Flow Model Research Articles

Heat transfer performance and startup characteristics of separated gravity heat pipe

Separated gravity heat pipes, with distinct arrangements of evaporating and condensing sections, offer low thermal resistance, high heat transfer efficiency, and a simple structure, making them suitable for passive cooling of spent fuel pools through gravity-driven processes. In this study, a steady-state, one-dimensional, two-phase flow model is developed to analyze phase change heat transfer in a separated gravity heat pipe. The research investigates the impact of liquid filling rate and vacuum level on heat pipe operation. The findings reveal a notable increase in pressure drop inside the tube with higher liquid filling rates, which diminishes the adaptability of the heat pipe as pressure rises, resulting in a narrower range of effective liquid filling rates. Specifically, the liquid filling rate of the heat pipe ranges from 38 % to 72 % at P = 13.75 kPa and from 44 % to 68 % at P = 15.75 kPa. Additionally, a startup prediction model is formulated based on a thermal resistance network model using the ideal gas assumption. Two startup states—namely, the initial startup state and the subsequent startup state—are proposed for large-scale separated gravity heat pipe arrays. The heat pipe achieves the large-temperature-difference initial startup state at a 50 % liquid filling rate within 7 min before transitioning to the subsequent startup state. The vapor mass, heat transfer coefficient, and working fluid temperature initially increase and then decrease over time, with varying peak times. As the liquid filling rate increases, the maximum vapor mass also increases. The heat transfer coefficient peaks at a 60 % liquid filling rate before subsequently declining. The optimal liquid filling rate of 60 % is identified based on startup time, heat transfer coefficient, and overall heat transfer efficiency.

Two-group interfacial area concentration model for dispersed gas-liquid flows in large-diameter pipes

Interfacial area concentration (IAC) plays a critical role in heat and mass transfers between gas and liquid phases through the interfaces. As interfacial area increases, mass and heat transfers between phases increase. Hence, a reliable IAC estimation is important for two-phase flow numerical simulations to conduct engineering designs and safety analyses. Gas bubbles show different behavior according to their shapes and sizes. Based on the size, gas bubbles can be classified into two groups that show different characteristics, such as IAC. Hence, two-group modeling helps to achieve a general approach for estimating the IAC in bubbly to beyond-bubbly flow regimes. Available models in the literature use empirical correlations to obtain group one and group two void fractions. These empirical approaches are not reliable for different flow conditions. In addition, these models are usually complex with several empirical constants. This study aims to develop a two-group area-averaged IAC model for upward vertical dispersed flows through large-diameter pipes. In addition, this study proposes using a general approach based on the two-group drift-flux model to calculate two-group void fractions rather than applying empirical correlations. The models are evaluated using 156 two-group measured data points in dispersed flow conditions through large-diameter pipes. The resulting prediction errors for group one and group two IAC models are 24.1 % and 34.2 %, and the errors for group one and group two void fraction predictions are 22.8 % and 25.6 %, respectively.

On the hydrothermal features of MHD nanofluid flow over a differently shaped thin needle influenced by Hall current with nonlinear thermal radiation

PurposeThe investigation has appraised the problem of an incompressible laminar steady magnetohydrodynamic (MHD) nanofluid stream over three distinct slendering thin isothermal needles of paraboloid, cylindrical and cone shapes. Water as a base liquid is assumed in this flow model. The influences of the Hall current and variable sorts of magnetic forces have enriched our investigation. Energy and concentration expressions consist of thermophoresis and Brownian migration phenomena. The analysis of thermal and mass slips of the presumed model has also been performed.Design/methodology/approachA relevant transformation is implemented for the alteration of the leading partial differential equations (PDEs) to the equations with nonlinear ordinary form. Due to the strong nonlinearity of the foremost equations, the problem is solved numerically by embedding the well-known RK-4 shooting practice. The software MAPLE 2017 has been exploited in reckoning the entire computation. To enunciate the investigated upshots, some graphical diagrams have been regarded here. According to technological interest, we measured the engineering quantities like the Sherwood number, the coefficient of drag friction and the Nusselt number in tabular customs.FindingsThe obtained consequences support that Hall current intensifies fluid movement when the needle is in a cone shape, while the superior velocity is noticed for cylindrical-shaped needles. The transference of heat responds inversely along with the growths of thermal and mass slip factors.Originality/valueNo work has been performed on the flow model of radiated nanofluid over a variable-shaped thin needle under Hall current, the variable magnetic field and different slip factors.

