One-phase Flow Research Articles

Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models

The development of reliable mathematical models and numerical discretization methods is important for the understanding of salt precipitation in porous media, which is relevant for environmental problems like soil salinization. Models on the pore scale are necessary to represent local heterogeneities in precipitation and to include the influence of solution-air-solid interfaces. A pore-network model for saturated flow, which includes the precipitation reaction of salt, is presented. It is implemented in the open-source simulator DuMuX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\ extrm{X}}$$\\end{document}. In this paper, we restrict ourselves to one-phase flow as a first step. Since the throat transmissibilities determine the flow behaviour in the pore network, different concepts for the decreasing throat transmissibility due to precipitation are investigated. We consider four concepts for the amount of precipitation in the throats. Three concepts use information from the adjacent pore bodies, and one employs a pore-throat model obtained by averaging the resolved pore-scale model in a thin-tube. They lead to different permeability developments, which are caused by the different distribution of the precipitate between the pore bodies and throats. We additionally apply two different concepts for the calculation of the transmissibility. One obtains the precipitate distribution from analytical assumptions, the other from a geometric minimization principle using a phase-field evolution equation. The two concepts do not show substantial differences for the permeability development as long as simple pore-throat geometries are used. Finally, advantages and disadvantages of the concepts are discussed in the context of the considered physical problem and a reasonable effort for the implementation and computational costs.

Estimation of Friction for a Hydrodynamic Sliding Bearing for the Turbulent Regime From Single-Phase and Two-Phase Fluid Flow Behaviour

The hydrodynamic plain bearing relies on the generation of a lubricant film through the rotational movement of the journal. As the journal rotates, it creates a layer of lubricant between the bearing and journal surfaces. This lubricant film separates the two surfaces, preventing direct contact and minimizing friction and wear. The high speeds can lead to severe conditions such as cavitation due to rapid oil evaporation, which introduces a new phase into the flow. In this study, it is anticipated that a two-phase flow will occur through the shaft-bushing conjunction because of the rupture of the lubricating film near the contact outlet. Pressure disturbances above these rupture zones may induce vapor-cavity formation at a small scale. A numerical analysis was conducted by solving Navier–Stokes continuity equations and vapor-transport equations. The k-epsilon model was used to analyze friction at the fluid-bearing interface for the turbulent regime. The results indicate that higher flow velocity values and pressure were observed in the case of two-phase flow compared to one-phase flow.

Velocity of viscous fingers in miscible displacement: Intermediate concentration

We investigate one-phase flow in porous medium corresponding to a miscible displacement process in which the viscosity of the injected fluid is smaller than the viscosity in the reservoir fluid, which frequently leads to the formation of a mixing zone characterized by thin fingers. The mixing zone grows in time due to the difference in speed between its leading and trailing edges. The transverse flow equilibrium (TFE) model provides estimates of these speeds. We propose an enhancement for the TFE estimates, and provide its theoretical justification. It is based on the assumption that an intermediate concentration exists near the tip of the finger, which allows to reduce the integration interval in the speed estimate. Numerical simulations were conducted that corroborate the new estimates within the computational fluid dynamics model. The refined estimates offer greater accuracy than those provided by the original TFE model.

Comparing Different Coupling and Modeling Strategies in Hydromechanical Models for Slope Stability Assessment

The dynamic interaction between subsurface flow and soil mechanics is often simplified in the stability assessment of variably saturated landslide-prone hillslopes. The aim of this study is to analyze the impact of conventional simplifications in coupling and modeling strategies on stability assessment of such hillslopes in response to precipitation using the local factor of safety (LFS) concept. More specifically, it investigates (1) the impact of neglecting poroelasticity, (2) transitioning from full coupling between hydrological and mechanical models to sequential coupling, and (3) reducing the two-phase flow system to a one-phase flow system (Richards’ equation). Two rainfall scenarios, with the same total amount of rainfall but two different relatively high (4 mm h−1) and low (1 mm h−1) intensities are considered. The simulation results of the simplified approaches are compared to a comprehensive, fully coupled poroelastic hydromechanical model with a two-phase flow system. It was found that the most significant difference from the comprehensive model occurs in areas experiencing the most transient changes due to rainfall infiltration in all three simplified models. Among these simplifications, the transformation of the two-phase flow system to a one-phase flow system showed the most pronounced impact on the simulated local factor of safety (LFS), with a maximum increase of +21.5% observed at the end of the high-intensity rainfall event. Conversely, using a rigid soil without poroelasticity or employing a sequential coupling approach with no iteration between hydromechanical parameters has a relatively minor effect on the simulated LFS, resulting in maximum increases of +2.0% and +1.9%, respectively. In summary, all three simplified models yield LFS results that are reasonably consistent with the comprehensive poroelastic fully coupled model with two-phase flow, but simulations are more computationally efficient when utilizing a rigid porous media and one-phase flow based on Richards’ equation.

