scholarly journals On unsteady flows of pore pressure-activated granular materials

Author(s):  
Anna Abbatiello ◽  
Miroslav Bulíček ◽  
Tomáš Los ◽  
Josef Málek ◽  
Ondřej Souček

AbstractWe investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.

1983 ◽  
Vol 105 (4) ◽  
pp. 509-511 ◽  
Author(s):  
M. M. Carroll ◽  
N. Katsube

It has been shown that the overall strain of a fluid-filled porous elastic solid is not governed by the Terzaghi effective stress law. We show, in the context of anisotropic linear elasticity, that the overall strain may be resolved into a component which is the average strain of the solid matrix and a component due to change in relative pore geometry, and that the latter is determined by the Terzaghi effective stress. This leads to a simple form of the response laws and, in particular, to effective stress laws for overall strain (obtained previously) and for strain of the pore space.


Author(s):  
Miroslav Bulíček ◽  
Erika Maringová ◽  
Josef Málek

We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone [Formula: see text]-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.


2010 ◽  
Vol 297-301 ◽  
pp. 960-965 ◽  
Author(s):  
Jean Michel Hugo ◽  
Emmanuel Brun ◽  
Frédéric Topin ◽  
Jérôme Vicente

This numerical study focuses on the determination of macroscopic (effective) properties from pore scale calculation. These results will be applied to heat exchangers design. The computational domain -representative of heat exchanger section- is a parallelepiped filled with metallic foam, heated on one face and crossed by a forced fluid flow. Conjugate heat transfer and fluid flow are computed using finite volume approach on the actual solid matrix and pore space topology obtained from X-ray tomograms. Calculated heat transfer coefficient and flow law parameters are in good agreement with literature data. An active foam length is defined and measured in order to provide optimal design characteristic for foamed heat exchanger.


2020 ◽  
Vol 8 (3) ◽  
pp. T515-T524
Author(s):  
Zhaoyun Zong ◽  
Man Jiang ◽  
Miaomiao Xu

With the continuous petroleum exploration around the world, the target of exploration is converting from conventional to deep, unconventional reservoirs. The pressure condition on those new target layers is different from the conventional reservoir, and pressure is one of the important factors affecting the elastic moduli and velocities of shale reservoirs. Therefore, it is necessary to take pressure effects into consideration in rock-physics modeling. We initially adopted a novel iterative rock-physical modeling approach on the basis of pore space stiffness theory to analyze pressure’s influence on shale. Pore space stiffness theory assumes that pores own their own stiffness like the solid matrix of rocks, which is related to the effective pressure. We have implemented plenty of numerical analysis on the effect of pressure on shale and found out the most contributive factor to the moduli and velocities of shale. Our result indicates that when the effective pressure is smaller than the critical value, the elastic moduli and elastic wave velocities of shale increase significantly with the increase of effective pressure. The elastic moduli and velocities tend to be constant when the effective pressure goes beyond that critical value. By comparison, we found that the most contributive mineral in shale is clay, and the porosity has the greatest effect on elastic moduli and velocities when the mineral composition of shale stays unchanged. The influence of pressure is not as obvious as other factors in shale reservoirs with low porosity (lower than 10%) because pores occupy a relatively small percentage of the total volume.


1971 ◽  
Vol 11 (03) ◽  
pp. 306-314 ◽  
Author(s):  
B.B. Williams ◽  
M.E. Whiteley

