scholarly journals Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale

2016 ◽  
Vol 374 (2078) ◽  
pp. 20150418 ◽  
Author(s):  
Viet T. Chau ◽  
Zdeněk P. Bažant ◽  
Yewang Su
Keyword(s):  
Solid Phase ◽  
Three Dimensional ◽  
Cohesive Crack ◽  
Rock Joints ◽  
Recent Analysis ◽  
Band Model ◽  
Two Phase ◽  
Strength Limit ◽  
Crack Wall ◽  
Phase Medium

Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10 5 –10 6 almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot’s two-phase medium and Terzaghi’s effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model. This article is part of the themed issue ‘Energy and the subsurface’.

SYNTHESIS OF HYDROGEN IN ACOUSTOPLASMA DISCHARGE IN A LIQUID-PHASE STREAM

2019 ◽  
pp. 42-48 ◽  
Author(s):  
N. A. Bulychev
Keyword(s):  
Liquid Phase ◽  
Organic Compounds ◽  
Electrode Materials ◽  
Solid Phase ◽  
Plasma Discharge ◽  
Raw Material ◽  
Two Phase ◽  
Reduced Pressure ◽  
External Power Source ◽  
Phase Medium

In this paper, the plasma discharge in a high-pressure fluid stream in order to produce gaseous hydrogen was studied. Methods and equipment have been developed for the excitation of a plasma discharge in a stream of liquid medium. The fluid flow under excessive pressure is directed to a hydrodynamic emitter located at the reactor inlet where a supersonic two-phase vapor-liquid flow under reduced pressure is formed in the liquid due to the pressure drop and decrease in the flow enthalpy. Electrodes are located in the reactor where an electric field is created using an external power source (the strength of the field exceeds the breakdown threshold of this two-phase medium) leading to theinitiation of a low-temperature glow quasi-stationary plasma discharge.A theoretical estimation of the parameters of this type of discharge has been carried out. It is shown that the lowtemperature plasma initiated under the flow conditions of a liquid-phase medium in the discharge gap between the electrodes can effectively decompose the hydrogen-containing molecules of organic compounds in a liquid with the formation of gaseous products where the content of hydrogen is more than 90%. In the process simulation, theoretical calculations of the voltage and discharge current were also made which are in good agreement with the experimental data. The reaction unit used in the experiments was of a volume of 50 ml and reaction capacity appeared to be about 1.5 liters of hydrogen per minute when using a mixture of oxygen-containing organic compounds as a raw material. During their decomposition in plasma, solid-phase products are also formed in insignificant amounts: carbon nanoparticles and oxide nanoparticles of discharge electrode materials.

Application of Two Phase Eulerian CFD Model to Simulate High Velocity Jet Induced Scour

2020 ◽  
Author(s):  
Nicholas S. Tavouktsoglou ◽  
Aggelos Dimakopoulos ◽  
Jeremy Spearman ◽  
Richard J. S. Whitehouse
Keyword(s):  
Numerical Model ◽  
High Velocity ◽  
Stokes Equations ◽  
Solid Phase ◽  
Three Dimensional ◽  
Water Jet ◽  
Ocean Engineering ◽  
Two Phase ◽  
Water Jets ◽  
Good Agreement

Abstract Submerged water jet causing soil excavation is a typical water-soil interaction process that occurs widely in many engineering disciplines. In hydraulic engineering for instance, a typical example would be scour downstream of headcuts, culverts, or dam spillways. In port and waterway engineering, erosion of the channel bed or quay wall by the propellers of passing ships are also typical water jet/soil interaction problems. In ocean engineering, trenching by impinging high-velocity water jets has been used as an efficient method for cable and pipeline burial. At present, physical modelling and simple prediction equations have been the main practical engineering tool for evaluating scour in these situations. However, with the increasing computational power of modern computers and the development of new Computational Fluid Dynamics (CFD) solvers, scour prediction in such engineering problems has become possible. In the present work three-dimensional (3D) numerical modelling has been applied to reproduce the capability of a pair of water jets to backfill an excavated trench. The simulations are carried out using a state-of-the-art three-dimensional Eulerian two-phase scour model based on the open source CFD software OpenFOAM. The fluid phase is resolved by solving modified Navier-Stokes equations, which take into consideration the influence of the solid phase, i.e., the soil particles. This paper first presents a validation of the numerical model against vertical jet erosion tests from the literature and conducted at HR Wallingford. The results of the model show good agreement with the experimental tests, with the numerical model predicting the scour hole depth and extent with good accuracy. The paper then presents a validation of the model’s ability to reproduce deposition which is evaluated through a comparison with settling velocity data and empirical formulations found in literature, again with the model showing good agreement. Finally, the model is applied to a prototype cable burial problem using a commercially available controlled flow jet excavator. The study found that the use of water jets can be effective (subject to confirmation of the time-scale required for real operations) for performing backfill operations but that the effectiveness is closely related to the type of sediment and selection of an appropriate jet discharge. As a result, in order for the water jet method to be effective for backfill, there is a requirement for a good description of the variation in sediment type along the trench and a requirement for the jet discharge to be varied as different sediment types are encountered.

