Radial Flow Model Research Articles

Analysis of Fluid Flow in a Radial Centrifugal Pump

The paper presents a validation of the results of a numerical model of radial centrifugal pump flow using a PIV (Particle Image Velocimetry) experimental method. For this purpose, a 3D model of the pump was created in Inventor, which was then used to design a numerical flow model in Ansys in the CFX module. The performance characteristics of the same pump were measured on an experimental test circuit, and vector maps of the flow in the suction pipe were obtained using the PIV method. The results of the experiment—vector fields of fluid velocity distribution in a suction pipe—were then compared with the outputs of the numerical Ansys model, namely the streamlines and pressure distributions. This comparison demonstrated that the numerical model is most consistent with reality if the input variables are the pressure in front of the pump and the mass flow behind the pump. In this case, the model can determine the pressure at the pump inlet with a deviation of 1% to 10% and create streamlines in the suction pipe corresponding to the results of PIV measurements.

Characterizing the radius of influence during pumping tests using the absolute critical drawdown criterion: Cases of integer flow dimensions

Determining the radius of influence r0 of wells during pumping tests is critical for the characterization of aquifers and the management of groundwater. However, because a convenient analytical interpretative framework is lacking, this is a very difficult task during routine investigations. Practicing hydrogeologists have resorted to using semi-empirical equations developed by certain authors. Most studies aiming to characterize the radius of influence are based on radial flow models. In this study, we propose to investigate, from an analytical standpoint, the radius of influence equation for integer flow dimensions (n=1,2,3), using both Barker’s generalized radial flow model and Theis’ radial flow model. The current approach may thus be considered valid for those hydrogeological contexts (fractured or granular aquifer media) that produce the specified flow dimension. The radius of influence is defined as the maximum distance from the pumping well at which the drawdown reaches its critical value of detectability: the absolute critical drawdown criterion sc. The radius of influence is a theoretical, non-intrinsic and variable parameter that reflects the ability of drawdown recording systems to measure very small variations. Our investigations show that the radius of influence equation can be generalized as follows: r0=Ctγ where the coefficients C and γ depend not only on the flow dimension parameter n, but also on the criterion sc, the pumping flow rate Q, the hydraulic conductivity K and the aquifer thickness b. The specificities of the radius of influence equation for each flow dimension are also discussed. Finally, results obtained from this analytical approach are verified against numerical simulations.

Characterization of Dissolution-Permeation System using Hollow Fiber Membrane Module and Utility to Predict in Vivo Drug Permeation Across BCS Classes

A dissolution-permeation system has potential to provide insight into the kinetic contributions of dissolution and permeation to overall drug absorption. The goals of the study were to characterize a dissolution-hollow fiber membrane (D-HFM) system and compare its resulting in vitro drug permeation constants (Kp′) to in vivo clinical permeation constants (kp), for four drugs in various Biopharmaceutics Classification System (BCS) classes. Model predictions for D-HFM were made based on derived mixing tank (MT) and complete radial (CRM) flow models and independent measurement of membrane permeability. Experimental D-HFM studies included donor flow rate and donor volume sensitivity studies, and drug permeation profile studies. Additionally, for the four drugs, Kp′from D-HFM system was compared to (kp) from literature, as well as Kp′ values from side-by-side diffusion cell and dissolution/Caco-2 system. Results show progressive D-HFM system development as a dissolution-permeation tool. Results indicated that D-HFM models using MT or CRM provided close agreement between predicted and observed drug permeation profiles. Drug permeation in D-HFM system was volume dependent, as predicted. Favorably, more drug permeated through the D-HFM system (10–20% in 60 min) compared to side-by-side diffusion cell (1%) and dissolution/Caco-2 system (0.1%). Kp′ from D-HFM system was also closer to in vivo kp; the two other in vitro models showed lower Kp′. Overall, studies reflect that HFM module has potential to incorporate drug permeation into the in vitro assessment of in vivo tablet and capsule performance.

