Fluid Flow Research Articles

Quasi-3D fracture acidizing simulation based on discrete virtual internal bond method

Fracture acidizing (FA) is the most effective stimulation technique for carbonate reservoirs. It involves the hydro-chemical coupling process. To more efficiently simulate FA, a quasi-3D discretized virtual internal bond (DVIB) is developed, in which a certain height is assigned to each bond and the rock is considered to consist of heterogeneous quasi-3D bond cells. The fracture is allowed to transversely cut through these bond cells. The macro fracture aperture fluctuation is characterized by the various apertures embedded in micro bonds. As the acid fluid flows through the fracture, the acid dissolves the bond to widen the aperture. The bond permeability is associated with the its aperture. Through this approach, the complicated hydro-chemical coupling process is reduced to 1D bond dissolution problem, which significantly improves the efficiency of FA simulation. The simulation examples show that the acid reactant transportation, the acid etching behaviors and the fracture acidizing process can be well simulated. It provides an efficient approach to FA simulation.

Koopman dynamic-oriented deep learning for invariant subspace identification and full-state prediction of complex systems

One strategy for predicting the state of nonlinear dynamical systems (typically of high dimensionality) is global linearization, such as utilizing the Koopman analysis model to transform the system state into an invariant subspace that evolves linearly. A critical challenge in the Koopman model is designing or deriving observation functions, typically nonlinear, to linearize the dynamical systems. To address the challenge, this study proposes a model called SKCAE (Skip-connected Koopman Convolutional AutoEncoder) that combines guidance of physics and data to learn observation functions accurately and efficiently. The novelties of SKCAE are twofold: (1) a coordinate-transforming main network for the construction of nonlinear observation functions, enabling the explicit identification of the low-dimensional dynamics that dominate the system's dynamical evolution, and (2) a Koopman dynamics-oriented subnetwork for quantitatively interpreting the system's intrinsic mechanisms from the frequency perspective and efficiently predicting the system state. Four numerical cases with discrete/continuous spectra on Eulerian/Lagrangrian descriptions are studied, i.e., fixed-point attractor, Duffing oscillator, fluid flow past a cylinder, and channel turbulence. Results demonstrate that SKCAE achieves significant improvement (up to a hundred times) in accuracy compared to conventional models and possesses remarkable capability in handling scenarios with data noises and/or loss, owing to its intrinsic advantage in retaining a broad range of frequency components of a dynamical system.

Experimental investigation of the performance attributes of a double pipe heat exchanger equipped with baffles of conventional or flower layouts

In industrial heat management, the design of baffles within heat exchangers is crucial. They guide fluid flow and enhance turbulence, optimizing heat transfer. Yet, their configuration must be carefully considered to balance thermal efficiency with energy expenditure and pressure management. This research conducts practical tests on the hydrothermal attributes of a counter-flow double-pipe heat exchanger. It evaluates two baffle layouts: segmental and flower, considering baffle cut-off ratio (16.7 %≤δ ≤ 50 %), pitch ratio (8.3 %≤λ ≤ 22.2 %), flower-design relative angle (30°≤γ ≤ 90°), and operating conditions of annulus-side (2660 ≤ Rean ≤ 13110, 5.21 ≤ Pran ≤ 7.48). The findings assure that installing the baffles results in notable increases in both Nu¯an and fan. Besides, lowering baffle cut-off and pitch ratios, and increasing the relative angle of flower baffles lead to additional increases. Moreover, raising the annulus-fluid temperature reduces Nu¯an with a negligible effect on fan. Increasing Rean leads to a reduced fan and greater Nu¯an. Compared with no baffles, the maximum recorded increases in the Nu¯an and fan are 147.4 % and 60.2 %, respectively, realized by incorporating flower layout. On average, the flower baffles boost the Nu¯an by 20.8 % more than those using conventional baffles, with an average increase of 4.3 % in the fan. To judge the benefit of utilizing baffles, the Hydrothermal Performance Index (HTPI) is calculated, and its highest value is recorded as 2.23, attained by running the annular pipe at the lowest flow rate and temperature, with inserting flower baffles (δ = 16.7 %, λ = 8.3 %, γ = 90°). Finally, correlations for Nu¯an, HTPI, and fan prediction are suggested.

