The impact of Brinkman's extension of Darcy's law in the neighborhood of a circular preferential flow pathway

1999 ◽  
Vol 14 (5) ◽  
pp. 427-435 ◽  
Author(s):  
Aaron A. Jennings ◽  
Ramagopal Pisipati
Keyword(s):  
Preferential Flow ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
The Impact ◽  
Flow Pathway

scholarly journals Analysis of elastic viscoplastic consolidation of sand drain foundations with exponential seepages

2021 ◽  
Vol 248 ◽  
pp. 01039
Author(s):  
Duanyang Yang ◽  
Fengyuan Li ◽  
Yangyang Xia ◽  
Mingsheng Shi ◽  
Yanjie Hao ◽  
...  
Keyword(s):  
Pore Pressure ◽  
External Load ◽  
Permeability Coefficient ◽  
Numerical Solutions ◽  
Darcy’S Law ◽  
Soft Clay ◽  
Darcy's Law ◽  
Consolidation Process ◽  
Soil Skeleton ◽  
The Impact

Studies have shown that the pore seepage in soft clay deviates from Darcy's law, with the compressibility and permeability of the soil demonstrating obvious nonlinear characteristics during the consolidation process. These factors will affect the sand drain foundation consolidation process. In order to explore the consolidation mechanism of sand drain foundation in saturated clay, this paper introduces the UH model considering the time effect to describe the nonlinear deformation relation of the soil skeleton under the Barron free strain assumption and introduces the exponential seepage equation as an alternative to Darcy's law. Additionally, the impact of the permeability coefficient and the smearing effect is considered which is used to re-derive the conventional sand drain consolidation equation, and then the finite difference method is adopted to give the implicit numerical solutions of the equation. By comparing with literature results, the validity of the method developed in this paper is verified. Then, the effects of the soil nonlinearity, construction disturbance, and external load on the sand drain foundation nonlinear consolidation process are studied as a function of time. The current results reveal that due to the viscous effect of soil, the pore pressure near the undrained boundary of the sand drain foundation during the pre-loading period increases. The above phenomenon is more evident when considering the non-Darcy seepage; meanwhile, the consolidation rate of the sand drain foundation also becomes increasingly slow. Moreover, the decrease of the permeability coefficient in the smear zone can significantly reduce the dissipation rate of the overall pore pressure of the sand drain foundation, while the increase of the external load accelerates foundation consolidation.

scholarly journals An extension of Darcy’s law incorporating dynamic length scales

2019 ◽  
Vol 129 ◽  
pp. 70-79 ◽  
Author(s):  
Yuhang Wang ◽  
Saman A. Aryana ◽  
Myron B. Allen
Keyword(s):  
Darcy’S Law ◽  
Darcy's Law ◽  
Length Scales ◽  
Dynamic Length

scholarly journals The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

2001 ◽  
Vol 19 (4) ◽  
pp. 177-188
Author(s):  
B Eitzinger ◽  
G Ederer
Keyword(s):  
Pressure Drop ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Constitutive Equations ◽  
Darcy’S Law ◽  
Stationary Flow ◽  
Darcy's Law ◽  
Nonlinear Behaviour ◽  
Cigarette Paper ◽  
Drop Flow

AbstractThis study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

scholarly journals Simulation of Water Filtration in Porous Zone Based on Darcy's Law

2013 ◽  
Vol 36 ◽  
pp. 163-168
Author(s):  
Mohammed Amine Kendouci ◽  
Benali Kharroubi ◽  
Rachid Khelfaoui ◽  
Ali Bendida ◽  
Brahim Dennai ◽  
...  
Keyword(s):  
Darcy’S Law ◽  
Darcy's Law ◽  
Water Filtration ◽  
Porous Zone

Contrasting facies patterns between river-dominated and symmetrical wave-dominated delta deposits

2021 ◽  
Vol 91 (3) ◽  
pp. 262-295
Author(s):  
BRIAN J. WILLIS ◽  
TAO SUN ◽  
R. BRUCE AINSWORTH
Keyword(s):  
Sea Level Rise ◽  
Sea Level ◽  
Preferential Flow ◽  
Return Flow ◽  
Lateral Migration ◽  
Littoral Drift ◽  
Delta Front ◽  
Reference Case ◽  
Depositional Processes ◽  
The Impact

Abstract Process-physics-based, coupled hydrodynamic–morphodynamic delta models are constructed to understand preserved facies heterogeneities that can influence subsurface fluid flow. Two deltaic systems are compared that differ only in the presence of waves: one river dominated and the other strongly influenced by longshore currents. To understand an entire preserved deltaic succession, the growth of multiple laterally adjacent delta lobes is modeled to define delta axial to marginal facies trends through an entire regressive–transgressive depositional succession. The goal is to refine a facies model for symmetrical wave-dominated deltas (where littoral drift diverges from the delta lobe apex). Because many factors change depositional processes on deltas, the description of the river-dominated example is included to provide a direct reference case from which to define the impact of waves on preserved facies patterns. Both systems display strong facies trends from delta axis to margin that continued into inter-deltaic areas. River-dominated delta regression preserved a dendritic branching of compensationally stacked bodies. Transgression, initiated by sea-level rise, backfilled the main channel and deposited levees and splays on the submerging delta top. Wave-dominated deltas developed dual clinoforms: a shoreface clinoform built as littoral drift carried sediment away from the river month and onshore, and a subaqueous delta-front clinoform composed of sediment accumulated below wave base. Although littoral drift in both directions away from the delta axis stabilized the position of the river at the shoreline, distributary-channel avulsions and lateral migration of river flows across the subaqueous delta top produced heterogeneities in both sets of clinoform deposits. Separation of shoreface and subaqueous delta-front clinoforms across a subaqueous delta top eroded to wave base produced a discontinuity in progradational vertical successions that appeared gradual in some locations but abrupt in others. Littoral drift flows away from adjacent deltas converged in inter-deltaic areas, producing shallow water longshore bars cut by wave-return-flow channels with associated terminal mouth bars. Transgression initiated by sea-level rise initially led to vertical aggradation of wave-reworked sheet sands on the subaqueous delta top and then retreating shoreface barrier sands as the subaerial delta top flooded. Pseudo inter-well flow tests responded to local heterogeneities in the preserved deposits. As expected, abandoned channels in the river-dominated case defined shoreline-perpendicular preferential flow paths and wave-dominated delta deposits are more locally homogeneous, but scenarios for development of more pronounced shore-parallel heterogeneity patterns for wave-influenced deltas are discussed. The results highlight the need to consider the dual clinoform nature of wave-dominated delta deposition for facies prediction and subsurface interpretation.

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