Exploiting the determinant factors on the available flexibility area of ADN's at TSO‐DSO interface

AbstractActive distribution networks (ADNs) are consistently being developed as a result of increasing penetration of distributed energy resources (DERs) and energy transition from fossil‐fuel‐based to zero carbon era. This penetration poses technical challenges for the operation of both transmission and distribution networks. The determination of the active/reactive power capability of ADNs will provide useful information at the transmission and distribution systems interface. For instance, the transmission system operator (TSO) can benefit from reactive power and reserve services which are readily available by the DERs embedded within the downstream ADNs, which are managed by the distribution system operator (DSO). This article investigates the important factors affecting the active/reactive power flexibility area of ADNs such as the joint active and reactive power dispatch of DERs, dependency of the ADN's load to voltage, parallel distribution networks, and upstream network parameters. A two‐step optimization model is developed which can capture the P/Q flexibility area, by considering the above factors and grid technical constraints such as its detailed power flow model. The numerical results from the IEEE 69‐bus standard distribution feeder underscore the critical importance of considering various factors to characterize the ADN's P/Q flexibility area. Ignoring these factors can significantly impact the shape and size of Active Distribution Networks (ADN) P/Q flexibility maps. Specifically, the Constant Power load model exhibits the smallest flexibility area; connecting to a weak upstream network diminishes P/Q flexibility, and reactive power redispatch improves active power flexibility margins. Furthermore, the collaborative support of reactive power from a neighboring distribution feeder, connected in parallel with the studied ADN, expands the achievable P/Q flexibility. These observations highlight the significance of accurately characterizing transmission and distribution network parameters. Such precision is fundamental for ensuring a smooth energy transition and successful integration of hybrid renewable energy technologies into ADNs.

Nonlinear twofold saddle point-based mixed finite element methods for a regularized μ(I)-rheology model of granular materials

We propose and analyze new mixed finite element methods for a regularized μ(I)-rheology model of granular flows with an equivalent viscosity depending nonlinearly on the pressure and the Euclidean norm of the symmetric part of the velocity gradient. To this end, and besides the velocity, the pressure and the aforementioned strain rate, we introduce a modified stress tensor that includes the convective term, and the skew-symmetric vorticity, as auxiliary tensor unknowns, thus yielding a mixed variational formulation within a Banach spaces framework. Then, the pressure is obtained through an iterative postprocess suggested by the incompressibility condition of the fluid, which allows us to express this unknown in terms of the aforementioned stress and the velocity. A fixed-point strategy combined with a solvability result for a class of nonlinear twofold saddle point operator equations in Banach spaces, is employed to show, along with the classical Banach fixed-point theorem, the well-posedness of the continuous and discrete formulations. In particular, PEERS and AFW elements of order ℓ⩾0 for the stress, the velocity, and the skew-symmetric vorticity, and piecewise polynomials of degree ⩽ℓ+n (resp. ⩽ℓ+1) for the strain rate with PEERS (resp. with AFW), yield stable Galerkin schemes. Optimal a priori error estimates are derived and associated rates of convergence are established. Finally, numerical results confirming the latter and illustrating the good performance of the methods, are reported.

Nonlinear parametric models of viscoelastic fluid flows

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate W i , we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows.