Nonlinear radiative thermal analysis of magneto-micropolar fluid over a bidirectionally extending sheet with varied thermal conditions

Thermal fluid flow analysis occasioned by stretching surfaces offers practical industrial and engineering applications, such as extrusion and drawing processes and materials experiencing heating and cooling conditions. Thus, this study explores magnetohydrodynamic micropolar fluid flow under varied thermal conditions and nonlinear thermal radiation over a dually stretched sheet subject to surface mass flux and an internal heat source. The study thus provides insight into the dynamics of heat transfer mechanisms for improving material processing techniques in many engineering processes. The flow dynamics with the thermal analysis are evaluated by applying two thermal conditions in the heat equation: the prescribed surface temperature (PST) and the prescribed heat flux (PHF). The formulated partial derivative equations that describe the current problem are changed into ordinary derivatives using some similarity quantities, while the converted equations are tackled with the combined techniques of shooting and Runge–Kutta Fehlberg. Consequently, diverse tables and figures are displayed to deliberate on the impacts of the physical terms on the dynamics of flow and heat transmission processes. The consequence of the analysis reveals a higher heat gradient in the prescribed surface temperature case than the uniform temperature distribution, as the Prandtl number magnifies. The micropolar material term reduces the surface frictional factor and depletes heat transmission, but the magnetic field term raises the skin friction coefficient.

The Design and Investigation of Hybrid a Microfluidic Micromixer

Today, microfluidics has become a revolutionary interdisciplinary topic with considerable attention in a wide range of biotechnology applications. In this research work, a numerical investigation of a microfluidic micromixer is carried out using a hybrid actuation approach with different micropillar shapes and gaps. For this purpose, COMSOL Multiphysics v.5.2. is used with three different physics, such as thermoviscous acoustic physics to solve acoustic governing equations, laminar physics to solve fluid flow governing equations, and diluted transport species to solve mixing governing equations. The simulations were carried out at different Reynolds numbers such as 2, 4, 6, 8, 10, and 12 with an oscillation frequency of 15 kHz. The results were in the form of acoustic characteristics such as acoustic pressure, acoustic velocity, acoustic stream, mixing index, and fluid flow behaviour at various Reynolds numbers. The results revealed that the inclusion of micropillars improved the mixing performance and strength of the acoustic field, resulting in an improvement of the mixing performance compared to the case without micropillars. In addition, the mixing performance is also investigated at different Reynolds numbers, and a higher mixing index is investigated at lower Reynolds numbers. Moreover, it was also investigated that blade-shaped micropillars with 0.150 mm gaps deliver the best results compared to the other cases, and the maximum and minimum values of the mixing index are 0.97 and 0.72, respectively, at Reynolds number 2. The main reason behind this larger mixing index at low Reynolds numbers is due to the inclusion of micropillars that enhance the diffusion rate and contact area, leading to the homogenisation of the heterogeneous fluids in the microchamber. The obtained results can be extremely helpful for the design and modifications of a hybrid microfluidics micromixer.

Free convection in a square wavy porous cavity with partly magnetic field: a numerical investigation

Natural convection in a square porous cavity with a partial magnetic field is investigated in this work. The magnetic field enters a part of the left wall horizontally. The horizontal walls of the cavity are thermally insulated. The wave vertical wall on the right side is at a low temperature, while the left wall is at a high temperature. The Brinkman-Forchheimer-extended Darcy equation of motion is utilized in the construction of the fluid flow model for the porous media. The Finite Element Method (FEM) was used to solve the problem’s governing equations, and the current study was validated by comparing it to earlier research. On streamlines, isotherms, and Nusselt numbers, changes in the partial magnetic field length, Hartmann number, Rayleigh number, Darcy number, and number of wall waves have been examined. This paper will show that the magnetic field negatively impacts heat transmission. This suggests that the magnetic field can control heat transfer and fluid movement. Additionally, it was shown that heat transfer improved when the number of wall waves increased.

About this title - The Bowland Shale Formation, UK: Processes and Resources

This volume showcases recent geological, geophysical and geochemical research on the UK Mississippian Bowland Shale Formation. Here, the Bowland Shale and equivalent units are described and interpreted in terms of sedimentary, geochemical, and mechanical properties and processes, basin-forming events, hydrocarbon prospectivity, mineralization, and heat and fluid flow in the subsurface.

