Fluid Pressure Gradient Research Articles

Squirt flow in partially saturated cracks: a simple analytical model

SUMMARY Obtaining the seismic response of rocks containing cracks whose scales are much smaller than the prevailing wavelengths is a classic and important problem in rock physics. Seminal analytical models yield the seismic signatures of cracked rocks saturated with a single fluid phase. However, in a wide variety of practically relevant scenarios, cracks may be partially saturated with multiple immiscible fluids of contrasting compressibilities, such as gas and water. When a passing seismic wave deforms the medium, fluid pressure gradients arise within such partially saturated cracks, which, in turn, tend to relax through a process commonly known as squirt flow. The corresponding viscous dissipation may greatly affect the seismic amplitudes and velocities, as well as the anisotropic behaviour of the medium. To date, extensions of classical analytical models to include squirt flow occurring within isolated partially saturated cracks remain limited either in the saturation or in the frequency range. In this work, we present a simple analytical model to compute the seismic response of rocks containing partially saturated aligned cracks accounting for squirt flow effects. First, we solve the linearized Navier–Stokes equations within a partially saturated penny-shaped crack subjected to an oscillatory strain. Then, we obtain a closed analytical expression for a complex-valued frequency-dependent effective fluid bulk modulus which accounts for the stiffness variations of each crack due to squirt flow. Using classic effective medium models, together with such an effective saturating fluid, we retrieve the effective compliance matrix of the probed partially saturated cracked rock. The proposed analytical solution is validated by comparison with corresponding 3-D numerical simulations and existing analytical models.

Physical Simulation and Mathematical Model of the Porous Flow Characteristics of Gas-Bearing Tight Oil Reservoirs

The separation of solution gas has great influence on the development of gas-bearing tight oil reservoirs. In this study, physical simulation and high-pressure mercury intrusion were used to establish a method for determining the porous flow resistance gradient of gas-bearing tight oil reservoirs. A mathematical model suitable for injection–production well networks is established based on the streamline integral method. The concept of pseudo-bubble point pressure is proposed. The experimental results show that as the back pressure decreases from above the bubble point pressure to below the bubble point pressure, the solution gas separates out. During this process, the porous flow resistance gradient is initially equal to the threshold pressure gradient of the oil single-phase fluid, then it becomes relatively small and stable, and finally it increases rapidly and exponentially. The lower the permeability, the higher the pseudo-bubble point pressure, and the higher the resistance gradient under the same back pressure. For tight reservoirs, the production pressure should be maintained above the pseudo-bubble point pressure when the permeability is lower than a certain value. When the permeability is higher than a certain value, the pressure can be reduced below the pseudo-bubble point pressure, and there is a reasonable range. The mathematical results show that after degassing, the oil production rate and the effective utilization coefficient of oil wells decline rapidly. These declines occur later and have a flat trend for high permeability formations, and the production well pressure can be reduced to a lower level. Fracturing can effectively increase the oil production rate after degassing. A formation that cannot be utilized before fracturing because of the blocked throats due to the separation of the solution gas can also be utilized after fracturing. When the production well pressure is lower than the bubble point pressure, which is not too large, the fracturing effect is better.

Development and analytical validation of a finite element model of fluid transport through osteochondral tissue

Fluid transport is critical to joint health. In this study we evaluate an unexplored component of joint fluid transport –fluid transport between cartilage and bone. Such transport across the cartilage-bone interface could potentially provide chondrocytes with an additional source of nutrients and signaling molecules. A biphasic viscoelastic model using an ellipsoidal fiber distribution was created with three distinct layers of cartilage (superficial zone, middle zone, and deep zone) along with a layer of subchondral bone. For stress-relaxation in unconfined compression, our results for compressive stress, radial stress, and effective fluid pressure were compared with established biphasic analytical solutions. Our model also shows the development of fluid pressure gradients at the cartilage-bone interface during loading. Fluid pressure gradients that develop at the cartilage-bone interface show consistently higher pressures in cartilage following the initial loading to 10% stain, followed by convergence of the pressures in cartilage and bone during the 400 s relaxation period. These results provide additional evidence that fluid is transported between cartilage and bone during loading and improves upon estimates of the magnitude of this effect through incorporating a realistic distribution and estimate of the collagen ultrastructure. Understanding fluid transport between cartilage and bone may be key to new insights about the mechanical and biological environment of both tissues in health and disease.

