Radial Fluid Research Articles

Laboratory investigation on fracture initiation and propagation behaviors of hot dry rock by radial borehole fracturing

Creating complex and interconnected fracture networks between injection and production wells is crucial for exploiting hot dry rock (HDR) geothermal energy. However, the simple planar fractures created by conventional hydraulic fracturing, primarily controlled by in situ stress, fail to connect directionally with the target well. This study proposes a novel stimulation method, i.e. radial borehole fracturing, which shows great potential for guiding the directional propagation of fractures. The fracture initiation and propagation behaviors of high-temperature granite under radial borehole fracturing are investigated and compared with those of conventional fracturing. Three-dimensional morphological scanning and reinjection tests are used to quantitatively evaluate fracturing performance. Additionally, the influences of key parameters, including rock temperature, in situ stress, injection rate, fluid viscosity, azimuth of the radial borehole, and the number of radial boreholes on the fracture morphology and breakdown pressure are investigated. The results show that radial borehole fracturing can effectively guide the initiation and propagation of fractures along the radial borehole. The breakdown pressure of radial borehole fracturing can be reduced by 14.1%-43.7% compared to conventional fracturing. A higher fluid-rock temperature difference reduces the directional propagation range of fractures guided by the radial borehole. Increases in the vertical density of radial boreholes, injection rate, and fluid viscosity enhance the guiding ability of radial boreholes. Furthermore, there is a competitive relationship between in situ stress and the azimuth of radial boreholes in controlling fracture propagation. This research provides a viable alternative for the directional connection of injection-production wells in HDR reservoirs.

Dynamic stress response in reservoirs stimulated by fluctuating fluid pressure during pulsating hydraulic fracturing

Determining the most effective scheme for fracturing operations depends on accurate calculations of reservoir stress. Traditional fracturing theories usually focus on stable fluid injection modes, which employ static assumptions in modelling and analysis. However, pulsating hydraulic fracturing (PHF) introduces fluctuating fluid pressure to stimulate reservoirs, which requires considering dynamic factors and exploring the dynamic stress response within the reservoir. Furthermore, reservoirs are often classified as homogeneous continuous or porous media materials, but the boundaries between these classifications are sometimes apparent. This paper investigated the development of both an elastodynamics model and a poroelastodynamics model for calculating dynamic stress responses during PHF. The staggered grid finite difference method addressed these models, with the outer boundary employing the perfectly matched layer (PML) method to simulate an infinite reservoir. The numerical simulation results were extensively verified and compared with analytical solutions, and the differences between various models and their relevant conditions were thoroughly analyzed. Analyzing fluid pressure fluctuation parameters revealed noteworthy insights into reservoir stress response characteristics. Results indicate that as the Biot coefficient and permeability increase, the disparities between the elastodynamics and poroelastodynamics models become prominent. In practical terms, high Biot coefficient or high permeability reservoirs necessitate using the poroelastodynamics model for accurate reservoir stress analysis. As the frequency of fluid pressure fluctuation increases, the amplitude of response of reservoir circumferential stress also increases, while the response amplitude of radial stress and fluid pressure decreases. These findings offer valuable theoretical guidance for parameter design in engineering applications during PHF.

Spatio-temporal analysis of power deposition and vibrational excitation in pulsed N2 microwave discharges from 1D fluid modelling and experiments

Vibrational excitation of N2 beyond thermodynamic equilibrium enhances the reactivity of this molecule and the production of radicals. Experimentally measured temporal and spatial profiles of gas and vibrational temperature show that strong vibrational non-equilibrium is found in a pulsed microwave discharges at moderate pressure (25 mbar) in pure N2 outside the plasma core and as an effect of power pulsing. A one dimensional radial time-resolved self-consistent fluid model has been developed to study the mechanism of formation of vibrationally excited N2. In addition to the temperature maps, time-resolved measurements of spontaneous optical emission, electron density and electron temperature are used to validate the model and the choice of input power density. The model reveals two regions in the plasma: a core where chemistry is dominated by power deposition and where vibrational excitation starts within the first ∼10 µs and an outer region reliant on radial transport, where vibrational excitation is activated slowly during the whole length of the pulse (200 µs). The two regions are separated by a sharp gradient in the estimated deposited power density, which is revealed to be wider than the emission intensity profile used to estimate the plasma size. The low concentration of excited species outside the core prevents the gas from heating and the reduced quenching rates prevent the destruction of vibrationally excited N2, thereby maintaining the observed high non-equilibrium.