Inertial migration of cylindrical micelles formed by comb-like copolymer in Poiseuille flow

By combining the lattice Boltzmann model of fluid flow with the molecular dynamics model of copolymers, we investigate the inertial migration of cylindrical micelles, which is obtained by controlling the length ratios of hydrophilic and hydrophobic segments in a comb-like copolymer. Our results demonstrate that cylindrical micelles gradually deviate from the center of the nanochannel with increasing Reynolds number (Re). For the same Re, the larger the cylindrical micelle is, the closer it is to the center of the nanochannel. Importantly, we find that the change in the equilibrium position is particularly pronounced at Re less than 0.1, while the trend becomes smoother at Re greater than 0.1, which is because of the transition of micelles from cylindrical to disk-like shapes when Re is smaller than 0.1, and does not change as Re further increases. This work provides an understanding of cylindrical micelles' inertial migration, particularly in identifying the effect of morphological changes on the equilibrium position, which could lead to significant advancements in the inertial migration of polymer micelles.

Inundation Processes with Active Sediment Transportation in the Floodplain of West Rapti River, Nepal

The present study discusses flood hazard characteristics in the lower reaches of the West Rapti River based on the results obtained from field surveys and numerical computations using depth averaged 2-D numerical models for flood flow and associated sediment transportation. To evaluate the inundation process with sediment erosion and deposition in the floodplain, a new erosion term was introduced into the mass conservation equations for suspended sediment and bed sediment. The results obtained from numerical computations indicated that field data on the spatial distributions of depths for inundation, and sediment erosion and deposition can be evaluated by the numerical model. Thus, numerical predictions were performed for the inundated areas, and the accumulated volumes of sediment erosion/deposition for floods with return periods of 50, 100, and 200 years, as a step towards damage assessment and risk assessment due to floods with active sediment transportation in the floodplains.

A two-fluid multiphase flow model coupled with the population balance equations for the flow of a multidispersed particle system

SummaryWe present a two-fluid multiphase flow model that can be applied to the flow of polydisperse particle systems. In the model, the flow of polydisperse particle systems with different N particle sizes is considered only as two phases of fluid and particle phases, without considering the individual N phases, and the motion of particles with different diameters is represented by the motion characteristics of fluid and granular phases. The equations for the granular phase are obtained by averaging the Euler equations for the particles of different particle sizes. And the velocity of particles of different particle sizes is calculated by an explicit approximation, similar to determining the slip velocity in a mixed model of multiphase flow without solving the Eulerian momentum equation. Also, the conservation equation of particles of different particle sizes was obtained by adding the source term to the population balance equation, which is caused by the difference in the particle velocity of the particles with different particle sizes. The proposed method was compared with the results of experimental studies presented in the previous study to verify the validity of the method. The method has the advantage of not only visualizing the particle size fraction distribution but also of being stable in calculation and not increasing the computational effort significantly in studying the flow of polydisperse particle systems with particle size distribution.

Bayesian inference of coupled groundwater flow and radiogenic helium-4 production and transport at the catchment scale

