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.
•A nonlinear model of thermoelastic wave propagation in porous media is studied.•The role of the boundaries between of two adjacent rocks on the evolutions of the pressure and temperature fields is ...discussed in details.•The analysis of exact explicit solutions is given and the estimate of the velocity propagation is discussed for different rocks.
The dynamics of transients of fluid-rock temperature, pore pressure, pollutants in porous rocks are of vivid interest for fundamental problems in hydrological, volcanic, hydrocarbon systems, deep oil drilling. This can concern rapid landslides or the fault weakening during coseismic slips and also a new field of research about stability of classical buildings. Here we analyze the transient evolution of temperature and pressure in a thin boundary layer between two adjacent homogeneous media for various types of rocks. In previous models, this boundary was often assumed to be a sharp mathematical plane. Here we consider a non-sharp, physical boundary between two adjacent rocks, where also local steady pore pressure and/or temperature fields are present. To obtain a more reliable model we also investigate the role of nonlinear effects as convection and fluid-rock “frictions”, often disregarded in early models: these nonlinear effects in some cases can give remarkable quick and sharp transients. All of this implies a novel model, whose solutions describe large, sharp and quick fronts. We also rapidly describe transients moving through a particularly irregular boundary layer.
By integrating groundwater, surface water and vadose zone systems, the terrestrial hydrologic system can be used to spatially map water balance characteristics spanning local to global scales, even ...when long-term stream gauge data are unavailable. The Watershed Characteristics Approach (WCA) is a hydrologic estimation model developed using a system-based approach focused on the regionalization of landscape characteristics to define unique hierarchical hydrogeological units (HHUs) and establish their link to hydrologic characteristics. Although the WCA can be used to map any hydrologic variable, its validity is demonstrated by summarizing results generated by applying the methodology to quantify the renewable groundwater flux at a spatial scale lacking long-term stream gauge monitoring data. Landscape components for 97 East-Central Minnesota (ECM) watersheds were summarized and used to identify which unique combinations of characteristics statistically influenced mean annual minimum groundwater recharge. These resulting combinations of landscape characteristics defined each HHU; as additional characteristics were applied, units were refined to create a hierarchical organization. Results were mapped to spatially represent the renewable groundwater flux for ECM, demonstrating how hydrologic regionalization can address knowledge gaps in multi-scale processes and aid in quantifying water balance components, an essential key to sustainable water resources management.
In this paper we analyze the presence of “Burgers solitons” in geologic porous rocks. These are quick, strong transients of combined fluid pressure and solute density that are generated from an ...adjacent matrix, characterized by an intense pressure and contaminant density. The effect that produces such transients is a nonlinear advection process that is not often taken into account in hydrologic science. A brief analysis of solitons in Pierre Shale is also shown in the paper.
In this paper we propose the application of a new model of transients of pore pressure p and solute density \r{ho} in geologic porous media. This model is rooted in the non-linear waves theory, the ...focus of which is advection and effect of large pressure jumps on strain (due to large p in a non-linear version of the Hooke law). It strictly relates p and \r{ho} 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 non-linear Burgers solitons. We therefore propose that the actual transport process in porous rocks for large signals is not the linear diffusion, but could be governed by solitons. A test of an eventual presence of solitons in a rock is here proposed, and then applied to Pierre Shale, Bearpaw Shale, Boom Clay and Oznam-Mugu silt and clay. A quick analysis showing the presence of solitons for nuclear waste disposal and salty water intrusions is also analyzed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in Jordan and St. Peter sandstones, thus suggesting the occurrence of osmosis in these rocks.
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