Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations
Abstract
:1. Introduction
2. Experimental
2.1. Materials
2.2. Experimental Setup
2.3. Experimental Procedures
2.3.1. Gas Permeability Measurement
2.3.2. PMI Experiments and Thin Section Analysis
3. Results and Discussions
3.1. Experimental Measurements
3.2. Pore-Throat Structure Type
3.3. Klinkenberg Permeability
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Notations | |
cross-sectional area of the core sample, cm2. | |
Klinkenberg constant, MPa. | |
throat radius, μm. | |
gas permeability, mD. | |
absolute permeability, mD. | |
length of the core sample, cm. | |
atmospheric pressure, 100 kPa. | |
the absolute pressures of inlet and outlet respectively, 100 kPa. | |
mean flow pressure (equal to ), MPa. | |
capillary pressure, MPa. | |
volumetric flow rate at the standard condition, cm3/s. | |
average pore radius, μm. | |
throat radius, µm. | |
throat radius, μm. | |
cumulative mercury saturation of throat radius . | |
pore-throat sorting coefficient. | |
Greek Letter | |
gas viscosity, mPa·s. |
References
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Samples Number | Gas Permeabilities at Different Mean Pore Pressure * (mD) | Klinkenberg Permeability (mD) | Porosity (%) | Characteristic Parameters of Capillary Pressure Curve | Pore-Throat Type | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
0.230 MPa | 0.370 MPa | 0.480 MPa | 0.620 MPa | 0.880 MPa | Threshold Capillary Pressure (MPa) | Median Saturation Pressure (MPa) | Maximum Mercury Injection Saturation (%) | Mean Pore-Throat Radius (μm) | ||||
#1 | 0.016 | 0.012 | 0.010 | 0.009 | 0.007 | 0.004 | 7.34 | 1.026 | 21.643 | 85.95 | 0.086 | BSMT |
#2 | 0.093 | 0.073 | 0.065 | 0.058 | 0.053 | 0.039 | 9.49 | 0.713 | 4.269 | 89.95 | 0.209 | MSMFT |
#3 | 0.215 | 0.179 | 0.155 | 0.144 | 0.130 | 0.101 | 15.44 | 0.495 | 2.732 | 89.07 | 0.341 | GSMFT |
#4 | 0.161 | 0.136 | 0.123 | 0.115 | 0.108 | 0.089 | 15.95 | 0.558 | 13.976 | 86.40 | 0.104 | BSMT |
#5 | 0.136 | 0.118 | 0.107 | 0.102 | 0.093 | 0.079 | 14.64 | 0.545 | 8.738 | 91.05 | 0.158 | BSMT |
#6 | 0.185 | 0.153 | 0.142 | 0.131 | 0.123 | 0.120 | 13.16 | 1.024 | 9.419 | 89.01 | 0.118 | BSMT |
#7 | 0.104 | 0.083 | 0.073 | 0.067 | 0.059 | 0.044 | 13.24 | 1.083 | 9.765 | 80.63 | 0.107 | BSMT |
#8 | 0.132 | 0.111 | 0.101 | 0.094 | 0.085 | 0.070 | 10.85 | 0.355 | 2.539 | 88.20 | 0.361 | GSMFT |
#9 | 0.170 | 0.141 | 0.125 | 0.114 | 0.096 | 0.075 | 10.67 | 0.342 | 2.658 | 88.69 | 0.359 | GSMFT |
#10 | 0.216 | 0.185 | 0.168 | 0.158 | 0.145 | 0.121 | 10.13 | 0.345 | 2.548 | 87.30 | 0.357 | GSMFT |
#11 | 0.304 | 0.266 | 0.248 | 0.234 | 0.226 | 0.189 | 13.43 | 0.338 | 2.663 | 87.15 | 0.344 | GSMFT |
#12 | 0.192 | 0.175 | 0.162 | 0.152 | 0.134 | 0.119 | 12.52 | 0.342 | 2.055 | 87.71 | 0.475 | GSMFT |
#13 | 0.082 | 0.070 | 0.061 | 0.057 | 0.051 | 0.041 | 7.34 | 0.713 | 2.672 | 89.20 | 0.343 | GSMFT |
#14 | 0.114 | 0.098 | 0.090 | 0.084 | 0.075 | 0.064 | 11.89 | 0.714 | 13.936 | 90.21 | 0.146 | MSMFT |
