An accurate analytical model for squirt flow in anisotropic porous rocks - Part 1: Classical geometry

Geophysics ◽  
2021 ◽  
pp. 1-81 ◽  
Author(s):  
Yury Alkhimenkov ◽  
Beatriz Quintal
Keyword(s):  
Numerical Solution ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Pore Space ◽  
Quantitative Description ◽  
Companion Paper ◽  
Analytical Models ◽  
Porous Rocks ◽  
Classical Geometry ◽  
Dispersion And Attenuation

Seismic wave propagation in porous rocks that are saturated with a liquid exhibits significant dispersion and attenuation due to fluid flow at the pore scale, so-called squirt flow. This phenomenon takes place in compliant flat pores such as microcracks and grain contacts that are connected to stiffer isometric pores. Accurate quantitative description is crucial for inverting rock and fluid properties from seismic attributes such as attenuation. Up to now, many analytical models for squirt flow were proposed based on simplified geometries of the pore space. These models were either not compared with a numerical solution or showed poor accuracy. We present a new analytical model for squirt flow which is validated against a three-dimensional numerical solution for a simple pore geometry that has been classically used to explain squirt flow; that is why we refer to it as classical geometry. The pore space is represented by a flat cylindrical (penny-shaped) pore whose curved edge is fully connected to a toroidal (stiff) pore. Compared with correct numerical solutions, our analytical model provides very accurate predictions for the attenuation and dispersion across the whole frequency range. This includes correct low- and high-frequency limits of the stiffness modulus, the characteristic frequency, and the shape of the dispersion and attenuation curves. In a companion paper (Part 2), we extend our analytical model to more complex pore geometries. We provide as supplementary material Matlab and symbolic Maple routines to reproduce our main results.

scholarly journals Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks

2021 ◽  
Vol 11 (6) ◽  
pp. 2495
Author(s):  
Belén Ferrer ◽  
María-Baralida Tomás ◽  
David Mas
Keyword(s):  
Cross Correlation ◽  
Pore Space ◽  
Digital Camera ◽  
Experimental Methods ◽  
Image Correlation ◽  
Rock Surface ◽  
Experimental Setup ◽  
Porous Rocks ◽  
Porous Sandstone ◽  
Variable Displacement

Some materials undergo hygric expansion when soaked. In porous rocks, this effect is enhanced by the pore space, because it allows water to reach every part of its volume and to hydrate most swelling parts. In the vicinity, this enlargement has negative structural consequences as adjacent elements support some compressions or displacements. In this work, we propose a normalized cross-correlation between rock surface texture images to determine the hygric expansion of such materials. We used small porous sandstone samples (11 × 11 × 30 mm3) to measure hygric swelling. The experimental setup comprised an industrial digital camera and a telecentric objective. We took one image every 5 min for 3 h to characterize the whole swelling process. An error analysis of both the mathematical and experimental methods was performed. The results showed that the proposed methodology provided, despite some limitations, reliable hygric swelling information by a non-contact methodology with an accuracy of 1 micron and permitted the deformation in both the vertical and horizontal directions to be explored, which is an advantage over traditional linear variable displacement transformers.

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

scholarly journals Novel Structure and Thermal Design and Analysis for CubeSats in Formation Flying

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 150
Author(s):  
Yeon-Kyu Park ◽  
Geuk-Nam Kim ◽  
Sang-Young Park
Keyword(s):  
Analytical Model ◽  
Formation Flying ◽  
Thermal Environment ◽  
Thermal Analyses ◽  
Thermal Design ◽  
Analytical Models ◽  
Test Results ◽  
Solar Panels ◽  
Novel Structure ◽  
Micro Propulsion

The CANYVAL-C (CubeSat Astronomy by NASA and Yonsei using a virtual telescope alignment for coronagraph) is a space science demonstration mission that involves taking several images of the solar corona with two CubeSats—1U CubeSat (Timon) and 2U CubeSat (Pumbaa)—in formation flying. In this study, we developed and evaluated structural and thermal designs of the CubeSats Timon and Pumbaa through finite element analyses, considering the nonlinearity effects of the nylon wire of the deployable solar panels installed in Pumbaa. On-orbit thermal analyses were performed with an accurate analytical model for a visible camera on Timon and a micro propulsion system on Pumbaa, which has a narrow operating temperature range. Finally, the analytical models were correlated for enhancing the reliability of the numerical analysis. The test results indicated that the CubeSats are structurally safe with respect to the launch environment and can activate each component under the space thermal environment. The natural frequency of the nylon wire for the deployable solar panels was found to increase significantly as the wire was tightened strongly. The conditions of the thermal vacuum and cycling testing were implemented in the thermal analytical model, which reduced the differences between the analysis and testing.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

