Pore structure fractal characteristics and its relationship with reservoir properties of the first Member of Lower Shihezi Formation tight sandstone in Hangjinqi area, Ordos Basin
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摘要: 基于物性、铸体薄片、电镜扫描和高压压汞等测试分析资料，利用汞饱和度法和含水饱和度法对杭锦旗地区盒1段致密储层孔隙结构分形维数进行了计算，并分析其与储层物性的关系。结果表明：盒1段储层平均孔隙度、渗透率分别为9.83%、1.03×10-3 μm2，储集空间以粒间溶孔、粒内溶孔和残余粒间孔为主。汞饱和度法计算的整体分形维数分布在2.138 4~2.829 2，平均值为2.396 5，含水饱和度法计算的整体分形维数分布在2.529 4~2.879 7，平均值为2.679 1。相比于含水饱和度法，汞饱和度法计算的分形维数与孔隙度、渗透率及各孔隙结构参数之间具有更好的相关性，是因为含水饱和度法易对孔喉较小的样品产生偏差。基于汞饱和度法分形维数，将盒1段储层孔隙结构分为四类：Ⅰ类（Df≤2.31），Ⅱ类（2.31 < Df < 2.4），Ⅲ类（2.4≤Df < 2.52），Ⅳ类（Df≥2.52），研究区主要孔隙结构类型为Ⅱ、Ⅲ类。选取分形维数（Df）、平均孔喉半径（Rm）和孔隙度（φ）等参数，对渗透率进行多元回归计算，计算值与实测值相关系数在0.9以上，表明计算模型在本区较为适用。Abstract: Based on physical property, casting thin section, scanning electron microscope, high-pressure mercury injection and other test analysis data, the fractal dimension of pore structure of tight sandstone reservoir was calculated by the method of mercury saturation and water saturation in the first Member of Lower Shihezi Formation in Hangjinqi area, and the relationship between fractal dimension and the physical properties of reservoir was analyzed.The results have shown that the average porosity and permeability of the Lower Shihezi Formation reservoir were 9.83% and 1.03×10-3 μm2, respectively.The reservoir space is mainly composed of intergranular dissolved pores, intragronular dissolved pores and residual intergranular pores.The overall fractal dimension calculated by the mercury saturation method is distributed in 2.138 4-2.829 2 with an average value of 2.396 5 while calculated by the water saturation method is distributed in 2.529 4-2.879 7 with an average value of 2.679 1.Compared with the water saturation method, the fractal dimension calculated by the mercury saturation method has a better correlation with the porosity, permeability and pore structure parameters, because the water saturation method tends to produce deviation on samples with smaller pore throat.The pore structure was divided into four types based on fractal dimension: Type Ⅰ(Df≤2.31), Type Ⅱ(2.31 < Df < 2.4), Type Ⅲ(2.4≤Df < 2.52), Ⅳ(Df≥2.52).Fractal dimension(Df), averoged radius of pore throct(Rm) and porosity(φ) were selected to calculate permeability by multiple nonlinear regression.The calculated permeability by multiple nonlinear regression shows strong correlation with measured permeability, whose correlation coefficient squared is more than 0.9, which means the permeability estimation model is suitable for the study area.
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图 1 杭锦旗地区构造位置及地层综合柱状图
Figure 1. Tectonic location and generalized stratigraphy of the Hangjinqi area, Ordos Basin
图 2 杭锦旗地区盒1段储层物性特征
Figure 2. Reservoir properties of the first Member of Lower Shihezi Formation in Hangjinqi area
图 3 杭锦旗地区盒1段砂岩分类