Theoretical Research on Grouting in Deep Loose Layers Based on the Cylindrical Diffusion Model of Radial Tube Flow

Grouting in deep, loose layers are a complex process in which many modes such as infiltration, splitting, and compaction coexist. It is of great significance to establish a realistic, simplified physical model to study the law of slurry diffusion. Herein, a cylindrical diffusion model of radial tube flow is established, and the control differential equations of both the Bingham slurry diffusion velocity in a single tube and the diffusion velocity of the radial tube flow are deduced. Additionally, the calculation formulas for the diffusion radius and slurry pressure distribution function are obtained. The rationality of the theory is verified by combining our results with those of the field grouting test of the Guotun coal mine. The results show that the cylindrical diffusion model of radial tube flow can successfully characterize the slurry diffusion law of grouting in a deep, loose layer. The slurry pressure attenuation shows distinguishable stages: within the first 30% of the diffusion radius, the slurry pressure decreased sharply by approximately 70%, and the slurry pressure decreases slowly in the later stages. Furthermore, the diffusion radius has a nonlinear, negative correlation with the height of the grouting section and the comprehensive injection rate of formation; the change rate is relatively more gradual, and there are no distinguishable stages. The research results provide a theoretical basis for reasonably determining the grouting parameters of deep, loose layers in the future.

Numerical investigation on heat transfer characterization of liquid lithium metal in pipe

Liquid Li metal is a promising nuclear reactor coolant; however, relevant research regarding its heat transfer characteristics remains insufficient. In this study, a steady-state two-dimensional mathematical model is established to describe the heat transfer process of liquid Li in a straight pipe. A numerical analysis is conducted to investigate the effects of inlet velocity, inlet temperature, and wall heat flux on heat transfer in liquid Li. The results indicate the advantage of using liquid Li for improving heat transfer at high inlet temperatures (> 1000 K) compared with using liquid sodium and lead–bismuth eutectic. Considering the mechanism of the outlet radial heat flow model, the ratio of turbulent to molecular diffusion coefficients presents a parabolic distribution along the radius of the pipe. Increasing the inlet velocity, decreasing the inlet temperature, and decreasing the wall heat flux can effectively weaken the dominant role of molecular heat transfer owing to the low Prandtl number of liquid Li. The heat transfer of liquid Li is investigated comprehensively in this study, and the results provide a basis for the practical application of liquid Li as a promising coolant.

Theoretical study of micropolar fluid flow in porous media

In this paper, a mathematical model of Hele-Shaw flow was developed on the basis of the field equation of micropolar fluid. The motion equation of micropolar fluid was extended to flow in porous media, contributing to the mathematical model of the unsteady radial flow of micropolar fluid in an infinite reservoir. The relations between flow velocity, pressure gradient and flow rate were obtained by solving the mathematical model under fixed production internal boundary and fixed-pressure external boundary conditions. In addition, the effect of the physical properties of micropolar fluid on its flow was analyzed. The results indicated a significant dependence between the apparent permeability and physical properties of micropolar fluid, which clearly deviated from the Newtonian fluid. The results showed that, as the ratio of rotational viscous force to Newtonian viscous force in the micropolar parameter and the characteristic length of the micropolar metamaterial increase, the non-Newtonian characteristics of the fluid become gradually more significant. The non- Newtonian behavior of micropolar fluid consequently becomes unneglected, leading to a decreasing apparent permeability. Compared with a Newtonian fluid, a micropolar fluid causes obvious flow resistance, resulting in larger energy consumption and lower flow rate. This study can provide an academic reference for nonlinear rheology and the flow of heterogeneous fluids in the fields of petroleum engineering and biofluid flow. Cited as: Zhu, W. Theoretical study of micropolar fluid flow in porous media. Advances in Geo-Energy Research, 2021, 5(4): 465-472, doi: 10.46690/ager.2021.04.11

Modeling transient flow behavior with the high velocity non-Darcy effect in composite naturally fractured-homogeneous gas reservoirs