A microscopic study of sand arches and sand skeletons under hydrodynamic force based on the CFD-DEM model

Sand production is one of the oldest challenges in the oil and gas industry, causing billions of dollars of losses every year. The main aim of the research reported here is to use our validated 3-D numerical model (Song et al., 2020) based on computational fluid dynamics (CFD) coupled with the discrete element method (DEM) to investigate sand arching under hydrodynamic force in oil and gas production wells. The main findings are as follows:The sand arches observed in our 3-D model have complex 3-D backbones. Sand arches with fewer sand grains are more stable and more common than those with more sand grains. Sand arches contain particles that are coarser than the average size of sand in reservoirs. Most associated angles in arches are less than 180°. For a concave arch with an associated angle greater than 180°, a bead hanging from the equator can be compensated by neighboring particles. A concave sand arch exists only when static friction is introduced. The two arch abutments of sand arches bear the maximum contact force. The critical drawdown pressure gradient of the reservoir increases when the frictional coefficient between sand and screen/liner material increases from 0.0 to 0.75. However, simply increasing the frictional coefficient does not enhance the stability of sand arches if the frictional coefficient is greater than 0.75. The sand skeleton generates greater inner contact force when a higher fluid pressure gradient is introduced. If the drag force exceeds the maximum strength of the sand arch, catastrophic sand production occurs without a new sand arch forming. The collapse and reconstruction of sand arches cause the fall and rebound respectively of the mean coordination number. The greater the mass of the sand production, the greater the mean coordination number's maximum retracement. The proposed method is sufficiently robust and efficient for application to the simulation of fluid-particle interactions for a wide variety of problems in granular systems.

Electro-osmatic flow of Jeffrey fluid in an asymmetric micro-channel under the effect of Magnetic field

In this article, we have investigated the peristaltic transport of electro-osmotic flow of Jeffrey fluid in an asymmetric channel, in which the walls are modulated by the peristaltic array of patches. In the presence of Electrical Debye Layer (EDL), the Poisson Boltzmann equation for the electrical potential within the micro channel is considered. To evaluate the electrical potential, Debye-Huckel linearization is employed the governing equations are modeled and reduce by small Reynolds number and long wavelength approximation and solved the exact solution. The axial fluid velocity, temperature, pressure gradient, pressure rise and stream functions are discussed with the effects of pertinent parameters (Hartmann number, Phase angle, relaxation time parameter) through the graphs.

Numerical investigation of a biomimetic elastic valve for microfluidic pumping

We use three-dimensional simulations to study the fluid–solid interactions between a highly-deflective biomimetic valve and a viscous fluid within a microfluidic channel, so as to guide the effective design of a biomimetic micropump. We study the steady state and dynamic behavior of the valve and fluid in response to applied fluid pressure gradients using a steady pressure drop and a trapezoidal pressure gradient waveform, respectively. We use dimensionless parameters to characterize the effect of various physical parameters on pumping performance. We determine the range of parameters in which valves can be designed to provide microfluidic pumping that is independent of the period of oscillation of pressure gradients driving the flow. Our findings guide the effective design of such a biomimetic microvalve for harnessing physiological motion to passively provide pumping in an implantable biosensor.

