Applied Pressure Gradient Research Articles

Accelerated test of ingress of chloride ions in concrete under pressure and concentration gradients

This paper describes the experimental and numerical work carried out to study the ingress of chloride ions in concrete under pressure and concentration gradients. The proposed accelerated water and chloride permeability tests together with long-term soaking tests are used to develop a pressure gradient model, a concentration gradient model and the combination of the two f or the prediction of ingress of chloride ions in concrete. It is found that the experimental results, based on OPC concrete with a water-cement ratio of 0·6 tested in the pressure range 0·30 MPa, agree well with the finite element solutions derived under similar conditions. The design and application of the specially built testing equipment for the accelerated permeability tests are presented. The repeatability of these tests, expressed as the coefficient of variation, is satisfactory. This confirms that the proposed test apparatus and method can be used with confidence. It is also observed that the applied pressure gradient has little effect on the water permeability coefficient in the experimental range 0–30 MPa.

Comparison of the Cooling Performance of Staggered and In-Line Arrays of Electronic Packages

The cooling performance of in-line and staggered regular arrays of simulated electronic packages is compared for both sparse and dense packaging configurations. At equal flow rates, staggered arrays exhibit higher element heat transfer coefficients and friction factors than in-line arrays. Furthermore, an increase in the packaging density of the elements results in a moderate reduction in the friction factor with negligible change in the heat transfer coefficient. However, when performance is expressed in terms of heat transfer rate per unit packaging system volume, dense arrays are found to out perform sparse arrays at equal flow rate, applied pressure gradient or pumping power. Furthermore, no significant difference in performance is observed between staggered and in-line configurations when they are compared on the basis of either equal coolant flow pressure drop or pumping power.

The characterization of fluid transport in a porous solid by pulsed gradient stimulated echo NMR

Pulsed magnetic field gradient stimulated echo NMR measurements are reported for the flow and diffusion of an aqueous phase within a sample of Fontainebleau sandstone. The stimulated echo dependence on the gradient pulse area, q, for a fixed observation time Δ, is used to derive the displacement probability distributions, P Δ(X), where X, the direction of the field gradient, is arranged to be parallel or perpendicular to the applied pressure gradient driving the flow. The shape of the P Δ(X) as a function of Δ is modelled in terms of laminar flow within a set of randomly oriented capillaries. For small Δ, molecules remain largely within the capillaries they occupy at the beginning of the time Δ and, as a consequence, the P Δ(X) for small Δ are dominated by the orientational distribution of the capillaries. For large Δ, the evolution of the P Δ(X) is reproduced only when diffusion of molecules across the velocity gradients within the capillaries is introduced and, in addition, the fluid transfers between differently oriented capillaries through the action of the overall flow.

Wetting front instability in randomly stratified soils

A probabilistic criterion is derived for the onset of wetting front instability during surface water infiltration into a randomly stratified soil. It is based on the common assumption that the natural log hydraulic conductivity of the soil is a random, multivariate Gaussian function of space. Whereas the mean (expectation) of this function may exhibit a drift, its fluctuations about the mean are statistically homogeneous with constant variance and autocorrelation scale. The wetting front is taken to form a sharp boundary. Closed-form expressions for the probability of instability, and for the mean critical wave number, are obtained either directly or via a first-order reliability method. Monte Carlo simulations are used to verify these analytical solutions as well as to determine the mean maximum rate of incipient finger growth and corresponding mean wave number. The effects of applied pressure gradient, capillary pressure head at the wetting front, and statistical parameters of the hydraulic conductivity field on instability and incipient finger growth are investigated for a wide range of these variables.

Laminar pulsatile two-phase non-Newtonian flow through a pipe

A lighter, less viscous lubricating Newtonian fluid lies above and does not mix with a non-Newtonian fluid whose constitutive equation is either a power law or a modified Bingham plastic. In steady flow, the flux of the non-Newtonian fluid can be significantly larger than in the corresponding single-phase fully filled flow. Here it is shown that such flux gains can be further enhanced by introducing an oscillatory component into the applied pressure gradient and at a cost in terms of additional power that is significantly less than in the corresponding fully filled (single phase) pipe flow.

The long-wave interfacial instability of two liquid layers stratified by thermal conductivity in an inclined channel

The flow of two liquid layers with different thermal conductivities confined in a rigid inclined channel cooled from below is susceptible to a long-wave interfacial instability. The results of Yih [Phys. Fluids 29, 1769 (1986)] on this problem are corrected and extended to layers of unequal thickness and to an arbitrary applied pressure gradient. The effects of direct liquid expansion and contraction as described in the conservation of mass equation are also included.

Highly Overbalanced Perforating

This article briefly describes a new perforating technique that will result in clean, open perforations. The well is normally stimulated when highly overbalanced perforation techniques are used. This perforation process improves formation evaluation because the well flows better and is easier to test.