#15 | 0.071 | 0.057 | 0.051 | 0.048 | 0.044 | 0.035 | 7.84 | 0.712 | 5.319 | 86.00 | 0.190 | MSMFT |
#16 | 0.168 | 0.144 | 0.132 | 0.121 | 0.113 | 0.095 | 10.04 | 0.716 | 3.660 | 88.75 | 0.253 | MSMFT |
#17 | 0.100 | 0.086 | 0.073 | 0.067 | 0.059 | 0.046 | 9.79 | 0.714 | 13.548 | 92.70 | 0.120 | BSMT |
#18 | 0.140 | 0.117 | 0.101 | 0.093 | 0.078 | 0.060 | 13.32 | 0.498 | 3.545 | 89.91 | 0.327 | GSMFT |
#19 | 0.261 | 0.218 | 0.200 | 0.188 | 0.169 | 0.140 | 13.93 | 0.494 | 2.603 | 85.62 | 0.382 | GSMFT |
#20 | 0.151 | 0.133 | 0.118 | 0.110 | 0.101 | 0.085 | 13.62 | 0.714 | 3.412 | 89.17 | 0.303 | GSMFT |
#21 | 0.092 | 0.073 | 0.065 | 0.057 | 0.050 | 0.037 | 6.44 | 0.483 | 2.611 | 86.61 | 0.383 | GSMFT |
#22 | 0.135 | 0.111 | 0.101 | 0.093 | 0.084 | 0.067 | 8.85 | 0.465 | 4.933 | 84.69 | 0.231 | MSMFT |
#23 | 0.105 | 0.088 | 0.074 | 0.070 | 0.063 | 0.047 | 9.98 | 0.723 | 14.236 | 92.50 | 0.119 | BSMT |
#24 | 0.165 | 0.143 | 0.132 | 0.124 | 0.113 | 0.097 | 11.39 | 1.023 | 7.058 | 86.54 | 0.245 | MSMFT |
#25 | 0.095 | 0.080 | 0.070 | 0.066 | 0.056 | 0.045 | 12.58 | 0.511 | 17.019 | 86.69 | 0.098 | BSMT |
#26 | 0.052 | 0.041 | 0.038 | 0.033 | 0.030 | 0.023 | 7.02 | 0.714 | 5.994 | 86.34 | 0.157 | MSMFT |
#27 | 0.079 | 0.064 | 0.053 | 0.046 | 0.042 | 0.027 | 9.26 | 0.713 | 5.942 | 82.48 | 0.198 | MSMFT |
#28 | 0.147 | 0.121 | 0.111 | 0.104 | 0.092 | 0.075 | 13.92 | 0.735 | 17.156 | 84.12 | 0.091 | BSMT |
#29 | 0.097 | 0.079 | 0.072 | 0.066 | 0.058 | 0.046 | 9.83 | 0.712 | 4.362 | 92.17 | 0.200 | MSMFT |
#30 | 0.114 | 0.096 | 0.088 | 0.080 | 0.073 | 0.060 | 9.69 | 0.711 | 2.713 | 87.25 | 0.324 | GSMFT |
#31 | 0.034 | 0.027 | 0.024 | 0.021 | 0.019 | 0.014 | 10.85 | 1.026 | 10.382 | 88.48 | 0.099 | BSMT |
#32 | 0.144 | 0.116 | 0.107 | 0.101 | 0.089 | 0.071 | 11.50 | 0.496 | 5.122 | 87.69 | 0.228 | MSMFT |
#33 | 0.145 | 0.111 | 0.102 | 0.095 | 0.084 | 0.062 | 11.50 | 1.158 | 10.561 | 88.59 | 0.096 | BSMT |
#34 | 0.228 | 0.201 | 0.187 | 0.178 | 0.162 | 0.142 | 9.43 | 0.347 | 2.373 | 88.38 | 0.406 | GSMFT |
#35 | 0.093 | 0.073 | 0.065 | 0.058 | 0.053 | 0.039 | 9.49 | 0.356 | 2.366 | 88.56 | 0.415 | GSMFT |
#36 | 0.273 | 0.241 | 0.223 | 0.214 | 0.195 | 0.172 | 9.79 | 0.494 | 2.065 | 84.56 | 0.413 | GSMFT |
#37 | 0.188 | 0.158 | 0.141 | 0.129 | 0.113 | 0.092 | 10.78 | 0.496 | 3.128 | 91.58 | 0.293 | GSMFT |
#38 | 0.147 | 0.125 | 0.118 | 0.108 | 0.098 | 0.084 | 14.01 | 0.619 | 17.239 | 85.91 | 0.089 | BSMT |
#39 | 0.100 | 0.080 | 0.070 | 0.065 | 0.058 | 0.043 | 11.53 | 0.598 | 17.125 | 86.53 | 0.094 | BSMT |
#40 | 0.160 | 0.130 | 0.120 | 0.109 | 0.091 | 0.073 | 13.97 | 0.585 | 17.028 | 86.67 | 0.095 | BSMT |
#41 | 0.118 | 0.095 | 0.084 | 0.077 | 0.068 | 0.052 | 10.57 | 0.902 | 16.522 | 91.38 | 0.109 | BSMT |
#42 | 0.078 | 0.061 | 0.055 | 0.049 | 0.044 | 0.033 | 9.17 | 0.695 | 16.513 | 91.26 | 0.107 | BSMT |
#43 | 0.007 | 0.005 | 0.004 | 0.004 | 0.003 | 0.002 | 6.44 | 0.686 | 16.429 | 91.63 | 0.102 | BSMT |
#44 | 0.123 | 0.107 | 0.096 | 0.088 | 0.080 | 0.067 | 12.10 | 0.715 | 4.797 | 91.81 | 0.236 | MSMFT |
