scholarly journals Semi-analytical solution for the problem of extended Pom-Pom fluid flow in a round pipe

2021 ◽  
Vol 2057 (1) ◽  
pp. 012007
Author(s):  
A I Kadyirov ◽  
E K Vachagina
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Solution Method ◽  
Parametric Method ◽  
Single Equation ◽  
Weissenberg Number ◽  
Normal Stresses ◽  
Rheological Equation ◽  
Rheological Equation Of State

Abstract A semi-analytical solution to the problem of the steady flow of viscoelastic single equation eXended Pom-Pom (XPP) fluid in a round pipe using the four-mode rheological equation of state of XPP is presented. An original parametric method for solving the set problem is used. The resulting method is applicable for solving a similar problem in a flat slit. The developed solution method is tested by comparing it with numerical results and experimental data. Using a polyacrylamide solution as an example, the influence of the Weissenberg number on the axial velocity profiles and the components of normal stresses is studied.

Role of kinetics on the couplings between fluid flow, deformation and reaction

2020 ◽  
Author(s):  
Benjamin Malvoisin ◽  
Yury Y. Podladchikov
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Numerical Modelling ◽  
Reaction Rate ◽  
Slow Slip ◽  
Slow Slip Events ◽  
Classical Formalism ◽  
Flow Deformation

<p>Short timescale processes such as earthquakes, tremors and slow slip events may be influenced by reactions, which are known to proceed rapidly in the presence of water (typically several days). Here, we developed a theoretical framework to introduce the influence of mineralogical reactions on fluid flow and deformation. The classical formalism for dissolution/precipitation reactions is used to consider the influence of the distance from equilibrium and of temperature on the reaction rate and a dependence on porosity is introduced to model the evolution of the reacting surface area during reaction. The thermodynamic admissibility of the derived equations is checked and an analytical solution is derived to test the model. The fitting of experimental data for three reactions typically occurring in metamorphic systems (serpentine dehydration, muscovite dehydration and calcite decarbonation) indicates a systematic faster kinetics on the dehydration side than on the hydration side close from equilibrium. This effect is amplified through the porosity term in the reaction rate. Numerical modelling indicates that this difference in reaction rate close from equilibrium plays a key role in microtextures formation during dehydration in metamorphic systems. The developed model can be used in a wide variety of geological systems where couplings between reaction, deformation and fluid flow have to be considered.</p>

Generalized Scaling Approach for Spontaneous Imbibition: An Analytical Model

2006 ◽  
Vol 9 (03) ◽  
pp. 251-258 ◽  
Author(s):  
Kewen Li ◽  
Roland N. Horne
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Capillary Pressure ◽  
Driving Force ◽  
Water Injection ◽  
Spontaneous Imbibition ◽  
Dimensionless Time ◽  
Water Imbibition ◽  
Oil Water

Summary Scaling the experimental data of spontaneous imbibition without serious limitations has been difficult. To this end, a general approach was developed to scale the experimental data of spontaneous imbibition for most systems (gas/liquid/rock and oil/water/rock systems) in both cocurrent and countercurrent cases. We defined a dimensionless time with almost all the parameters considered. These include porosity, permeability, size, shape, boundary conditions, wetting- and nonwetting-phase relative permeabilities, interfacial tension (IFT), wettability, and gravity. The definition of the dimensionless time was not empirical; instead, it was based on theoretical analysis of the fluid-flow mechanisms that govern spontaneous imbibition. The general scaling method was confirmed against the experimental data from spontaneous water imbibition conducted at different IFTs in oil-saturated rocks with different sizes and permeabilities. A general analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition was derived. The analytical solution predicts a linear correlation between the imbibition rate and the reciprocal of the recovery by spontaneous imbibition in most fluid/fluid/rock systems. Introduction An important fluid-flow phenomenon during water injection or aquifer invasion into reservoirs is spontaneous water imbibition. Scaling the experimental data of spontaneous water imbibition in different fluid/fluid/rock systems is of essential importance in designing the water-injection projects and predicting the reservoir production performances. Ignoring the effects of relative permeability, capillary pressure, and gravity in the dimensionless time might be the reason that the existing scaling methods do not always function successfully. It is known that these parameters influence the spontaneous imbibition in porous media significantly. For that reason, these parameters should be honored properly in the scaling. Many papers have been published to characterize and scale spontaneous water imbibition in both oil/water/rock systems (Li et al. 2002; Tong et al. 2001; Zhou et al. 2001; Babadagli 2001; Kashchiev and Firoozabadi 2002; Civan and Rasmussen 2001; Akin et al. 2000; Cil et al. 1998; Perkins and Collins 1960; Mattax and Kyte 1962; Du Prey 1978; Hamon and Vidal 1986; Reis and Cil 1993; Cuiec et al. 1994; Ma et al. 1995; Chen et al. 1995; Zhang et al. 1996; Al-Lawati and Saleh 1996; Babadagli 1997; Li and Horne 2002) and gas/liquid/rock systems (Li and Horne 2001, 2004a; Li et al. 2006; Handy 1960). However, few have included the effects of capillary pressure, relative permeability (both wetting and nonwetting phases), wettability, and gravity simultaneously. This is important because all the parameters may play an important role in many cases and may not be ignored. For example, a number of enhanced-/improved-oil-recovery processes relate to low IFT. In these cases, capillary pressure as a driving force may be small, and gravity may not be neglected. In some cases, gravity may also be a driving force, as pointed out by Schechter et al. (1991).