Spectrum of density fluctuations in a particlefluid system—II. Polydisperse spheres

This paper presents an extension of the analysis shown in Part I to a polydisperse particle-fluid system. The density autocorrelation is shown to be a function of two quantities, a generalized Overlap function for which an analytical expression is derived, and the radial distribution function (RDF). In Fourier transform space, the density spectrum again appears to be a strong function of the mean particle size, and secondarily the mean particle separation distance. One unusual result is previously observed oscillations in the density spectrum of a monodisperse system of particles are severely dampened or even eliminated in the polydisperse case, depending on the width of the particle size distribution. Apparently contributions from different particle correlations interfere with each other, thereby reducing the coherent oscillations seen in the monodisperse particle-fluid system. Furthermore at large wavenumbers, the spectrum decays with a −2 power-law, independent of the shape of the particle size distribution. This behavior can be traced to the Overlap function which controls the behavior of the spectrum beyond the first peak. Remarkably the −2 power-law spectrum is determined by the shape of the particles (i.e. spheres) rather than their spatial distribution (RDF). The effect of an asymptotically large pressure gradient on the correlation of several important higher-order moments is revisited for the polydisperse system. The relatively simple relationships developed for the monodisperse system are lost in the polydisperse case because particles of different sizes will be influenced differently by an applied pressure gradient. The result is moments that are of different order in velocity can no longer be related to each other (as they were in the monodisperse system), even in this idealized flow. A more comprehensive understanding of this phenomenon can only be achieved through direct numerical simulation or experiment.

Observations of purely elastic instabilities in the Taylor–Dean flow of a Boger fluid

An experimental and theoretical investigation of the stability of the viscoelastic flow of a model Boger fluid between rotating cylinders with an applied pressure gradient is presented. In our theoretical study, a linear stability analysis based on the Oldroyd-B fluid model which predicts the critical conditions and the structure of the vortex flow at the onset of instability is developed. Our results reveal that certain non-axisymmetric modes are more unstable than the previously studied axisymmetric mode when the shearing by the cylinder rotation is the dominant flow-driving force. This is consistent with recent results presented by Beris & Avgousti (1992) on the stability of elastic Taylor–Couette flow. On the other hand, the axisymmetric mode is more unstable when the pressure gradient becomes dominant. Furthermore, we investigate the mechanism of purely elastic Taylor–Dean instability with respect to non-axisymmetric disturbances through an examination of the disturbance-energy equation. It is found that the mechanism of the elastic Taylor–Dean instability is associated with the coupling between the disturbance polymeric stresses due to the azimuthal variation of the disturbance flow and the base state velocity gradients. In our experimental study, evidence of non-inertial, cellular instabilities in the Taylor–Dean flow of a well-characterized polyisobutylene/polybutene Boger fluid is presented. A stationary, meridional obstruction is placed between independently rotating, concentric cylinders to generate an azimuthal pressure gradient in opposition to the shearing flow. Flow visualization experiments near the critical conditions show the transition from purely azimuthal flows to secondary vortex flows, and the development of evenly spaced, banded vortex structures. The critical wavenumber obtained from spectral image analysis of the visualizations, and the critical Deborah number are presented for various ratios of the pressure gradient to the shear driving force. Although there is a quantitative discrepancy between data and theory, the qualitative trends in the data are in agreement with our theoretical predictions. In addition, laser-Doppler velocimetry (LDV) measurements show that the instability is a stationary mode when the pressure gradient is the dominant flow-driving force, while it is an oscillatory instability when the shearing is dominant, again as predicted by the theory.

Streaming Potential across a Charged Membrane

An expression for the streaming potential across a uniformly charged membrane under an applied pressure gradient is derived that is different from the usual streaming potential in a porous plug or a capillary. It is predicted that for typical membranes, this streaming potential should be observed as a membrane potential, the magnitude of which is comparable to that of the usual membrane potential induced by the electrolyte concentration gradient.

Flow of viscoplastic fluids in a rotating concentric annulus

A difficulty in any flow calculation with viscoplastic fluids such as Bingham fluids is the determination of possible plug zones in which no deformation occurs. This paper investigates the flow in a concentric annulus when there is both an axial and tangential flow, the tangent flow arising from rotation of the inner cylinder of the annulus. The flow is analyzed by considering flow in a slot, for which an analytical solution is given, and by solving the full problem numerically. It is shown that when the boundary is set in motion an applied pressure gradient will always cause flow. If the applied pressure gradient is small compared to the yield stress of the fluid then the full solution predicts the existence of plugs attached to the outer wall of the annulus. The slot approximation fails to predict this feature. For larger pressure gradients the two solutions are in good agreement. The analytical calculation gives a simple expression for the critical rate at which the wall has to move to reduce the plug size to zero.

