## Study of the starting pressure gradient in branching network.(English)Zbl 1383.76018

Summary: In order to increase the production of oil in low permeability reservoirs with high efficiency, it is necessary to fully understand the properties and special behaviors of the reservoirs and correctly describe the flow in the reservoirs. This paper applies the branching network mode to the study of the starting pressure gradient of nonlinear Newtonian fluid (Bingham fluid) in the reservoirs with low permeability based on the fact that the fractured network may exist in the reservoirs. The proposed model for starting pressure gradient is a function of yield stress, microstructural parameters of the network. The proposed model may have the potential in further exploiting the mechanisms of flow in porous media with fractured network.

### MSC:

 76A05 Non-Newtonian fluids 76S05 Flows in porous media; filtration; seepage
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### References:

 [1] Lorente S, Wechsatol W, Bejan A. Tree-shaped flow structures designed by minimizing path lengths. Int J Heat Mass Transf, 2002, 45: 3299–3312 · Zbl 1021.76008 [2] Bear J. Dynamics of Fluids in Porous Media. NewYork: Elsevier, 1972 · Zbl 1191.76001 [3] Barenblatt G E, Entov B M, Rizhik B M. Flow of Liquids and Gases in Natural Formations. Moscow: Nedra, 1984 [4] Vradis G C, Dougher J, Kumar S. Entrance pipe flow and heat transfer for a Bingham plastic. Int J Heat Mass Transf, 1993, 36(3): 543–552 [5] Hammad K J, Vradis G C. Creeping flow of a Bingham plastic through axisymmetric sudden contractions with viscous dissipation. Int J Heat Mass Transf, 1996, 39(8): 1555–1567 · Zbl 0964.76501 [6] Nascimento U C S, Macêdo E N, Quaresma J N N. Thermal entry region analysis through the finite integral transform technique in laminar flow of Bingham fluids within concentric annular ducts. Int J Heat Mass Transf, 2002, 45(4): 923–929 · Zbl 0991.76515 [7] Khatyr R, Ouldhadda D, Idrissi A II. Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts. Int J Heat Mass Transf, 2003, 46: 589–598 · Zbl 1121.76390 [8] Blackery J, Mitsoulis E. Creeping motion of a sphere in tubes filled with a Bingham plastic material. J Non-Newtonian Fluid Mech, 1997, 70: 59–77 [9] Roquet N, Saramito P. An adaptive finite element method for Bingham fluid flows around a cylinder. Comput Methods Appl Mech Eng, 2003, 192(31): 3317–3341 · Zbl 1054.76053 [10] Balhoff M T, Thompson K E. Modeling the steady flow of yieldstress fluids in packed beds. AICHE J, 2004, 50(12): 3034–3048 [11] Prada A, Civan F. Modification of Darcy’s law for the threshold pressure gradient. J Pet Sci Eng, 1999, 22(4): 237–240 [12] {$$\Gamma$$}орщуноВ A T. 1987. The Development of the Singular Oil Field (in Chinese). Translated by Zhang S B. Beijing: Petroleum Industry Press, 1987. 18–184 [13] Li F H, Liu, C Q. Pressure transient analysis for unsteady porous flow with start-up pressure derivative (in Chinese). Well Testing, 1997, 6(1): 1–4 [14] Mu X Y, Liu Y X. Study of starting pressure gradient in low-peameability oilfield (in Chinese). Oil & Gas Recov Technol, 2001, 8(5): 58–60 [15] Liu Y W, Ding Z H, He F Z. Three kinds of methods for determining the start-up pressure gradients in low permeability reservoir (in Chinese). Well Testing, 2002, 11(4): 1–4 [16] Song F Q, Liu C Q, Li F H. Transient pressure of percolation through one dimension porous media with threshold pressure gradient (in Chinese). Appl Math Mech, 1999, 20(1): 25–32 · Zbl 0933.76506 [17] Mandelbrot B B. The Fractal Geometry of Nature. New York: Freeman, 1982 · Zbl 0504.28001 [18] Zamir M. Arterial branching within the confines of fractal L-System formalism. J Gen Physiol, 2001, 118: 267–275 [19] Uylings H B M. Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull Math Biol, 1977, 39: 509–519 · Zbl 0403.92011 [20] Bejan A, Rocha L A O, Lorete S. Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluid streams. Int J Therm Sci, 2000, 39: 949–960 [21] Acuna J A, Ershagghi I, Yortsos Y C. Practical application of fractal pressure transient analysis of naturally fractured reservoir. SPEFE, 1995, 10(3): 173–179 [22] Tian J, Tong D K. The flow analysis of fluids in fractal reservoir with the fractional derivative. J Hydrodyn, 2006, 18(3): 287–293 · Zbl 1203.76151 [23] Scherdegger A E. The Physics of Flow in Porous Media. New York: Elsevier, 1972
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