T2 incremental and cumulative spectrum for echo spacing of 1.2 and 0.6 ms, respectively. Note the bimodal behaviors of the T2 spectrum.

components and short T2 components can be observed in the T2 spectrum. However, the T2 spectrum is characterized by right-skewed (lower left peak but higher right peak) distributions due to the dominance of large intergranular pore systems. Most of the T2 components are higher than 100 ms which are most likely related to the remaining larger pores,48 and there are long T2 components even larger than 1000 ms. In contrast, there are very weak short T2 components. In addition, the signal amplitudes of the left peak, which represents micropores with small pore sizes, are much lower than that of right peak (Figure 5). As can be observed in Figure 4, the NMR spectra measured at echo spacing of 0.6 ms are different from those measured at 1.2 ms echo spacing. More small pores, which are associated with short T2 values, can be detected through using a short echo spacing, and it can be observed that, at shorter T2 values (10 ms), the crossover and overlap of the two spectra can be detected, implying that large pores may have varied transverse relaxation time distributions at various echo spacings. In addition, the full signal amplitudes, i.e., the total NMR porosity measured at 0.6 ms echo spacing, can be higher or lower than that measured at 1.2 ms echo spacing (Figures 4 and 5). However, both of the parameters T2gm (the geometric mean of the T2 distribution) measured at 0.6 and 1.2 ms echo spacings show good correlation with permeability (Figure 6). It can be concluded that the higher the T2gm parameter, the better D


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Figure 6. Plots of permeability versus T2gm at echo spacing of 1.2 and 0.6 ms, respectively.

Figure 7. Plots of T2peak versus T2gm at echo spacing of 1.2 and 0.6 ms, respectively.

the reservoir quality will be (Figure 6). Both the T2 values and T2 amplitudes are higher in high permeability samples. Another NMR parameter T2peak, which is defined as the value of T2 that shows the highest frequency on the T2 spectrum,42,47 also shows strongly positive correlation with T2gm (Figure 7). A high T2peak value commonly indicates that the T2 amplitudes are higher, which results in a high T2gm value. Additionally, the parameter T2gm also reveals a relatively strong positive relationship with the RQI values (Figure 8). Parameter reservoir quality index (RQI), which is defined as the ratio of permeability to fractional porosity under the square root (eq 3),27,49 is an important parameter in addressing the reservoir quality in various scales50−52 and is commonly used for formation classification and pore structure evaluation.27,37 Regression analysis reveals that RQI is positively correlated with T2gm with a high correlation coefficient (R2) larger than 0.68 (Figure 8). Therefore, according to NMR pore size distribution, the T2gm is a sensitive parameter for characterizing the pore size distribution and microscopic pore structure.27 RQI =

K φ

(3)

where RQI is the reservoir quality index, μm, K is the permeability, μm2, and φ is the fractional porosity. 3.3. Fractal Analysis. Equation 2 foresees that the relationship between the cumulative porosity distribution and NMR transverse relaxation time distribution (T2) is linear on a log−log plot. log(Vp) − log(T2) plots were constructed for all of the 28 samples (Figures 9 and 10). The results reveal that all of the plots show good fitting (correlation coefficients >0.9), indicating that Donghetang sandstone samples are fractal and can be described by the fractal model in eq 2. The fractal

Figure 8. Plots of reservoir quality index versus T2gm at echo spacing of 1.2 and 0.6 ms, respectively.

dimension can therefore be derived from the slope of the best fitting line. However, by plotting log(Vp) against log(T2) for all E


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Figure 9. Double-logarithm coordination showing the relationship between the cumulative pore volume Vp (%) and the T2 (ms) at echo spacings of 1.2 and 0.6 ms, respectively. The T2 spectrum is presented in Figure 4.

Figure 10. Double-logarithm coordination showing the relationship between the cumulative pore volume Vp (%) and the T2 (ms) at echo spacings of 1.2 and 0.6 ms, respectively. The T2 spectrum is presented in Figure 5.

of the samples, not a straight line but instead two straight lines with an evident inflection point are observed (Figure 9), and this is in accordance with the previous results.11,12,17,27,35 In fact, all of the fractal curves (log(Vp) − log(T2)) break into two segments at a certain T2 values (Figures 9 and 10). For instance, Figure 9 shows that an evident inflection point exists in the fractal curve for the sample whose T2 spectrum is presented in Figure 4. The fractal curves break into two segments at a T2 value of 1.0 ms for echo spacing of 1.2 and 0.6 ms (Figure 9). In addition, the accuracy of the fractal model is measured based on coefficient of determination, R2,53,54 and the high values of R2 indicate that it is sufficient to use the fractal models for the fractal dimension calculation in the Donghetang sandstones (Figure 9). Another example is shown in Figure 10, in which the T2 spectrum is presented in Figure 5. It can be concluded that the fractal curves break into two segments at a T2 value of 0.63 ms for echo spacing of 1.2 and 0.6 ms, respectively (Figure 10), and the correlation coefficients of the four straight lines are all larger than 0.95, which implies the accuracy of the fractal model (Figure 10). From eq 2, it can be concluded that the fractal dimensions can be derived from the slope of the best fitting line, and the fractal dimensions of small pores (short T2 values) and large pores (long T2 values) can be obtained respectively through regression analysis. The slopes of the log(Vp) − log(T2) plots give the fractal dimensions for large pores Dmax of 2.3473 (3.0− 0.6527), which is measured at an echo spacing of 1.2 ms (Figure 9A). This is a signature of a volume fractal since it is in

