Multi-method characterization of sandstone pore size distribution heterogeneity and its influence on porosity and permeability variation

Abstract

Pore volume/surface area and size distribution heterogeneity are two important parameters of pore structures, which restrict the gas-water-oil migration process in sandstone reservoirs. The fractal theory has been proved to be one of the most effective methods to quantify pore distribution heterogeneity. However, the dynamic variation of porosity and permeability due to fractal characteristics has been rarely studied. In this paper, physical properties, mineral composition, and pore distribution of 18 groups of sandstone samples were analyzed using scanning electron microscope (SEM) and high-pressure mercury injection tests. Then, Sierpinski model, Menger model, thermodynamic model, and multi-fractal model were used to calculate the fractal dimension of the pore volume. Thus, the relationship between fractal dimension and porosity/permeability variation rate, and pore compressibility were studied. The results are as follows. 1) All samples can be divided into three types based on pore volume (0.9 cm³∙g⁻¹) and mercury removal efficiency (35%), i.e., Type A (< 0.9 cm³∙g⁻¹and < 35%); Type B (> 0.9 cm³∙g⁻¹ and <35%); Type C ( > 0.9 cm³∙g⁻¹ and > 35%). 2) Four fractal models had poor applicability in characterizing fractal characteristics of different sample types. The fractal dimension by the Sierpinski model had a good linear correlation with that of other models. Pores with smaller volumes dominated the overall pore distribution heterogeneity by multi-fractal dimension. The pore diameter between 200−1000 nm and larger than 1000 nm was the key pore size interval that determined the fractal characteristics. 3) With the increase of confining pressures, porosity and permeability decreased in the form of a power function. The compressibility coefficient of typical samples was 0.002−0.2 MPa⁻¹. The compressibility of Types A and B was significantly higher than that of Type C, indicating that the total pore volume was not the key factor affecting the pore compressibility. The correlation of compressibility coefficient/porosity variation rate with pore volume (total and different size pore volume), fractal value and mineral component were not significant. This indicates that these three factors comprehensively restricted pore compression.

Graphical abstract

Keywords

tight sandstone / pore size distribution / fractal dimension / multi-fractal model / permeability-porosity

References

[1] AnguloR, Alvarado V, GonzalezH (1992). Fractal dimensions from mercury intrusion capillary tests. In: SPE Latin America Petroleum Engineering Conference. Society of Petroleum Engineers

[2] Cai Y, Li Q, Liu D, Zhou Y, Lv D (2018). Insights into matrix compressibility of coals by mercury intrusion porosimetry and N₂ adsorption.Int J Coal Geol, 200: 199–212

[3] Cai Y, Liu D, Pan Z, Che Y, Liu Z (2016). Investigating the effects of seepage-pores and fractures on coal permeability by fractal analysis.Transp Porous Media, 111(2): 479–497

[4] Cai Y, Liu D, Yao Y, Li J, Liu J (2011). Fractal characteristics of coal pores based on classic geometry and thermodynamics models.Acta Geol Sin Engl Ed, 85(5): 1150–1162

[5] Friesen W I, Mikula R J (1987). Fractal dimensions of coal particles.J Colloid Interface Sci, 120(1): 263–271

[6] Gao L (2016). Sedimentary Reservoir Study of Permian Shang Wuerhe Formation in Well Block Jinlong-2 of Junggar Basin. Dissertation for Master’s Degree. Qingdao: China University of Petroleum

[7] He H, Li S, Liu C, Kong C, Jiang Q, Chang T (2020). Characteristics and quantitative evaluation of volcanic effective reservoirs: a case study from Junggar Basin, China.J Petrol Sci Eng, 195: 107723

[8] Hou X, Zhu Y, Chen S, Wang Y, Liu Y (2020). Investigation on pore structure and multifractal of tight sandstone reservoirs in coal bearing strata using LF-NMR measurements.J Petrol Sci Eng, 187: 106757

[9] Hu Y, Guo Y, Zhang J, Shangguan J, Li M, Quan F, Li G (2020). A method to determine nuclear magnetic resonance T₂ cutoff value of tight sandstone reservoir based on multifractal analysis.Energy Sci Eng, 8(4): 1135–1148

[10] Lai J, Wang G, Fan Z, Chen J, Wang S, Zhou Z, Fan X (2016). Insight into the pore structure of tight sandstones using NMR and HPMI measurements.Energy Fuels, 30(12): 10200–10214

[11] Lai J, Wang G, Wang Z, Chen J, Pang X, Wang S, Zhou Z, He Z, Qin Z, Fan X (2018). A review on pore structure characterization in tight sandstones.Earth Sci Rev, 177: 436–457

[12] Li J, Wang S, Lu S, Zhang P, Cai J, Zhao J, Li W (2019). Micro-distribution and mobility of water in gas shale: a theoretical and experimental study.Mar Pet Geol, 102: 496–507

[13] Li K (2010). Analytical derivation of Brooks-Corey type capillary pressure models using fractal geometry and evaluation of rock heterogeneity.J Petrol Sci Eng, 73(1−2): 20–26

[14] Li W, Liu H, Song X (2015). Multifractal analysis of Hg pore size distributions of tectonically deformed coals.Int J Coal Geol, 144–145: 138–152

[15] Liu G, Meng Z, Luo D, Wang J, Gu D, Yang D (2020). Experimental evaluation of interlayer interference during commingled production in a tight sandstone gas reservoir with multi-pressure systems.Fuel, 262: 116557

[16] Liu K, Ostadhassan M, Kong L (2019). Fractal and multifractal characteristics of pore throats in the Bakken shale.Transp Porous Media, 126(3): 579–598