Entropy generation and heat transfer characteristics in MHD Casson fluid flow over a wedge with viscous dissipation and thermal radiation

AbstractThis investigation outlines the significance of MHD Falkner–Skan flow of non‐Newtonian fluid flow over a wedge. To study the non‐Newtonian flow, Casson fluid is taken. Additionally, this study explores heat and mass transport under the influence of viscous dissipation, Joule heating, and thermal radiation. This heat and mass transport investigation is carried out under the influence of thermal and concentration slip factors. Moreover, the entropy generation is also computed using the second law of thermodynamics. A set of nonlinear partial differential equations arises from the mathematical formulation of the problem. Similarity variables are then introduced to achieve a similarity solution. The leading differential equations are solved numerically using the Runge–Kutta‐4 method in conjunction with shooting techniques. Graphical representations are employed to demonstrate the physical significance of relevant parameters. The investigation presents and discusses the impact of various parameters on velocity, temperature, concentration and entropy profiles for three different positions of the wedge: stationary, forward‐moving, and backward‐moving. The main conclusions of the study are as follows: (1) Enhancing the magnetic parameter and wedge angle parameter leads to higher fluid velocity, (2) elevating both the Eckert and magnetic number results in a rapid escalation of fluid energy, (3) Skin friction coefficient increases gradually with an increase in the power law Falkner–Skan parameter.

A Review of Fracturing and Enhanced Recovery Integration Working Fluids in Tight Reservoirs

Tight reservoirs, characterized by low porosity, low permeability, and difficulty in fluid flow, rely on horizontal wells and large-scale hydraulic fracturing for development. During fracturing, a significant volume of fracturing fluid is injected into the reservoir at a rate far exceeding its absorption capacity. This not only serves to create fractures but also impacts the recovery efficiency of tight reservoirs. Therefore, achieving the integration of fracturing and enhanced recovery functions within the working fluid (fracturing-enhanced recovery integration) becomes particularly crucial. This study describes the concept and characteristics of fracturing-enhanced recovery integration and analyzes the types and features of working fluids. We also discuss the challenges and prospects faced by these fluids. Working fluids for fracturing-enhanced recovery integration need to consider the synergistic effects of fracturing and recovery; meet the performance requirements during fracturing stages such as fracture creation, proppant suspension, and flowback; and also address the demand for increased recovery. The main mechanisms include (1) enlarging the effective pore radius, (2) super-hydrophobic effects, and (3) anti-swelling properties. Fracturing fluids are pumped into fractures through pipelines, where they undergo complex flow in multi-scale fractures, ultimately seeping through capillary bundles. Flow resistance is influenced by the external environment, and the sources of flow resistance in fractures of different scales vary. Surfactants with polymerization capabilities, biodegradable and environmentally friendly bio-based surfactants, crosslinking agents, and amino acid-based green surfactants with outstanding properties will unleash their application potential, providing crucial support for the effectiveness of fracturing-enhanced recovery integration working fluids. This article provides important references for the green, efficient, and sustainable development of tight oil reservoirs.

Controls on fracture propagation in bioturbated carbonate rocks: Insights from the Aruma formation, central Saudi Arabia

Previous research has explored the linkage between bioturbation, porosity, and permeability in carbonate reservoir rocks. The impact of bioturbation on natural fractures in such rocks remains relatively unexplored, however, but is crucial for effective subsurface resource management. This study focuses on the relationship between bioturbation and fracture characteristics in a well-exposed outcrop, the upper Cretaceous Khanasir Member of the Aruma Formation, central Saudi Arabia. The approach includes field investigation, petrography, imaging analysis, and CT scanning to quantify the relationship between burrows and fracture characteristics at scales from thin section to outcrop scale. At the outcrop scale, the Khanasir Member comprises three distinct units based on their fracture and burrow characteristics. These units reveal two primary categories of fractures: (1) burrow-related fractures, influenced and controlled by bioturbation; and (2) non-burrow-related fractures, unaffected by bioturbation. The characteristics of fractures within these units are influenced by multiple factors including: if burrows are filled; composition of the burrow fillings; mineralogy of host rock matrix; texture of the host rock matrix; and burrow percentage. The interplay of these factors affects fracture attributes such as density, length, and spacing, all of which have a direct impact on fluid flow behavior within subsurface reservoirs.

