scholarly journals Frequency-dependent attenuation and dispersion caused by squirt flow: Three-dimensional numerical study

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. MR129-MR145 ◽  
Author(s):  
Yury Alkhimenkov ◽  
Eva Caspari ◽  
Boris Gurevich ◽  
Nicolás D. Barbosa ◽  
Stanislav Glubokovskikh ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Numerical Study ◽  
Numerical Models ◽  
Pore Space ◽  
Fluid Pressure ◽  
Frequency Dependent ◽  
Attenuation And Dispersion ◽  
Dispersion And Attenuation

Seismic waves may exhibit significant dispersion and attenuation in reservoir rocks due to pore-scale fluid flow. Fluid flow at the microscopic scale is referred to as squirt flow and occurs in very compliant pores, such as grain contacts or microcracks, that are connected to other stiffer pores. We have performed 3D numerical simulations of squirt flow using a finite-element approach. Our 3D numerical models consist of a pore space embedded into a solid grain material. The pore space is represented by a flat cylinder (a compliant crack) whose edge is connected with a torus (a stiff pore). Grains are described as a linear isotropic elastic material, whereas the fluid phase is described by the quasistatic linearized compressible Navier-Stokes momentum equation. We obtain the frequency-dependent effective stiffness of a porous medium and calculate dispersion and attenuation due to fluid flow from a compliant crack to a stiff pore. We compare our numerical results against a published analytical solution for squirt flow and analyze the effects of its assumptions. Previous interpretation of the squirt flow phenomenon based mainly on analytical solutions is verified, and some new physical effects are identified. The numerical and analytical solutions agree only for the simplest model in which the edge of the crack is subjected to zero fluid pressure boundary condition while the stiff pore is absent. For the more realistic model that includes the stiff pore, significant discrepancies are observed. We identify two important aspects that need improvement in the analytical solution: the calculation of the frame stiffness moduli and the frequency dependence of attenuation and dispersion at intermediate frequencies.

The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Wave Equation ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
P Wave ◽  
Fluid Properties ◽  
Permeability Anisotropy ◽  
Attenuation And Dispersion ◽  
Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

Attenuation and dispersion of P-waves in fluid-saturated porous rocks with a distribution of coplanar cracks - scattering approach

Geophysics ◽  
2020 ◽  
pp. 1-54
Author(s):  
Yongjia Song ◽  
Jun Wang ◽  
Hengshan Hu ◽  
Bo Han
Keyword(s):  
Quality Factor ◽  
Scattering Problem ◽  
Crack Density ◽  
Relaxation Frequency ◽  
P Wave ◽  
Frequency Dependent ◽  
Low Frequencies ◽  
Attenuation And Dispersion ◽  
Dispersion And Attenuation ◽  
Coplanar Cracks

Wave-induced fluid flow (WIFF) between cracks and micro-pores is one of the major mechanisms in causing attenuation and dispersion within seismic frequency ranges. Previous non-interaction-approximation (NIA) models often assume the distribution of cracks is dilute, neglecting the influences of interacting cracks on dispersion and attenuation. To overcome this restriction, we investigate the interaction between coplanar cracks and their influences on seismic dispersion and attenuation. First, a scattering problem for a longitudinal (P) wave normally impinging on a plane with equally distributed coplanar cracks in a porous medium is solved using integral transform approach. Then, based on the solution, an effective wavenumber is derived for P-wave propagation in a porous material with coplanar cracks. It is found that the magnitude of dispersion and attenuation can significantly increase when the spacing between adjacent cracks decreases even if the crack density is unchanged. Moreover, frequency-dependent asymptotic behavior of inverse quality factor is also different from that of the NIA models at frequencies lower than the WIFF relaxation frequency. Specifically, the inverse quality factor scales with the square root of frequency at low frequencies. When the spacing between adjacent cracks is large, an additional frequency-dependent scale occurs at relatively higher frequencies (but still lower than the WIFF relaxation frequency) with inverse quality factor scales with the first power of frequency. When the spacing becomes much larger so that the interaction between the adjacent cracks is negligible, the present model exactly reduces to a NIA model for a distribution of aligned slit cracks and the first power scale can prevail attenuation within low frequencies.