Numerical modelling of saturated boundless media with infinite elements

Based on the elastic theory assumptions and averaging theories, an infinite element boundary which is frequency independent is derived for saturated soil media. The infinite element development is based on mapping functions and viscous layers for damping propagating waves of both solid and water phases. The newly developed infinite element is able to simulate the boundaries of fully saturated soil medium considering both soil displacement and fluid pressures. The main point is that the fluid pressure gradient at infinity is taken to equal to zero thus enabling the realistic consideration of the fluid pressures in numerical simulations. In numerical modelling, the general finite element software ANSYS using its User Programmable Features is used. Related comparisons are done with references. In simulation of propagating waves, the numerical approach is verified considering different models. The verification models include wave propagation through a saturated soil column. The implementation of the newly developed infinite element is done by simulation of an earth fill dam boundaries while the dam body is simulated as a three-phase medium. The obtained results from simulations show promising results and are thoroughly discussed.

Squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids.

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation can significantly affect the waves' amplitudes and velocities. This, in turn, implies that corresponding measurements contain key information about flow-related properties of the probed medium. In many natural and applied scenarios, pore fluids are effectively non-Newtonian, for which squirt flow processes have, as of yet, not been analyzed. In this work, we present a numerical approach to model the attenuation and modulus dispersion of compressional waves due to squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids. In particular, we explore the effective response of a medium comprising an elastic background with interconnected cracks saturated with a Maxwell-type non-Newtonian fluid. Our results show that wave signatures strongly depend on the Deborah number, defined as the relationship between the classic Newtonian squirt flow characteristic frequency and the intrinsic relaxation frequency of the non-Newtonian Maxwell fluid. With larger Deborah numbers, attenuation increases and its maximum is shifted towards higher frequencies. Although the effective plane-wave modulus of the probed medium generally increases with increasing Deborah numbers, it may, however, also decrease within a restricted region of the frequency spectrum.

Modeling In-situ tectonic stress state and maximum horizontal stress azimuth in the Central Algerian Sahara – A geomechanical study from El Agreb, El Gassi and Hassi Messaoud fields

Central Algerian Sahara hosts many prolific hydrocarbon accumulations in the Paleozoic successions. In this work a contemporary stress field of the Saharan platform has been evaluated using the dataset from recently drilled wells in El Agreb, El Gassi and Hassi Messaoud fields. A pore fluid pressure gradient of 0.56 PSI/feet is interpreted from the in-situ measurements in the Paleozoic reservoir units. Vertical stress (Sv) modeled from the bulk-density data indicates an average of 1.02 PSI/feet gradient. Rock elastic property-based approach is employed to model the magnitudes of minimum (Shmin) and maximum horizontal stress (SHmax) components, which were calibrated with leak off test/minifrac and breakout widths, respectively. Paleozoic stress profiles reveal Shmin/Sv range of 0.74–0.84, while SHmax/Sv varies between 1.1 and 1.33. Subsurface stress distribution indicates that the present-day stress field in the Saharan platform is principally strike-slip faulting (SHmax > Sv > Shmin). A cumulative 1490 m of B-D quality wellbore breakouts, inferred from the acoustic image logs, suggest a NW-SE/WNW-ESE SHmax orientation, which is parallel to the absolute African plate motion and Africa-Eurasia plate convergence direction, implying ridge push force to be the dominant contributor to the tectonic stress field. Mean SHmax orientation shows slightly anticlockwise rotation (126°N to 144°N) from south (El Agreb) to north (Hassi Messaoud field). Inferences are discussed regarding the fault slip potential and hydrocarbon reservoir development.

Compressibility effects in turbulent transport of the temperature field.

Compressibility effects in a turbulent transport of temperature field are investigated by applying the quasilinear approach for small Péclet numbers and the spectral τ approach for large Péclet numbers. The compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature field similarly to that for the particle number density and magnetic field. However, expressions for the turbulent diffusion coefficient for the mean temperature field in a compressible turbulence are different from those for the mean particle number density and the mean magnetic field. The combined effect of compressibility and inhomogeneity of turbulence causes an increase of the mean temperature in the regions with more intense velocity fluctuations due to a turbulent pumping. Formally, this effect is similar to a phenomenon of compressible turbophoresis found previously [J. Plasma Phys. 84, 735840502 (2018)JPLPBZ0022-377810.1017/S0022377818000983] for noninertial particles or gaseous admixtures. The gradient of the mean fluid pressure results in an additional turbulent pumping of the mean temperature field. The latter effect is similar to the turbulent barodiffusion of particles and gaseous admixtures. The compressibility of a fluid flow also causes a turbulent cooling of the surrounding fluid due to an additional sink term in the equation for the mean temperature field. There is no analog of this effect for particles.

