含水合物沉积物渗透率分形模型
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摘要
天然气水合物是一种重要的替代能源,被国务院列为新矿种,但是现阶段的开采技术仍然难以达到商业开采标准.渗透率是判断水合物矿体是否具有开发潜力的重要指标,是水合物开采流程优化等工作的基础参数.然而,现有的渗透率理论模型在定量描述沉积物有效孔隙结构演化过程时仍有不足.因此,本文从定量描述沉积物有效孔隙结构演化过程出发,采用分形分析的方法,提出了一个含水合物沉积物渗透率理论模型;将模型预测结果与前人实验数据进行对比,以验证模型的适用性;最后分析了模型参数对渗透率演化过程的影响关系.结果表明,提出的渗透率分形模型较好地重现了水合物含量及其赋存形式对含水合物沉积物渗透率的影响过程;水合物赋存形式以及由此决定的最大孔径演化关系是影响沉积物渗透率演化过程的关键因素;本模型具有良好的工程应用潜力,为今后含水合物沉积物渗透率研究提供了新的思路.
Natural gas hydrates, ice-like crystals composed of water and natural gas, are widely distributed in marine sediments along the continental margin and permafrost regions. Natural gas hydrates are of great significance as a future energy resource, and have been officially authorized as a new kind of mineral in China. For now, however, the gas production rate of all the existing technologies is far below the commercial criterion. The permeability of hydrate-bearing sediments is a critical parameter that determines the economic feasibility of gas production from hydrate deposits, and it is one of the basic parameters needed for varieties of numerical simulators. However, most of the existing theoretical models for the permeability prediction are lack of quantitative descriptions of the pore space for fluids flow. In this work, a fractal theory based theoretical model is proposed to predict the permeability of hydrate-bearing sediments. In the proposed model, the pore space for fluids flow is equivalent to a bundle of capillary tubes with their diameters obeying the fractal scaling law. A hydrate saturation dependent area fractal dimension is applied to describe how the capillary tube diameters evolve during hydrate dissociation. The theoretically predicted curves are compared with published experimental data to verify its feasibility, and sensitivity analyses on model parameters are performed. The results suggest that the proposed theoretical model can describe the hydrate saturation and pore-scale behavior dependent permeability of hydrate-bearing sediments. The maximum diameter of the pore for fluids flow which is affected by the pore-scale behavior of gas hydrate is the key influence parameter determining the permeability of hydrate-bearing sediments. The proposed model is of great potential for engineering applications.
Natural gas hydrates, ice-like crystals composed of water and natural gas, are widely distributed in marine sediments along the continental margin and permafrost regions. Natural gas hydrates are of great significance as a future energy resource, and have been officially authorized as a new kind of mineral in China. For now, however, the gas production rate of all the existing technologies is far below the commercial criterion. The permeability of hydrate-bearing sediments is a critical parameter that determines the economic feasibility of gas production from hydrate deposits, and it is one of the basic parameters needed for varieties of numerical simulators. However, most of the existing theoretical models for the permeability prediction are lack of quantitative descriptions of the pore space for fluids flow. In this work, a fractal theory based theoretical model is proposed to predict the permeability of hydrate-bearing sediments. In the proposed model, the pore space for fluids flow is equivalent to a bundle of capillary tubes with their diameters obeying the fractal scaling law. A hydrate saturation dependent area fractal dimension is applied to describe how the capillary tube diameters evolve during hydrate dissociation. The theoretically predicted curves are compared with published experimental data to verify its feasibility, and sensitivity analyses on model parameters are performed. The results suggest that the proposed theoretical model can describe the hydrate saturation and pore-scale behavior dependent permeability of hydrate-bearing sediments. The maximum diameter of the pore for fluids flow which is affected by the pore-scale behavior of gas hydrate is the key influence parameter determining the permeability of hydrate-bearing sediments. The proposed model is of great potential for engineering applications.