Figure 3. Sandstone classification of the first Member of Lower Shihezi Formation in Hangjinqi area
图 4 杭锦旗地区盒1段储层储集空间类型
A.锦62井，3 455.94 m，残余粒间孔和粒间溶孔，单偏光；B.锦27井，2 265.4 m，长石溶孔沿节理发育，单偏光；C.锦7井，2 821 m，蜂窝状岩屑溶孔，裂缝穿过岩屑颗粒，单偏光；D.锦126井，2 933.48 m，溶蚀强烈，发育铸膜孔和超大复合孔；E.锦27井，2 319.45 m，贴粒缝和粒内缝，单偏光；F.锦89井，3 087.05 m，残余粒间孔；G.锦75井，2 753.99 m，粒内溶孔；H.锦89井，3 082.34 m，自生高岭石晶间孔，具一定连通性；I.锦89井，3 082.34 m，伊利石与绿泥石晶间孔
Figure 4. Reservoir space types of the first Member of Lower Shihezi Formation in Hangjinqi area
图 5 汞饱和度法计算的典型分形曲线
Figure 5. Representative fractal curve calculated by mercury saturation method
图 6 含水饱和度法计算的典型分形曲线
Figure 6. Representative fractal curve calculated by water saturation method
图 7 汞饱和度法分形维数与储层物性关系
Figure 7. Relationship between reservoir properties and fractal dimension calculated by mercury saturation method
图 8 含水饱和度法分形维数与储层物性关系
Figure 8. Relationship between reservoir properties and fractal dimension calculated by water saturation method
图 9 汞饱和度法分形维数与孔隙结构参数关系
Figure 9. Relationship between pore structure parameters and fractal dimension calculated by mercury saturation
图 10 4类储层毛管压力曲线和孔喉半径分布特征
Figure 10. Capillary pressure curves and pore throat radius distributions for four types of reservoir
图 11 盒1段储层实测渗透率与孔隙度及计算渗透率的关系
Figure 11. Relationship between measured permeability vs. porosity and calculated permeability
表 1 盒1段致密储层孔隙结构分形维数计算结果
Table 1. Fractal dimension of first Member of Lower Shihezi Formation tight sandstone reservoir
样品编号 孔隙度/% 渗透率/10-3 μm2 汞饱和度法分形维数 含水饱和度法分形维数 D1 D2 Df D1 D2 Df J116-1 0.1 0.148 / / 2.829 2 2.942 7 2.746 4 2.844 6 J122-3 9.0 1.640 / / 2.372 7 2.855 8 2.430 5 2.643 2 J32-6 3.9 0.802 / / 2.440 2 2.931 7 2.627 1 2.779 4 J33-6 10.0 1.340 / / 2.417 5 2.795 8 2.335 0 2.565 4 J7-6 5.9 1.500 / / 2.409 3 2.913 8 2.468 0 2.690 9 J74-5 14.3 5.830 / / 2.168 0 2.709 6 2.605 2 2.664 4 J77-6 5.8 1.090 / / 2.471 3 2.901 5 2.462 5 2.639 3 J102-2 9.8 1.900 2.474 8 2.129 7 2.302 3 2.708 7 2.533 4 2.649 4 J102-5 11.6 3.480 2.217 8 2.084 0 2.150 7 2.708 7 2.533 4 2.678 0 J102-6 6.6 0.574 2.593 8 2.152 3 2.373 1 2.672 0 2.515 2 2.623 3 J107-2 5.4 0.942 2.502 8 2.331 1 2.417 0 2.831 7 2.085 5 2.577 1 J107-5 6.4 2.090 2.524 3 2.275 5 2.399 9 2.810 8 2.506 3 2.698 8 J107-8 1.2 0.165 2.877 2 2.495 9 2.686 6 2.901 9 2.622 8 2.754 3 J107-9 6.6 0.921 2.503 6 2.263 2 2.383 4 2.803 3 2.513 7 2.698 0 J107-13 9.7 1.020 2.496 3 2.200 9 2.348 6 2.712 3 2.310 4 2.556 2 J107-16 2.0 0.616 2.558 2 2.495 9 2.527 1 2.927 9 2.711 6 2.805 6 J122-5 1.8 0.577 2.800 6 2.274 6 2.537 6 2.940 5 2.801 1 2.879 7 J126-2 17.0 11.340 2.385 7 2.035 0 2.210 4 2.493 1 2.770 0 2.529 4 J126-4 14.8 3.920 2.404 2 2.086 0 2.244 2 2.632 2 2.689 0 2.641 3 J27-3 12.6 1.860 2.566 8 2.086 1 2.326 5 2.664 5 2.536 9 2.625 7 J27-7 13.4 5.840 2.648 7 2.122 5 2.385 6 2.668 7 2.486 9 2.611 1 J30-3 6.10 2.23 2.498 0 2.179 2 2.338 6 2.801 2 2.627 2 2.726 3 J30-5 9.20 1.42 2.499 8 2.174 2 2.337 0 2.765 6 2.471 6 2.641 3 J33-4 13.80 