Gravitational and Finite‐Size Effects On Pressure Saturation Curves During Drainage

Abstract

We experimentally and numerically study the influence of gravity and finite-size effects on the pressure-saturation relationship in a given porous medium during slow drainage. The effect of gravity is systematically varied by tilting the system relative to the horizontal configuration. The use of a quasi two-dimensional porous media allows for direct spatial monitoring of the saturation. Exploiting the fractal nature of the invasion structure, we obtain a relationship between the final saturation and the Bond number S F nw = Bo 0.097 using percolation theory. Moreover, the saturation, pressure, and Bond number are functionally related, allowing for pressure-saturation curves to collapse onto a single master curve, parameterized by the representative elementary volume size and by the Bond and capillary numbers. This allows to upscale the pressure-saturation curves measured in a laboratory to large representative elementary volumes used in reservoir simulations. The large-scale behavior of these curves follows a simple relationship, depending on Bond and capillary numbers, and on the flow direction. The size distribution of trapped defending fluid clusters is also shown to contain information on past fluid flow and can be used as a marker of past flow speed and direction.

Burst Dynamics, Upscaling and Dissipation of Slow Drainage in Porous Media

“…Figure 11 shows a two-dimensional invasion percolation simulation with a gravitational field together with drainage experiments performed by Ayaz et al [81]. The red dash-dotted line confirms the predictions of the theoretical scaling in Eq.…”

“…Such a measurement remains to be done. An experimental verification of the theoretical scaling of the invasion front and the saturation behind the front for three-dimensional porous media is also of great interest for future work [81]. Experiments involving changing the gravitational effects in a geophysical centrifuge could be one way to accomplish this.…”

“…Let L be the length of the porous model and assume L > w. The final saturation behind the front of the invading fluid and its dependence on the pressure across the model has been studied in Ref. [81]. In this study, we considered the volume of the invaded fluid in boxes with size corresponding to the width of the invading front.…”

“…On length scales below this size, the structure of the invading fluid is fractal, while on length scales larger than this size, the structure is homogeneous. For sufficiently large F, when η is the characteristic length scale of the front, the saturation S F nw of the nonwetting fluid behind the front becomes [81].…”

“…The capillary number Ca qμ 2 a 2 /(ckA) 1.2 • 10 -4 is kept fixed while the Bond number Bo Δρga 2 /c is changed in the experiments. Numerical and experimental data from[81].…”