Hydrogeological numerical models are essential for assessing radioactive waste disposal by understanding groundwater flow systems. These models typically rely on hydraulic head data, with other state variables often underutilized in model inversions. In Flanders' Neogene aquifer, where safety studies for Boom Clay are ongoing, existing models face uncertainties due to dependence on hydraulic heads alone. This study aims to: i) develop a conceptual model of radiogenic Helium-4 (4Herad) production and transport to reproduce observed concentrations; ii) evaluate the usefulness of 4Herad observations as an additional state variable for inverse conditioning; and iii) assess how including 4Herad affects model calibration and uncertainty reduction. We address these objectives by incorporating radiogenic Helium-4 (4Herad) as an unconventional state variable in model inversion to tackle parameter non-uniqueness. Utilizing a Bayesian approach, we employ two 3D models: a groundwater flow (GWF) model conditioned by hydraulic heads and a coupled GWF model with 4Herad production and transport, conditioned by both hydraulic heads and 4Herad concentrations. We hypothesize that integrating 4Herad will improve model accuracy and reduce uncertainties compared to using hydraulic head data alone. Findings indicate that major 4Herad sources include crustal fluxes (~57 %) and in situ Boom Clay production (~25 %). The coupled inference narrows the posterior distributions of parameters, especially for hydraulic conductivity (e.g., Mol, Diest, Berchem formations, and the Rauw Fault) and recharge, showing that 4Herad observations effectively reduce uncertainty beyond hydraulic head data. Including 4Herad improves model reliability and prediction accuracy, highlighting its importance for refining groundwater flow parameters and derived fluxes. To the best of our knowledge, this study marks the first-ever attempt at harnessing 4Herad quantitative insights into flow and transport parameters following a Bayesian approach at a catchment scale, setting a precedent for future research and emphasizing the innovative nature of this work. This study showcases a state-of-the-art approach in hydrogeological modelling, demonstrating the effectiveness of integrating 4Herad with hydraulic head observations to produce more reliable model predictions. By reducing uncertainties in crucial groundwater fluxes, this approach offers significant potential for improving geological disposal safety studies. This pioneering work advocates for the continued use of 4Herad in hydrogeological modelling, emphasizing its innovative contribution to future research and safety studies. Plain language summaryUnderstanding how groundwater flows is crucial for safely storing radioactive waste. Traditionally, models used to study groundwater rely mostly on measurements of water pressure, while other valuable data often go unused. In the Neogene aquifer in Flanders, where researchers are studying the Boom Clay formation for potential waste storage, relying only on water pressure has created uncertainties in the models. This study explores a new approach by using a different type of measurement: radiogenic Helium-4 (4Herad). The goals of the study are threefold: first, to build a model that accurately represents how 4Herad is produced and moves through the groundwater; second, to test whether including 4Herad as an additional measurement improves the model compared to using only water pressure data; and third, to see how using 4Herad affects the accuracy and reliability of the model. The study uses two types of models: one that relies only on water pressure data and another that includes both water pressure and 4Herad measurements. The idea is that 4Herad could provide additional insights and help reduce uncertainties in the model. The findings show that 4Herad comes mainly from two sources: the surrounding crust and the Boom Clay itself. Including 4Herad in the model helps narrow down uncertainties, particularly regarding how water moves through different layers and how much water is being replenished. This research is the first to use 4Herad in this way, using a formal statistical method to improve groundwater models. The results suggest that 4Herad is a valuable addition for making more accurate predictions and improving safety assessments for radioactive waste storage.

Prospects of Detecting a Jet in Sagittarius A* with Very-long-baseline Interferometry

Abstract Event Horizon Telescope (EHT) images of the horizon-scale emission around the Galactic center supermassive black hole Sagittarius A* (Sgr A*) favor accretion flow models with a jet component. However, this jet has not been conclusively detected. Using the “best-bet” models of Sgr A* from the EHT Collaboration, we assess whether this nondetection is expected for current facilities and explore the prospects of detecting a jet with very-long-baseline interferometry (VLBI) at four frequencies: 86, 115, 230, and 345 GHz. We produce synthetic image reconstructions for current and next-generation VLBI arrays at these frequencies that include the effects of interstellar scattering, optical depth, and time variability. We find that no existing VLBI arrays are expected to detect the jet in these best-bet models, consistent with observations to date. We show that next-generation VLBI arrays at 86 and 115 GHz—in particular, the EHT after upgrades through the ngEHT program and the ngVLA—successfully capture the jet in our tests due to improvements in instrument sensitivity and (u, v) coverage at spatial scales critical to jet detection. These results highlight the potential of enhanced VLBI capabilities in the coming decade to reveal the crucial properties of Sgr A* and its interaction with the Galactic center environment.