Determination of Hydrocarbon-bearing Property of Deep-water Sandstone by Fluid Pressure Gradient from Seismic Attributes

In the same hydrodynamic system, because the densities of oil and gas are smaller than that of water, their pressure gradients are also smaller. Therefore, the pressure gradient can determine fluid properties. Based on seismic data and well logging data, this paper attempts to apply the equivalent medium theory to predict the pressure gradient, and then to identify fluids. Firstly, the upper and lower limits of bulk modulus and shear modulus of rocks can be obtained by using wellbore and well logging interpretation data. Secondly, based on the equivalent medium theory, the fluid velocity (when rock rigidity approaching zero) and the rock matrix velocity (when porosity approaching zero) are predicted. Thirdly, the predicted two types of velocity curves and the original acoustic curves are used for seismic inversion. Finally, according to the inversion results, the formation pressure and pressure gradient can be obtained by using the Fillippone pressure formula, and the hydrocarbon-bearing property of reservoirs can be determined according to the theoretical pressure gradients of different fluids. For offshore deep-water sandstone in an overseas block, when the frequency attributes for hydrocarbon detection cannot reflect hydrocarbons well, the fluid pressure gradient attribute is used to predict hydrocarbons, and the prediction coincidence rate reaches 70%.

Fluid filtration through the media with random sets of crack-like inclusions

Fluid filtration through homogeneous permeable media containing random sets of thin crack-like inclusions is considered. One of the characteristic sizes of such inclusions is much smaller than the others, and filtration coefficients of the inclusion material are much larger than the coefficients of the host medium. First, a homogeneous medium with an isolated crack-like inclusion subjected to a constant external fluid pressure gradient is considered (the one-particle problem). Using the method of matching of asymptotic expansions, the problem is reduced to a 2D-integral equation for the fluid flux along the middle surface of the inclusion. Analytical solutions of this equation for thin inclusions with elliptical middle surfaces are presented. Then, the solution of the one-particle problem is used in the framework of the self-consistent effective field method for calculation of effective filtration coefficients of the medium with crack-like inclusions. The method takes into account statistical characteristics of random sets of the inclusions. Detailed equations for the tensors of effective filtration coefficients of the heterogeneous media are presented for inclusions of the same orientations and for a homogeneous distribution of the inclusion over the orientations. Predictions of the method are compared with numerical solutions of the homogenization problem presented in the literature.

Tidal Grounding‐Line Migration Modulated by Subglacial Hydrology

AbstractWe present a mathematical model of the hydrology of grounding‐line migration on tidal timescales, in which the ice acts elastically, overlying a connected hydrological network, with the ocean tides modeled by an oscillating far‐field fluid height. The upstream grounding‐line migration is driven by a fluid pressure gradient through the grounding zone, while the downstream migration is limited by fluid drainage through the till. The two processes are described using separate travelling‐wave solutions, based on a model of fluid flow under an elastic sheet. The asymmetry between the upstream and downstream motion allows the grounding line to act as a nonlinear filter on the tidal forcing as the pressure signal propagates upstream, and this frequency modulation is discussed in the context of velocity data from ice streams across Antarctica to provide a novel constraint on till permeability.

Effects of pulsating heat source on interstitial fluid transport in tumour tissues.

