Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media

1997 ◽  
Vol 119 (3) ◽  
pp. 700-706 ◽  
Author(s):  
J. L. Lage ◽  
B. V. Antohe ◽  
D. A. Nield
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Hydrostatic Pressure ◽  
Pressure Gradient ◽  
Fluid Velocity ◽  
Rate Of Change ◽  
Transition To Turbulence ◽  
Abnormal Behavior ◽  
Hydrostatic Pressure Gradient ◽  
Transition Speed

Previous reports of experiments performed with water (Fund et at., 1987 and Kececioglu and Jiang, 1994) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been termed “transition to turbulence in a porous medium.” We investigate the relationship between the hydrostatic pressure gradient of a fluid (air) through a porous medium and the average seepage fluid velocity. Our experimental results, reported here, indicate an increase in the hydrostatic pressure rate beyond a certain transition speed, not a decrease. Physical arguments based on a consideration of internal versus external incompressible viscous flow are used to justify this distinct behavior, a consequence of the competition between a form dominated transition and a viscous dominated transition. We establish a criterion for the viscous dominated transition from consideration of the results of three porous media with distinct hydraulic characteristics. A theoretical analysis based on the semivariance model validation principle indicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.

scholarly journals Electromyography of the Respiratory Muscles and Gill Water Flow in the Dragonet

1968 ◽  
Vol 49 (3) ◽  
pp. 583-602
Author(s):  
G. M. HUGHES ◽  
C. M. BALLINTIJN
Keyword(s):  
Hydrostatic Pressure ◽  
Stroke Volume ◽  
Pressure Gradient ◽  
Time Course ◽  
Respiratory Muscles ◽  
Adverse Pressure Gradient ◽  
Pressure Head ◽  
Volume Flow ◽  
Frequency Change ◽  
Hydrostatic Pressure Gradient

1. An account is given of the main skeletal elements and muscles involved in the respiratory movements of the dragonet, Callionymus lyra. 2. Using electromyographic techniques it has been shown that the muscles chiefly involved in rapid ejection of water out of the opercular slit are the adductor mandibulae, protractor hyoideus, and hyohyoideus. During the expansion phase of the cycle, which is about six times the duration of the contraction phase, the levator hyomandibulae and sternohyoideus are active, though in some cases the latter only comes in at higher levels of pumping. 3. Changes in volume flow across the gills have been produced by either (a) altering the hydrostatic pressure gradient (Δp) across the system, or (b) altering the oxygen or carbon dioxide content of the water inspired by the fish. With (a), the volume flow decreases linearly at a rate of about 30 ml./min./cm. H2O static pressure head until an inflexion is reached in the curve at which rate of flow decreases and is normally when Δp is zero. That the relative increase in flow rate with negative Δp's is due to the activity of the fish pumping against the adverse pressure gradient has been confirmed by electromyogram recordings during such experiments. With (b), it was possible to demonstrate a clear relationship between stroke volume and the level of electrical activity as measured by the height of the integrated electromyogram. The integrated EMG increases more than linearly with increasing stroke volume during PO2 changes, but this relationship seems to be more nearly linear during changes in CO2 concentration. 4. The respiratory frequency is scarcely affected by changes in flow produced by altering the hydrostatic pressure gradient, but following a decrease in PO2 or an increase in CO2 there is a significant fall in frequency which accompanies the increased electromyogram. The time course of these changes during recovery from a decrease in PO2 or an increase in PCOCO2 suggests that the gas tensions of the inspired water are detected by receptors on the gills and thus influence the electromyogram activity, but the frequency change observed is due to a change in the blood affecting receptors in the brain.

The Growth of Mixing Zone in Heterogeneous Porous Media

2012 ◽  
Author(s):  
M. R. Othman ◽  
R. Badlishah Ahmad ◽  
Z. May
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Short Duration ◽  
Dispersion Coefficient ◽  
Fluid Velocity ◽  
Heterogeneous Porous Media ◽  
Mixing Zone ◽  
Zone Size ◽  
Model Mixing ◽  
Dispersive Mixing