A gas reservoir with composite properties contains two distinct regions, where one develops natural fractures and the other does not. To investigate the pressure transient behavior of the non-Darcy flow in composite naturally fractured-homogeneous gas reservoirs, a radial bi-zonal composite non-Darcy flow model was developed based on Izbash's equation. The inner region was considered as a dual-porosity medium to simulate the non-Darcy flow, whereas the outer region was considered as a homogeneous medium to simulate the Darcy flow. This model was solved using the Laplace transform, linearization and Stehfest numerical inversion. Then, the standard bi-logarithmic characteristic curves of the non-Darcy flow model were plotted. The flow stages were recognized and the influence of vital characteristic parameters on the transient behavior was analyzed and discussed in detail, such as the empirical constant, radius of the non-Darcy region, storage ratio, crossflow coefficient, etc. It is found that the values of the empirical constant n have a significant influence on the pressure transient behavior of the non-Darcy region. Moreover, three reduced models of the model proposed in this study were analyzed and discussed. Finally, it was found from the field application that this model had an excellent agreement between the measured and simulated pressure responses. The research results can be a helpful guide for researchers in the related fields when studying the transient behavior of high-velocity non-Darcy gas flow in composite naturally fractured-homogeneous gas reservoirs.

The extended generalized radial flow model and effective conductivity for truncated power law variograms

Pumping tests are established for characterizing spatial average properties of aquifers. At the same time, they are promising tools to identify heterogeneity characteristics such as log-conductivity variance and correlation scales. We present the extended Generalized Radial Flow Model (eGRF) which combines the characterization of well flow in fractal geometry with an upscaled conductivity for pumping tests in heterogeneous media. We show that the eGRF is a generalization of previously solutions, such as that of Barker, Butler and Neuman. We derive effective conductivities for uniform and well flow conditions in heterogeneous log-normal media with a truncated power law correlation structure through the upscaling procedure Coarse Graining. The radial-dependent effective conductivity for well flow reflects the gradual change of heterogeneity impact on average pumping test drawdowns. We then combine upscaled conductivities with the eGRF model to determine the effective pumping test solution. We provide a proof of concept by comparing theoretical upscaling results with Monte Carlo well flow simulations in heterogeneous fractal fields. The eGRF and upscaling results are implemented and made freely available as python code for transport simulation as well as pumping test analysis.

A Transactive Retail Market Mechanism for Active Distribution Network Integrated With Large-Scale Distributed Energy Resources

The burgeoning integration of distributed energy resources (DER) poses new challenges for the economic and safe operation of the electricity system. The current distribution-side policy is largely based on mandatory regulations and incentives, rather than the design of a competitive market mechanism to arouse DERs to freely compete in the retail market. To address this issue, we proposed a transactive retail market mechanism to attract the active participation of profit-driven DER retailers in a deregulated way. Considering the limited competitive property of the retail market, a bi-level DSO-dominated framework is constructed to simulate the virtual game between distribution system operator (DSO) and DER retailers. Specifically, the flexible interval pricing of retailers is modeled as a series of binary revenue constraints to influence the DSO's centralized economic dispatch decisions, where the time-varying distribution locational marginal price is adopted to settle energy activities at different locations over the time horizon. Due to the uncertain power flow path during the coordinated decision-making process, we proposed a general undirected second-order cone-based AC radial power flow model and provided sufficient conditions to ensure its exactness. Also, we applied a series of approximation and relaxation techniques to transform the bi-level mixed-integer quadratic framework with highly discrete induced domains into a solvable mixed-integer semidefinite programming problem. It is demonstrated in the case study that the proposed mechanism not only improves market efficiency but also eliminates market power and the resulting market failures.

Modeling the coseismic groundwater level increase in the Oi well, central Japan

A model for coseismic groundwater level increase is presented for understanding hydrological responses of wells to seismic waves. Three types of coseismic groundwater level changes were observed in six wells 300–500 m in depth, operated by the Hot Spring Research Institute of Kanagawa Prefecture, central Japan. The first change was a sustained increase uniquely appearing at the Oi well. The second, a sustained decrease observed at most wells following the 2011 off the Pacific Coast of Tohoku Earthquake, and the third was an oscillatory response appearing in all six wells. In this study, we focused on the first response at the Oi well. We analyzed digital data at 1-Hz sampling rate of 12 events including shallow and deep earthquakes, and local to remote earthquakes from 2011 to 2016. There were 11 earthquakes which generated a sustained increase in the groundwater level in the Oi well from 5 to 10 cm. The time series of the sustained increase in the Oi well was well approximated by the decaying exponential function, characterized by a time constant ranging from 156 to 363 s. The slug test model for radial flow adequately represents the time curves observed in the Oi well, for which possible values of specific storage and hydraulic conductivity were used. The success of the application of the slug test model indicates a sudden increase in pore-pressure in the aquifer surrounding the well during the passage of seismic waves. We examined several candidates for the cause of the earthquake-triggered pore-pressure increase around the Oi well. We found that the poroelastic static strain change due to earthquake is not suitable for the sustained groundwater level increase at the Oi well. Qualitative examination suggests that following three models possibly explain the observed buildup times at the Oi well, but that all of them are not definitive: (a) permeability change due to barrier removal on the fracture surface, (b) undrained consolidation, and (c) gas bubble nucleation and growth.

