scholarly journals Modeling the Movement of Groundwater VOD in a Rectangular Jumper with a Screen

2021 ◽  
Vol 2 (2) ◽  
pp. 069-073
Author(s):  
EN Bereslavsky
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Analytical Solution ◽  
Incompressible Fluid ◽  
Darcy’S Law ◽  
Exact Analytical Solution ◽  
Darcy's Law

Within the framework of planar steady-state filtration of incompressible fluid according to Darcy’s law, an exact analytical solution of the problem of flow in a rectangular cofferdam with a screen in the presence of evaporation from the free surface of groundwater is given. The limiting cases of the considered motion - filtration in unconfined reservoir to imperfect gallery, as well as the flow in the absence of evaporation - are noted.

scholarly journals On periodic Stokesian Hele-Shaw flows with surface tension

2008 ◽  
Vol 19 (6) ◽  
pp. 717-734 ◽  
Author(s):  
J. ESCHER ◽  
B.-V. MATIOC
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Incompressible Fluid ◽  
Classical Solution ◽  
Small Perturbation ◽  
Darcy’S Law ◽  
Viscous Incompressible Fluid ◽  
Darcy's Law ◽  
Two Dimensional ◽  
Unique Classical Solution

In this paper we consider a 2π-periodic and two-dimensional Hele-Shaw flow describing the motion of a viscous, incompressible fluid. The free surface is moving under the influence of surface tension and gravity. The motion of the fluid is modelled using a modified version of Darcy's law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution for a domain which is a small perturbation of a cylinder. Moreover, we identify the equilibria of the flow and study their stability.

Compressible Advection Through an Elastomer Seal: A Porous Media Approach to Seals for Space Applications

2009 ◽  
Author(s):  
Nicholas G. Garafolo ◽  
Christopher C. Daniels
Keyword(s):  
Darcy’S Law ◽  
Gas Permeability ◽  
Exact Analytical Solution ◽  
Darcy's Law ◽  
Leak Rate ◽  
Molecular Flow ◽  
Space Applications ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Elastomer Seal

Gas permeability characterization is of the utmost importance in space seals applications. Space seals must maintain acceptable mass losses in harsh environments where temperatures widely vary under vacuum conditions. Silicone elastomers are commonly used in space as they offer significant sealing performance at temperature extremes and are capable of meeting stringent outgassing requirements necessary for vacuum environments. Traditional models of leak rates solely rely on a diffusive transport mechanism; mass is transported across a membrane through molecular flow induced by a concentration gradient under isostatic conditions. In the application of space seals, the pressure gradients are large, resulting in advection dominated transport. Conventional applications of advection utilize Darcy’s law; however, the fluid is assumed incompressible and fails to capture the nonlinear pressure gradient under compressible situations. Consequently, employing Darcy’s law incorrectly predicts the leak rate. A novel model in compressible advection through an elastomer seal is presented. A phenomenological approach is taken to determine the specific discharge. Through the conservation of mass, the governing equation for pressure is derived. An exact analytical solution exists for one-dimensional flow in the form of a Generalized Emden-Fowler equation and as a result, an analytical expression for mass flow is developed. A series of experiments is presented to deduce permeability constants and Klinkenberg parameter of silicone S0383-70 under one-dimensional flow conditions. The leak rates of the model and experiments are compared. Through the presented compressible advection model, the mass leak rate of any candidate seal geometry can be evaluated.

scholarly journals Analytical solution of freeze-drying mathematical model based in Darcy’s law: application to an orange juice-based cake

2021 ◽  
Vol 19 (1) ◽  
pp. 265-272
Author(s):  
Mariana Aziyadé Uscanga-Ramos ◽  
Erik Lopez-Sanchez ◽  
Nuria Martínez-Navarrete ◽  
Miguel Angel García-Alvarado ◽  
Marco Antonio Salgado-Cervantes
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Orange Juice ◽  
Freeze Drying ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Model Based

scholarly journals Incompressible Fluid flow through free andporous areas

2021 ◽  
pp. 99-102
Author(s):  
Mohamed Saif AlDien ◽  
Hussam M.Gubara
Keyword(s):  
Fluid Flow ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Continuity Equation ◽  
Flow Problem ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Incompressible Fluid Flow ◽  
Flow Through

In this paper we discussedincompressiblefluid flow problem through free and porous areas by using Darcy's law and continuity equation, by apply the boundary conditions required to specify the solutio

Quasi-static hydraulic crack growth driven by Darcy’s law

2018 ◽  
Vol 11 (2) ◽  
pp. 161-191 ◽  
Author(s):  
Stefano Almi
Keyword(s):  
Incompressible Fluid ◽  
Crack Growth ◽  
Darcy’S Law ◽  
Fluid Pressure ◽  
Energy Functional ◽  
Darcy's Law ◽  
Variational Model ◽  
Equilibrium Conditions ◽  
Griffith’S Criterion ◽  
Weak Notion

AbstractIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain {\epsilon\in\mathbb{R}} and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V, and ϵ. Then we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

scholarly journals On the validity of modeling concepts for (the simulation of) groundwater flow in lowland peat areas – case study at the Zegveld experimental field