#45 | 0.146 | 0.118 | 0.107 | 0.101 | 0.090 | 0.071 | 13.67 | 0.499 | 2.172 | 88.91 | 0.404 | GSMFT |
#46 | 0.081 | 0.068 | 0.061 | 0.055 | 0.050 | 0.040 | 11.56 | 0.713 | 5.570 | 91.82 | 0.184 | MSMFT |
#47 | 0.048 | 0.039 | 0.036 | 0.033 | 0.030 | 0.025 | 7.10 | 0.715 | 13.884 | 89.75 | 0.154 | MSMFT |
#48 | 0.100 | 0.083 | 0.077 | 0.071 | 0.066 | 0.055 | 8.90 | 0.495 | 12.537 | 89.97 | 0.176 | MSMFT |
#49 | 0.136 | 0.110 | 0.103 | 0.096 | 0.087 | 0.071 | 9.96 | 0.495 | 7.560 | 85.97 | 0.147 | MSMFT |
#50 | 0.150 | 0.131 | 0.118 | 0.112 | 0.100 | 0.085 | 11.73 | 0.716 | 5.408 | 88.12 | 0.242 | MSMFT |
Type | Pore-Throat Sorting Coefficient | Entry Pressure (MPa) | Median Saturation Pressure (MPa) | Mean Throat Radius (μm) | Maximum Mercury Injection Saturation (%) |
---|---|---|---|---|---|
GSMFT | 1.175–2.027 | 0.338–0.714 | 2.05–3.55 | 0.293–0.475 | 84.56–92.70 |
MSMFT | 1.308–2.133 | 0.465–1.023 | 3.66–13.94 | 0.146–0.253 | 82.48–92.17 |
BSMT | 1.583–2.788 | 0.511–1.464 | 8.74–39.03 | 0.070–0.158 | 79.30–91.58 |
Type | Parameter | Mean Pore Pressure (MPa) | ||||
---|---|---|---|---|---|---|
0.230 | 0.370 | 0.480 | 0.620 | 0.880 | ||
GSMFT | slope | 0.6718 | 0.7430 | 0.7985 | 0.8333 | 0.8858 |
intercept | −0.0235 | −0.0164 | −0.0135 | −0.0108 | −0.0068 | |
MSMFT | slope | 0.6205 | 0.7064 | 0.7606 | 0.8021 | 0.8723 |
intercept | −0.0115 | −0.0079 | −0.0065 | −0.0050 | −0.0041 | |
BSMT | slope | 0.5578 | 0.6602 | 0.7133 | 0.7663 | 0.8384 |
intercept | −0.0079 | −0.0061 | −0.0047 | −0.0040 | −0.0030 |
Samples Number | Type | Mean Pore Pressure (MPa) | Measured Results | Calculated Results and Relative Error with Measured Results | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Gas Permeability (mD) | Klinkenberg Permeability (mD) | GSMFT Equation | MSMFT Equation | BSMT Equation | ||||||
Klinkenberg Permeability (mD) | Relative Error (%) | Klinkenberg Permeability (mD) | Relative Error (%) | Klinkenberg Permeability (mD) | Relative Error (%) | |||||
#51 | GSMFT | 0.230 | 0.147 | 0.073 | 0.075 | 2.74 | 0.082 | 12.33 | 0.078 | 6.85 |
#52 | 0.207 | 0.117 | 0.116 | 0.85 | 0.120 | 2.56 | 0.113 | 3.42 | ||
#53 | MSMFT | 0.230 | 0.092 | 0.050 | 0.038 | 24.00 | 0.048 | 4.00 | 0.047 | 6.00 |
#54 | 0.103 | 0.054 | 0.046 | 14.81 | 0.055 | 1.85 | 0.053 | 1.85 | ||
#55 | BSMT | 0.230 | 0.144 | 0.076 | 0.074 | 2.63 | 0.077 | 1.32 | 0.077 | 1.32 |
#56 | 0.094 | 0.047 | 0.040 | 14.89 | 0.050 | 6.38 | 0.048 | 2.13 |
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Liu, G.; Bai, Y.; Fan, Z.; Gu, D. Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations. Energies 2017, 10, 1575. https://doi.org/10.3390/en10101575
Liu G, Bai Y, Fan Z, Gu D. Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations. Energies. 2017; 10(10):1575. https://doi.org/10.3390/en10101575
Chicago/Turabian StyleLiu, Guangfeng, Yaoxing Bai, Zhaoqi Fan, and Daihong Gu. 2017. "Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations" Energies 10, no. 10: 1575. https://doi.org/10.3390/en10101575