Use of Hydraulic Test Data to Recognize Fracture Network Pattern of Rock Mass in Taiwan Mountainous Areas

Comprehensive information on fracture network properties around a borehole is indispensable for developing a hydrogeological site descriptive model. However, such information usually relies on various cross-hole field tests at a high cost. This study presents a cost-effective option regarding the identification of fracture network density around a borehole. Based on packer-test and drilling-core data from 104 boreholes in Taiwan mountainous areas, Barker’s generalized transient radial flow model and the concept of fractal flow dimension were used to reanalyze the existing hydraulic test data for obtaining the n value related to the geometry of groundwater flow for each test section. The analyzed n value was utilized to explain the characteristics of the fracture network in the adjacent area of each packer inspection section. The interpretation results were verified, using five hydrogeological indicators, namely rock-quality designation, fracture aperture, fracture density, hydraulic conductivity, and fracture/matrix permeability ratio. All hydrogeological indices have high correlations with flow dimension n values. Based on the verification results from using these indices, the proposed method in exploring such information was proven to be feasible. Finally, three practical relations were established, to provide additional information for designing and planning groundwater-related engineering systems in Taiwan mountainous areas.

Flow Physics of Wicking into Woven Screens with Hybrid Micro-/Nanoporous Structures.

Wicking within woven screens has attracted considerable attention due to its important role in applications concerning phase-change heat transfer and phase separation. In the present study, horizontal spreading experiments are conducted to investigate the wicking performance of woven screens by measuring the volumetric liquid intake into the screens and the liquid propagation fronts through two perpendicular high-speed cameras. Woven screens with micro (single- and multilayer)- and nano (plain, etched, and fluoridated)-porous structures are manipulated through diffusion bonding and chemical processes. The macroscopic observation indicates the substantial enhancement of the wicking capability in multilayer structures, where the interlayer microchannels could compensate for the essential deficiency of single-layer screens by providing low-resistance flow passages. Wicking capability of water is enhanced by the hydrophilic nanograsses along the wires. Furthermore, flow mechanisms within the screens are analyzed by comparisons between apparent and saturated wicking distances. In multilayer structures, the liquid spreads along the entire cross-sectional area in etched screens, while it spreads primarily along the interlayer microchannels in plain and fluoridated screens. The influence of various fluids on the wicking behavior within the woven screens is found to be fully represented by a unique parameter that captures the effects of surface tension and dynamic viscosity in the radial flow model. This work deepens the understanding of the capillary-driven flow within the woven screens with hybrid micro-/nanoporous structures and provides guidance for the design and manufacture of highly efficient wicking structures.

Rheological and workability effects of bottom ash usage as a mineral additive on the cement based permeation grouting method

This study presents the effects of rheological and fluidity features of cement based grouts incorporated with bottom ash (BA) as mineral additive on permeation grouting method. In this context, some experimental and analytical analyses were conducted and their results were presented. In terms of rheological and workability tests, the test program included 28 different mixtures having 0% (for control purposes), 5%, 10%, 15%, 20%, 25% and 30% bottom ash content and four water to binder ratios (w/b = 0.75, 1.00, 1.25 and 1.50). Plastic viscosity, apparent viscosity, and the yield stress of the mixtures based on rheological properties were measured for all mixtures. At the same time, marsh cone flow time, plate cohesion, and mini slump diameter in terms of workability features were obtained. In second part of this study, all rheological properties obtained from the mixtures were used for evaluating permeation grout method based on two analytical flow models (radial and spherical flow models). All test results showed that rheological parameters (especially plastic viscosity) and workability properties of the cement based grouts incorporated with BA are very important for determining of the permeation grouting design parameters such as injection pressure.