Three-Dimensional Numerical Simulation of Convective Melting of Solid Particles in a Fluid

1999 ◽  
Author(s):  
Y. L. Hao ◽  
Y.-X. Tao
Keyword(s):  
Volume Fraction ◽  
Solid Phase ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Phase Changes ◽  
Solid Particles ◽  
Preliminary Calculation ◽  
Two Phase ◽  
Closed Set ◽  
Gravity Effects

Abstract A physical model of two-phase flow and heat-mass transfer with the phase changes based on the theory of interacting continua is proposed. All terms in the conservation equations are analyzed and the constitutive equations are presented. A closed set of governing equations describing the convective melting of solid particles in a fluid is obtained. The numerical method is developed for the solution of velocity, temperature, and volume fraction of solid phase for the three-dimensional melting in a rectangular cross-section channel. Preliminary calculation, including gravity effects, shows that the result is reasonable. This study provides a basis for the theoretical and experimental investigation of convective melting of solid particles in a fluid.

scholarly journals Numerical model of heat transfer in three phases of the poroelastic medium

2016 ◽  
Vol 38 (2) ◽  
pp. 53-59
Author(s):  
Anna Uciechowska-Grakowicz ◽  
Tomasz Strzelecki
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Solid Phase ◽  
Irreversible Thermodynamics ◽  
Pore Fluid ◽  
Gas Filtration ◽  
Two Phase ◽  
Phase Medium ◽  
Thermal Consolidation ◽  
The Mathematical Model

Abstract In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

scholarly journals Experimental Investigation and CFD Modeling of Slush Cryogen Flow Measurement Using Circular Shape Capacitors

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 2117 ◽  
Author(s):  
Bogdan Florian Monea ◽  
Eusebiu Ilarian Ionete ◽  
Stefan Ionut Spiridon
Keyword(s):  
Flow Measurement ◽  
High Performance ◽  
Solid Phase ◽  
Experimental Testing ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Cfd Modeling ◽  
Two Phase ◽  
Circular Shape ◽  
Experimental Stand

The measurement of two-phase cryogenic fluid mixtures flow, also known as slush cryogen flow, with its most attractive form (liquid and solid) is of great interest for various applications, due to its thermodynamic advantages. This paper presents a newly developed device, under the form of a circular capacitor prototype, together with an experimental stand for slush formation. Slush nitrogen was used as testing fluid during the experimental work. Then, the experimental data for slush cryogen flow measurement using the proposed circular shape capacitor were compared with theoretical results obtained by simulation. A three-dimensional flow field model was built and solved for the innovative design slush flowmeter using a computational fluid dynamic (CFD) model. Nitrogen slush density of 874 kg/m3, representing approximately 30% solid fraction, was reported for both the modeling and experimental testing, although the numerical investigation is not limited to these values. By comparing experimental vs. simulation results, a deeper view on the designed configuration can be achieved, thus improving the progress in producing high-performance next generation devices for two-phase flow measurement in terms of physical dimensions, length and space between armatures. Even so, the mathematical model has limitations when mixtures with higher percentages of solid phase and particle sizes are encountered.

scholarly journals DISSIPATION OF THE ACOUSTIC OSCILLATIONS IN TWO-PHASE MEDIUM OF GAS-SOLID PARTICLES TYPE

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 67-72
Author(s):  
Anatoly Kochergin ◽  
Grigory Pavlov ◽  
Ksenia Valeeva
Keyword(s):  
Solid Phase ◽  
Sound Intensity ◽  
Solid Particles ◽  
Acoustic Energy ◽  
Effective Diameter ◽  
Frequency Noise ◽  
Acoustic Oscillations ◽  
Two Phase ◽  
River Sand ◽  
Phase Medium

The presented work is devoted to the study of the absorption of acoustic energy by a two-phase medium such as gas-solid particles. An experimental method was chosen for the study the effect on the distribution of acoustic pressure oscillations of various frequencies in a two-phase medium consisting of suspended solids (river sand, various powders, etc.), geometric and physical characteristics of the suspension. To determine the density of the created two-phase curtain was used capacitive concentration meterthat was developed by the employees of KNRTU-KAI named after A.N. Tupolev. It was also established that with a decrease in the effective diameter of the solid phase, the acoustic resistance of the studied curtain increases at frequencies of more than 800 Hz, while oscillations in the frequency range of 100 ÷ 400 Hz propogate almost unchanged. As a result of interference phenomena, a decrease in sound intensity occurs. Consequently, an increase in the number of particles in the path of wave propogation due to an increase in the amount of suspended matter and the thickness of the curtain contributes to a decrease in the radiation intensity. It has been experimentally proven that the effectiveness of reducing the intensity of acoustic oscillations in a two-phase medium such as "gas-solid particles" increases as a result of: -increasing the mass content of particles in the medium; -increasing the thickness of the medium; - reducing the density and particle size. To assess the reduction in the intensity of frequency noise when oscillations propogate in a two-phase medium, an empirical dependence was obtained.