Radial Steam Flow in Two-Phase Geothermal Reservoirs - Comparison of Analytical and Finite Difference Solutions

1980 ◽  
Vol 20 (05) ◽  
pp. 359-362 ◽  
Author(s):  
Allen F. Moench
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Analytical Solution ◽  
Nonlinear Equations ◽  
Liquid Water ◽  
Numerical Study ◽  
Transient Pressure ◽  
Closed Form Analytical Solution ◽  
Finite Difference Solution ◽  
Difference Solution

Abstract A linear closed-form analytical solution for the radial flow of steam toward a producing well in a vapor-dominated geothermal reservoir is compared with a finite difference solution to the nonlinear equations of fluid flow and energy change. Assumptions used in the development of the equations are that (1) the liquid phase, initially uniformly distributed within the reservoir, is immobile, (2) the relative permeability to steam is constant (3) local thermal equilibrium exists within the reservoir, (4) temperature changes are due only to phase change, and (5) effects of vapor-pressure lowering are negligible. With the onset of production, vigorous vaporization of liquid water in the reservoir near the wellbore creates a dry region that increases in volume as production continues. This behavior produces a circular moving boundary that separates superheated steam in the dry zone from saturated steam in the wet zone. The rate of movement of this boundary, the pressure drawdown, and the temperature and saturation distributions are obtained analytically by applying the solution to the linearized equations of flow in radial coordinates. Results obtained numerically using a finite difference solution to the nonlinear equations of fluid flow and energy agree closely with the analytical approach in spite of the nonlinearities involved. Introduction Methods of analysis of transient pressure data from geothermal steam reservoirs until recently have been limited to techniques developed for noncondensible gas reservoirs (for example, see Ramey). These techniques generally assume that isothermal conditions prevail in the reservoir. In vapor-dominated geothermal reservoirs, steam and liquid water are believed to coexist, with the liquid component being relatively immobile (White et al.). Under conditions of fluctuating pressure, phase changes result, and the assumption of isothermal flow is no longer valid. Therefore several authors have included nonisothermal flow theory in the analysis of steam pressure transients in porous media. Evidence for liquid vaporization within the reservoir is indirect; however, there are laboratory experiments, well test data, and chemical studies that support the contention. Moench and Atkinson presented results of a numerical study of transient pressure behavior in geothermal steam reservoirs. Their study involved a finite difference solution to the nonlinear equations of radial fluid flow and energy change. They found that it was possible to explain some, but not all, of their computational results by combining the energy and flow equations, thereby deriving an equation similar to the gas flow equation but with an apparent hydraulic diffusivity that was many times reduced. This report extends the analysis to a linear closed-form analytical solution for pressure drawdown, fully accounting for the results of the numerical study. Mathematical Model The geothermal reservoir is conceptualized as a horizontal aquifer partially filled with liquid water in which steam flows radially toward a discharging well. With the onset of production, vigorous vaporization of liquid water in the reservoir near the wellbore creates a dry region that increases in volume as production continues.

Analytical Solution of Unsteady Casson Fluid Flow Through a Vertical Cylinder with Slip Velocity Effect

2021 ◽  
Vol 87 (1) ◽  
pp. 68-75
Author(s):  
Wan Faezah Wan Azmi ◽  
Ahmad Qushairi Mohamad ◽  
Lim Yeou Jiann ◽  
Sharidan Shafie
Keyword(s):  
Fluid Flow ◽  
Analytical Solution ◽  
Newtonian Fluid ◽  
Analytical Solutions ◽  
Slip Velocity ◽  
Fluid Velocity ◽  
Real Life ◽  
Casson Fluid ◽  
Flow Through ◽  
Velocity Effect