An integrated distributionally robust model for two-echelon patient appointment scheduling

We develop a distributionally robust optimization (DRO) model for the outpatient appointment scheduling problem of a set of patients served in two serial stages, consultation and examination. The arrival sequence of patients is known, and the problem of scheduling is to assign appointment time for each patient to minimize total cost with random service time for two serial stages. A max–min problem is formulated for the two-stage appointment scheduling as a whole, in which the waiting time exhibits a high degree of coupling due to the continuous two-stage process. To address this, we devise a two-stage network maximum flow model that provides an equivalent linear expression for the waiting time. For the inner maximum problem, we employ a conic programming approach for equivalent representation, incorporate the scheduling decision of the outer minimum problem, and convert the model to its equivalent copositive programming by taking the conic duality. We conduct numerical experiments and sensitivity analysis using real and simulated data, and the results verify the effectiveness of our proposed DRO model.

Analysis of dominant flow in tectonic coal during coalbed methane transport

Diffusion and seepage are the main flow forms of coal seam gas transport, and are one of the key factors in the selection of gas extraction improvement methods. Changes in the physical structure of tectonic coal make gas transport more complex during coalbed methane extraction. In this paper, we develop a multi-field coupled model of methane transport in coal seams, taking into account the effects of tectonics, and theoretically analyze the dominant flow patterns for methane extraction. Then, the evolution of gas dominated flow is analyzed for different initial pressures, initial permeabilities, and initial diffusion coefficients of tectonic and intact coal seams. The results show that the amount of daily methane seepage in tectonic coal increases with the initial pressure of the coal reservoir, but decreases with the initial diffusion coefficient of the coal reservoir. Methane seepage in tectonic coal has a longer control time than in intact coal at different initial pressures, initial permeabilities, and initial diffusion coefficients of the coal reservoir. For different coal reservoir initial pressures, coal reservoir initial permeabilities, and coal reservoir initial diffusion coefficients, the maximum seepage control time for tectonic coal is 20, 17, and 15 times longer than for intact coal, respectively. Finally, the discrepancies of methane dominant flow in tectonic coal and intact coal during methane extraction were analyzed by using the double bottleneck flow model, and methods for methane enhanced extraction in tectonic coal and intact coal were discussed. The results presented in this paper may provide a theoretical reference for the extraction of differentiated gas in coal seams.

Comparison of rotor hovering aerodynamic performance in free-surface and ground effects using numerical methods

The aerodynamic performance of the rotor hovering on the air–water free-surface, which is significant for cross-medium unmanned aerial vehicles, is merely studied. In this study, a compressible two-phase flow model is used to compare the aerodynamic performance in the free-surface effect (FSE) and the ground effect (GE) with various dimensionless distances, γ, between the rotor and the ground (or free-surface). According to the results, the vortex core in FSE moves further in both vertical and radial directions than in GE for the early stages. Additionally, the blade surface is separated into three parts. In zone I, the aerodynamic performance is mostly determined by proximity effects. For both FSE and GE, the downward induced velocity at the rotor disk rises with increasing γ, leading to a decrease in the sectional thrust coefficient CT,S. By the way, CT,S is larger in FSE. In zone III, the aerodynamic performance is mostly governed by the blade tip vortex. The trend of aerodynamic performance with γ is reversed compared with zone I. The above-mentioned two opposing tendencies result in a smaller rotor thrust in FSE than in GE within the range of 0.60≤γ≤3.00, but a higher rotor thrust in FSE within the range of γ≤0.60.

