Abstract
We here analyze a new model of transients of pore pressure p and solute density ρ in geologic porous media. This model is rooted in the nonlinear wave theory, its focus is on advection and effect of large pressure jumps on strain. It takes into account nonlinear and also time-dependent versions of the Hooke law about stress, rate and strain. The model solutions strictly relate p and ρ evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e., the nonlinear “Burgers solitons”. We, therefore, show that the actual transport process in porous rocks for large signals is not only the linear diffusion, but also a solitons presence could control the process. A test of a presence of solitons is applied to Pierre shale, Bearpaw shale, Boom clay and Oznam-Mugu silt and clay. An application about the presence of solitons for nuclear waste disposal and salt water intrusions is also discussed. Finally, in a kind of “theoretical experiment” we show that solitons could also be present in higher permeability rocks (Jordan and St. Peter sandstones), thus supporting the idea of a possible occurrence of osmosis also in sandstones.
Highlights
Recent research of geologic porous media has revealed how semi-permeable membranes can create chemical gradients, generated by osmosis (Marine and Fritz 1981; Alexander 1990; House and Pritchett 1995; Nunn 1997; Neuzil 2000; Neuzil and Provost 2009; HartElectronic supplementary material The online version of this article contains supplementary material, which is available to authorized users.2012)
To quantify the effect of chemical gradients, Ghassemi and Diek (2003, hereafter GD03) developed non-Osanger (Onsager 1931) analytical models to describe fluid transport forced by osmosis and pore pressure unbalances around a borehole
Rather surprising that solitons can be present for such small b. These findings support the idea of some presence of osmosis in relatively higher permeability rocks
Summary
Recent research of geologic porous media has revealed how semi-permeable membranes can create chemical gradients, generated by osmosis Among the solutions of a nonlinear version of the GD03 model, MSV found quick and sharp transients of p and q, the ‘‘Burgers solitons’’ (Whitham 1974). The hypothesis of homogeneity of the matrix implies to disregard the natural rock variability, but allows a much simpler analysis. To address this topic, we here analyze the evolution of q and p in clay, shale, silt and sandstones to validate if solitons can occur in these rocks. The occurrence of solitons can support the presence of osmosis in geologic porous media, in low permeability deposits, and in highly permeable rocks, such as sandstones.
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