Characteristics and effectiveness of deep and ultradeep tight sandstone fractures: Insights from geological and geophysical data analysis

“Effective” natural fractures are those that contribute to reservoir storage and conductivity. In this paper, the effectiveness of fractures in deep and ultradeep reservoirs (gt;6 km depth) is evaluated by using geophysical image log data, core, microstructures, mechanical tests, and geological evidence of tectonic context (including current in situ stress) and sedimentary faces and diagenesis. Intraformational open mode fractures are the most common type in this tectonically active region, and their effectiveness is affected by the coupling between past tectonic activity, in situ stress, and chemical reactions such as mineral precipitation or dissolution (diagenesis). Our results show that the effectiveness of fractures is mainly related to the aperture and filling, and fractures formed by early tectonic movement are more likely to be filled by minerals, reducing their effectiveness. Near orogenic belts in strongly cemented tight diagenetic facies exhibit a greater abundance of mineral-filled fractures, while dissolution can increase the fracture aperture and produces secondary pores in host rocks and roughen fracture walls. The effective normal stress acting on the fracture surface decreases when the fracture is parallel to the maximum horizontal stress component, so the fracture has a large aperture and therefore is more effective. The laboratory measurement results reveal that the contribution of fractures to reservoir space is limited, and the reservoir space provided by fractures accounts for only 13% of all types of reservoir space, while the development of fractures increases reservoir permeability by 1-2 orders of magnitude. Fractures improve the effectiveness of reservoir by connecting the dispersed pores in the reservoir matrix. Fractures with a low angle to the maximum horizontal stress component direction have greater apertures and permeabilities, and are the main channels for fluid flow.

Numerical analysis of a parallel triple-jet of liquid-sodium in a turbulent forced convection regime

In the present study, we have applied a combined wall-resolving dynamic Large-Eddy Simulation (LES) (for the velocity field) and Direct Numerical Simulation (DNS) (for the temperature field) approach for mixing of parallel triple-jets with different temperatures of liquid sodium in a turbulent forced convection regime. Because of the high thermal conductivity of sodium (a low-Prandtl fluid), we adopted the dynamic Smagorinsky subgrid closure for the unresolved velocity scales, while the thermal scales are fully resolved. Furthermore, the Time-dependent Reynolds-Averaged Navier-Stokes (T-RANS) approach with the high-Reynolds number variant (i.e. with the wall functions as boundary conditions along solid boundaries) of the four-equation eddy viscosity model (k−ε−kθ−εθ) was applied. The fine-mesh LES/DNS provided a close agreement with the experimental data for both velocity and temperature fields (for both first- and second-moments). In contrast, the coarse-mesh LES/DNS overestimated the turbulent kinetic energy profiles at different distances from the inlet plane. The T-RANS results confirmed a good agreement with the mean streamwise velocity and turbulent kinetic energy, as well as the mean temperature profiles. Finally, the analysis of power spectral density distributions of the temperature signal revealed that all simulation techniques captured a dominant flow frequency originating from the induced Kelvin-Helmholtz instabilities between the side and central jets. The presented combined dynamic LES/DNS approach is recommended for future simulations of the turbulent forced convection flows of low Prandtl fluids, especially if thermal fatigue effects need to be predicted correctly.

Exploring Unsteady Three-Dimensional Casson Fluid Flow through a Stretching Surface with Heat Source/Sink: A Numerical Investigation

This research aims to examine the effects of a heat source or sink and viscous dissipation on an MHD unsteady three-dimensional Casson fluid flow across a stretched sheet. Using similarity transformations, the governing partial differential equations are transformed into coupled ordinary differential equations, which are then solved numerically in Matlab. The numerical findings for several physical parameters that impact velocity and temperature profiles are described in tables and graphs. The interesting finding are recorded as follows: When the Magnetic parameter increases, the skin friction coefficient increases along x and z directions, but when the Casson parameter lowers, it decreases. The Nusselt number increases with the enhancement of viscous dissipation parameter and heat source or sink parameter. Understanding the behavior of non-Newtonian fluids in the presence of heat transfer is crucial in a number of domains, including chemical engineering, biomechanics, and material processing. These applications might benefit from this kind of study.

Analysis of MHD third-grade hybrid nanofluid model in Darcy-Forchheimer porous medium: Evaluation of the thermal performance of [formula omitted]-[formula omitted] cylindrical nanoparticles dispersed in ethylene glycol fluid