Macromolecules and drug delivery to solid tumours is strongly influenced by fluid flow through interstitium, and pressure-induced tissue deformations can have a role in this. Recently, it has been shown that temperature-induced tissue deformation can influence interstitial fluid velocity and pressure fields, too. In this paper, the effect of modulating-heat strategies to influence interstitial fluid transport in tissues is analysed. The whole tumour tissue is modelled as a deformable porous material, where the solid phase is made up of the extracellular matrix and cells, while the fluid phase is the interstitial fluid that moves through the solid matrix driven by the fluid pressure gradient and vascular capillaries that are modelled as a uniformly interspersed fluid point-source. Pulsating-heat generation is modelled with a time-variable cosine function starting from a direct current approach to solve the voltage equation, for different pulsations. From the steady-state solution, a step-variation of vascular pressure included in the model equation as a mass source term via the Starling equation is simulated. Dimensionless 1D radial equations are numerically solved with a finite-element scheme. Results are presented in terms of temperature, volumetric strain, pressure and velocity profiles under different conditions. It is shown that a modulating-heat procedure influences velocity fields, that might have a consequence in terms of mass transport for macromolecules or drug delivery.

Embedded discontinuity approach for coupled hydromechanical analysis of fractured porous media

SummaryIn this paper, a new continuum approach for the coupled hydromechanical analysis of fractured porous media is proposed. The methodology for describing the hydraulic characteristics invokes an enriched form of Darcy's law formulated in the presence of an embedded discontinuity. The constitutive relations governing the hydromechanical response are derived by averaging the fluid pressure gradient and the discontinuous displacement fields over a selected referential volume of the material, subject to some physical constraints. The framework incorporates an internal length scale which is explicitly embedded in the definition of gradient operators. The respective field equations are derived following the general form of balance equations in interacting continua. The conventional finite element method is then employed for the spatial discretization, and the generalized Newmark scheme is used for the temporal discretization. The proposed methodology is verified by some numerical examples dealing with a steady‐state flow through fractured media as well as a time‐dependent consolidation in the presence of a discontinuity.

Mechanisms of melt extraction during lower crustal partial melting

AbstractProgressive vapour‐absent partial melting of a closed rock system increases melt pressure due to an expansion in the volume of the mineral plus melt assemblage. For a locally closed system, we quantify the melt pressure increase per increment of partial melting of a metapelite using phase equilibria modelling and combine it with Mohr–Coulomb theory to examine the interplay between melt pressure and fracture behaviour. It is shown that very small increments of vapour‐absent partial melting (<1%) increase melt pore pressure by tens of MPa leading to inevitable brittle failure of locally closed systems. Fracturing will affect these systems, even if initially limited to the scale of a few grains, and a connected microfracture network will enhance permeability as partial melting progresses. This will lead to a conditionally open system, potentially limiting accumulation of melt in the source. Repeated and cyclic fracture as temperature progressively increases will drive migration of the melt into sites of low fluid pressure at all scales. Crystal‐plastic creep processes create deformation‐induced dilatancy gradients that dominate over buoyancy forces at all scales in the melt source. Brittle and ductile deformation therefore cooperate in the extraction of melt. Enhanced porosity and permeability in ductile shear zones result in lower fluid pressure, providing a potentially important driving force for melt migration and drainage ‘up’ shear zones and along larger scale fluid pressure gradients in the crust.

Numerical solution of a generalized Falkner–Skan flow of a FENE-P fluid

The purpose of this article is to introduce a novel strategy for the numerical solution of a viscous boundary layer flow past a flat plate at a non-zero pressure gradient for a viscoelastic fluid governed by the FENE-P model. The stream function of this problem obeys a generalized Falkner–Skan equation. The fundamental method is based on embedding an integral operator, expressed in terms of Green's function of the corresponding linear differential operator, into well-known fixed-point iterative procedures, including Picard's and Mann's. Estimates of the skin friction coefficient are computed. The numerical solutions obtained from the proposed method are compared with the analytical and numerical solutions that exist in the literature. The convergence of the iterative scheme is proved via manipulation of the contraction principle. Numerical experiments and calculations ascertain that the introduced scheme handles the governing equation very efficiently, provides rapid convergence, and yields highly accurate results.