2011 ◽  
Vol 8 (1) ◽  
pp. 2065-2101
Author(s):  
P. Trambauer ◽  
J. Nonner ◽  
J. Heijkers ◽  
S. Uhlenbrook
Keyword(s):  
Steady State ◽  
Groundwater Flow ◽  
Darcy’S Law ◽  
Single Layer ◽  
Darcy's Law ◽  
Layer Model ◽  
Peat Soils ◽  
Slug Tests ◽  
Flow Models ◽  
Humified Peat

Abstract. The groundwater flow models currently used in the western part of The Netherlands and in other similar peaty areas are thought to be a too simplified representation of the hydrological reality. One of the reasons is that due to the schematization of the subsoil, its heterogeneity cannot be represented adequately. Moreover, the applicability of Darcy's law in these types of soils has been questioned, but this law forms the basis of most groundwater flow models. With the purpose of assessing the typical heterogeneity of the subsoil and to verify the applicability of Darcy's law fieldwork was completed at a research site in the western part of The Netherlands. The assessments were carried for the so called Complex Confining Layer (CCL), which is the Holocene peaty to clayey layer overlying Pleistocene sandy deposits. Borehole drilling through the CCL with a hand auger was completed and revealed the typical heterogeneous character of this layer showing a dominance of muddy, humified peat which is alternated with fresher peat and clay. Slug tests were carried out to study the applicability of Darcy's law given that previous studies suggested the non validity for humified peat soils given by a variable hydraulic conductivity K with the hydraulic gradient. For higher humification degrees, the experiments indeed suggested a variable K, but this seems to be the result of the inappropriate use of steady-state formulae for transient experiments in peaty environments. The muddy peat sampled has a rather plastic nature, and the high compressibility of this material leads to transient behavior. However, using transient formulae, the slug tests conducted for different initial hydraulic heads showed that there was hardly any evidence of a variation of the hydraulic conductivity with the hydraulic gradient. Therefore, Darcy's law can be used for peat soils. The heterogeneity of the subsoil and the apparent applicability of Darcy's law were taking into account for the detailed heterogeneous model that was prepared for the research site. A MODFLOW model consisting of 13 layers in which 4 layers represent the heterogeneous CCL was set up for an average year assuming steady state conditions and for the winter of 2009 to 2010 adopting transient conditions. The transient model was then extended for a whole hydrological year and for an eight year period with the objective of visualizing the flowpaths through the CCL. The results from these models were compared with a 10 layer model whereby the CCL is represented by a single layer assuming homogeneity. From the comparison of the two model types the conclusion could be drawn that a single layer schematization of the CCL produces flowpath patterns which are not the same but still quite similar to a 4 layer representation of the CCL. However, the single layer schematization results in a considerable underestimation of the flow velocity, and subsequently a longer travel time, through the CCL. Therefore, a single layer model of the CCL seems quite appropriate to represent the flow behavior of the shallow groundwater system, but would be inappropriate for transport modeling through the CCL.

Carbon Dioxide Effects on Wellbore-Pressure Response During Injection/Falloff Test

SPE Journal ◽  
2018 ◽  
Vol 23 (03) ◽  
pp. 919-936 ◽  
Author(s):  
Cíntia G. Machado ◽  
Mohammadreza M. Firoozabad ◽  
Albert C. Reynolds
Keyword(s):  
Carbon Dioxide ◽  
Steady State ◽  
Incompressible Flow ◽  
Analytical Solutions ◽  
Darcy’S Law ◽  
Co2 Concentration ◽  
Darcy's Law ◽  
Pressure Solution ◽  
Wellbore Pressure ◽  
Carbonated Water

Summary We provide analytical solutions for the wellbore pressure during an injection/falloff-test problem under radial-flow conditions in homogeneous porous media where the injected fluid is carbonated water. For both the injection and falloff periods, we assume an isothermal process with thermodynamic equilibrium, a linear adsorption isotherm, and viscosities that depend only on the carbon dioxide (CO2) concentration. We also neglect CO2 diffusion, gravity effects, and capillarity effects. For the injection period, we first determine the saturation and concentration distributions with time in the reservoir by applying the method of characteristics to solve the appropriate system of hyperbolic conservation equations, where we assume incompressible fluids. In solving for water saturation and CO2 concentration in water, we neglect the change in water volume caused by the variation of the CO2 concentration in water. After solving for the saturation and concentration profiles, the pressure solution can be obtained by integrating Darcy's law, from the wellbore radius to infinity, while assuming an infinite-acting reservoir and invoking the Thompson-Reynolds steady-state theory (Thompson and Reynolds 1997b). Because Darcy's law does not assume incompressible flow, the pressure solution generated does not assume incompressible flow. To obtain an analytical expression for the wellbore pressure, however, we do assume that for injection and falloff, the total flow-rate profile in the reservoir is constant in a region from the wellbore to a radius greater than the radius of the flood front. The region within this radius increases with time and it is referred to as the steady-state region or zone (Thompson and Reynolds 1997b). During the falloff stage, it is assumed that there is no change in saturation in the reservoir, which is reasonable because we neglect capillary pressure, the gravity force, and fluid compressibilities when determining the saturation profile. Using these assumptions, we generate analytical solutions for a carbonated-water-injection (CWI)/falloff test and compare these solutions with those obtained with a commercial reservoir simulator using very fine spatial grids and very small timesteps. This comparison suggests that the analytical solutions presented can be used reliably to analyze pressure data obtained during CWI/falloff tests.

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