Some Authors believe that a minimum pressure gradient (called threshold pressure gradient (TPG)) is required before a liquid starts to flow in a porous medium. In a tight or shale oil formation, this TPG phenomenon becomes more important, as it is more difficult for a fluid to flow. In this paper, experimental data on TPG published in the literature are carefully reviewed. What we found is that a very low flow velocity corresponding to a very low pressure gradient cannot be measured in the experiments. Experiments can only be done above some measurable flow velocities. If these flow velocities and their corresponding pressure gradients are plotted in an XY plot and extrapolated to zero velocity, a non-zero pressure gradient corresponds to this zero velocity. This non-zero pressure gradient is called threshold pressure gradient in the literature. However, in the regime of very low velocity and very low pressure gradient, the data gradually approach to the origin of the plot, demonstrating a non-linear relationship between the pressure gradient and the velocity. But the data do not approach to a point of zero velocity and a threshold pressure gradient. Therefore, the concept of threshold pressure gradient is a result of data misinterpretation of available experimental data.
The correct interpretation is that there are two flow regimes: nonlinear flow regime (non-Darcy flow regime) when the pressure gradients are low, and linear flow regime (Darcy flow regime) when the pressure gradient is intermediate or high. The nonlinear flow regime starts from the origin point. As the pressure gradient is increased, the curve becomes a straight line demonstrating the linear flow regime. We have verified our views by first analyzing the causes of non-Darcy flow, and then systematically analyzed typical experimental data and correlations in the literature. We conclude that TPG does not exist. We also use several counter examples to support our conclusion.
Acknowledgements
The work presented in this paper is Supported by the U.S. Department of Energy under Award Number DE-FE0024311.
| [1] |
M. Majumder, N. Chopra, R. Andrews, B.J. Hinds, Nanoscale hydrodynamics: enhanced flow in carbon nanotubes, Nature 438 (7064) (2005), 44-44.
|
| [2] |
M. Whitby, N. Quirke, Fluid flow in carbon nanotubes and nanopipes, Nat. Nanotechnol. 2 (2) (2007) 87-94.
|
| [3] |
S. Li, M. Dong, Z. Li, Measurement and revised interpretation of gas flow behavior in tight reservoir cores, J. Pet. Sci. Eng. 65 (1) (2009) 81-88.
|
| [4] |
M. Dong, Z. Li, S. Li, J. Yao, Permeabilities of tight reservoir cores determined for gaseous and liquid CO2 and C2H6 using minimum backpressure method, J. Nat. Gas Sci. Eng. 5 (2012) 1-5.
|
| [5] |
A.A. Moghadam, R. Chalaturnyk, Analytical and experimental investigations of gas-flow regimes in shales considering the influence of mean effective stress, SPE J. 21 (2) (2015) 557-572. SPE-178429.
|
| [6] |
E. Secchi, S. Marbach, A. Nigués, D. Stein, A. Siria, L. Bocquet, Massive radius-dependent flow slippage in carbon nanotubes, Nature 537 (7619) (2016) 210-213.
|
| [7] |
Y. Huang, Z. Yang, Y. He, X. Wang, Y. Luo, Nonlinear porous flow in low permeability porous media, Mech. Pract. 35 (5) (2013) 1-8.
|
| [8] |
R. Miller, P. Low, Threshold gradient for water flow in clay systems, Soil Sci. Soc. Am. J. 27 (6) (1963) 605-609.
|
| [9] |
A. Prada, F. Civan, Modification of Darcy's law for the threshold pressure gradient, J. Pet. Sci. Eng. 22 (4) (1999) 237-240.
|
| [10] |
Y. Huang, Mechanism of Flow in Low Permeability Reservoirs, Petroleum Industrial Press, 1998.
|
| [11] |
Z. Yang,Porous Media Flow Mechanics for Low Permeability Reservoirs and its Application, Doctoral Dissertation, Chinese Academy of Sciences, 2005.
|
| [12] |
A. Li, S. Zhang, M. Liu, W. Wang, L. Zhang, A new method of measuring starting pressure for low permeability reservoir, J. China Univ. Pet. Ed. Nat. Sci. 32 (1) (2008) 68-71.
|
| [13] |
S. Li, L. Cheng, X. Li, F. Hao, Nonlinear seepage flow of ultralow permeability reservoirs, Pet. Explor. Dev. 35 (5) (2008) 606-612.