Electrokinetic dissipation induced by seismic waves

When a fluid electrolyte moves relative to a solid, an electric field is generated that migrates ions and thus dissipates energy. This “electrokinetic” dissipation is theoretically compared to the viscous shear dissipation for fluid flow generated by a fixed time harmonic pressure gradient in a planar quartz duct. It is shown that, regardless of frequency, it is safe to ignore the electrokinetic losses when the electrolyte molarity is on the order of 0.1 M or greater. For low molarity electrolytes [Formula: see text], however, the electrokinetic losses do become significant compared to the viscous losses for flow in sufficiently tight pores. The ratio of electrokinetic dissipation [Formula: see text] to viscous dissipation [Formula: see text] is always a maximum when the electrokinetic radius (the duct haft‐width divided by the Debye length) is ≈1.5. The maximum value of [Formula: see text] does not exceed 0.5 for the NaCl, KCl, and quartz systems considered. The generated electric field pushes on the excess ions in the duct in a direction opposite to the applied pressure gradient, thus giving rise to an apparent viscosity enhancement. This enhancement is ⩽45 percent for the systems considered here, and can be directly obtained from the [Formula: see text] ratio. Indeed, the central effect of a large [Formula: see text] ratio is that the amount of relative fluid flow is reduced, and thus, the amount of wave attenuation is reduced.

Permeability estimation from velocity anisotropy in fractured rock

Cracks in a rock mass subjected to a uniaxial stress will be preferentially closed depending on the angle between the fracture normal vectors and the direction of the applied stress. If the prestress fracture orientation distribution is isotropic, the effective elastic properties of such a material after application of the stress are then transversely isotropic due to the overall alignment of the cracks still open. Velocity measurements in multiple directions are used to invert for the probability density function describing orientations of crack normals in such a rock. This is accomplished by expanding the crack orientation distribution function into generalized spherical harmonics. The coefficients in this expansion are functions of the crack density and the crack aspect ratio distribution. The information on fracture distribution obtained from the velocity inversion allows an estimation of the anisotropic permeability of the fractured rock system. Permeability estimates are based on the number of cracks open of each aspect ratio, and the contribution of a given crack is weighted by the cosine of the angle between the crack and the direction of the applied pressure gradient. This approach yields a prediction of permeability as a function of the angle from the uniaxial stress axis. The inversion for crack orientation is applied to ultrasonic velocity measurements on Barre granite, and permeability predictions for this sample are presented. The inversion results are good and reproduce velocity measurements well, and the permeability predictions show some of the expected trends. Initial comparisons of the predictions with available permeability data, however, show deviations, suggesting that further information on partial crack closure and connectivity of cracks should be included into the permeability model.

Lubricated pipelining. Part 3 Stability of core-annular flow in vertical pipes

The stability of core-annular flow in vertical pipes is analysed using the linearized theory of stability. In previous studies instabilities due to interfacial friction, interfacial tension and Reynolds stresses in the bulk fluid were identified and associated with observed instabilities. In this study we include and analyse the effects of gravity. In one case gravity opposes and in the other aids the applied pressure gradient. Some preliminary results from our experiments are also presented. The prediction of stability for perfect core-annular flow in a carefully selected window of parameters is verified for the case of free fall in which the applied pressure gradient vanishes.

Linear problem of water-ice phase transitions in unsaturated soils

The approach proposed by Menot is developed. The problem of the freezing of an unsaturated soil is formulated for a compressible gas and equal component pressures. An analytic solution is obtained in the linear approximation. The results indicate the strong dependence of the ice saturation on the permeability of the soil and the applied pressure gradient.

The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders

Flow fields within spatially periodic arrays of cylinders arranged in square and hexagonal lattices are calculated, with microscale Reynolds number ranging between zero and 200, employing a finite element numerical scheme. The terminology of an ‘‘apparent permeability’’ is introduced to establish a relationship existing between mean velocity and macroscopic pressure gradient characterized by a finite Reynolds number flow. In contrast with the low Reynolds number ‘‘true ’’ permeability, the apparent permeability is shown here to generally depend upon the direction of the applied pressure gradient, owing to nonlinearities existing within the local fluid motion. The orientation-dependent permeabilities of both square and hexagonal monodisperse arrays are observed to diminish with increasing Reynolds number. Similar behavior is also observed for a bidisperse square array, though the apparent permeability of the latter is shown less sensitive to Darcy velocity orientation at large Reynolds numbers in comparison to the corresponding monodisperse square array, for all cylinder concentrations examined.

