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TECHNICAL PAPERS

# Fluid Flows Through Some Geological Discontinuities

[+] Author and Article Information
D. B. Ingham, A. K. Al-Hadhrami, L. Elliott

Department of Applied Mathematics,  University of Leeds, Leeds LS2 9JT, UK

X. Wen

School of the Environment,  University of Leeds, Leeds LS2 9JT, UK

J. Appl. Mech 73(1), 34-40 (May 06, 2005) (7 pages) doi:10.1115/1.1991861 History: Received May 24, 2004; Revised May 06, 2005

## Abstract

In this paper the fluid flow through some composite channels has been investigated in the physical parameter ranges appropriate to some flows in geological applications. In particular, we have considered the fluid flow through a composite channel that has undergone a vertical fracture. The vertical connecting channel is also composed of a composite material. In such physical situations, the materials undergo several orders of magnitude changes in their Darcy numbers. This results in very large changes in the pressure in the vicinity of the interfaces between these materials. Therefore it is necessary to develop mathematical and numerical techniques to deal with such situations and in this paper an approach is presented.

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## Figures

Figure 1

A schematic diagram of the problem when fluid flows through a two-dimensional geometrical configuration consisting of inlet and outlet composite channels which are linked by a vertical channel

Figure 2

The geometry of a horizontal fluid flow across an arbitrary vertical porous media composed of two Darcy parameters α¯1 and α¯1 of thicknesses Δl1 and Δl2, and cross-sectional areas S1 and S2, where S1+S2=S

Figure 3

The streamlines where the light shaded regions have Da=10−16, shale, while elsewhere Da=10−10, sand. The nondimensional values associated with the two vertical barriers, positioned in the regions 1.3<x<1.9 and 4.7<x<5.3, respectively, are height 2 and width 0.6, while the values associated with the horizontal barrier positioned in the region 3.1<y<3.7 are height 0.6 and width 1.0

Figure 4

The variation of the nondimensional fluid pressure along the axis of the three channels, namely, (a) the inlet, (b) the vertical, and (c) the outlet, channels, see Fig. 3

Figure 5

The convergence history for the mass residual Rmass as a function of number of iterations in the CVM with the APC, (−×−), and without the APC, (-o-), for the configuration shown in Fig. 3, where in (a) the light shaded regions have Da=10−16, while elsewhere Da=10−10, and (b) the light shaded regions have Da=10−14, while elsewhere Da=10−10

Figure 6

The streamlines where the light shaded regions have Da=10−16, shale, while elsewhere Da=10−10, sand, and the nondimensional values associated with the vertical barrier positioned in the region 3.4<x<3.6 are height 7 and width 0.2

Figure 7

The pressure contours in the vertical channels which correspond to: (a) Fig. 6, where there is a vertical barrier of height 7, width 0.2 and positioned in the region 3.4<x<3.4, (b) Fig. 8, where there are vertical and horizontal barriers of heights 7 and 0.2, widths 0.2 and 1.0, respectively, and positioned in the region 3.4<x<3.4 and 3.2<y<3.4, respectively, and (c) Fig. 9, where there are two thin vertical barriers each of height 4.5, width 0.1, and at a distance 0.2 apart, and positioned in the region 3.3<x<3.4 and 3.5<x<3.6, respectively. All the barriers have Da=10−16, shale, while elsewhere Da=10−10, sand, and the values of the pressure presented are scaled by a factor 1012.

Figure 8

The streamlines where the light shaded regions have Da=10−16, shale, while elsewhere Da=10−10, sand, and the nondimensional values associated with the vertical barrier, positioned in the region 3.4<x<3.6, are height 7 and width 0.2, while the nondimensional values associated with the horizontal barrier, positioned in the region 3.2<y<3.4, are height 1.0 and width 0.2

Figure 9

The streamlines where the light shaded regions have Da=10−16, shale, while elsewhere Da=10−10, sand, and the nondimensional values associated with the two thin vertical barriers, positioned in the regions 3.3<x<3.4 and 3.5<x<3.6, respectively, are height 5.5, width 0.1, and at a distance 0.2 apart

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