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Investigation of Pressure Pulse Distribution in Porous Media | ||
| Journal of Chemical and Petroleum Engineering | ||
| مقاله 4، دوره 46، شماره 1، شهریور 2012، صفحه 41-52 اصل مقاله (293.29 K) | ||
| نوع مقاله: Original Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jchpe.2012.1892 | ||
| نویسندگان | ||
| Monir Taherkhani؛ Peyman Pourafshary* | ||
| Institute of Petroleum Engineering, University of Tehran, Tehran, Iran | ||
| چکیده | ||
| Diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in Navier-Stokes momentum equation. From mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. This issue may caused by numerous assumptions that has been implemented for developing diffusivity equation. However, if we omit two main assumptions of steady state condition and constant velocity and consider linear approximation for velocity field, the pressure propagation differential equation would be hyperbolic which is called Telegraph Equation. The propagation speed is limited for this equation. In this work, these equations are compared in prediction of pressure pulse propagation in Cartesian coordination with different parameters. The results show that the telegraph equation has minor correction in some cases as: far distances from pressure pulse source, when the fluid has high viscosity and for the rocks with low porosity and permeability; so considering common parameters in hydrocarbon reservoirs, the diffusivity equation has sufficient accuracy for reservoir engineering applications. | ||
| کلیدواژه‌ها | ||
| Diffusivity equation؛ Darcy equation؛ Pressure distribution equation؛ Porous media؛ Telegraph equation | ||
| مراجع | ||
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[4] Fatt, I. (1956)."A Demonstration of the effect of dead-end volume on pressure transient in porous medium.” Trans. AIME. Vol. 216.
[5] Jeffreys, G. V. and Jenson, V.G. (1977). “Mathematical Methods in Chemical Engineering.” Second Edition.
[6] Foster, W. R., McMillen, J. M. and Odeh, A. S. (1967). “The equation of motion of fluids in porous media: I. Propagation velocity of pressure pulses.” Society of Petroleum Engineering. [7] Foster, W. R., McMillen, J. M. and Odeh, A. S. (1967). “The equation of motion of fluids in porous media: II. Shape of pressure pulses.” Society of Petroleum engineering journal.
[8] Ockendon, J., Howison, S., Lacey, A. and Movchan, A. (1999). “Applied Partial Differential Equation.” Oxford University Press.
[9] Garabedian, P. R. (1998). “Partial Differential Equation.” AMS Chelsea Publishing. Second edition. | ||
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