Modeling of residual stresses by correlating surface topography in machining of AISI 52100 steel

2021 ◽  
pp. 1-26
Author(s):  
Chao Liu ◽  
Yan He ◽  
Yufeng Li ◽  
Yulin Wang ◽  
Shilong Wang ◽  
...  
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Cutting Force ◽  
Surface Topography ◽  
Analytical Model ◽  
Analytical Models ◽  
Workpiece Surface ◽  
Dynamic Cutting Force ◽  
Intermittent Cutting ◽  
Effect Of Surface

Abstract The residual stresses could affect the ability of components to bear loading conditions and also the performance. The researchers considered workpiece surface as a plane and ignored the effect of surface topography induced by the intermittent cutting process when modeling residual stresses. The aim of this research develops an analytical model to predict workpiece residual stresses during intermittent machining by correlating the effect of surface topography. The relative motions of tool and workpiece are analyzed for modeling thermal-mechanical and surface topography. The influence of dynamic cutting force and thermal on different positions of surface topography is also considered in analytical model. Then the residual stresses model with the surface topography effect can be developed in intermittent cutting. The analytical models of dynamic cutting force, surface topography and residual stresses are verified by the experiments. The variation trend of evaluated values of the residual stress of workpiece is basically consistent with that of measured values. The compressive residual stress of workpiece surface in highest point of the surface topography are higher than that in the lowest point.

Subpixel determination of wormhole tip position in 4D tomography of dissolving limestone cores

2021 ◽  
Author(s):  
Rishabh Prakash Sharma ◽  
Max P. Cooper ◽  
Anthony J.C. Ladd ◽  
Piotr Szymczak
Keyword(s):  
Flow Field ◽  
Pore Space ◽  
Nonlinear Process ◽  
Linear Interpolation ◽  
Flow Fields ◽  
Porous Rocks ◽  
Dissolution Experiment ◽  
Novel Approach ◽  
Highly Nonlinear ◽  
Computed Microtomography

<p>Dissolution of porous rocks by reactive fluids is a highly nonlinear process resulting in a variety of dissolution patterns, the character of which depends on physical conditions such as flow rate and reactivity of the fluid. Long, finger-like dissolution channels, “wormholes”, are the main subject of interest in the literature, however, the underlying dynamics of their growth remains unclear. </p><p>While analyzing the tomography data on wormhole growth.  one open question is to define the exact position of the tip of the wormhole. Near the tip the wormhole gradually thins out and the proper resolution of its features is hindered by the finite spatial resolution of the tomographs. In particular, we often observe in the near-tip region several disconnected regions of porosity growth, which - as we hypothesized - are connected by the dissolution channels at subpixel scale. In this study, we show how these features can be better resolved by using numerically calculated flow fields in the reconstructed pore-space. </p><p>We used 70 micrometers, 16-bit grayscale X-ray computed microtomography (XCMT) time series scans of limestone cores, 14mm in diameter and 25mm in length. Scans were performed during the entire dissolution experiment with an interval of 8 minutes. These scans were further processed using a 3-phase segmentation proposed by Luquot et al.[1], in which grayscale voxels are converted to macro-porosity, micro-porosity and grain phases from their grayscale values. The macro-porous phase is assigned a porosity of 1, while the grain phase is assigned 0. Micro-porous regions are assigned an intermediate value determined by linear interpolation between pore and grain threshold using grayscale values. An OpenFOAM based, Darcy-Brinkman solver, porousFoam, is then used to calculate the flow field in this extracted porosity field. </p><p>Porosity contours reconstructed from the tomographs show some disconnected porosity growth near the tip region which later become part of the wormhole in subsequent scans. We have used a novel approach by including the micro-porosity phase in pore-space to calculate the flow-fields in the near-tip region. The calculated flow fields clearly show an extended region of focused flow in front of the wormhole tip, which is a manifestation of the presence of a wormhole at the subpixel scale. These results show that micro-porosity plays an important role in dissolution and 3-phase segmentation combined with the flow field calculations is able to capture the sub-resolved dissolution channels. </p><p> </p><p> [1] Luquot, L., Rodriguez, O., and Gouze, P.: Experimental characterization of porosity structure and transport property changes in limestone undergoing different dissolution regimes, Transport Porous Med., 101, 507–532, 2014</p>