Dengan menggunakan penyelesaian analitikal yang merangkumi fraktal eksponen, pembesaran jarak pencampuran telah dapat ditentukan bagi model satu dimensi. Size zon pencampuran didapati meningkat apabila media berliang menjadi semakin heterogen. Dalam media berliang yang heterogen, saiz zon pencampuran meningkat apabila pemalar penyerakan meningkat terutama sekali pada aliran jangkamasa singkat relatif. Terdapat tiga faktor penting mempengaruhi saiz zon pencampuran penyerakan, ΔxD. Perkara terpenting dalam kajian ini ialah keheterogenan takungan, yang dipersembahkan oleh fraktal eksponen, β. Hasil kajian mendapati bahawa apabila β menjadi kecil (media berliang menjadi semakin heterogen), saiz zon pencampuran meningkat. Satu lagi faktor mempengaruhi ΔxD ialah pemalar penyerakan bersandar masa, Κ(tD). Di dalam takungan heterogen, zon pencampuran meningkat dengan peningkatan nilai pemalar penyerakan pada aliran jangkamasa singkat relatif. Bagi aliran jangkamasa panjang relatif, bagaimanapun, ΔxD terus meningkat walaupun Κ(tD) menjadi tetap. Faktor ketiga ialah purata kelajuan bendalir, ν. Zon pencampuran mempunyai perkaitan songsang dengan kelajuan bendalir dengan cara ΔxD meningkat apabila ν berkurangan. Kata kunci: Kehomogenan; keheterogenan; pekali penyerakan; eksponen fraktal; zon pencampuran; media berliang Utilizing currently available analytical solutions that incorporate fractal exponent, the growth of mixing length of injected solvent was determined for a one-dimensional model. Mixing zone size was found to increase as porous medium becomes increasingly heterogeneous. In a heterogeneous porous media, mixing zone size increases as dispersion coefficient increases particularly at relatively short duration of flow. There are three important factors influencing the size of the dispersive mixing zone, ΔxD. Of particular importance in this study is reservoir heterogeneity, which is represented by a fractal exponent, β. It was discovered that as β becomes smaller (porous medium becomes increasingly heterogeneous), the size of the mixing zone increases. Another factor affecting ΔxD is time dependent dispersion coefficient, Κ(tD). In a heterogeneous reservoir, mixing zone increases with increasing value of dispersion coefficient at relatively short duration of flow. For relatively long period of flow, however? ΔxD continues to increase even though Κ(tD) remains constant. The third factor is average fluid velocity, ν. Mixing zones have inverse relationship with fluid velocity in that ΔxD increases as ν decreases. Key words: Homogeneity; heterogeneity; dispersion coefficient; fractal exponent; mixing zone; dimensionless concentration; porous media

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

A cloned renal epithelial Na+ channel protein displays stretch activation in planar lipid bilayers

1995 ◽  
Vol 268 (6) ◽  
pp. C1450-C1459 ◽  
Author(s):  
M. S. Awayda ◽  
I. I. Ismailov ◽  
B. K. Berdiev ◽  
D. J. Benos
Keyword(s):  
Hydrostatic Pressure ◽  
Pressure Gradient ◽  
Lipid Bilayers ◽  
Single Channel ◽  
Na Channel ◽  
Planar Lipid Bilayers ◽  
Stretch Activation ◽  
Hydrostatic Pressure Gradient ◽  
Epithelial Na Channel

We have previously cloned a bovine renal epithelial channel homologue (alpha-bENaC) belonging to the epithelial Na+ channel (ENaC) family. With the use of a rabbit nuclease-treated in vitro translation system, mRNA coding for alpha-bENaC was translated and the polypeptide products were reconstituted into liposomes. On incorporation into planar lipid bilayers, in vitro-translated alpha-bENaC protein 1) displayed voltage-independent Na+ channel activity with a single-channel conductance of 40 pS, 2) was mechanosensitive in that the single-channel open probability was maximally activated with a hydrostatic pressure gradient of 0.26 mmHg across the bilayer, 3) was blocked by low concentrations of amiloride [apparent inhibitory constant of amiloride (K(i)amil approximately 150 nM], and 4) was cation selective with a Li+:Na+:K+ permselectivity of 2:1:0.14 under nonstretched conditions. These pharmacological and selectivity characteristics were altered to a lower amiloride affinity (K(i)amil > 25 microM) and a lack of monovalent cation selectivity in the presence of a hydrostatic pressure gradient. This observation of stretch activation (SA) of alpha-bENaC was confirmed in dual electrode recordings of heterologously expressed alpha-bENaC whole cell currents in Xenopus oocytes swelled by the injection of 15 nl of a 100 mM KCl solution. We conclude that alpha-bENaC, and by analogy other ENaCs, represent a novel family of cloned SA channels.

Analysis of the Influence of Fluid Flow on the Plasticity of Porous Rock Under an Axially Symmetric Punch

1974 ◽  
Vol 14 (03) ◽  
pp. 271-278 ◽  
Author(s):  
Milos Kojic ◽  
J.B. Cheatham
Keyword(s):  
Plastic Deformation ◽  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Unit Volume ◽  
Fluid Pressure ◽  
The Body ◽  
Axially Symmetric

