A phenomenological description of the transient single-phase pore velocity period using the resistance force-velocity relationship
Abstract view|82|times PDF download|38|times
Abstract
A new approach to determine the transient period towards steady state pore flow velocity for fluids propagating through porous media under constant pressure condition is presented. The transient expression relates to the mean pore velocity rather than the fluid pressure conventional considered when characterizing transient behavior in porous media. It is based on the general, resistance force-velocity relationship, and is therefore analogous to the approach used when calculating transient periods for objects falling through resisting air and for the increase in electric currents towards respective steady state values. The transient is caused by inertia forces and characterized by a relaxation time comprising fluid density and viscosity together with porous medium properties as porosity and absolute permeability. Results show that the transient period increases with decreasing medium porosity and fluid viscosity and with increasing fluid density and absolute permeability of the medium. The transient period is negligibly small for typical fluid/medium property values characterizing typical subterrain sandstone reservoirs. Significant transient periods, occasionally observed during laboratory fluid injection tests, are therefore caused by other time-dependent processes not captured by the transient expression presented herein, e.g., fines migration or electrokinetic phenomena.
Cited as: Standnes, D. C. A phenomenological description of the transient single-phase pore velocity period using the resistance force-velocity relationship. Advances in Geo-Energy Research, 2022, 6(2): 104-110. https://doi.org/10.46690/ager.2022.02.03
Keywords
Full Text:
PDFReferences
Alonso, M., Finn, E. J. Fundamental University Physics, 2nd Edition. Massachusetts, USA, Addison-Wesley Publishing Company, 1983.
Batchelor, C. K., Batchelor, G. K. An Introduction to Fluid Mechanics. Cambridge, UK, Cambridge University Press, 2000.
Bear, J. Dynamics of Fluids in Porous Media. North Chelmsford, USA, Courier Corporation, 1988.
Berg, S., van Wunnik, J. Shear rate determination from porescale flow fields. Transport Porous Media, 2017, 117(2): 229-246.
Bijeljic, B., Raeini, A., Mostaghimi, P., et al. Predictions of non-Fickian solute transport in different classes of porous media using direct simulation on pore-scale images. Physical Review E, 2013, 87: 013011.
Brace, W. F., Walsh, J. B., Frangos, W. T. Permeability of granite under high pressure. Journal of Geophysical Research, 1968, 73(6): 2225-2236.
Callen, H. B., Welton, T. A. Irreversibility and generalized noise. Physical Review, 1951, 83(1): 34-40.
Darcy, H. Les Fontaines Publiques de la Ville de Dijon, Dalmont. Paris, France, 1856.
Delgado, A. V., González-Caballero, F., Hunter, R. J., et al. Measurements and interpretation of electrokinetic phenomena. Journal of Colloid and Interface Science, 2007, 309: 194-224.
Dey, S., Zeeshan Ali, S., Padhi, E. Terminal fall velocity: The legacy of Stokes from the perspective of fluvial hydraulics. Proceedings of the Royal Society A, 2019, 475(2228): 20190277.
Dullien, F. A. L. Single phase flow through porous media and pore structure. The Chemical Engineering Journal, 1975, 10(1): 1-34.
Foster, W. R., McMillen, J. M., Odeh, A. S. The equations of motion of fluids in porous media: I. propagation velocity of pressure pulses. Society of Petroleum Engineers Journal, 1967, 7(4): 333-341.
Kittel, C., Kroemer, H. Thermal Physics. New York, USA, W. H. Freeman and Company, 1980.
Kubo, R. The fluctuation-dissipation theorem. Reports on Progress in Physics, 1966, 29(1): 255-284.
Kuila, U., Prasad, M., Kazemi, H. Assessing Knudsen flow in gas-flow models of shale reservoirs. Canadian Society of Exploration Geophysicists, 2013, 38: 23-27.
Landau, L. D., Lifshitz, E. M. Fluid Mechanics, Second Edition. Oxford, UK, Pergamon Press, 1987.
Lin, D., Wang, J., Yuan, B., et al. Review on gas flow and recovery in unconventional porous rocks. Advances in Geo-Energy Research, 2017, 1(1): 39-53.
Neuman, S. P. Theoretical derivation of Darcy’s law. Acta Mechanica, 1977, 25: 153-170.
Odeh, A. S., McMillen, J. M. Pulse testing: Mathematical analysis and experimental verification. Society of Petroleum Engineers Journal, 1972, 12(5): 403-409.
Rosenbrand, E., Kjøller, C., Riis, J. F., et al. Different effects of temperature and salinity on permeability reduction by fines migration in Berea sandstone. Geothermics, 2015, 53: 225-235.
Slattery, J. C. Single-phase flow through porous media. AIChE Journal, 1969, 15(6): 866-872.
Smith, R. J. Circuits, Devices and Systems, 4th Edition. NewYork, USA, John Wiley & Sons, 1984.
Standnes, D. C. Implications of molecular thermal fluctuations on fluid flow in porous media and its relevance to absolute permeability. Energy & Fuels, 2018, 32: 8024-8039.
Standnes, D. C. Dissipation mechanisms for fluids and objects in relative motion described by the Navier-Stokes Equation. ACS Omega, 2021, 6(29): 18598-18609.
Standnes, D. C. Derivation of the conventional and a generalized form of Darcy’s Law from the Langevin Equation.Transport in Porous Media, 2022, 141(1): 1-15.
Stokes, G. G. On the numerical calculation of a class of definite integrals and infinite series. Transactions of the Cambridge Philosophical Society, 1851, 9: 166-187.
Taherkhani, M., Pourafshary, P. Investigation of pressure pulse distribution in porous media. Journal of Chemical and Petroleum Engineering, 2012, 46(1): 41-52.
Whitaker, S. Flow in porous media I: A theoretical derivation of Darcy’s Law. Transport in Porous Media, 1986, 1(1): 3-25.
Yang, D., Wang, W., Chen, W., et al. Revisiting the methods for gas permeability measurements in tight porous medium. Journal of Rock Mechanics and Geotechnical Engineering, 2019, 11: 263-276.
Zimmerman, R. W. Imperial College Lectures in Petroleum Engineering, The-Volume 5: Fluid Flow in Porous Media. Singapore, World Scientific, 2018.
Zwanzig, R. Time-correlation functions and transport coefficients in statistical mechanics. Annual Review of Physical Chemistry, 1965, 16(1): 67-102.
DOI: https://doi.org/10.46690/ager.2022.02.03
Refbacks
- There are currently no refbacks.
Copyright (c) 2022 The Author(s)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.