Abstract A procedure is developed for predicting changes in the porosity distribution in a sandstone resulting from reaction with hydrofluoric acid. This procedure is based on a theory for slow heterogeneous reactions in a porous solid where the solid matrix is consumed in the reaction Process. Reaction-rate data for use in this theory are obtained from experiments where acid is injected through short cores and effluent concentration measured using a fluoride specific ion electrode. This rate is found to be first order in hydrofluoric acid concentration. Variations in rate with temperature and quantity of rock dissolved are shown. Introduction Mixtures of hydrofluoric and hydrochloric acid are used to stimulate gas and oil production from sandstone reservoirs by increasing formation porosity and permeability near the wellbore. This porosity and permeability near the wellbore. This acid will react with almost all constituents of naturally occurring sandstones, such as silica, feldspar, clays, and calcareous material. In order to utilize this acid effectively, it is necessary to predict where acid reacts and changes that occur predict where acid reacts and changes that occur with reaction. Chemical reactions between hydrofluoric acid and silica or calcite in the rock matrix are simple, well known reactions. However, reactions with silicates such as clays or feldspars are complex since these minerals occur as three-dimensional lattices with only average empirical formulas. Examples are kaolinite ([A Fe +3 Mg]-Si O1.8 0.1 0.1 2 5 [OH]. Ca), montmorillonite (A Mg Si4 0.05 1.67 0.33 4 O [OH] . NA), and feldspars such as albite10 2 0.33 ([NaSi A ]). In the reactions shown below the3 8 reaction of sodium silicate is used to represent hydrofluoric acid reaction with silicates found in the matrix. REACTION WITH SILICA SiO + 4HF SiF + 2H O2 4 2 SiF + 2HF H SiF4 2 6 REACTION WITH SILICATES (FELDSPAR OR CLAYS) Na SiO + 8HF SiF + 4NaF + 4H O4 4 4 2 2NaF + SiF Na SiF4 2 6 2HF + SiF H SiF4 2 6 REACTION WITH CALCITE CaCO + 2HF CaF + H O + CO3 2 2 2 Reaction of HF-HCl mixtures with silicates and quartz has been the subject of studies by Blumberg, Blumberg and Stavinou, Gatewood et al. and Smith and Hendrickson. These studies indicate that the reaction is first order in HF concentration and that reaction rate with silicates is at least 10 times faster than reaction with silica. To dare, a reliable method for relating reaction data taken on finely ground silica, dispersed clays, or glass slides to the acidization process in a sandstone formation has not been developed Figs. 1 and 2 are photomicrographs of a Berea sandstone core illustrating the system in which acid reaction occurs. In these photomicrographs silica grains are black, and a few feldspar grains are apparent because of their internal porosity, which gives a streaked appearance. Unfortunately, clay or calcite cannot be differentiated from the pore space since all appear as an area shading from pore space since all appear as an area shading from gray to white. It is apparent that the heterogeneous nature of the porous material greatly complicates the reaction problem. For this reason, a theory including mass problem. For this reason, a theory including mass transport, surface kinetics, and a statistical representation for the porous material is required to describe acid reaction. SPEJ P. 306


2016 ◽  
Vol 26 (05) ◽  
pp. 987-1024 ◽  
Author(s):  
Michael Winkler

We consider the chemotaxis system [Formula: see text] as originally introduced in 1971 by Keller and Segel in the second of their seminal works. This system constitutes a prototypical model for taxis-driven pattern formation and front propagation in various biological contexts such as tumor angiogenesis, but in the higher-dimensional context any global existence theory for large-data solutions is yet lacking. In this work it is shown that in bounded planar domains [Formula: see text] with smooth boundary, for all reasonably regular initial data [Formula: see text] and [Formula: see text], the corresponding Neumann initial-boundary value problem possesses a global generalized solution. Thus particularly addressing arbitrarily large initial data, this goes beyond previously gained results asserting global existence of solutions only in spatial one-dimensional problems, or under certain smallness conditions on the initial data. The derivation of this result is based on a priori estimates for the quantities [Formula: see text] and [Formula: see text] in spatio-temporal [Formula: see text] spaces, where further boundedness and compactness properties are derived from the former by relying on the planar spatial setting in using an associated Moser–Trudinger inequality. Furthermore, some further boundedness and relaxation properties are derived, inter alia indicating that for any such solution we have [Formula: see text] in [Formula: see text] as [Formula: see text] for all finite [Formula: see text], and that in an appropriate generalized sense the quantities [Formula: see text] and [Formula: see text] eventually enter bounded sets in [Formula: see text] and [Formula: see text], respectively, with diameters only determined by the total population size [Formula: see text]. Finally, some numerical experiments illustrate the analytically obtained results.