Investigation on intermittent flow characteristics in horizontal pipe by visualization measurement method

Accurate measurement and prediction of the intermittent flow characteristics in horizontal pipes is important for constructing multiphase flow models and ensuring pipe flow safety. In this paper, a quantitative image post-processing technique for intermittent flow characteristics based on gray histogram image similarity is proposed, which can realize the measurement of slug frequency. In addition, the technique also has the ability to classify a large number of images, and can quickly find the elongated bubble head, liquid film area and liquid slug area of intermittent flow. On the basis of this technique, combined with image post-processing methods such as gas–liquid interface feature analysis, a set of intermittent flow image processing technique with perfect route is formed. Based on this post-processing technique, the similarity image oscillation trajectories of plug flow and slug flow are obtained. There are differences in the similarity image oscillation trajectories of the two intermittent sub-flow patterns, and the similarity image of the plug flow has an obvious platform period and trailing rising line, which can be used as a basis for the classification of the two intermittent sub-flow patterns. A correlation for predicting the slug frequency of intermittent sub-flow patterns is developed. The accuracy of this slug frequency prediction correlation can be improved by about 10 % compared to not dividing the sub-flow patterns. When the mixture Froude number Frm is less than 5.0, the radial position of the elongated bubble head decreases linearly as the Frm increases. When the Frm is greater than 5.0, the elongated bubble head oscillates near the middle of the pipe. Prediction correlations for the radial position of the elongated bubble head and the slug velocity are established separately, and the maximum error is ± 10 %. The modified mixed Froude number is proposed, and based on this, a new prediction model for the transition from plug flow to slug flow is established.

Analysis of Production Decline Type Curves Considering Water Influx in Naturally Fractured Gas Reservoirs

Abstract In the development of fractured gas reservoirs with edge and bottom water, water invasion is a pervasive issue. However, most production decline analysis models focus on primary depletion with closed boundaries rather than secondary depletion with water influx. Therefore, this paper aims to develop decline type curves for analyzing and interpreting production data from existing natural water influx in fractured gas reservoirs. Firstly, a transient dual porosity flow model is developed considering water influx in naturally fractured gas reservoirs, the functions of Blasingame decline type curves are derived and obtained. Subsequently, the Blasingame production decline type curves of a vertical well in naturally fractured reservoirs experiencing natural water influx are plotted. These new type curves can estimate water invasion and dual medium parameters, offering valuable insights for production decline analysis in fractured reservoirs with water influx. The Blasingame production decline curves are divided into six regimes based on characteristics. Then, the effects of various formation parameters and water invasion cases on the type curves are discussed and analyzed. Compared with Blasingame type curves without water influx at the external boundary, the behaviors of those presented in this paper are quite different at the boundary responses. Finally, through the analysis of a case well, it is found that theoretical type curves considering dual-medium and water invasion are more consistent with actual production data. This suggests that these new type curves provide more accurate estimation for understanding and managing issues related to water invasion in fractured gas reservoirs.

Simulation of bench-scale CO2 injection using a coupled continuum-discrete approach

Unintended releases of CO2 from carbon capture and storage operations presents the risk of atmospheric emissions and groundwater or surface water quality impacts. Given the potential impacts, it is valuable to have tools capable of predicting groundwater concentrations and likely pathways of CO2 migration in the subsurface. Traditional multiphase flow models struggle to simulate the discontinuous flow expected at leakage sites. This work applied a coupled continuum-discrete model, ET-MIP, to simulate a bench-scale injection of CO2. Results demonstrate the capability of ET-MIP to accurately capture gas fingering behaviour, and the complexity of multicomponent mass transfer observed in the experiment. Simulations were computationally efficient, allowing for the use of multiple displacement pressure realizations. CO2 migration in the subsurface was shown to be sensitive to mass transfer, as i) increased groundwater velocity can dissolve leaked CO2 prior to reaching the surface and ii) background dissolved gases in the subsurface can impact the rate of upwards gas movement, gas distribution, and the composition and persistence of the gas phase. The sensitivity to mass transfer suggests it may be preferable to monitor for low-solubility gases in the source mixture rather than CO2. These findings are applicable to other gases in the subsurface, such as hydrogen or methane migrating from geoenergy wells.