Introduction A number of problems occur in the fields of drilling and rock mechanics for which consideration must be given to the interaction of fluid flow and rock deformation. Such problems include those of borehole stability, chip removal from under a drill bit, drilling in the presence of a fluid pressure gradient between the drilling fluid and formation fluid, and drilling by use of hydraulic jets. We have recently developed a general theory of the influence of fluid pressure gradients and gravity on the plasticity of porous media. The solution of the problem considered here serves as an example of the application of that theory. The illustrative problem is to determine the load required on a flat problem is to determine the load required on a flat axially symmetric punch for incipient plasticity of the porous medium under the punch when fluid flows through the bottom face of the punch. The rock is assumed to behave as a Coulomb plastic material under the influence of body forces plastic material under the influence of body forces due to fluid pressure gradients and gravity. Numerical methods that have been used by Cox et al. for analyzing axially symmetric plastic deformation in soils with gravity force are applied to the problem considered here. Involved is an iterative process for determining the slip lines. The fluid flow field ‘used for calculating the fluid pressure gradient is based upon the work by Ham pressure gradient is based upon the work by Ham in his study of the potential distribution ahead of the bit in rotary drilling. The effective stresses in the porous rock and the punch force for incipient plasticity are computed in terms of the fluid plasticity are computed in terms of the fluid pressure and the cohesive strength and internal pressure and the cohesive strength and internal friction of the rock. PLASTICITY OF POROUS MEDIA PLASTICITY OF POROUS MEDIA A recently developed general theory of plasticity of porous media under the influence of fluid flow is summarized in this section. The equation of motion for the porous solid for the case of incipient plastic deformation reduces to the following equilibrium equation:(1) where Ts is the partial stress tensor of the solid; Fs is the body force acting on the solid per unit volume of the solid material; P is the interaction force between the solid and the fluid; and is the porosity, which is defined as the ratio of the pore porosity, which is defined as the ratio of the pore volume to the total volume of the solid-fluid mixture. The partial stress tensor Ts can be considered as the effective stress tensor that is used in sod mechanics. With the acceptance of the effective stress principle defined in Ref. 5, the yield function, f, in the following form is satisfied for plastic deformation of the porous medium. plastic deformation of the porous medium.(2) where EP is the plastic strain tensor and K and the work-hardening parameter. From the equation of motion for the fluid, the interaction force P can be expressed in the form(3) where is the inertial force of the fluid per unit volume of the mixture and F is the body force acting on the fluid per unit volume of fluid. For the case of incipient plastic deformation the solid can be considered static (velocities of the solid particles are zero), and the problem of determining particles are zero), and the problem of determining the fluid flow field is the one usually analyzed in petroleum engineering. petroleum engineering. Consider a flow of be fluid such that the inertial forces of the fluid can be neglected and assume that Darcy's law is applicable. SPEJ P. 271

Theory of Plasticity of Porous Media With Fluid Flow

1974 ◽  
Vol 14 (03) ◽  
pp. 263-270 ◽  
Author(s):  
Milos Kojic ◽  
J.B. Cheatham
Keyword(s):  
Plastic Deformation ◽  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
General Theory ◽  
Pressure Gradient ◽  
Yield Criterion ◽  
Solid Particles ◽  
Fluid Mixture ◽  
Moving Fluid

Abstract Plastic deformation of a porous medium containing moving fluid is analyzed as a motion of a solid-fluid mixture. The fluid is considered to be Newtonian, and the porous material consists of interconnected pore spaces and of solid particles that can deform pore spaces and of solid particles that can deform elastically. The effective stress principle and a general form of the yield function-including work-hardening characteristics-and general stress-strain relations are applied to describe the plastic deformation of the solid. The system of plastic deformation of the solid. The system of governing equations with the number of unknowns being equal to the number of equations is formed. A possible method of solution of a general problem is described. Some simplification such as problem is described. Some simplification such as the assumptions of quasi-static plastic deformation and incipient plastic deformation with the application of Darcy's law for the fluid flow are discussed. To illustrate an application of the theory, the problem of incipient plane plastic deformation of a Coulomb material is presented. Introduction The motion of fluid through a porous medium and the deformation of a porous medium containing fluid have been the subjects of many investigations. For problems concerning fluid flow through porous media in petroleum and civil engineering literature, the porous material is usually considered undeformable and Darcy's law is taken as the governing relation between the velocity and the pressure of the fluid. pressure of the fluid. Most of the effort concerning fluidization of porous media has been experimental; here the task porous media has been experimental; here the task is to find the critical pressure gradient or the critical velocity of the fluid that will cause fluidization. Only the one-dimensional equilibrium equation, which relates Ne pressure gradient of the fluid and densities of solid and fluid, has been analyzed in most fluidization studies. Recently, a more general theoretical approach has been taken and equations of motion of fluid and solid have been established. Some of the results of this theory are used in the present study. Previous investigations of the deformation of porous media containing fluid have been both porous media containing fluid have been both empirical and theoretical. In the domain of elastic deformation much of the published material has dealt with experimental work aimed at finding the relation between a change in fluid pressure and stresses and deformation of the solid phase. A general theory of elasticity of porous media containing moving fluid was established by Biot. However, that theory is approximate since Darcy's law is considered as a governing relation for the fluid, and the change of permeability with the deformation of the solid is neglected. A simplification of this theory was presented by Lubinski. Experimental work has been carried out in the domain of plastic deformation of porous media containing fluid. The effective stress principle has been established as a result of experiments using saturated sand and porous rocks with various pore pressures (fluid is static in these experiments. pressures (fluid is static in these experiments. This principle, which is considered as a fundamental principle in soil mechanics, states that the pore principle in soil mechanics, states that the pore pressure does not affect the yield criterion of the pressure does not affect the yield criterion of the solid. In other words, the yield condition of the solid depends only on stresses transmitted among the solid particles. The influence of fluid flow on plasticity of porous media was indicated by Lambe and Whitman porous media was indicated by Lambe and Whitman in the analysis of stability of an infinite slope of a soil. In the equilibrium equation of a so-called "free body" a term equal to the negative pressure gradient is added. There is no general theory for plasticity of porous media containing moving fluid. plasticity of porous media containing moving fluid. GENERAL THEORY Consider the motion of a solid-fluid mixture and suppose that the motion of the solid is a plastic deformation. Then the problem reduces to the following: define the motion of a solid-fluid mixture so that the yield criterion of the solid is satisfied. The mechanical model can be described as follows. 1. The system comprises one fluid and one should constituent. SPEJ P. 263

