By Hui-Hai Liu
This booklet provides a scientific try and generalize a number of primary actual legislation relating to subsurface fluid circulation which are very important for a few modern functions within the parts of hydrogeology, reservoir engineering and rock mechanics. It additionally covers the heritage of studying those actual legislation, their respective scope of validity, and their generalizations or extensions.
The actual legislation mentioned contain Darcy’s legislations, Darcy-Buckingham legislations and Hooke’s legislations. Darcy’s legislations is the elemental legislation for subsurface fluid movement. For low-permeability media, it isn't regularly sufficient a result of powerful fluid–solid interplay. even though the Darcy-Buckingham legislation is frequently used for modeling subsurface multiphase circulation, it's only legitimate less than the neighborhood equilibrium . This situation doesn't carry in lots of situations, specially whilst fingering circulation happens. it's renowned that subsurface fluid move is coupled with mechanical deformation of subsurface media; in a few purposes, this coupling can play a dominant function. The continuum-scale elastic deformation of common rock, even if, doesn't constantly stick to the conventional type of Hooke’s law.
The ebook additionally offers functions of the proposed generalizations of the actual legislation to numerous very important engineering projects.
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Additional resources for Fluid Flow in the Subsurface: History, Generalization and Applications of Physical Laws
7 Case Studies 29 condition generally exhibits stronger non-Darcian flow behavior than that under the saturated condition, because the former corresponds to smaller sizes of pores occupied by water. For demonstration purposes, and because of the lack of alternatives, we assume that kr in Eq. 37 can be represented by Eq. 34. When hydraulic gradient (i) in a test is given, krM can be calculated from Eq. 37 with Iun and kr obtained from Eqs. 34, respectively. 6 (Zheng et al. 2012). 14 shows the calculated krM curves as a function of the effective saturation.
11). This layer contributes to the second half of the total flux for the layered system. ) For the second porous medium, the relationship between the magnitude of total flux q and hydraulic gradient i is the additive combination of L2 and L3 in Fig. 11. The thick black line (with two segments from L2 and L1 respectively) is the q(i) curve for the second medium (the layered system). Note that I1 is the same as the hydraulic gradient at the intersection between L1 and L2, because the two ideal porous media have the same threshold gradient (I).
17), which is consistent with the results of Hu and Ewing (2014). 47 in Fig. 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.