Numerical simulation study on impact factors to dynamic filtration loss

During drilling operations, naturally, fractured formations are prone to show serious mud losses, which hinder drilling and increase nonproductive time and costs. The influencing factors of dynamic fluid loss are important for optimizing drilling parameters, reducing drilling fluid loss, and protecting oil and gas reservoirs. In this study, we simulated the dynamic filtration loss of drilling fluid during drilling under formation conditions using commercial software CMG (Computer Modelling Group). The effects of filtration time, filtrate viscosity, pressure difference, internal filter cake permeability, and external filter cake permeability on filtration loss were investigated. The simulation results showed that the permeability of the external mud cake is an important factor to control the fluid loss, and the pressure consumed by the external mud cake with low permeability can account for more than 90% of the total pressure difference. When the permeability of the external mud cake is high, the permeability of the internal mud cake also has a significant influence on the dynamic fluid loss. Under formation conditions, the dynamic fluid loss of radial fluid loss is still proportional to the filtration time and pressure difference, and inversely proportional to the filtrate viscosity of drilling fluid. Under the simulated conditions, the pressure will quickly transfer to the boundary, and the formation pressure at the same position in the formation will gradually increase, while the increase is relatively small with a constant filtration rate. The results of this paper can be used to the real site for drilling optimization. This numerical analysis method can be easily applied to filtrate loss analysis, formation damage area calculation, and other radial flow-related study.

Simulation and parametric optimal design of active radial magnetic fluid bearing

Simulation and parametric optimal design of active radial magnetic fluid bearing

Simulation and parametric optimal design of active radial magnetic fluid bearing

Simulation and parametric optimal design of active radial magnetic fluid bearing

Numerical analysis of seepage law for radial fluid flow in a single fracture: Comparison between smooth and rough fractures

This paper investigated the differences for the hydraulic characteristics in a single fracture between using the Navier–Stokes (N–S) equation and Darcy's law, which would be benefit to understand the seepage mechanism in the fracture. A numerical model of the radial flow was established considering the aperture size and water injection flow rate. Some conclusion could be given. First, the Darcy's law only described the seepage characteristics when the flow rate was small when the flow rate and pressure response have a linear relationship. While the N–S equation could describe the linear and nonlinear seepage characteristics, resulting in a better model of the actual fracture seepage flow. Second, the aperture size had a limited influence on the water pressure and seepage velocity inside the fracture when the flow rate was small. It began to have a significant impact influence on the seepage characteristics inside the fracture with the aperture increased. Third, the flow–pressure response conformed to the Forchheimer equation in the fracture. The critical Reynold number would decrease from 1.2 to 0.0116 when fracture aperture decreased from 3 to 0.5 mm using the N–S equation. The degree of nonlinearity of the fluid flow increases with fracture roughness increasing. This work gave a guidance to the difference in the two seepage theories and correction for the result by Darcy law, which was widely used in the engineering calculation.

Semianalytical Modeling for Multiphase Flow in a Fractured Low-Permeability Gas Condensate Reservoir.