Researchers and scientists became interested in the newly developed idea of hybrid nanofluids because of their exceptional thermal conductivities, which resulted in enhanced thermal performance. These fluids have a wide range of uses in the industrial and technical fields. This novel class of fluids is playing a vital role in solar energy, automotive industry, cooling of the machine and manufacturing, heating and ventilation systems, electronic cooling, nuclear systems cooling, biomedical fields, space, ships, and defense systems. In light of the physical significance of the above-mentioned class of fluids, the current investigations are carried to examine the thermal performance of the mixture of cylindrical shaped aluminum oxide Al2O3 and copper Cu nanoparticles suspended in ethylene glycol using third-grade non-Newtonian fluid flow model. The fluid flow is induced by the stretching of the permeable sheet in exponential manner that is embedded in a Dacry-Forchheimer porous medium. The effects of Lorentz force applied normal to the flow and suction impacts have been incorporated in the current proposed model. The solutions of the flow model transformed to ordinary differential equations are computed using MATLAB built-in solver bvp4c. The solutions are presented in graphical representations. Graphical solutions reflect that fluid velocity slows down by growing the volume fractions of the nanoparticles. Increasing values of viscoelastic parameters reflect that there is a reduction in velocity and intensification in profiles of temperature and concentration have been noted. Rising values of cross-diffusion parameter is leading to the reduction in magnitude of velocity, and augmenting behavior of temperature and concentration has been seen. Observations indicate rising third-grade fluid parameter and porosity parameter lead to reduction in velocity. Increasing Schmidt number gives reduced Sherwood number, and magnetic field parameter improves the rate of hear transfer (Nusselt number) and skin friction coefficient for both Al2O3/ethylene glycol nanofluid and Al3O3-Cu/ethylene glycol-based hybrid nanofluid. The suggested model's validity is confirmed through comparison with previously released findings. Additionally, a grid independence test (sensitivity analysis) has been performed to verify the accuracy and verification of the numerical model.

Effect of magnetic needle magnetic particle grinding process on the performance of metal aluminum plates

Magnetic needle grinding processing technology is one of the magnetic grinding processing techniques. It possesses the characteristics of micro-cutting removal, small increase in processing temperature, flexible processing, high-quality, and high-precision processing. It is mainly utilized to remove burrs at the edge of the workpiece and the edge of the hole, as well as to finish the surface of the workpiece. It is frequently employed in civil, aerospace, navigation, and other fields. Due to the randomness and complexity of magnetic needle movement in magnetic abrasive finishing, it is difficult to quantify the processing parameters and predict processing effects. Therefore, this paper establishes a simulation model of magnetic needle in magnetic abrasive finishing by the coupling numerical simulation method of fluid dynamics discrete element method (CFD-DEM) to analyze the working state parameters of the magnetic needle. Through the simulation of actual working conditions, the machining process and parameters of magnetic abrasive finishing are quantified and analyzed, and the motion trend of magnetic needles during the machining process is studied. Then, the residual stress of single magnetic needle impact is analyzed with ABAQUS, and the performance enhancement of the workpiece is predicted. Finally, observations of surface morphology and validation of residual stress prediction were conducted through experiments on an aluminum plate. The results show that the residual stress of the aluminum plate is positively correlated with the number of strikes of the magnetic needle. The residual stress changes from tensile stress (+0.1 MPa) to compressive stress (-16.5 MPa). The comparison between simulation results and experimental results is good, indicating that the simulation model can comprehensively consider multiple factors such as magnetic field, particle motion, and fluid flow, and establish a magnetic needle magnetic grinding process model that is suitable for actual working conditions.

Modulation instability analysis, and characterize time-dependent variable coefficient solutions in electromagnetic transmission and biological field

This study integrates the telegraph model with the traveling wave coefficient. This model characterizes planar random motion of particles in fluid flow, pressure waves from pulsatile blood flow in arteries, electrical impulses in nerve and muscle cell axons, and electromagnetic waves in superconducting media. Using the efficient and well-established Enhanced Modified Simple Equation (EMSE) method, we investigate solitary wave solution with the variable coefficient of the telegraph model. To investigate the variable coefficient solitary wave solution, we apply a transformation variable η = h(t)x + g(t), which is dependent on the time variable function. The diverse functions of h(t) and g(t) yield many novel and exclusive solutions. Numerical solutions are plotted in 3D, density, and 2D. instanton soliton, kinky periodic wave, lump wave, kink wave, anti-kink wave, double periodic wave, diverse types periodic wave, lump with bell wave periodic wave, periodic lump wave, etc. Solitary waves explain complex wave phenomena through nonlinear effects like self-interaction and dispersion. Due to the classical nonlinear telegraph model's wave dynamics, they are used in brain function and communication system design. We conclude by testing the governing model's modulation instability. Dispersive and nonlinear processes modulating the stable state cause instability in high-order nonlinear equations. Examining the wave movement role and modulation instability analysis to assess solution stability shows that all solutions are accurate and stable. The computational difficulties and results demonstrate the approaches' clarity, effectiveness, and simplicity, suggesting they can be applied to evolutionary dynamic and static nonlinear equations in computational physics, other real-world situations, and numerous academic disciplines.