the range from 2.0 to 3.0, and this is in accordance with the fractal dimensions of three-dimensional pore spaces.14,24,32 For the spectrum measured at 0.6 ms echo spacing, the fractal dimensions of the large pores, which are associated with large T2 values, are also in the range from 2.0 to 3.0 (Figure 9B). For instance, Figure 9B gives a fractal dimension of 2.4671 in the large pore system realm. The calculated results show that the fractal dimensions of these samples are between 2.18 and 2.59 with an average of 2.41, indicating the low to moderate complexity of pore structure for the Donghetang sandstones. However, it should be noted that the slopes of the best fitting lines for the small pore realm are commonly larger than 1.0, or even they could be higher than 6.0 (Figures 9 and 10). Consequently, negative fractal dimensions will be obtained by using the fractal models illustrated in eq 2. Actually, the fractal dimension in the very small-scale range of pore size ( 0.7 support a strong positive relationship between T2gm and the fractal dimensions (Figure 13). However, as can be noted in Figures 12 and 13, generally

Figure 12. Plots of T2peak versus fractal dimension at echo spacing of 1.2 and 0.6 ms, respectively. G


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dominate the pore systems. Samples with the highest reservoir quality are characterized by a combination of primary intergranular and secondary dissolution pores. The pore throats are dominantly of laminated and curved lamellar types with minor amounts of control shape pore throats. The coexistence of large intergranular pores and dissolution pores results in a heterogeneous pore structure and a high value of fractal dimension. The NMR T2 pore size distributions are either uni- or bimodal (right-skewed) due to the abundance in large intergranular pores. NMR parameter T2gm and T2peak show good correlations with reservoir quality (permeability and reservoir quality index), and they are suggested to be sensitive parameters for pore structure evaluation.42 By using a short echo spacing of 0.6 ms, much more smaller pores can be detected. Fractal analysis was performed on the NMR T2 spectrum measured at echo spacings of 0.6 and 1.2 ms, respectively. There are clear inflection points on the fractal curves of log(Vp) versus log(T2), and the small pore systems including the pore throats and clay-dominated micropores, which are associated with very small T2 values, may not be self-similar. The fractal dimensions of the larger pore systems show strong positive relationships with the NMR T2peak and T2gm values and can be used to quantitatively characterize the complexity degree and heterogeneity of thte pore structure.

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Figure 13. Plots of T2gm versus fractal dimension at echo spacing of 1.2 and 0.6 ms, respectively.

AUTHOR INFORMATION

Corresponding Authors

*Tel.: +8615210877985. E-mail: [email protected]. *E-mail: [email protected].

the higher T2gm and T2peak are, the higher the fractal dimensions will be (Figures 12 and 13). This indicates that the samples with high T2gm and T2peak values, which are suggested to have good reservoir quality (high porosity and permeability), tend to have higher fractal dimensions and therefore high complexity degree of pore structures (Figures 12 and 13). As discussed above, the thin section and SEM analysis show that samples with the highest reservoir quality are those containing abundant large intergranular pores and secondary dissolution pores (Figure 3). The coexistence of intergranular pores and secondary dissolution pores results in a high complexity degree of pore throat structure and therefore fractal dimension. On the contrary, samples which contain only primary intergranular pores or secondary pores tend to have poorer reservoir quality and therefore lower T2gm and T2peak values. Consequently, the fractal dimensions will be lower since one type of pore dominates the pore systems. Fractal dimensions can be used here to represent the complexity degree and heterogeneity of the pore structure. The coexistence of dissolution pores and large intergranular pores contributes to a heterogeneous pore throat distribution and a high value of fractal dimension. The fractal dimension is an ideal parameter to comprehensively describe the regularity and complexity degree of the pore throat structure, and it is also an effective approach to characterize the macroscopic behaviors of reservoir rocks.

ORCID

Ziyuan Wang: 0000-0002-5288-793X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank PetroChina Tarim Oilfield Company for providing samples and data access. This work was financially supported by the National Basic Research Program of China (973 Program; Grant No. 2009CB219302), and we thank the sponsors of these projects. We thank three anonymous reviewers for their constructive comments, which improve the paper significantly. We also thank Dr. Ryan P. Rodgers (associate editor of Energy and Fuels) for his enthusiasm, patience, and tireless efforts.

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REFERENCES

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5. CONCLUSIONS Based on the present work, the following conclusions may be drawn. The Donghetang sandstones have moderate reservoir quality, and the primary pores and secondary dissolution pores H


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Fractal Analysis of Donghetang Sandstones Using NMR Measurements

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