1.94 2.412 0 2.141 0 2.276 5 2.827 3 2.366 4 2.610 8 J39-4 15.00 6.44 2.374 1 2.055 6 2.214 9 2.586 2 2.749 6 2.604 5 J44-4 13.00 8.79 2.376 6 2.064 0 2.220 3 2.613 0 2.769 3 2.631 4 J62-3 4.40 0.69 2.594 5 2.123 8 2.359 2 2.707 4 2.665 6 2.695 0 J62-5 10.70 4.54 2.554 2 2.048 9 2.301 6 2.510 3 2.794 2 2.537 6 J7-4 4.50 0.74 2.625 4 2.343 6 2.484 5 2.908 8 2.731 2 2.818 7 J7-10 2.90 0.52 2.625 4 2.352 2 2.488 8 2.904 2 2.688 2 2.791 6 J91-6 1.60 0.95 2.490 6 2.263 5 2.377 1 2.926 7 2.657 9 2.821 0 J91-8 7.80 1.65 2.608 9 2.156 1 2.382 5 2.809 6 2.629 8 2.728 4 J91-10 4.90 1.09 2.616 7 2.160 1 2.388 4 2.851 2 2.773 7 2.816 0 J91-13 4.50 1.18 2.616 7 2.231 2 2.424 0 2.844 7 2.571 3 2.703 0 J98-2 13.50 7.25 2.550 9 2.064 5 2.307 7 2.567 8 2.784 9 2.589 6 
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表 2 孔隙结构参数与物性及分形维数相关性
Table 2. Relationship between pore structure parameters and reservoir property and fractal dimension
特征参数 参数类型 孔隙度 渗透率 汞饱和度法分形维数 含水饱和度法分形维数 孔喉大小 Rd y=3.99lnx+7.95, R2=0.38 y=1.47x1.135, R2=0.62 y=3 897e-4.41x, R2=0.76 y=4 066e-3.088x, R2=0.16 Rave y=3.83lnx+16.5, R2=0.47 y=14.86x1.035, R2=0.69 y=5 836e-5.51x, R2=0.88 y=269 6e-3.759x, R2=0.19 R50 y=2.7lnx+17.22, R2=0.65 y=11.15x0.591 1, R2=0.62 y=4×108e-9.672x, R2=0.85 y=109e-9.051x, R2=0.33 DM y=3.53lnx+16.92, R2=0.59 y=14.09x0.887 5, R2=0.74 y=106e-9.672x, R2=0.93 y=106e-6.123x, R2=0.32 孔喉分布 Sp y=3.66lnx+15.77, R2=0.47 y=12.25x0.990 1, R2=0.69 y=82 935e-5.617x, R2=0.84 y=9 653e-4.206x, R2=0.20 DR y=-10.94lnx+12.4, R2=0.41 y=3.39x-2.042, R2=0.29 y=0.071 6e1.269x, R2=0.74 y=0.008 6e1.923x, R2=0.43 α y=7.59lnx+12.4, R2=0.41 y=80.89x1.572 6, R2=0.45 y=29.526e-2.482x, R2=0.72 y=275.3e-3.039x, R2=0.40 Sk y=-7.03lnx+14.01, R2=0.30 y=4.85x-1.381, R2=0.23 y=4.229x-7.628, R2=0.58 y=5.946x-13.45, R2=0.40 孔喉连通 Pd y=-3.99lnx+6.8, R2=0.38 y=4.45x-1.058, R2=0.59 y=2×10-5e4.409 5x, R2=0.80 y=0.000 2e3.088x, R2=0.16 P50 y=2.63lnx+16.3, R2=0.62 y=9.91x-0.616, R2=0.63 y=2×10-9e9.658 7x, R2=0.85 y=3×10-9e9.658 7x, R2=0.28 Smax y=14.4lnx-54.43, R2=0.61 y=0.043x0.045 9, R2=0.49 y=-83.08x+276.1, R2=0.64 y=-150x+479.7, R2=0.75 We y=-2.7lnx+17.7, R2=0.012 y=14.09x-0.627, R2=0.013 y=-0.35x+37.6, R2=0.000 06 y=-4.64x+49.7, R2=0.005 注：Rd.最大孔喉半径；Rave.平均孔喉半径；R50.中值孔喉半径；DM.半径均值；Sp.分选系数；DR.相对分选系数；α.均质系数；Sk.歪度；Pd.排驱压力；P50.中值压力；Smax.最大进汞饱和度；We.退汞效率
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表 3 杭锦旗地区盒1段储层孔隙结构类型
Table 3. Pore structure types of the first Member of Lower Shihezi Formation reservoir in Hangjinqi area
孔隙结构类型 样品数 分形维数 孔隙度/% 渗透率/10-3 μm2 排驱压力/MPa 平均孔喉半径/μm 最大进汞饱和度/% Ⅰ类 8 2.138 4~2.302 3 9.8~17.0 1.90~11.34 0.28~0.53 0.19~0.63 86.9~91.1 Ⅱ类 13 2.314 4~2.399 9 4.4~13.8 0.57~5.84 0.60~1.14 0.06~0.14 66.6~91.5 Ⅲ类 9 2.409 3~2.488 8 1.6~10.0 0.52~1.86 0.58~1.66 0.05~0.13 56.2~89.4 Ⅳ类 5 2.527 1~2.829 2 0.1~5.4 0.15~1.09 0.82~11.31 0.01~0.10 32.6~80.1
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