Casson fluid is a non-Newtonian fluid with its unique fluid behaviour because it behaves like an elastic solid or liquid at a certain condition. Recently, there are several studies on unsteady Casson fluid flow through a cylindrical tube have been done by some researchers because it is related with the real-life applications such as blood flow in vessel tube, chemical and oil flow in pipelines and others. Therefore, the main purpose of the present study is to obtain analytical solutions for unsteady flow of Casson fluid pass through a cylinder with slip velocity effect at the boundary condition. Dimensional governing equations are converted into dimensionless forms by using the appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid parameters. Then, the dimensionless equations of velocity with the associated initial and boundary conditions are solved by using Laplace transform with respect to time variable and finite Hankel transform of zero order with respect to the radial coordinate. Analytical solutions of velocity profile are obtained. The obtained analytical result for velocity is plotted graphically by using Maple software. Based on the obtained result, it can be observed that increasing in Casson parameter, time and slip velocity will lead to increment in fluid velocity. Lastly, Newtonian fluid velocity is uniform from the boundary to the center of cylinder while Casson fluid velocity is decreased when approaching to the center of cylinder. The present result is validated when the obtained analytical solution of velocity is compared with published result and found in a good agreement.

Elastomer Seal With Frictional Contact: Analytical Solution

2013 ◽  
Author(s):  
Moosa S. M. Al-Kharusi ◽  
Sayyad Zahid Qamar ◽  
Tasneem Pervez ◽  
Maaz Akhtar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Numerical Models ◽  
Fluid Pressure ◽  
Closed Form Solution ◽  
Field Conditions ◽  
Design Parameters ◽  
Sealing Pressure ◽  
Elastomer Seal

Main motivation for this work is the need for performance evaluation of swelling (and inert) elastomer seals used in petroleum applications. Closed-form (analytical) solutions are derived for sealing pressure distribution along the elastomer seal as a function of material properties of the elastomer, seal geometry and dimensions, seal compression, and differential fluid pressure acting on the seal ends. Seal performance is also modeled and simulated numerically. Good agreement between analytical and numerical results gives confidence that the analytical solution can be used for reliable prediction of sealing behavior of the elastomer. Detailed investigation is then carried out to find out the effect of variation in seal design parameters on seal performance. For both analytical and numerical models, properties of the seal material at various stages of swelling are needed. Therefore, a series of experiments were also designed and conducted to study the effect of swelling on mechanical properties (E, G, K, and ν) of the sealing material. One major finding is that sealing pressure distribution along the seal is not constant but varies nonlinearly depending on seal parameters and loading conditions, with maximum sealing pressure occurring at the center of the seal length. Longer seals are not necessarily better; after a certain seal length, sealing pressure reaches a steady value for a given set of field conditions. As expected, higher seal compression gives higher sealing pressure. Seal compression can be increased either by tubular expansion or by selecting an elastomer that swells more, or a combination of the two. Experimental evaluation of swelling-elastomer seal performance can be very costly, and is not even possible in many cases. Numerical simulations, if validated, can be more convenient, but computational effort and cost can be high as simulations have to be run for each set of conditions. Analytical approach presented here not only gives an elegant closed-form solution, but can give reasonably accurate and much faster prediction of elastomer performance under various actual oil and gas field conditions.

Faults and magma reservoirs along the Southern Andes Volcanic zone (SAVZ): linking oservations and numerical models of stress change controlling magmatic and hydrothermal fluid flow

2020 ◽  
Author(s):  
Javiera Ruz ◽  
Muriel Gerbault ◽  
José Cembrano ◽  
Pablo Iturrieta ◽  
Camila Novoa Lizama ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Stress Field ◽  
Fault Zone ◽  
Numerical Models ◽  
Fluid Pressure ◽  
Seismic Inversion ◽  
Fault Zones ◽  
Fault System ◽  
Far Field ◽  
Trigger Failure