引文
1 Numasawa M,Yamamoto K,Yasuda M,et al.Objectives and operation overview of the 2007 JOGMEC/NRCAN/AURORA Mallik 2L-38 gas hydrate production test.In:Proceedings of the International Conference on Gas Hydrates.Vancouver,2008
2 Schoderbek D,Farrell H,Hester K,et al.ConocoPhillips gas hydrate production test final technical report.ConocoPhillips Company,2013
3 Yamamoto K.Overview and introduction:Pressure core-sampling and analyses in the 2012-2013 MH21 offshore test of gas production from methane hydrates in the eastern Nankai Trough.Mar Pet Geol,2015,66:296-309
4 Cyranoski D.Japanese test coaxes fire from ice.Nature,2013,496:409
5 Wu N Y,Huang L,Su Z,et al.A study of geological evaluation indicators for the exploitation potential of marine natural gas hydrates:Theory and methodology(in Chinese).Nat Gas Ind,2013,33:11-17[吴能友,黄丽,苏正,等.海洋天然气水合物开采潜力地质评价指标研究:理论与方法.天然气工业,2013,33:11-17]
6 Konno Y,Masuda Y,Hariguchi Y,et al.Key factors for depressurization-induced gas production from oceanic methane hydrates.Energy Fuels,2010,24:1736-1744
7 Liu L,Lu X,Zhang X,et al.Numerical simulations for analyzing deformation characteristics of hydrate-bearing sediments during depressurization.Adv Geo-Energ Res,2017,1:135-147
8 Kleinberg R L,Flaum C,Griffin D D,et al.Deep sea NMR:Methane hydrate growth habit in porous media and its relationship to hydraulic permeability,deposit accumulation,and submarine slope stability.J Geophys Res,2003,108:2508
9 Mahabadi N,Dai S,Seol Y,et al.The water retention curve and relative permeability for gas production from hydrate-bearing sediments:Porenetwork model simulation.Geochem Geophys Geosyst,2016,17:3099-3110
10 Wang J,Zhao J,Zhang Y,et al.Analysis of the effect of particle size on permeability in hydrate-bearing porous media using pore network models combined with CT.Fuel,2016,163:34-40
11 Mandelbrot B.How long is the coast of Britain?Statistical self-similarity and fractional dimension.Science,1967,156:636-638
12 Coleman S W,Vassilicos J C.Transport properties of saturated and unsaturated porous fractal materials.Phys Rev Lett,2008,100:035504
13 Yu B,Li J.Some fractal characters of porous media.Fractals,2001,9:365-372
14 Yu B M,Li J H.A geometry model for tortuosity of flow path in porous media.Chin Phys Lett,2004,21:1569-1571
15 Cai J,Perfect E,Cheng C L,et al.Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures.Langmuir,2014,30:5142-5151
16 Wei W,Cai J,Hu X,et al.An electrical conductivity model for fractal porous media.Geophys Res Lett,2015,42:4833-4840
17 Xia Y,Cai J,Wei W,et al.A new method for calculating fractal dimensions of porous media based on pore size distribution.Fractals,2018,26:1850006
18 Xu P,Li C,Qiu S,et al.A fractal network model for fractured porous media.Fractals,2016,24:1650018
19 Xu P,Qiu S,Cai J,et al.A novel analytical solution for gas diffusion in multi-scale fuel cell porous media.J Power Sources,2017,362:73-79
20 Wang H,Liu Y,Song Y,et al.Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging.J Appl Geophys,2012,86:70-81
21 Daigle H.Relative permeability to water or gas in the presence of hydrates in porous media from critical path analysis.J Pet Sci Eng,2016,146:526-535
22 Ning F L,Li C,Cai J C,et al.Study on the relative permeability of hydrate-bearing sediments by a fractal parallel capillary model.In:Proceedings of the International Conference on Gas Hydrates.Denver,2017
23 Chaouachi M,Falenty A,Sell K,et al.Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographic microscopy.Geochem Geophys Geosyst,2015,16:1711-1722
24 Yu B,Cheng P.A fractal permeability model for bi-dispersed porous media.Int J Heat Mass Transfer,2002,45:2983-2993
25 Iversen N,J?rgensen B B.Diffusion coefficients of sulfate and methane in marine sediments:Influence of porosity.Geochim Cosmochim Acta,1993,57:571-578
26 Kumar A,Maini B,Bishnoi P R,et al.Experimental determination of permeability in the presence of hydrates and its effect on the dissociation characteristics of gas hydrates in porous media.J Pet Sci Eng,2010,70:114-122
27 Delli M L,Grozic J L H.Experimental determination of permeability of porous media in the presence of gas hydrates.J Pet Sci Eng,2014,120:1-9
28 Zhang H Y,Liu L L,Liu C L,et al.Experimental investigation on permeability of hydrate bearing sediments based on pressure pulse method(in Chinese).J Exp Mech,2018,33:263-271[张宏源,刘乐乐,刘昌岭,等.基于瞬态压力脉冲法的含水合物沉积物渗透性实验研究.实验力学,2018,33:263-271]
29 Li G,Wu D M,Li X S,et al.Experimental measurement and mathematical model of permeability with methane hydrate in quartz sands.Appl Energy,2017,202:282-292
30 Comiti J,Renaud M.A new model for determining mean structure parameters of fixed beds from pressure drop measurements:Application to beds packed with parallelepipedal particles.Chem Eng Sci,1989,44:1539-1545
31 Fujii T,Suzuki K,Takayama T,et al.Geological setting and characterization of a methane hydrate reservoir distributed at the first offshore production test site on the Daini-Atsumi Knoll in the eastern Nankai Trough,Japan.Mar Petgeol,2015,66:310-322