The development of simultaneous transducer ultrasonic with dual-transducer to measure flow velocity in the pipe

There are still several obstacles to calculating fluid flow rate measurement on custody transfer, such as the distribution of one-phase fluid flow rate, less sTable pressure, and fluid flow rate changes, which are still the main problems in the process of a measuring system. To calculate the flow rate of one phase fluid, there is a method often used, namely transit time. In practice, the transit time works to send the ultrasonic pulse from upstream to downstream, which had to have a delay because the transducer must switch the function of a transducer to become transmitter or receiver. So, this paper proposed a new strategy of measurement multipath ultrasonic flowmeter (UFLW) with a simultaneous transit time method using a dual transmitter and receiver. The simultaneous method is a measuring technique that utilizes a pair of ultrasonic transducers as both trigger and receiver. The first transducer serves as the transmitter, while the second functions as the receiver, capturing the signal at the same time without changing their positions or roles. In order to implement the configuration setup, let’s try to use 3 paths configuration with 6 pairs of transducers, 3 on the upstream and 3 on the downstream. To estimate the flow velocity, let’s use long short-term memory (LSTM), which is one of the recurrent neural networks (RNN) architectures in the deep learning algorithm, and to evaluate the performance, let’s use the Bland-Altman plot and root mean squared error (RMSE) and validation loss of the LSTM model. The result shows RMSE 0.289 from the actual flow velocity, which means an LTSM with simultaneous multipath ultrasonic can reduce the error between prediction and actual measurement

Interaction of the fluid film with the oncoming steam flow in the thermosiphon transport zone

If the liquid film flows from the wall of the channel down and the core of the flow consists of one wind mixture of steam and small liquid drops, then this is called the flow mode of the steam-water mixture. In this case, a one-phase flow theory can be used, which provides the easiest way to study two-phase flows. Steam is a mixture of water, perceived as a quasicontinuum, for which the average properties of the flow are determined. The liquid film reacts with the approaching flow in the opposite direction of the phases with high humidification on their surfaces. In this case, external and internal problems of the flow of the hydrogen vapor mixture along the wall of the channel and the flow of the film will be considered. They can be expressed through the movement of velocities and phases on the surface of the film due to the increase in the interference between them.

Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions

In order to study the efficiency of the various forms of trapping including mineral trapping scenarios for CO2 storage behavior in deep layers of porous media, highly nonlinear coupled diffusion-advection-reaction partial differential equations (PDEs) including kinetic and equilibrium reactions modeling the miscible multiphase multicomponent flow have to be solved. We apply the globally fully implicit PDE reduction method (PRM) developed 2007 by Kräutle and Knabner for one-phase flow, which was extended 2019 to the case of two-phase flow with a pure gas in the study of Brunner and Knabner. We extend the method to the case of an arbitrary number of gases in gaseous phase, because CO2 is not the only gas that threats the climate, and usually is accompanied by other climate killing gases. The application of the PRM leads to an equation system consisting of PDEs, ordinary differential equations, and algebraic equations. The Finite Element discretized / Finite Volume stabilized equations are separated into a local and a global system but nevertheless coupled by the resolution function and evaluated with the aid of a nested Newton solver, so our solver is fully global implicit. For the phase disappearance, we use persistent variables which lead to a semismooth formulation that is solved with a semismooth Newton method. We present scenarios of the injection of a mixture of various gases into deep layers, we investigate phase change effects in the context of various gases, and study the mineral trapping effects of the storage technique. The technical framework also applies to other fields such as nuclear waste storage or oil recovery.

Hydraulic losses in cryogenic pipelines

The pressure loss in cryogenic pipelines for the cases with one-phase flow is specified via known hydraulic formulas for general fluids. The stream of two-phase flow causes troubles for hydraulic calculation of cryogenic pipeline. There are three main types of cryogenic flow in the pipelines. First type is characterized with quite equal distribution of liquid throughout stream phase of gas (homogenous gas-liquid mixture), second type – with the structure of gas and fluid in separate layers, and the third one – with the motion of fluid in the ring part of pipe walls and high speed of gas in its central part. The paper offers a calculation formula for the estimation of hydraulic resistance (losses) for hydraulic calculation of multi-phase cryogenic pipelines in the presence of thermal exchange with environment when pressure losses are associated with the force of gravity and friction.