Oscillatory forcing of flow through porous media. Part 2. Unsteady flow

2002 ◽  
Vol 465 ◽  
pp. 237-260 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Flow Through Porous Media ◽  
Mean Flow ◽  
Two Fluids ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Numerical computations are employed to study the phenomenon of oscillatory forcing of flow through porous media. The Galerkin finite element method is used to solve the time-dependent Navier–Stokes equations to determine the unsteady velocity field and the mean flow rate subject to the combined action of a mean pressure gradient and an oscillatory body force. With strong forcing in the form of sinusoidal oscillations, the mean flow rate may be reduced to 40% of its unforced steady-state value. The effectiveness of the oscillatory forcing is a strong function of the dimensionless forcing level, which is inversely proportional to the square of the fluid viscosity. For a porous medium occupied by two fluids with disparate viscosities, oscillatory forcing may be used to reduce the flow rate of the less viscous fluid, with negligible effect on the more viscous fluid. The temporal waveform of the oscillatory forcing function has a significant impact on the effectiveness of this technique. A spike/plateau waveform is found to be much more efficient than a simple sinusoidal profile. With strong forcing, the spike waveform can induce a mean axial flow in the absence of a mean pressure gradient. In the presence of a mean pressure gradient, the spike waveform may be employed to reverse the direction of flow and drive a fluid against the direction of the mean pressure gradient. Owing to the viscosity dependence of the dimensionless forcing level, this mechanism may be employed as an oscillatory filter to separate two fluids of different viscosities, driving them in opposite directions in the porous medium. Possible applications of these mechanisms in enhanced oil recovery processes are discussed.

scholarly journals Role of a Hydrostatic Pressure Gradient in the Formation of Early Ischemic Brain Edema

1986 ◽  
Vol 6 (5) ◽  
pp. 546-552 ◽  
Author(s):  
Shizuo Hatashita ◽  
Julian T. Hoff
Keyword(s):  
Hydrostatic Pressure ◽  
Pressure Gradient ◽  
Water Content ◽  
Brain Edema ◽  
Intraluminal Pressure ◽  
Tissue Pressure ◽  
Ischemic Brain ◽  
Hydrostatic Pressure Gradient ◽  
Arterial Blood ◽  
Ischemic Brain Edema

We studied whether a hydrostatic pressure gradient between arterial blood and brain tissue plays a role in the formation of early ischemic cerebral edema after middle cerebral artery (MCA) occlusion in cats. Tissue pressure, regional CBF, and water content were measured from the cortex in the core and the peripheral zone of brain normally perfused by the MCA. Intraluminal arterial pressure was altered at intervals by inflation of an aortic balloon to vary the blood–tissue pressure gradient in the ischemic zone. Brain water content in the ischemic core, where flow fell to 5.5 ml/100 g/min, increased within 1 h of occlusion. After occlusion tissue pressure rose from 7.95 ± 0.72 mm Hg at 1 h to 13.16 ± 1.13 mm Hg at 3 h. When intraluminal pressure was increased, water content increased further, but only at 1 h after occlusion. In the periphery where flow was 18.9 ml/100 g/min during normotension. neither water content nor tissue pressure rose within 3 h of occlusion. Increased intraluminal pressure was accompanied by increased water content only at 3 h. This study indicates that a hydrostatic pressure gradient is an important element in the development of ischemic brain edema, exerting its major effect during the initial phase of the edema process.

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