scholarly journals Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Fakharany ◽  
R. Company ◽  
L. Jódar
Keyword(s):  
Option Pricing ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Stable Process ◽  
Integration Formula ◽  
Pricing Models ◽  
Integral Term ◽  
Pricing Problems ◽  
Stability And Consistency ◽  
Partial Integrodifferential Equation

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.

scholarly journals On the development of instabilities in an annulus and a shell composed of a poro-hyperelastic material

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180239 ◽  
Author(s):  
A. P. S. Selvadurai ◽  
A. P. Suvorov
Keyword(s):  
Soft Tissues ◽  
Mechanical Response ◽  
Numerical Solutions ◽  
Pore Space ◽  
Stability Loss ◽  
Computational Approach ◽  
Hyperelastic Material ◽  
Porous Skeleton ◽  
Internal Pressures

The paper investigates the development of instability in an internally pressurized annulus of a poro-hyperelastic material. The theory of poro-hyperelasticity is proposed as an approach for modelling the mechanical behaviour of highly deformable elastic materials, the pore space of which is saturated with a fluid. The consideration of coupling between the mechanical response of the hyperelastic porous skeleton and the pore fluid is important when applying the developments to soft tissues encountered in biomechanical applications. The paper examines the development of an instability in a poro-hyperelastic annulus subjected to internal pressure. Using a computational approach, numerical solutions are obtained for the internal pressures that promote either short-term or long-term instability in a poro-hyperelastic annulus and a poro-hyperelastic shell. In addition, time-dependent effects of stability loss are examined. The analytical solutions are used to benchmark the accuracy of the computational approach.

scholarly journals Use of Jacobians for inverse kinematics of articulated robots : a study on approximate solutions

2020 ◽  
Author(s):  
◽  
Uriel Jacket Tresor Demby's
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Fuzzy Inference ◽  
Numerical Approach ◽  
Data Driven ◽  
Approximate Methods ◽  
Inference System ◽  
First Case

In the context of articulated robotic manipulators, the Forward Kinematics (FK) is a highly non-linear function that maps joint configurations of the robot to poses of its endeffector. Furthermore, while in the most useful cases these functions are neither injective (one-to-one) nor surjective (onto), depending on the robot configuration -- i.e. the sequence of prismatic versus revolute joints, and the number of Degrees of Freedom (DoF) -- the associated Inverse Kinematics (IK) problem may be practically or even theoretically impossible to be solved analytically. Therefore, in the past decades, several approximate methods have been developed for many instances of IK problems. The approximate methods can be divided into two distinct categories: data-driven and numerical approaches. In the first case, data-driven approaches have been successfully used for small workspace domains (e.g., task-driven applications), but not fully explored for large ones, i.e. in task-independent applications where a more general IK is required. Similarly, and despite many successful implementations over the years, numerical solutions may fail if an improper matrix inverse is employed (e.g., Moore-Penrose generalized inverse). In this research, we propose a systematic, robust and accurate numerical solution for the IK problem using the Unit-Consistent (UC) and the Mixed (MX) Inverse methods to invert the Jacobians derived from the Denavit-Hartenberg (D-H) representation of the FK for any robot. As we demonstrate, this approach is robust to whether the system is underdetermined (less than 6 DoF) or overdetermined (more than 6 DoF). We compare the proposed numerical solution to data driven solutions using different robots -- with DoF varying from 3 to 7. We conclude that numerical solutions are easier to implement, faster, and more accurate than most data-driven approaches in the literature, specially for large workspaces as in task-independent applications. We particularly compared the proposed numerical approach against two data-driven approaches: Multi-Layer Perceptron (MLP) and Adaptive Neuro-Fuzzy Inference System (ANFIS), while exploring various architectures of these Neural Networks (NN): i.e. number of inputs, number of outputs, depth, and number of nodes in the hidden layers.

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