During the production of fractured low-permeability gas condensate reservoir (FLPGCR), a phase transition takes place in both the formation and wellbore, resulting in multiphase flow when the pressure drops below the dew point pressure. Additionally, the presence of fractures causes the formation of stress-sensitive characteristics. Nevertheless, traditional analytical models, such as the two-region model or three-region model, overlook the coupling impact of the above factors, which could lead to incorrect pressure transient response and erroneous estimation of well and formation parameters. Therefore, this work presents a semianalytical model for an FLPGCR considering the effects of multiphase flow, stress-sensitive, and wellbore phase redistribution. The gas condensate reservoir is divided into N banks, and the radial fluid saturation variation is modeled by multiple annular reservoirs with a constant saturation in each annular reservoir. The behavior of a fractured reservoir is modeled by using the dual-porosity model. The Pedrosa transform was utilized to address the nonlinear differential equation arising from stress-sensitive behavior. To verify the semianalytical solution, it was compared with numerical simulation results from CMG. The results showed that there are 10 flow regimes for the proposed model. The shape of the type curve has the potential to identify the degree of blockage within the FLPGCR. The wellbore phase redistribution only affects the first transitional-flow regime, which slows the rate of pressure drop. The stress sensitivity will lead to the upward characteristic of the curve in a later stage. More attention should be paid to the upward pressure derivative curve at late times, which is conventionally regarded as the effect of a closed boundary when it may not be the case. In addition, the shape factor and composite radius may obscure the radial flow regime. Finally, the proposed model was applied to interpret the pressure measurements recorded from the Bohai field in China, which exhibits a better fitting quality than the traditional models.

Transient thermal management characteristics of a porous fin with radially outwards fluid flow

Thermal management and energy storage problems often utilize extended surfaces, also known as fins for enhanced heat transfer. While thermal conduction is usually the dominant mode of heat transfer in a solid fin, the use of porous fins that include advective thermal transport due to porous fluid flow has also been investigated. In particular, the steady state thermal performance of a porous fin with pressure-driven radially outwards flow has been studied. While such results are helpful for studying problems that are inherently steady state in nature, such results do not readily apply to problems where heat removal or energy storage occurs only over a short period of time. This work presents transient thermal analysis of a porous fin with radial porous fluid flow driven by a pressure gradient. It is shown that the transient temperature field in the fin is governed by a transient convection-diffusion-reaction (CDR) equation, the solution for which is derived in the form of Bessel functions. Based on this solution, the evolution of fin performance with time is examined. Comparison of heat removed by the porous fin with a baseline case without any fin is carried out. The time taken to reach steady state is calculated. Key non-dimensional parameters appearing in this problem are identified and their impact on fin performance over time is investigated. Since fin porosity improves advective thermal transport but suppresses diffusive transport at different rates at different times, therefore, it is shown that for a given operating time, there may exist an optimal porosity that maximizes the rate of heat removal. It is shown that the operating time period of the fin plays a key role in determining whether fin porosity strongly impacts heat removal rate or not. Consequently, it is shown that it is important to consider transient effects in determining whether the use of a porous fin is beneficial at all, and, if so, what is the optimal fin porosity to use. This work contributes towards porous fin theory, and offers practical design guidelines for improving and optimizing the transient performance of porous fins.

Induced flow and heat transfer due to inner stretching and outer stationary coaxial cylinders

The current pioneering research explores the development of fluid flow and heat transfer between two cylinders. The flow is induced solely by the stretching of inner cylinder enclosed by the stationary outer cylinder. The physical phenomenon occurs in polymer extrusion in engineering applications. A mathematical formulation based on the mass conservation, Navier-Stokes and energy equations is designed which reveals after non-dimensionalization that the motion is governed by the cylinder curvature, Prandtl number and distance/gap parameters between the concentric cylinders. Numerical simulations portray that deformation of the inner cylinder sets up a motion drifting axially the fluid above, which is compensated by a radial fluid to conserve the mass flow. When the gap limits to infinity, the model perfectly matches with the Crane's solution for vanishing curvature and with the Wang's solution for all curvature. An analytical flow/heat solution in the specific case of narrowing cylinders is also derived in elementary polynomial form, which shows up as stretching triggered Coutte-kind flow. Yet, another analytical solution of the flow in terms of rational function valid with a specific value of curvature parameter is detected when the flow over the inner cylinder expands to infinity. In particular, the gap size has prominent effect on the formation of momentum and thermal fields. Results also prove that a critical gap distance exist at which the heat transfer rate is at its minimum. From a pure mathematical point of view, the present authors believe that some of the published numerical results should be rechecked through comparisons with the exact solutions as provided here.