Analytical and Numerical Models of Transport in Porous Cementitious Materials

ABSTRACTFluid flow under applied pressure gradients and ionic diffusion under applied concentration gradients are important transport mechanisms that take place in the pore space of cementitious materials. This paper describes: 1) a new analytical percolation-theory-based equation for calculating the permeability of porous materials, 2) new computational methods for computing effective diffusivities of microstructural models or digitized images of actual porous materials, and 3) a new digitized-image mercury intrusion simulation technique.

Increase in electrical resistance of plasmodesmata of Chara induced by an applied pressure gradient across nodes

By insertion of microelectrodes into the vacuoles of two adjacent internodal cells of Chara corallina, the changes of the potential differences across the plasma membranes and node were noted when a current of 0.40 μA was passed through the cells bathed in artificial pond water. When the solution bathing one cell was changed to artificial pond water + 102 mol m−3 mannitol, a significant increase was detected both in the membrane potential difference response and in the nodal potential difference response. This indicates that the lowering of turgor on one cell by 0.24 MPa increased the electrical resistance of the membrane of that cell and also the resistance of the plasmodesmata connecting the two internodal cells via the node. This is evidence in support of valving in plasmodesmata when a pressure difference is induced across their ends.

The role of pressure in osmotic flow

Pressure-driven volume flow occurs at the expense of an external energy supply. This has been shown for pure liquid pressed through a rigid partition and for the reverse osmosis case. In contrast to these cases, the osmotic flow dissipation and work done against the applied pressure gradient are covered by free energy change brought about by dilution of the solution. A consistent energetic and mechanical description of osmosis has been achieved on recognizing that the occurrence of pressure gradient depends, according to the mechanical equilibrium condition, on whether there is a resultant external force acting on the solution. The pressure gradient, if at all present, is shown to be only a factor in osmotic flow and not the prime mover. The osmotic effect on course-porous membranes has been considered as resulting from physical adsorption on the pore wall. A force on the solution near the pore wall due to adsorption is derived on recognizing that it can perform work at the expense of the Gibbs free energy of the solution. This membrane-solution interaction force can cause a slip of the solution on the wall or pressure buildup if the flow has been stopped. Assuming diffusional type of flow in the wall-adjacent layer and viscous flow in the core of the channel, the resultant volume flow is expressed by the moment of adsorption, chemical potential gradients of the components, and by the applied pressure gradient. For non-Newtonian liquids a possibility of plug flow has been shown.

A Logical Approach to Fracture Fluid Selection

Abstract This paper presents a method of matching formation, rock and reservoir fluid characteristics to the properties of fracturing fluids for optimized stimulation treatments. Particular emphasis is placed on the role of the scanning electron microscope in formation characterization. The other rock and well properties can be determined utilizing standard industry practices. In addition to the traditional fracturing fluid parameters of rheology and fluid leak-off, the volatility, wetting tendencies, inter facial tensions and clay compatibility are discussed and are utilized in the selection process. Introduction Over the course of fracturing history, the decisions involved in choosing fracturing fluids have varied considerably. In earlier years, attempts were made to maximize created fracture area, with no real consideration for the geology and mineralogy of the reservoir. Rather, emphasis was placed on increasing the fracturing fluid efficiency and width generation capabilities. It has long been known that certain fluids give substantially better results on a particular formation than other: fluids, but the success or failure of the fluid selection was largely due to experience. With the advent of scanning electron microscopy, the emphasis shifted to damage occurring as a result of fracturing fluid interaction with authigenic materials in argillaceous reservoirs. The high demand for energy and the interest in low-permeability reservoirs have created a new mysticism involving clay mineralogy. This paper discusses a more detailed fracture selection process which will alleviate some of the misinterpretations. Permeability analysis of formation cores has been an important factor in determining whether a well was capable of commercial production. The fact that measurements are made with gas at pressures significantly different from the formation pressure, however, causes large errors in permeability values, always on the optimistic side. In addition, if a well hasn't been cored it is difficult to obtain permeability data until production has been established, and obtaining production may require stimulation. Permeability values however, can only give (Figure in full paper) a partial picture of pore geometry which should be supplemented by SEM studies, capillary pressure measurements, core flow tests and relative permeability measurements. The purpose of this paper is to combine geology, fluid flows and rock fluid interaction into a logical design process for fracture fluid selection. This process involves the microscopic properties of the rock, including permeability and fracture face damage, the formation heterogeneity, the formation pressures and saturation levels as well as the fracture fluid properties. Sandstone Geology and Permeability Permeability of a porous material characterizes the ease with which a fluid will flow with an applied pressure gradient. The physical parameters of a formation that contribute to permeability variances are the size and shape of the pore spaces, grain packing and fabric, and the degree of cementation. The fabric of a rock is the property concerned with the orientation in space of the component particles. Grains naturally tend to fall such that they lie with their greatest cross section in a horizontal pattern and with their longest axis parallel to water currents thus describing permeability as a directional property.