Elastic strain energy and forces on point defects in a two-phase medium

1986 ◽  
Vol 1 (1) ◽  
pp. 193-201 ◽  
Author(s):  
K. Jagannadham ◽  
J. Narayan
Keyword(s):  
Point Source ◽  
Point Defects ◽  
Elastic Strain ◽  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Second Phase ◽  
Two Phase ◽  
Phase Medium ◽  
Important Field

Elastic strain energy and forces on point defects in a two-phase medium with a planar interface are analyzed employing the surface dislocation analysis developed earlier for three-dimensional distortions. The important field components, namely, the tractions and the displacements arising due to the point source at the interface, are determined. Furthermore, the field components at the interface are used to determine the elastic strain energy associated with the point source in the two-phase medium and the elastic force exerted by the second phase on the point defect. The significance of these results to the force acting on a vacancy or an interstitial at the interface is emphasized.

scholarly journals Modeling of sand-water slurry flow through horizontal pipe using CFD

2016 ◽  
Vol 64 (3) ◽  
pp. 261-272 ◽  
Author(s):  
Manoj Kumar Gopaliya ◽  
D.R. Kaushal
Keyword(s):  
Solid Phase ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Particle Sizes ◽  
Slurry Flow ◽  
Two Phase ◽  
Horizontal Pipe ◽  
Water Slurry ◽  
Horizontal Orientation ◽  
Slurry Flows

Abstract The paper presents three-dimensional CFD analysis of two-phase (sand-water) slurry flows through 263 mm diameter pipe in horizontal orientation for mixture velocity range of 3.5-4.7 m/s and efflux concentration range of 9.95-34% with three particle sizes viz. 0.165 mm, 0.29 mm and 0.55 mm with density 2650 kg/m3. RNG k-ε turbulence closure equations with Eulerian multi-phase model is used to simulate various slurry flows. The simulated values of local solid concentration are compared with the experimental data and are found to be in good agreement for all particle sizes. Effects of particle size on various slurry flow parameters such as pressure drop, solid phase velocity distribution, friction factor, granular pressure, turbulent viscosity, turbulent kinetic energy and its dissipation have been analyzed.

SOME BOUNDS ON THE BULK CONDUCTIVITY OF A TWO-PHASE MEDIUM: A COMPARISON BETWEEN PERIODIC AND RANDOM STRUCTURE

1992 ◽  
Vol 02 (03) ◽  
pp. 283-294 ◽  
Author(s):  
ANDREA GAVIOLI
Keyword(s):  
Positive Constant ◽  
Percolation Theory ◽  
Effective Conductivity ◽  
Three Dimensional ◽  
Random Structure ◽  
Bulk Conductivity ◽  
Two Phase ◽  
Phase Medium

We prove that the effective conductivity of a three-dimensional medium with a periodic chessboard structure does not exceed [Formula: see text] where α and β are the values of the conductivity in the cells of the chessboard, and A is a positive constant; then we show how the corresponding “random” structure behaves in a quite different way, according to recent results in percolation theory.

3D Tomographic Transition of Particle Distribution in Microchannel

2011 ◽  
Author(s):  
Je-Eun Choi ◽  
Masahiro Takei
Keyword(s):  
Particle Concentration ◽  
Particle Distribution ◽  
Solid Phase ◽  
Flow Direction ◽  
Three Dimensional ◽  
Quantitative Result ◽  
Deionized Water ◽  
Two Phase ◽  
Cross Sectional ◽  
Reconstruction Image

The three dimensional cross-sectional particle concentrations of particle-liquid two phase flows in the two cross-seciton of microchannel has been reconstructed using process tomography. In the obtained 3D (2D space and time) reconstruction image, the dielectric particle-injected area appears to have a high particle concentration, and the deionized water-injected area appears to have a low particle concentration. Dielectric particles as the solid phase and non-conductive deionized water as the liquid phase are non-uniformly injected to the microchannel. The comparison between the qualitative result of 3D reconstruction image and the quantitative result of particle concentration in flow direction transition is that the particle is reasonably distributed in the particle injected area of the cross-section. Based on the reconstructed particle distribution image, it is easy to estimate the particle diffusion behaviors in microchannel.

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