<p> The Chilean margin is amongst the most active seismic and volcanic areas on Earth. It hosts active and fossil geothermal and mineralized systems of economic interest documenting significant geofluid migration through the crust. By comparing numerical models with field and geophysical data, we aim at pinning when and where fluid migration occurs through porous domains, fault zone conduits, or remains stored at depth awaiting a more appropriate stress field. <span>Dyking and volcanic activity occur within fault zones</span> <span>along the S</span><span>A</span><span>VZ, linked with stress field variations</span> <span>in spatial and temporal association with</span> –<span>short therm-</span> <span>seismicity</span> <span>and -long term- oblique </span><span>plate </span><span>convergence.</span> <span>Volcanoes and geothermal domains are mostly located along or at the intersection of margin-oblique fault zones (Andean Transverse Faults), and along margin-parallel strike slip zones, some which may cut the entire lithosphere (Liquiñe-Ofqui fault system). Wh</span><span>ereas</span><span> the big picture displays</span> <span>fluid flow straight to the surface, at close look significant offsets between crustal structures occur. 3D numerical models using conventional elasto-plastic rheology provide insights on the interaction of (i) an inflating magmatic cavity, (ii) a slipping fault zone, and (iii) regional tectonic stresses. Applying either (i) a magmatic overpressure or (ii) a given fault slip can trigger failure of the intervening rock, and generate either i) fault motion or ii) magmatic reservoir failure, respectively, but only for distances less than the structures' breadth even at low rock</span> <span>strength. However, at greater inter-distances the bedrock domain in between the fault zone and the magmatic cavity undergoes dilatational strain of the order of 1-5x10-5. This dilation opens the bedrock’s pore space and forms «pocket domains» that may store up-flowing over-pressurized fluids, which may then further chemically</span> interact<span> with the bedrock, for the length of time</span> <span>that</span> <span>these pockets remain open. These porous pockets</span> <span>can reach kilometric size, questioning their parental link with outcropping plutons along the margin. Moreover, bedrock permeability may also increase as fluid flow diminishes effective bedrock friction and cohesion. Comparison with rock experiments indicates that such stress and fluid pressure changes may eventually trigger failure at the intermediate timescale (repeated slip or repeated inflation). Finally, incorporating far field compression (iii)</span> <span>loads the bedrock to</span> <span>a state of stress at the verge of failure. Then, failure around the magmatic </span><span>reservoir</span><span> or </span><span>at</span> <span>the fault zone occurs for lower load</span><span>ing</span><span>.</span> <span>Permanent tectonic loading on the one hand, far field episodic seismic inversion of the stress field on the other, and localized failure all together promote a transient stress field, thus explaining the occurrence of transient fluid pathways on seemingly independent timescales. These synthetic models are then discussed with regards to specific cases along the SVZ, particularly the Tatara-San Pedro area (~36°S), where magnetotelluric profiles </span><span>document</span><span> conductive volumes at different depths underneath active faults, volcanic edifices and geothermal vents. We discuss the mechanical link between these deep sources and surface structures</span>.</p>

Conjugate Heat and Mass Transfer in Metal Foams: A Numerical Study for Heat Exchangers Design

2010 ◽  
Vol 297-301 ◽  
pp. 960-965 ◽  
Author(s):  
Jean Michel Hugo ◽  
Emmanuel Brun ◽  
Frédéric Topin ◽  
Jérôme Vicente
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Heat Exchanger ◽  
Heat Exchangers ◽  
Effective Properties ◽  
Numerical Study ◽  
Pore Space ◽  
Solid Matrix ◽  
Metallic Foam ◽  
Computational Domain

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.

Anisotropic P-SV-wave dispersion and attenuation due to inter-layer flow in thinly layered porous rocks

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA135-WA145 ◽  
Author(s):  
Fabian Krzikalla ◽  
Tobias M. Müller
Keyword(s):  
Wave Attenuation ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
P Wave ◽  
Angle Of Incidence ◽  
Porous Rocks ◽  
Frequency Dependent ◽  
Symmetry Properties ◽  
Wave Induced ◽  
Attenuation And Dispersion