2020 ◽  
Vol 16 (5) ◽  
pp. 1061-1083 ◽  
Author(s):  
Muhammad Sohail ◽  
Rabeeah Raza

PurposeThe current determination is committed to characterize the boundary layer flow of Williamson nanofluid prompted by nonlinear strained superficial under heat and mass transport mechanisms. Buongiorno model is presented to view the influence of nanoparticles in fluid flow. Scrutiny has been conceded under the action of the transversely smeared magnetic field. Heat and mass relocation exploration are conducted in the companionship of radiation effects and actinic compensation.Design/methodology/approachSimilarity variable is designated to transmute nonlinear partial differential equations of conservation laws of mass, momentum, energy and species into ordinary dimensional expressions. These constitutive and complicated ordinary differential expressions assessing the flow situation are handled efficaciously by manipulating Runge–Kutta–Fehlberg procedure (RK-5) with shooting routine.FindingsThe graphical demonstration is deliberated to scrutinize the variation in velocity, temperature and concentration profiles with respect to flow regulating parameters. Numerical data are displayed through tables in order to surmise variation in skin friction coefficient and Nusselt number. The augmenting values of fluid parameter and magnetic parameter reduces the horizontal fluid velocity, whereas normal velocity upsurges for mounting values of stretching ratio parameter. Moreover, mounting values of radiation parameter and thermophoresis parameter upsurges the temperature profile, whereas, growing values of Prandtl number lessen the temperature field.Practical implicationsThe current exploration is used in many industrial and engineering applications in order to discuss the transport phenomenon.Originality/valueFlow over a nonlinear stretched surface has numerous applications in the industry. The present attempt examines the combined influence of various physical characteristics for the flow of Williamson fluid and no such attempt exist in the available literature.


Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 195-203 ◽  
Author(s):  
Azra N. Tutuncu ◽  
Augusto L. Podio ◽  
Mukul M. Sharma

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe in detail the hysteresis in stress‐strain diagrams and to understand the influence of different fluids on the strain amplitude dependence of elastic moduli and attenuation. Cycling experiments were also conducted with sandstone samples saturated with CTAB, a cationic surfactant that renders the mineral surfaces hydrophobic. Hexadecane and CTAB were selected so as to investigate the relative contributions of adhesion hysteresis and stick‐slip sliding on attenuation in sedimentary granular rocks. Young’s moduli and Poisson’s ratios obtained from the cycling tests show a significant dependence on strain amplitude on dry as well as water and hexadecane saturated samples. Bow‐tie‐shaped diagrams are obtained when loading and unloading tangent moduli are plotted against strain. The type of fluid in the pore space and at the grain contacts has a large influence on the hysteresis observed in the stress‐strain diagrams.


2011 ◽  
Vol 48 (12) ◽  
pp. 1829-1840 ◽  
Author(s):  
I. Cavarretta ◽  
I. Rocchi ◽  
M.R. Coop

A new apparatus is described that measures interparticle friction between sand-sized grains over relatively large displacements and also under immersion in a fluid. Its relatively simple design allows the key calibrations to be checked by statics. An analysis of the geometry of simple spherical particle contacts and the forces at those contacts revealed that there are strict constraints on the permissible stiffness of the interparticle friction apparatus to avoid stick–slip behaviour. Tests on ball bearings gave highly repeatable data, while others on glass ballotini revealed a significant effect of ambient humidity on the data obtained. The interparticle friction was found to increase with the roughness of the ballotini. Immersion in water increased the interparticle friction slightly for both the ballotini and quartz sand particles, while immersion in oil reduced the friction considerably for the quartz sand, especially at higher contact force levels.


Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 766-772 ◽  
Author(s):  
Michel Küntz ◽  
Jean Claude Mareschal ◽  
Paul Lavallée

A 2-D lattice gas is used to calculate the effective electrical conductivity of saturated porous media as a function of porosity and conductivity ratio [Formula: see text] between the pore‐filling fluid and the solid matrix for various microscopic structures of the pore space. The way the solid phase is introduced allows the porosity ϕ to take any value between 0 and 1 and the geometry of the pore structure to be as complex as desired. The results are presented in terms of the formation factor [Formula: see text], with [Formula: see text] the effective conductivity of the saturated rock and [Formula: see text] the conductivity of the fluid. It is shown that the formation factor F as a function of the porosity ϕ follows a power law [Formula: see text], equivalent to the empirical Archie’s law. The exponent m varies with the microgeometry of the pore space and could therefore reflect the microstructure at the macroscopic scale. The prefactor a of the power law, however, is close to 1 regardless of the microstructure. For a given microgeometry of the pore space, the variation of the residual electrical conductivity of the solid matrix induced by a finite conductivity ratio [Formula: see text] does not significantly influence the variation of the effective conductivity of the fluid‐solid binary mixture unless the porosity is low.


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