Fracture Propagation Mechanism of Radial Well-Guided Preflush Fluid Acid Fracturing under Injection Discharge Control

In view of the low availability of carbonate reservoirs, a radial well-assisted preflush acid fracturing technology is proposed to help communicate oil and gas reservoirs in non-principal stress directions. The acid fracturing model of the auxiliary preflush in the radial well is established by using the extended finite element and the two-scale continuous model. The mechanism of fracture directional propagation under the control of injection discharge is analyzed, and the deflection coefficient is introduced to characterize the guiding effect quantitatively. The effects of different in-situ stress differences and injection discharge on the guiding effect and guiding mechanism of radial wells are studied emphatically. The results show that the induced stress field caused by radial wells and the high-pressure gradient at the end of fractures are the main reasons for the directional propagation of fractures. Horizontal in-situ stress difference is the main factor, which influences the guiding effect by controlling the induced stress field and pressure gradient. The radial well can effectively guide fracture propagation when the local stress difference is less than 3 MPa. The preflush fluid discharge and acid discharge are important factors affecting the guiding effect. The preflush fluid discharge affects the guiding effect by controlling the induced gravitational field and pressure gradient. The preflush fluid discharge between 2.5-3.5 m3·min-1 is most conducive to the directional expansion of acid fracturing cracks. The acid discharge affects the guiding effect by controlling the pressure gradient: the smaller the acid discharge, the more unfavorable the directional expansion of the acid fracture. Compared with the preflush fluid discharge, the influence of the acid discharge is smaller. The theoretical basis can be used in the field application of radial well-assisted preflush fluid acid fracturing technology through the article.

Low-Gradient Magnetophoresis of Nanospheres and Nanorods through a Single Layer of Paper.

The possible magnetophoretic migration of iron oxide nanoparticles through the cellulosic matrix within a single layer of paper is challenging with its underlying mechanism remained unclear. Even with the recent advancements of theoretical understanding on magnetophoresis, mainly driven by cooperative and hydrodynamics phenomena, the contributions of these two mechanisms on possible penetration of magnetic nanoparticles through cellulosic matrix of paper have yet been proven. Here, by using iron oxide nanoparticles (IONPs), both nanospheres and nanorods, we have investigated the migration kinetics of these nanoparticles through grade 4 Whatman filter paper with a particle retention of 20-25 μm. By performing droplet tracking experiments, the real-time stained area growth of the particle droplet on the filter paper, under the influences of a grade N40 NdFeB magnet, were recorded. Our results show that the spatial and temporal expansion of the IONP stain is biased toward the magnet and such an effect is dependent on (i) particle concentration and (ii) particle shape. The kinetics data were first analyzed by treating it as a radial wicking fluid, and later the IONP distribution within the cellulosic matrix was investigated by optical microscopy. The macroscopic flow front velocities of the stained area ranged from 259 μm/s to 16 040 μm/s. Moreover, the microscopic magnetophoretic velocity of nanorod cluster was also successfully measured as ∼214 μm/s. Findings in this work have indirectly revealed the strong influence of cooperative magnetophoresis and the engineering feasibility of paper-based magnetophoretic technology by taking advantage of magnetoshape anisotropy effect of the particles.

Numerical Analysis of Flow Characteristics in Impeller-Guide Vane Hydraulic Coupling Zone of an Axial-Flow Pump as Turbine Device

An axial-flow pump as a turbine (PAT), as compared to the conventional Francis turbine, has the advantages of not being restricted by the terrain and having lower cost to reverse the pump as a turbine for power generation. When an axial-flow pump is reversed as a turbine, the internal flow pattern is more complicated than when in the pump mode, which can cause instability in the whole system and result in degradation of the hydraulic performance and structural vibration. The impeller and guide vane are the core of the axial-flow PAT unit. This research compares the experimental and numerical simulation results in order to verify the energy performance and pressure pulsation signal of the axial-flow PAT. The unsteady flow regime, fluid force, and pressure pulsation characteristics of the impeller-guide vane hydraulic coupling zone are analyzed in detail. The findings demonstrate that both the dominant frequency of the fluid force pulsation signal and the flow field pressure pulsation signal appear at 3 times of the rotation frequency. The blade passing frequency (BPF) of the impeller is the dominant frequency, and other frequency components are also dominated by the harmonic frequency of the BPF. The impeller and guide vane are primarily subject to radial fluid force. Under partial working conditions, the pressure pulsation intensity in the flow field greatly increases, and the pressure pulsation amplitude at the guide vane outlet and impeller outlet appears to be more sensitive to the flow rate change.