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.

A General Correlation for Pool Film Boiling Heat Transfer From a Horizontal Cylinder to Subcooled Liquid: Part 2—Experimental Data for Various Liquids and Its Correlation

1990 ◽  
Vol 112 (2) ◽  
pp. 441-450 ◽  
Author(s):  
A. Sakurai ◽  
M. Shiotsu ◽  
K. Hata
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Analytical Solution ◽  
Boiling Heat Transfer ◽  
Radiation Effects ◽  
Approximate Analytical Solution ◽  
Horizontal Cylinder ◽  
Film Boiling ◽  
System Pressure ◽  
Horizontal Cylinders

Experimental data of pool film boiling heat transfer from horizontal cylinders in various liquids such as water, ethanol, isopropanol, Freon-113, Freon-11, liquid nitrogen, and liquid argon for wide ranges of system pressure, liquid subcooling, surface superheat and cylinder diameter are reported. These experimental data are compared with a rigorous numerical solution and an approximate analytical solution derived from a theoretical model based on laminar boundary layer theory for pool film boiling heat transfer from horizontal cylinders including the effects of liquid subcooling and radiation from the cylinder. A new correlation was developed by slightly modifying the approximate analytical solution to agree better with the experimental data. The values calculated from the correlation agree with the authors’ data within ± 10 percent, and also with other researchers’ data for various liquids including those with large radiation effects, though these other data were obtained mainly under saturated conditions at atmospheric pressure.

scholarly journals Узагальнення моделі Голанда і Рейсснера на випадок осьової симетрії

2021 ◽  
pp. 12-19
Author(s):  
Костянтин Петрович Барахов
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Bessel Functions ◽  
Classical Model ◽  
Adhesive Bond ◽  
Radial Coordinate ◽  
Round Hole ◽  
Normal Stresses

The purpose of this work is to create a mathematical model of the stress state of overlapped circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. To solve the problem, a simplified model of the adhesive bond of two overlapped plates is proposed. The simplification is that the movement of the layers depends only on the radial coordinate and does not depend on the angular one. The model is a generalization of the classical model of the connection of Holland and Reissner in the case of axial symmetry. The stresses are considered to be evenly distributed over the thickness of the layers, and the adhesive layer works only on the shift. These simplifications allowed us to obtain an analytical solution to the studied problem. The problem of the stress state of the adhesive bond of two plates is solved, one of which is weakened by a round hole, and the other is a round plate concentric with the hole. A load is applied to the plate weakened by a round hole. The discussed area is divided into three parts: the area of bonding, as well as areas inside and outside the bonding. In the field of bonding, the problem is reduced to third- and fourth-order differential equations concerning tangent and normal stresses, respectively, the solutions of which are constructed as linear combinations of Bessel functions of the first and second genera and modified Bessel functions of the first and second genera. Using the found tangential and normal stresses, we obtain linear inhomogeneous Euler differential equations concerning longitudinal and transverse displacements. The solution of the obtained equations is also constructed using Bessel functions. Outside the area of bonding, displacements are described by the equations of bending of round plates in the absence of shear forces. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations concerning the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

scholarly journals Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation

Polymers ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 334
Author(s):  
Ekaterina Vachagina ◽  
Nikolay Dushin ◽  
Elvira Kutuzova ◽  
Aidar Kadyirov
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Analytical Methods ◽  
Experimental Validation ◽  
Parametric Method ◽  
Fluid Flows ◽  
Parametric Representation ◽  
Viscoelastic Flow ◽  
Exponential Form ◽  
Image Velocimetry

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

scholarly journals Algorithm Scheme to Simulate the Distortions during Gas Quenching in a Single-Piece Flow Technology

Coatings ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 694 ◽  
Author(s):  
Jacek Sawicki ◽  
Krzysztof Krupanek ◽  
Wojciech Stachurski ◽  
Victoria Buzalski
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
High Pressure ◽  
Heat Transfer Coefficient ◽  
Fluid Flow ◽  
Transfer Coefficient ◽  
Single Piece ◽  
Gas Quenching ◽  
Complex Fluid ◽  
Algorithm Scheme

Low-pressure carburizing followed by high-pressure quenching in single-piece flow technology has shown good results in avoiding distortions. For better control of specimen quality in these processes, developing numerical simulations can be beneficial. However, there is no commercial software able to simulate distortion formation during gas quenching that considers the complex fluid flow field and heat transfer coefficient as a function of space and time. For this reason, this paper proposes an algorithm scheme that aims for more refined results. Based on the physical phenomena involved, a numerical scheme was divided into five modules: diffusion module, fluid module, thermal module, phase transformation module, and mechanical module. In order to validate the simulation, the results were compared with the experimental data. The outcomes showed that the average difference between the numerical and experimental data for distortions was 1.7% for the outer diameter and 12% for the inner diameter of the steel element. Numerical simulation also showed the differences between deformations in the inner and outer diameters as they appear in the experimental data. Therefore, a numerical model capable of simulating distortions in the steel elements during high-pressure gas quenching after low-pressure carburizing using a single-piece flow technology was obtained, whereupon the complex fluid flow and variation of the heat transfer coefficient was considered.

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