Elastic upscaling of thinly layered rocks typically is performed using the established Backus averaging technique. Its poroelastic extension applies to thinly layered fluid-saturated porous rocks and enables the use of anisotropic effective medium models that are valid in the low- and high-frequency limits for relaxed and unrelaxed pore-fluid pressures, respectively. At intermediate frequencies, wave-induced interlayer flow causes attenuation and dispersion beyond that described by Biot’s global flow and microscopic squirt flow. Several models quantify frequency-dependent, normal-incidence P-wave propagation in layered poroelastic media but yield no prediction for arbitrary angles of incidence, or for S-wave-induced interlayer flow. It is shown that generalized models for P-SV-wave attenuation and dispersion as a result of interlayer flow can be constructed by unifying the anisotropic Backus limits with existing P-wave frequency-dependent interlayer flow models. The construction principle is exact and is based on the symmetry properties of the effective elastic relaxation tensor governing the pore-fluid pressure diffusion. These new theories quantify anisotropic P- and SV-wave attenuation and velocity dispersion. The maximum SV-wave attenuation is of the same order of magnitude as the maximum P-wave attenuation and occurs prominently around an angle of incidence of [Formula: see text]. For the particular case of a periodically layered medium, the theoretical predictions are confirmed through numerical simulations.

scholarly journals A Mathematical Model of Gas and Water Flow in a Swelling Geomaterial—Part 1. Verification with Analytical Solution

Minerals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 30 ◽  
Author(s):  
Elias Ernest Dagher ◽  
Julio Ángel Infante Sedano ◽  
Thanh Son Nguyen
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Gas Flow ◽  
Numerical Models ◽  
Model Verification ◽  
Model Complexity ◽  
Gas Migration

Gas generation and migration are important processes that must be considered in a safety case for a deep geological repository (DGR) for the long-term containment of radioactive waste. Expansive soils, such as bentonite-based materials, are widely considered as sealing materials. Understanding their long-term performance as barriers to mitigate gas migration is vital in the design and long-term safety assessment of a DGR. Development and the application of numerical models are key to understanding the processes involved in gas migration. This study builds upon the authors’ previous work for developing a hydro-mechanical mathematical model for migration of gas through a low-permeable geomaterial based on the theoretical framework of poromechanics through the contribution of model verification. The study first derives analytical solutions for a 1D steady-state gas flow and 1D transient gas flow problem. Using the finite element method, the model is used to simulate 1D flow through a confined cylindrical sample of near-saturated low-permeable soil under a constant volume boundary stress condition. Verification of the numerical model is performed by comparing the pore-gas pressure evolution and stress evolution to that of the results of the analytical solution. The results of the numerical model closely matched those of the analytical solutions. Future studies will attempt to improve upon the model complexity and investigate processes and material characteristics that can enhance gas migration in a nearly saturated swelling geomaterial.

Evaluation of Turbulence Models for the Numerical Study of Reciprocating-Mechanism Driven Heat Loop

2016 ◽  
Author(s):  
Olubunmi T. Popoola ◽  
Ayobami A. Bamgbade ◽  
Y. Cao
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Numerical Study ◽  
Numerical Models ◽  
Turbulence Models ◽  
Boussinesq Approximation ◽  
High Heat ◽  
Working Fluid ◽  
High Heat Transfer ◽  
Transfer Device

A bellows-type Reciprocating-Mechanism Driven Heat Loops (RMDHL) is a novel heat transfer device that could attain a high heat transfer rate through a reciprocating flow of the working fluid inside the heat transfer device. Although the device has been tested and validated experimentally, analytical or numerical study have not been undertaken to understand its working mechanism and to provide guidance for the device design. In a bid to improve the accuracy of the numerical models of the RMDHL, seven turbulence models for fluid flow have been alternately adapted and implemented in an existing numerical RMDHL model. The obtained results were studied and compared with prior experimental results to gain confidence and select the most suitable turbulence modeling techniques. The Boussinesq approximation has been used and the governing equations have been numerically solved using the CFD solver FLUENT. For the three-dimensional fluid flow, the turbulence models were studied are the Standard, RNG, and Realizable k-ε Models, Standard and SST k-ω Models, Transition k-kL-ω Model and the Transition SST Model. The result of each numerical simulation have been analyzed and ranked using a numerical model calibration template. It was found that the standard k-ω Models provided the least accurate results while the RNG-k-ε Model provided the most accurate predictions. It is expected that the results will help improve the accuracy of the work on the RMDHL modeling.

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