|
| [14] |
B. Zeng, L. Cheng, F. Hao, Experiment and Mechanism Analysis on Threshold Pressure Gradient with Different Fluids, Society of Petroleum Engineers, 2010 January 1.
|
| [15] |
Z. Yang, R. Yu, Z. Su, Y. Zhang, D. Cui, Numerical simulation of the nonlinear flow in ultra-low permeability reservoirs, Pet. Explor. Dev. 37 (1) (2010) 94-98.
|
| [16] |
X. Wang, Z. Yang, Y. Sun, X. Liu, Experimental and theoretical investigation of nonlinear flow in low permeability reservoir, Proced. Environ. Sci. 11 (2011) 1392-1399.
|
| [17] |
Z. Yang, X. Liu, X. Xu, Y. Zhang, X. Wang, Study on Physical Simulation Experimental Technology of Ultra-low Permeability Large-scale Outcrop Model, International Petroleum Technology Conference, 2013 March 26.
|
| [18] |
J. Xu, R. Jiang, L. Xie, R. Wang, L. Shan, L. Li, Non-Darcy flow numerical simulation for low-permeability reservoirs, in: SPE Europec/EAGE Annual Conference, Society of Petroleum Engineers, 2012 January.
|
| [19] |
Z. Yang, X. Liu, Z. Zhang, Y. He, X. Wang, Ultra-low Permeability Reservoir Evaluation and Well Pattern Numerical Simulation Studies, Petroleum Press, 2012.
|
| [20] |
S. Xu, X. Yue, Experimental research on nonlinear flow characteristics at low velocity, J. China Univ. Pet. Ed. Nat. Sci. 31 (5) (2007) 60-63.
|
| [21] |
W. Xiong, Q. Lei, X. Liu, S. Gao, Z. Hu, H. Xue, Pseudo threshold pressure gradient to flow for low permeability reservoirs, Pet. Explor. Dev. 36 (2) (2009) 232-236.
|
| [22] |
S. Wang, Q. Feng, M. Zha, S. Lu, Y. Qin, T. Xia, C. Zhang, Molecular dynamics simulation of liquid alkane occurrence state in pores and slits of shale organic matter, Pet. Explor. Dev. 42 (6) (2015) 844-851.
|
| [23] |
S. Wang, F. Javadpour, Q. Feng, Molecular dynamics simulations of oil transport through inorganic nanopores in shale, Fuel 171 (2016) 74-86.
|
| [24] |
Y. Jin, X. Liu, Z. Liu, S. Lu, Q. Xue, Effect of interfacial layer on water flow in nanochannels: Lattice Boltzmann simulations, Phys. B Condens. Matter 487 (2016) 18-24.
|
| [25] |
R. Yang, R. Jiang, S. Liu, X. Zhang, H. Liu, Numerical simulation of nonlinear seepage in ultra-low permeability reservoirs, Acta Pet. Sin. 32 (2) (2011) 299-306.
|
| [26] |
H. Pascal, Nonsteady flow through porous media in the presence of a threshold gradient, Acta Mech. 39 (3-4) (1981) 207-224.
|
| [27] |
X. Wang, X. Hou, M. Hao, T. Yang, Pressure transient analysis in lowpermeable media with threshold gradients, Acta Pet. Sin. 32 (5) (2011) 847-851.
|
| [28] |
J. Lu, Pressure behavior of a hydraulic fractured well in tight gas formation with threshold pressure gradient, in: SPE Middle East Unconventional Gas Conference and Exhibition, Society of Petroleum Engineers, 2012 January.
|
| [29] |
F. Li, C. Liu, Transient pressure analysis for unsteady flow with start-up pressure gradient, Oil Gas Well Tests 1 (1997) 1-4.
|
| [30] |
C. Guo, J. Xu, M. Wei, R. Jiang, Experimental study and numerical simulation of hydraulic fracturing tight sandstone reservoirs, Fuel 159 (2015) 334-344.
|
| [31] |
Xue C., Large Physical Simulation Experimental Study on the Ultra-low Permeability Reservoir. Institute of Porous Flow and Fluid Mechanics, (Master Thesis, Chinese Academy of Sciences).
|
| [32] |
C. Li, S. Zhu, Another discussion on starting pressure gradient, Lithol. Reserv. 25 (4) (2013) 1-5.
|
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