[17] Lu G, Wang J, Wei C, Song Y, Yan G, Zhang J, Chen G (2018). Pore fractal model applicability and fractal characteristics of seepage and adsorption pores in middle rank tectonic deformed coals from the Huaibei coal field.J Petrol Sci Eng, 171: 808–817

[18] Mastalerz M, Hampton L, Drobniak A, Loope H (2017). Significance of analytical particle size in low-pressure N₂ and CO₂ adsorption of coal and shale.Int J Coal Geol, 178: 122–131

[19] Paz Ferreiro J, Vidal Vázquez E (2010). Multifractal analysis of Hg pore size distributions in soils with contrasting structural stability.Geoderma, 160(1): 64–73

[20] Peng C, Zou C, Yang Y, Zhang G, Wang W (2017). Fractal analysis of high rank coal from southeast Qinshui basin by using gas adsorption and mercury porosimetry.J Petrol Sci Eng, 156: 235–249

[21] Pfeifer P, Avnir D (1983). Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces.J Chem Phys, 79(7): 3558–3565

[22] Qiao J, Zeng J, Chen D, Cai J, Jiang S, Xiao E, Zhang Y, Feng X, Feng S (2022). Permeability estimation of tight sandstone from pore structure characterization.Mar Pet Geol, 135: 105382

[23] Qin L, Zhai C, Liu S, Xu J, Wu S, Dong R (2018). Fractal dimensions of low rank coal subjected to liquid nitrogen freeze-thaw based on nuclear magnetic resonance applied for coalbed methane recovery.Powder Technol, 325: 11–20

[24] Schmitt M, Fernandes C P, Da Cunha Neto J A B, Wolf F G, dos Santos V S S (2013). Characterization of pore systems in seal rocks using nitrogen gas adsorption combined with mercury injection capillary pressure techniques.Mar Pet Geol, 39(1): 138–149

[25] Shao P, Wang X, Song Y, Li Y (2018). Study on the characteristics of matrix compressibility and its influence factors for different rank coals.J Nat Gas Sci Eng, 56: 93–106

[26] Su P, Xia Z, Qu L, Yu W, Wang P, Li D, Kong X (2018). Fractal characteristics of low-permeability gas sandstones based on a new model for mercury intrusion porosimetry.J Nat Gas Sci Eng, 60: 246–255

[27] Wang X, Hou J, Song S, Wang D, Gong L, Ma K, Liu Y, Li Y, Yan L (2018). Combining pressure-controlled porosimetry and rate-controlled porosimetry to investigate the fractal characteristics of full-range pores in tight oil reservoirs.J Petrol Sci Eng, 171: 353–361

[28] Wang Y, Zhu Y, Chen S, Li W (2014). Characteristics of the nanoscale pore structure in northwestern Hunan shale gas reservoirs using field emission scanning electron microscopy, high-pressure mercury intrusion, and gas adsorption.Energy Fuels, 28(2): 945–955

[29] Yao Y, Liu D (2012). Comparison of low-field NMR and mercury intrusion porosimetry in characterizing pore size distributions of coals.Fuel, 95: 152–158

[30] Yao Y, Liu D, Tang D, Tang S, Huang W, Liu Z, Che Y (2009). Fractal characterization of seepage-pores of coals from China: an investigation on permeability of coals.Comput Geosci, 35(6): 1159–1166

[31] Yu S, Bo J, Pei S, Jiahao W (2018). Matrix compression and multifractal characterization for tectonically deformed coals by Hg porosimetry.Fuel, 211: 661–675

[32] Zhang J, Chu X, Wei C, Zhang P, Zou M, Wang B, Quan F, Ju W (2022). Review on the application of low-field nuclear magnetic resonance technology in coalbed methane production simulation.ACS Omega, 7(30): 25906–26992

[33] Zhang J, Wei C, Chu X, Vandeginste V, Ju W (2020a). Multifractal analysis in characterizing adsorption pore heterogeneity of middle- and high-rank coal reservoirs.ACS Omega, 5(31): 19385–19401

[34] Zhang J, Wei C, Ju W, Yan G, Lu G, Hou X, Kai Z (2019a). Stress sensitivity characterization and heterogeneous variation of the pore-fracture system in middle-high rank coals reservoir based on NMR experiments.Fuel, 238: 331–344

[35] Zhang J, Wei C, Zhao J, Ju W, Chen Y, Tamehe L S (2019b). Comparative evaluation of the compressibility of middle and high rank coals by different experimental methods.Fuel, 245: 39–51

[36] Zhang P, Lu S, Li J, Chang X (2020b). 1D and 2D Nuclear magnetic resonance (NMR) relaxation behaviors of protons in clay, kerogen and oil-bearing shale rocks.Mar Pet Geol, 114: 104210

[37] Zhu S, Du Z, Li C, Salmachi A, Peng X L, Wang C W, Yue P, Deng P (2018). A semi-analytical model for pressure-dependent permeability of tight sandstone reservoirs.Transp Porous Media, 122(2): 235–252

[38] Zou C, Zhu R, Liu K, Su L, Bai B, Zhang X, Yuan X, Wang J (2012). Tight gas sandstone reservoirs in China: characteristics and recognition criteria.J Petrol Sci Eng, 88–89: 82–91

[39] Zou M, Wei C, Zhang M, Shen J, Chen Y, Qi Y (2013). Classifying coal pores and estimating reservoir parameters by nuclear magnetic resonance and mercury intrusion porosimetry.Energy Fuels, 27(7): 3699–3708

Acknowledgements

This research was sponsored by the This research was sponsored by the Research Fund of Shandong Coalfield Geological Bureau (No. 2022-003), Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process of the Ministry of Education (China University of Mining and Technology) (No. 2023-007) and Shandong Coalfield Geological Bureau Research Special Project of 2024s (No. MTDZKY-2024-35).

Competing interests

The authors declare that they have no competing interests.

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