Effects of fluid composition in fluid injection experiments in porous media

Experiments on fluid flow in porous media, using fluids loaded with solids of various grain sizes, have been conducted in a modified Hele-Shaw setup. This setup utilised weakly cemented porous media with specific hydraulic and mechanical properties. Fluid injection in coarse granular media with clean or low-concentration fine particles, results in infiltration only, with pressure close to the material tensile strength, while injection in finer granular material causes damage alongside infiltration, with the fluid pressure still close to the material tensile strength. When larger particle sizes or higher particle concentrations are used in the mixture, the fluid travels further within the porous medium, primarily influenced by the grain size of the granular medium. In the latter case, the Darcy flow equation with an effective permeability term can be employed to determine the pressure differential. For the largest particle sizes included in the fluid, the equation is still applicable, but the effective permeability requires adjustment for particle size within the fluid rather than the granular medium. This is crucial when the injection point is locally clogged. The experiments show that fracturing conditions are controlled by different mechanisms. Dimensional and statistical analysis was used to classify the injection pressures to regimes predicted by fracturing theory or by Darcy law with modified effective permeabilities. The findings show that both the material properties and fluid composition are important designing parameters.

Optimization of the Laser Drilling Processing Parameters for Carbon Steel Based on Multi-Physics Simulation

The laser drilling of carbon steel is always suffered from the formation of slag, the presence of cutting burrs, the generation of a significant quantity of spatter, and the incomplete penetration of the substrate. In order to avoid these defects formed during the laser drilling of carbon steel, the COMSOL multi-physics simulation method was used to model and optimize the laser drilling process. Considering the splash evolution of the material during the complex drilling process, the transient evolution of the temperature field, the flow of the molten fluid, the geometrical changes, and the absorption of the laser energy during the laser drilling process were investigated. The simulated borehole dimensions are consistent with the experimental results. The process parameters have a great influence on the fluid flow pattern and material slag splashing. The laser power has a significant effect on the laser processing compared with the process parameters. With the increase in laser power and the decrease in laser heat source radius, the time required for perforation is reduced, the flow of melt is accelerated, the perforation efficiency is increased, and the hole wall is smoother, but the degree of spattering is greater. The optimized process parameters were obtained: laser heat source radius of 0.3 mm, laser power of 3000 W. These findings can help reduce the machining defects in carbon steel with excellent mechanical properties by optimizing the laser drilling processing parameters.

Dynamics and Chaos of Convective Fluid Flow

In this paper, a mathematical model of fluid flows in a convective thermal system is developed, and a five-dimensional dynamical system is developed for the investigation of the convective fluid dynamics. The analytical solutions of periodic motions to chaos of the convective fluid flows are developed for steady-state vortex flows, and the corresponding stability and bifurcations of periodic motions in the five-dimensional dynamical system are studied. The harmonic frequency-amplitude characteristics for periodic flows are obtained, which provide energy distribution in the parameter space. Analytical homoclinic orbits for the convective fluid flow systems are developed for the asymptotic convection through the infinite-many homoclinic orbits in the five-dimensional dynamical system. The dynamics of fluid flows in the convective thermal systems are revealed, and one can use such methodology to predict atmospheric and oceanic phenomena through thermal convections.

Dynamics of a cantilevered pipe conveying fluid and partially subjected to a confined counter-current external axial flow of a different fluid

A linear analytical model has been developed for prediction of fluid-elastic instabilities of brine-strings during product retrieval in salt-mined caverns. These caverns are utilized for storage and subsequent retrieval of hydrocarbons, hydrogen gas or compressed air in Compressed Air Energy Storage (CAES) plants. The retrieval operation involves pumping brine downwards through a long cantilevered pipe (“brine-string”) into the cavern, causing the lighter-than-brine gaseous or liquid “product” stored in the cavern to flow upwards and out of the cavern through a shorter annular passage formed by a concentric casing surrounding the upper portion of the pipe. The presence in the cavern of two different fluids with a variable interface level is taken into account. Employing a Newtonian derivation of the equation of motion solutions were obtained via the Galerkin modal decomposition technique, demonstrating that the brine-string may develop buckling or flutter at high-enough flow rates, depending on the system parameters. Extensive computations investigated the influence of system parameters on the dynamics. It is shown that simplifying the system by considering a single fluid in the cavern, and so for the flows within and around the brine-string, leads to unrealistically high critical flow velocity predictions.