Dispersion and mixing dynamics of complex oil-in-water emulsions in Taylor-Couette flows.

The seminal study by G. I. Taylor (1923) has inspired generations of work in exploring and characterizing Taylor-Couette (TC) flow instabilities and laid the foundation for research of complex fluid systems requiring a controlled hydrodynamic environment. Here, TC flow with radial fluid injection is used to study the mixing dynamics of complex oil-in-water emulsions. Concentrated emulsion simulating oily bilgewater is radially injected into the annulus between rotating inner and outer cylinders, and the emulsion is allowed to disperse through the flow field. The resultant mixing dynamics are investigated, and effective intermixing coefficients are calculated through measured changes in the intensity of light reflected by the emulsion droplets in fresh and salty water. The impacts of the flow field and mixing conditions on the emulsion stability are tracked via changes in droplet size distribution (DSD), and the use of emulsified droplets as tracer particles is discussed in terms of changes in the dispersive Péclet, Capillary and Weber numbers. For oily wastewater systems, the formation of larger droplets is known to yield better separation during a water treatment process, and the final DSD observed here is found to be tunable based on salt concentration, observation time and mixing flow state in the TC cell. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Study on Load-Bearing Characteristics of Converter Trunnion Bearing

In order to improve the load-bearing performance of converter trunnion bearing, this paper proposes magnetic-hydraulic bearing which is a new coupled support technology that combines electromagnetic support and hydrostatic support. It can be realized the active control of electromagnetic and hydraulic pressure, and is conducive to extending the bearing replacement period. Based on the magnetic-hydraulic coupling, a mathematical model of the initial state of the radial support system is established, the calculation formula of bearing capacity of radial magnetic fluid bearing is deduced, and Matlab software is used to analyze the variation trend of bearing capacity and stiffness with rotor displacement. The optimization of structural parameters was carried out according to analysis of bearing characteristics, and it was concluded that the bearing performance was the best when the diameter of the bearing cavity was 10 mm, and the bearing capacity increased significantly when the thickness of the oil film was 70 μm. It provides a theoretical basis for the innovative design of converter trunnion support system.

Comparison between 1D radial and 0D global models for low-pressure oxygen DC glow discharges

This work focuses on the comparison between a zero-dimensional (0D) global model (LoKI) and a one-dimensional (1D) radial fluid model for the positive column of oxygen DC glow discharges in a tube of 1 cm inner radius at pressures between 0.5 Torr and 10 Torr. The data used in the two models are the same, so that the difference between the models is reduced to dimensionality. A good agreement is found between the two models on the main discharge parameters (gas temperature, electron density, reduced electric field and dissociation fraction), with relative differences below 5%. The agreement on other species average number densities, charged and neutral, is slightly worse, with relative differences increasing with pressure from 11% at 0.5 Torr to 57% at 10 Torr. The success of the 0D global model in describing these plasmas through volume averaged quantities decreases with pressure, due to pressure-driven narrowing of radial profiles. Hence, in the studied conditions, we recommend the use of volume-averaged models only in the pressure range up to 10 Torr.

Design optimization and experimental evaluation of a large capacity magnetorheological damper with annular and radial fluid gaps.

This paper presents an optimal design of a large-capacity Magnetorheological (MR) damper suitable for off-road vehicle applications. The damper includes an MR fluid bypass valve with both annular and radial gaps to generate a large damping force and dynamic range. An analytical model of the proposed damper is formulated based on the Bingham plastic model of MR fluids. To establish a relationship between the applied current and magnetic flux density in the MR fluid active regions, an analytical magnetic circuit is formulated and further compared with a magnetic finite element model. The MR valve geometrical parameters are subsequently optimized to maximize the damper dynamic range under specific volume and magnetic field constraints. The optimized MR valve can theoretically generate off-state and on-state damping forces of 1.1 and 7.41 kN, respectively at 12.5 mm/s damper piston velocity. The proposed damper has been also designed to allow a large piston stroke of 180 mm. The proof-of-concept of the optimally designed MR damper was subsequently fabricated and experimentally characterized to investigate its performance and validate the models. The results show that the proposed MR damper is able to provide large damping forces with a high dynamic range under different excitation conditions.