Analytical solution of soil deformation and fluid pressure change for a two-layer system with an upper unsaturated soil and a lower saturated soil under external loading

Natural soils often exhibit stratification, thus resulting in distinct flow and deformation patterns within each stratum as acted on by applied compaction stress or induced fluid pressure gradient. A comprehensive theoretical model of poroelasticity is rigorously established in the current study, which provides a detailed mathematical treatment of soil deformation and pore fluid pressure change through the upper unsaturated and lower saturated zones caused by time-invariant external loads. This double-layer system consists of an upper soil layer bearing air and water simultaneously, whereas a lower soil layer remains entirely saturated. A linear transformation that exactly separates our coupled model equations into analytically solvable coordinates is first achieved. Then, a boundary-value problem involving these equations under a semipermeable drainage scenario is formulated as a representative example, which complies with the physical constraint to ensure the continuity of pore water flux and pressure at the interface. The problem is solved analytically using Laplace transformation, and next computed numerically with hydraulic and elasticity parameters corresponding to a saturated clay overlain by an unsaturated sand to evaluate the excess pore fluid pressure and total settlement in each zone. A parametric study is also performed to examine the effect of initial water content and soil texture on the deformation behavior of the soil as well as on the development of the pore fluid pressure. The excess pore water pressure in each zone is mutually affected; therefore, if the upper unsaturated zone has a lower hydraulic conductivity, it would hinder, as compared to the opposite condition, the dissipation of the excess pore water pressure in the lower saturated zone as a consequence of water drainage blockage occurring in the former. Thus, a significant implication of our results is that change in thickness of the lower saturated zone created by land surface stress loads will always be overestimated when its interaction with the hydromechanical behavior of the upper unsaturated zone is neglected.

Neurodegeneration in Alzheimer's disease and glaucoma: overlaps and missing links.

The eye is said to be the window into the brain. Alzheimer’s disease (AD) and glaucoma both being diseases of the elderly, have several epidemiological and histological overlaps in pathogenesis. Both these diseases are neurodegenerative conditions. Over the years, a consensus has developed that both may be two ends of a singular spectrum of diseases. Epidemiological studies have shown that more Alzheimer’s patients may be suffering from glaucoma than general healthy population. Retinal ganglion cell damage is a characteristic of both diseases, along with discovery of amyloid-β and tau protein deposition in the retina and aqueous humor of eye. The latter two proteins are known to be pathognomonic of AD. Other pathways such as the insulin receptor pathway also seem to be affected in both diseases similarly. In spite of these overlaps, there are few missing links which still need more evidence, namely, intraocular pressure mechanisms, cerebrospinal fluid pressure and trans-lamina cribrosa pressure gradients, vascular autoregulation factors, etc. Several factors point towards a common pathogenesis at some level for both diseases and prospective studies are necessary to study the natural course of both diseases.

Effects of Fluid Rheology and Pore Connectivity on Rock Permeability Based on a Network Model

AbstractPermeability is an important rock property in exploration geophysics. Darcy's law assumes a steady‐state regime and constant permeability. However, recent studies showed that the effects of fluid viscosity and pore geometry on permeability cannot be neglected. The periodic variation of pore fluid pressure gradient due to elastic wave propagation induces the oscillated fluid flow. We consider a Maxwell fluid in a 3‐D pore network subject to harmonic oscillations. The network is based on the Voronoi method, which provides a realistic connectivity. The permeability of polyethylene oxide and cetylpyridinium chloride and sodium salicylate solution have been simulated. The results show that permeability is constant at frequencies less than several kHz and rapidly decreases to extremely low values as frequency tends to infinite. In addition, we find that fluid mainly flows in sparse‐large pore networks at low frequencies and in dense‐small pore networks at high frequencies. The Maxwell fluid shows significant permeability peaks related to the mean coordination number, indicating that there exists an optimal network connectivity at which fluid flow is maximum. These results have been central to understand how fluid flows in natural reservoir rocks. The permeability variations versus frequency, fluid rheology, and pore connectivity provide key information of reservoir fluid properties and pore network structure. The results indicate that it is questionable whether Darcy static permeability can be applied at high frequencies.