32 Daigle H,Johnson A,Thomas B.Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients.Geophysics,2014,79:D425-D431
2 Schoderbek D,Farrell H,Hester K,et al.ConocoPhillips gas hydrate production test final technical report.ConocoPhillips Company,2013
3 Yamamoto K.Overview and introduction:Pressure core-sampling and analyses in the 2012-2013 MH21 offshore test of gas production from methane hydrates in the eastern Nankai Trough.Mar Pet Geol,2015,66:296-309
4 Cyranoski D.Japanese test coaxes fire from ice.Nature,2013,496:409
5 Wu N Y,Huang L,Su Z,et al.A study of geological evaluation indicators for the exploitation potential of marine natural gas hydrates:Theory and methodology(in Chinese).Nat Gas Ind,2013,33:11-17[吴能友,黄丽,苏正,等.海洋天然气水合物开采潜力地质评价指标研究:理论与方法.天然气工业,2013,33:11-17]
6 Konno Y,Masuda Y,Hariguchi Y,et al.Key factors for depressurization-induced gas production from oceanic methane hydrates.Energy Fuels,2010,24:1736-1744
7 Liu L,Lu X,Zhang X,et al.Numerical simulations for analyzing deformation characteristics of hydrate-bearing sediments during depressurization.Adv Geo-Energ Res,2017,1:135-147
8 Kleinberg R L,Flaum C,Griffin D D,et al.Deep sea NMR:Methane hydrate growth habit in porous media and its relationship to hydraulic permeability,deposit accumulation,and submarine slope stability.J Geophys Res,2003,108:2508
9 Mahabadi N,Dai S,Seol Y,et al.The water retention curve and relative permeability for gas production from hydrate-bearing sediments:Porenetwork model simulation.Geochem Geophys Geosyst,2016,17:3099-3110
10 Wang J,Zhao J,Zhang Y,et al.Analysis of the effect of particle size on permeability in hydrate-bearing porous media using pore network models combined with CT.Fuel,2016,163:34-40
11 Mandelbrot B.How long is the coast of Britain?Statistical self-similarity and fractional dimension.Science,1967,156:636-638
12 Coleman S W,Vassilicos J C.Transport properties of saturated and unsaturated porous fractal materials.Phys Rev Lett,2008,100:035504
13 Yu B,Li J.Some fractal characters of porous media.Fractals,2001,9:365-372
14 Yu B M,Li J H.A geometry model for tortuosity of flow path in porous media.Chin Phys Lett,2004,21:1569-1571
15 Cai J,Perfect E,Cheng C L,et al.Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures.Langmuir,2014,30:5142-5151
16 Wei W,Cai J,Hu X,et al.An electrical conductivity model for fractal porous media.Geophys Res Lett,2015,42:4833-4840
17 Xia Y,Cai J,Wei W,et al.A new method for calculating fractal dimensions of porous media based on pore size distribution.Fractals,2018,26:1850006
18 Xu P,Li C,Qiu S,et al.A fractal network model for fractured porous media.Fractals,2016,24:1650018
19 Xu P,Qiu S,Cai J,et al.A novel analytical solution for gas diffusion in multi-scale fuel cell porous media.J Power Sources,2017,362:73-79
20 Wang H,Liu Y,Song Y,et al.Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging.J Appl Geophys,2012,86:70-81
21 Daigle H.Relative permeability to water or gas in the presence of hydrates in porous media from critical path analysis.J Pet Sci Eng,2016,146:526-535
22 Ning F L,Li C,Cai J C,et al.Study on the relative permeability of hydrate-bearing sediments by a fractal parallel capillary model.In:Proceedings of the International Conference on Gas Hydrates.Denver,2017
23 Chaouachi M,Falenty A,Sell K,et al.Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographic microscopy.Geochem Geophys Geosyst,2015,16:1711-1722
24 Yu B,Cheng P.A fractal permeability model for bi-dispersed porous media.Int J Heat Mass Transfer,2002,45:2983-2993
25 Iversen N,J?rgensen B B.Diffusion coefficients of sulfate and methane in marine sediments:Influence of porosity.Geochim Cosmochim Acta,1993,57:571-578
26 Kumar A,Maini B,Bishnoi P R,et al.Experimental determination of permeability in the presence of hydrates and its effect on the dissociation characteristics of gas hydrates in porous media.J Pet Sci Eng,2010,70:114-122
27 Delli M L,Grozic J L H.Experimental determination of permeability of porous media in the presence of gas hydrates.J Pet Sci Eng,2014,120:1-9
28 Zhang H Y,Liu L L,Liu C L,et al.Experimental investigation on permeability of hydrate bearing sediments based on pressure pulse method(in Chinese).J Exp Mech,2018,33:263-271[张宏源,刘乐乐,刘昌岭,等.基于瞬态压力脉冲法的含水合物沉积物渗透性实验研究.实验力学,2018,33:263-271]
29 Li G,Wu D M,Li X S,et al.Experimental measurement and mathematical model of permeability with methane hydrate in quartz sands.Appl Energy,2017,202:282-292
30 Comiti J,Renaud M.A new model for determining mean structure parameters of fixed beds from pressure drop measurements:Application to beds packed with parallelepipedal particles.Chem Eng Sci,1989,44:1539-1545
31 Fujii T,Suzuki K,Takayama T,et al.Geological setting and characterization of a methane hydrate reservoir distributed at the first offshore production test site on the Daini-Atsumi Knoll in the eastern Nankai Trough,Japan.Mar Petgeol,2015,66:310-322
32 Daigle H,Johnson A,Thomas B.Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients.Geophysics,2014,79:D425-D431