By Hui-Hai Liu
This publication offers a scientific try and generalize a number of primary actual legislation relating to subsurface fluid stream which are very important for a couple of modern purposes within the components of hydrogeology, reservoir engineering and rock mechanics. It additionally covers the background of studying those actual legislation, their respective scope of validity, and their generalizations or extensions.
The actual legislation mentioned contain Darcy’s legislation, Darcy-Buckingham legislations and Hooke’s legislations. Darcy’s legislations is the elemental legislations for subsurface fluid circulate. For low-permeability media, it's not constantly enough due to the powerful fluid–solid interplay. even though the Darcy-Buckingham legislation is usually used for modeling subsurface multiphase move, it's only legitimate below the neighborhood equilibrium situation. This doesn't carry in lots of instances, in particular whilst fingering stream happens. it's renowned that subsurface fluid circulation is coupled with mechanical deformation of subsurface media; in a few functions, this coupling can play a dominant function. The continuum-scale elastic deformation of average rock, despite the fact that, doesn't continuously stick to the conventional kind of Hooke’s law.
The e-book additionally offers purposes of the proposed generalizations of the actual legislation to numerous very important engineering projects.
Read Online or Download Fluid Flow in the Subsurface: History, Generalization and Applications of Physical Laws PDF
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Additional info for Fluid Flow in the Subsurface: History, Generalization and Applications of Physical Laws
5, indicating that water flow is close to Darcian flow in this sample. Nevertheless, most shale samples are characterized by unconventional flow and our theory (discussed above) can be applied to both Darcian and non-Darcian flow processes. 36 1 Generalization of Darcy’s Law: Non-Darcian Liquid Flow … Fig. 17 Comparisons between the imbibition data of Roychaudhuri et al. (2013) and the theory (Eq. 50) (Liu et al. 2015) The non-equilibrium imbibition has also been reported to give slope values (in the log-log plots shown in Figs.
50. 7 Case Studies 35 Fig. 16 Observed cumulative imbibition as a function of time for a Barnett shale sample (from Hu and Ewing 2014) Hu and Ewing (2014) attributed the observed non-Darcian flow behavior to poor pore connectivity in low-permeability media. However, it is clearly demonstrated mathematically in the above derivation that the observed non-Darcian liquid flow is a direct result of the nonlinearity between imbibition flux and pressure gradient. We also believe that this nonlinearity is largely caused by the strong solid–liquid interaction (Miller and Low 1963; Hansbo 1960), rather than pore connectivity.
The key assumption is that liquid flux is a power function of capillary pressure gradient, or kÃ @pc nÀ1 @pc qx ¼ À l @x @x ð1:38Þ where kÃ is an analogue of permeability for unsaturated liquid flow (or permeability multiplied by relative permeability), pc is capillary pressure (that is negative), n is a positive parameter, x is location, and again l is fluid viscosity. 38 will be reduced to Darcy’s law for n = 1. Note that liquid flux qx can be positive or negative to represent its direction.