Flow mechanisms and solid flow rate prediction of powders discharged from hoppers with an insert

In this paper, lignite and glass beads with different particle size were selected as experimental materials. These powder materials were discharged from hoppers in the situations of without insert (NoIn), with confined insert (ConIn) and with unconfined insert (Ucon-In), respectively. The discharge processes were first discussed in detail and consequently, the solid flow rate of powders was obtained and analyzed. The flow zones in hoppers were divided based on the radial flow model of powder flow and the effects of inserts on the flow zone evolution were revealed. Experimental results show that both confined and unconfined inserts are beneficial to the increase of the solid flow rate, especially for the weaker flowability powders. The lignite, with the worst flowability, shows the largest increment of solid flow rate giving a value of 58% under ConIn. Considering characteristics of the inserted hopper structure as well as the development of flow zones, a modified model derived from the minimum energy theory was developed. The model was able to predict the solid flow rate through both the traditional hoppers and the inserted hoppers, with the deviation below than 10%.

Radial flow velocity profiles of a yield stress fluid between smooth parallel disks

In rock grouting, idealized 2D-radial laminar flow of yield stress fluids (YSF) is a fundamental flow configuration that is used for cement grout spread estimation. A limited amount of works have presented analytical and numerical solutions on the radial velocity profiles between parallel disks. However, to the best of our knowledge, there has been no experimental work that has presented measured velocity profiles for this geometry. In this paper, we present velocity profiles of Carbopol (a simple YSF), measured by pulsed ultrasound velocimetry within a radial flow model. We describe the design of the physical model and then present the measured velocity profiles while highlighting the plug-flow region and slip effects observed for three different apertures and volumetric flow rates. Although the measured velocity profiles exhibited wall slip, there was a reasonably good agreement with the analytical solution. We then discuss the major implications of our work on radial flow.

A CFD‐based design scheme for the perforated distributor with the control of radial flow

AbstractIn the present study, flow homogenization by distributors in chemical apparatus is studied as a process of flow control and its mechanism is reconsidered from the model of resistance to the model of radial flow. This process is composed of four consecutive behaviors: the generation, distribution, conversion of the radial flow and the momentum transfer of axial flow. Based on these flow behaviors, the novel distributor is designed as the combination of perforated plate in the center area and vertical guiding baffles around. Taking the wire‐screen catalytic reactor as a case study, numerical simulation is employed to optimize the structure of distributor and a CFD‐based design scheme called “flow field analysis scheme” is proposed. Numerical simulation is conducted in the apparatus with a diffuser (inlet D0 = 500 mm, main part D1 = 3,000 mm) under the gas velocity of 3.6 m/s (corresponding Re ≈ 12,000). The numerical results from optimized distributor show that compared with the traditional perforated plate, the flow field adjusted by the novel distributor can achieve a better flow uniformity with lower energy consumption. The theoretical analysis and numerical results are also validated and proved by the experimental results.

A review of analytical and semi-analytical fluid flow models for ultra-tight hydrocarbon reservoirs

In the last decade, numerous approaches, e.g., analytical and semi-analytical pressure solutions, production decline curve, reservoir-scale numerical models, have been used to increase our understanding of fluid transport in hydraulically fractured ultra-tight reservoirs and to improve predictions of well production. Among these approaches, analytical and semi-analytical methods have proved useful to petroleum engineers, because of the balance between the reliability of theoretical model outputs and the computational cost. Analytical or semi-analytical solutions can be used to analyze pressure-transient responses, to estimate hydraulic and induced fracture properties, to forecast production, and to optimize well spacing and multi-stage hydraulic fracking.This work reviews the development of analytical/semi-analytical multi-linear and radial flow models for hydraulically-fractured horizontal wells over the past decade. In particular, the review summarizes and compares the fundamental physics and mathematics of the gas transport mechanisms that are important in unconventional reservoirs. We highlight the analytical approaches that have successfully coupled 1) reservoir spatial heterogeneity, e.g., subdivision of the stimulated reservoir volume (SRV) and fractal SRV, 2) non-continuum flow mechanisms, e.g., Knudsen diffusion, surface diffusion, and gas slip, into diffusivity equations, and 3) the impact of pressure depletion on gas desorption, and pore size change in propped and unpropped fractures. We also discuss the gas permeability models that have been proposed in the past decade and the challenges that remain to the development of oil flow models. Our knowledge of fluid transport, especially for confined fluid at multiple reservoir scales, remains incomplete, and our understanding of flow contributions from different flow regions, and mass transfer between them remains limited.