Symmetries and Casimirs of radial compressible fluid flow and gas dynamics inn > 1 dimensions

Symmetries and Casimirs are studied for the Hamiltonian equations of radial compressible fluid flow inn>1dimensions. An explicit determination of all Lie point symmetries is carried out, from which a complete classification of all maximal Lie symmetry algebras is obtained. The classification includes all Lie point symmetries that exist only for special equations of state. For a general equation of state, the hierarchy of advected conserved integrals found in the recent work is proved to consist of Hamiltonian Casimirs. A second hierarchy that holds only for an entropic equation of state is explicitly shown to comprise non-Casimirs, which yield a corresponding hierarchy of generalized symmetries through the Hamiltonian structure of the equations of radial fluid flow. The first-order symmetries are shown to generate a non-abelian Lie algebra. Two new kinematic conserved integrals found in the recent work are likewise shown to yield additional first-order generalized symmetries holding for a barotropic equation of state and an entropic equation of state. These symmetries produce an explicit transformation group acting on solutions of the fluid equations. Since these equations are well known to be equivalent to the equations of gas dynamics, all of the results obtained forn-dimensional radial fluid flow carry over to radial gas dynamics.

Storing CO2 in geothermal reservoir rocks from the Kizildere field, Turkey: Combined stress, temperature, and pore fluid dependence of seismic properties

As part of a seismic monitoring project in a geothermal field, where the feasibility of re-injection and storage of produced CO2 is being investigated, a P- and S-wave seismic velocity characterisation study was carried out. The effect of axial and radial (up to 42 MPa) stress, pore pressure (up to 17 MPa), pore fluid (100% brine or supercritical CO2) and temperature (21–100 °C) on seismic properties were studied in the laboratory for the two main reservoir formations at the Kızıldere geothermal reservoir. Each (un)confined compressive strength test performed revealed a similar trend: rapidly increasing velocity at low stresses followed by a more moderate increase at higher stresses. The data implied that the stress-dependency of the velocity increased with temperature. Increasing temperatures resulted in decreasing P-wave velocities due to mineral thermal expansion. This temperature-dependency increased with reducing stress levels. The S-wave velocity seems to be more sensitive to changes in pore pressure than the P-wave velocity. On the other hand, the S-wave velocity is less affected by an increasing axial stress compared to the P-wave velocity. By performing multiple nonlinear regression on the velocity dataset, related to a brine-saturated fractured marble, second-degree polynomial trends were found for the P- and S-wave velocity, as a function of temperature, axial stress, and pore pressure, that can potentially be used for predicting velocities at Kızıldere, or other similar, geothermal site(s). For distinguishing between a 100% brine-saturated versus a fully supercritical CO2-saturated fracture, the arrival times of the first arrivals were too close to each other to allow their utilization. The fracture aperture was too small compared to the wavelength of the source signal. However, differences in P- and S-wave amplitudes of the first arrivals were seen, where the supercritical CO2-saturated crack revealed consistently lower peak and trough amplitudes compared to the brine-saturated scenario.

Investigation of radial heat conduction with 1D self-consistent model in helicon plasmas

A 1D radially self-consistent model in helicon plasmas has been established to investigate the influence of radial heat conduction on plasma transport and wave propagation. Two kinds of 1D radial fluid models, with and without considering heat conduction, have been developed to couple the 1D plasma–wave interaction model, and self-consistent solutions have been obtained. It is concluded that in the low magnetic field range the radial heat conduction plays a moderate role in the transport of helicon plasmas and the importance depends on the application of the helicon source. It influences the local energy balance leading to enhancement of the electron temperature in the bulk region and a decrease in plasma density. The power deposition in the plasma is mainly balanced by collisional processes and axial diffusion, whereas it is compensated by heat conduction in the bulk region and consumed near the boundary. The role of radial heat conduction in the large magnetic field regime becomes negligible and the two fluid models show consistency. The local power balance, especially near the wall, is improved when conductive heat is taken into account.