Dynamic fluid flow model for phosphate slurry pipeline: OCP main pipeline as case study

The transportation of phosphate slurry through large-scale pipelines presents significant challenges due to the complex behavior of multiphase flows, particularly with varying solid content, density, and dynamic viscosity. Efficient and accurate prediction of flow behavior is critical for optimizing the operation of such pipelines. This work aims to develop a dynamic computational model to simulate phosphate slurry flow in pipelines. The case study focuses on the OCP Group’s main slurry pipeline, which links the mining sites at Khouribga to the industrial plants at Jorf Lasfar, Morocco. This pipeline system spans a total length of 187.124 km, consisting of 5237 pipes with an inner diameter ranging from 0.8546 m to 0.8578 m, and features several elevation changes along its ground level. Using a section-averaged, dynamic approach and the Finite Volume scheme, the model computes essential flow parameters, including density, dynamic viscosity, and pressure, for the incompressible and non-Newtonian slurry and process water flows. The model’s accuracy is validated against on-site measured data, showing an average deviation of ±0.32% for outlet density, and below 10% for pressure along the pipeline, underscoring the model’s reliability. Additionally, a sensitivity analysis was conducted to illustrate the impact of key parameters on the predicted head losses and pressures along the pipeline. This analysis shows that the slurry viscosity is the most critical parameter, significantly influencing these predictions. This model provides high accuracy and reasonable CPU time for real-time simulation and monitoring, while also offering significant potential for optimizing pipeline operations and ensuring the reliability of phosphate transport.

Numerical simulation of carbon dioxide flooding in fractured reservoirs using generic projection-based embedded discrete fracture model

This paper, for the first time, integrates the generic projection-based embedded discrete fracture model (pEDFM) with the commercial reservoir simulator ECLIPSE for carbon dioxide (CO2) flooding in fractured reservoirs. The integrated method first obtains inter-grid connections and corresponding transmissibilities within the reservoir model based on the generic pEDFM. It then constructs an equivalent CO2 flooding ECLIPSE model to the original pEDFM reservoir model, thereby calculating the global equations of the compositional flow model to obtain distributions of pressure, saturation, component concentrations, and well performance data. We implemented three numerical examples to verify that the proposed method can achieve significantly higher computational accuracy compared to the widely used embedded discrete fracture model in both high and low permeability fracture scenarios, while also avoiding the difficulties associated with generating matching grids for complex fracture networks. Furthermore, the proposed integrated method uses the solver within ECLIPSE to solve the global equations, thus avoiding the high cost of developing a robust nonlinear solver for complex compositional model of CO2 flooding. This demonstrates the practicality of the method and its significant potential for subsequent application to various reservoir models.

On the mechanics of conducting micropolar fluids with magnetic particles: Vorticity–microrotation difference

In this paper, mechanisms that differentiate microrotation (i.e., particles' internal rotation) and vorticity in magnetohydrodynamic micropolar flows with magnetic particles are examined. Micropolar fluids are characterized by the asynchronization of the microrotation and the vorticity of the liquid carrier. When the microrotation is equal to the fluid's vorticity, the flow is purely Newtonian. In this context, two classical examples of micropolar magnetohydrodynamic fluids with magnetic particles are used, namely, blood and ferrofluid. The effect of all dimensionless parameters associated with the mathematical model is examined in terms of differentiating microrotation and vorticity. These dimensionless parameters are specifically calculated using the physical properties of the ferrofluid and blood. It was shown that higher values of the rotational viscosity (which are associated with smaller values of the spin relaxation time), higher values of channel's height, and higher values of the microrotation wall parameter tend to equalize microrotation and vorticity. On the other hand, the spin viscosity and the micromagnetorotation (magnetic torque) are mechanisms that differentiate microrotation and vorticity. Lorentz force does not seem to have any noticeable effect on the microrotation–vorticity difference. It is anticipated that this study will reveal the cases where a magnetohydrodynamic micropolar fluid with magnetic particles, such as blood and ferrofluid, can be simplified to a Newtonian one, which brings many benefits associated with a simplified mathematical flow model (such as smaller computational cost and less time).