Analysis of the impact of hydraulic properties and climate change on estimations of borehole yields

Understanding the impact of climate change on borehole yields from fractured aquifers is essential for future water resources planning and management. Although variation in hydraulic conductivity with depth (VKD) in fractured aquifers is a well-known phenomenon, the relative significance of climate change and VKD on borehole yield estimates is poorly understood. We hypothesize that VKD exerts a significant additional control on borehole yields under climate change that has not been considered in yield assessments to date. We developed a simple two-layered radial groundwater flow model of an idealised pumping borehole in the fractured Chalk aquifer of south-east England, and applied 11 VKD profiles based on a simple conceptual representation of variation in hydraulic conductivity with depth in the Chalk. For each time step, the transmissivity is calculated by integrating the VKD profile over the saturated depth calculated at the previous time step. For each VKD profile and resulting transmissivity, we applied 20 climate scenarios and six constant pumping rates for the period 1962–2014. We then estimated borehole yields based on the derived lowest pumping water levels during key drought years (e.g. 1976). We show that the hydraulic properties of the aquifer are more significant (p < 0.001) than changes in climate (p > 0.1) in controlling lowest pumping groundwater levels when abstraction rates are <9000 m3/day, and that both are significant when abstraction ≥9000 m3/day. Hydraulic conductivity is as significant a control as climate on borehole yields, although responses are non-linear associated with whether pumping water level-pumping rate curves intersect key yield constraints (e.g. pump intake depth, major inflow horizons). It is recommended that variations in hydraulic conductivity with depth are taken into consideration in future assessments of borehole yields under climate change. The approach presented is generic and can be applied across different aquifers where vertical heterogeneity is present and affects transmissivity.

Production performance analysis of fractured vertical wells with SRV in triple media gas reservoirs using elliptical flow

The stimulated reservoir volume (SRV) exists near hydraulic fractures in gas reservoirs after hydraulically fracturing stimulation, which creates one region with distinct gas reservoir properties from initial formation. Due to strong anisotropy, compared with radial flow model, the elliptical flow model is important for the optimal exploitation of triple media gas reservoirs (TMGR) consisting of matrix, vugs and fractures. The paper presents a composite elliptical flow model to analyse the fractured vertical well transient pressure and rate performance in TMGR with SRV. The inter-porosity flow from matrix to fractures is transient flow. Modified Mathieu functions is employed to solve the mathematical model. There are nine flow regimes based on dimensionless pseudo-pressure curves' characteristics and the comparison of transient inter-porosity flow with steady inter-porosity flow is illustrated. Sensitivity analysis for relevant parameters are conducted, such as well radius, SRV radius, mobility ratio, storativity ratio and inter-porosity flow coefficient.

Deriving the Oil-Water Seepage Pressure Distribution from Two-Phase Oil-Water Flow Stress Gradient

The characteristics of oil-water two-phase flow in low-permeability reservoirs have been insufficiently studied. In the present article, we estimate the oil-water seepage parameters using a flow stress gradient model with a nonuniform radial distribution of the water saturation coefficient in a low-permeability reservoir. We apply the oil-water relative permeability curves and the Buckley-Leverett equation to determine the oil-water mobility ratio and the functional relationship between the two-phase flow stress gradient, the radial distribution, and the oil saturation. In this way, we construct an oil-water radial flow model based on the oil-water two-phase flow stress to derive the pressure distribution equation. Calculation results show that there is a linear relationship between the oil-water two-phase flow stress gradient and the oil saturation and a quadratic relationship between the oil-water two-phase mobility ratio and the oil saturation. The strata/ pressure distribution for low-permeability reservoirs is highly sensitive to the oil-water two-phase flow stress gradient, and the effect is more noticeable near the wellbore.