A Direct Numerical Simulation Investigation of the One-Phase Flow in a Simplified Emulsification Device

Abstract More detailed investigation of the flow inside emulsification devices, e.g., High-pressure homogenizers (HPHs) helps the industry to broaden the fundamental understanding of the working principle of these machines which in turn will pave the road to increase the breakup efficiency of emulsification processes. Direct numerical simulation (DNS) is not deemed as a practical method in industry due to the high computational cost and time. This study is the first DNS carried out on a model of an emulsification device model. The goal of this study is to set a benchmark for future CFD investigations using industrially favorable tools (RANS, LES, etc.). A scale-up model HPH is designed and the results show a successful modeling of the flow field mimicking the flow behavior inside a typical HPH.

A Comparison of Computational and Experimental Fluid Dynamics Studies between Scaled and Original Wing Sections, in Single-Phase and Two-Phase Flows, and Evaluation of the Suggested Method

The correlation between computational fluid dynamics (CFD) and experimental fluid dynamics (EFD) is crucial for the behavior prediction of aerodynamic bodies. This paper’s objective is twofold: (1) to develop a method that approaches commercial CFD codes and their link with EFD in a more efficient way, using a downscaled model, and (2) to investigate the effect of rain on the aerodynamic behavior of a wing. More specifically, we investigate the one-phase and two-phase flow over a typical wing section NACA 641-212 airfoil, in the commercial code Ansys Fluent. Two computational models were developed; the first model represents the original dimensions of the wing, while the second is downscaled to 23% of the original. The response of the models in air and air–water flow were primarily studied, as well as the impact on aerodynamic efficiency due to the existence of the second phase. For the computational fluid dynamics simulations, a pressure-based solver with a second-order upwind scheme for the spatial discretization and the Spalart–Allmaras (SA) turbulence model were utilized. Meanwhile, for the two-phase flow of air–water, the discrete phase model (DPM) with wall–film boundary conditions on the surface of the wing and two-way coupling between continuous and discrete phase was considered. The second phase was simulated as water droplets injected in the continuous phase, in a Euler–Lagrange approach. The experimental model was constructed in accordance with the downscaled model and tested in a subsonic wind tunnel, using 3D printing technology which reduced the experiment expenses. The presence of water in two-phase flow was proven to deteriorate the aerodynamic factors of the wing compared to one-phase flow, as expected. The three-stage comparison of CFD and EFD results showed a very good convergence, in both single and two-phase flow. This can lead to the conclusion that a rapid and low-cost study for the estimation of the aerodynamic performance of objects with high accuracy is feasible with the suggested method.

A combined volume of fluid and immersed boundary method for free surface simulations induced by solitary waves

A combined volume of fluid and immersed boundary method is developed to simulate free surface flow induced by solitary waves. The simulations of problems involving free boundaries with large deformations are known to be challenging due to the discontinuity of density and momentum flux across the interface. In order to reduce the spurious velocities and prevent unphysical tearing of the interface, an extra velocity field is designed to extend the velocity of the water into the air and to enforce a new boundary condition near the free surface. The free surface is captured using a new Volume of Fluid (VOF) method and a boundary layer is built on the air side by an immersed boundary method. A density-weight smoothing approach is used to reconstruct the velocities inside the boundary layer. The accuracy of the new solver is verified by two benchmark problems, the propagation of a solitary wave in constant depths and run-up of a solitary wave on a slope. The performances of the new solver are compared with the original VOF solver, analytical solutions and one-phase flow solver results, and better results are obtained. The simulation of a plunging wave breaking on a slope further demonstrates the capability of the new solver to capture strong air-water interactions. It is shown to improve the robustness and stability of two-phase flow simulations and higher accuracy can be obtained on a relatively coarse grid compared to the original volume of fluid method.

Forecasting the impact of formation damage on relative permeability during low-salinity waterflooding

Low-salinity waterflooding is considered to be an advanced oil recovery method, but the main mechanism behind the increase in oil recovery factor is still under investigation. Fines migration has been recognized to be one of the mechanisms responsible for the increase in oil production. In this case, the increase in oil recovery happens as a result of increased sweep efficiency and consequent reduction of residual oil. The release of particles due to reduction of electrostatic forces results in flux diversion to previously unswept areas in the reservoir, increasing oil recovery. This paper provides a better understanding of the effects of formation damage during low-salinity water injection in Berea sandstones and proposes a methodology to forecast its effects on water relative permeability. We have performed one- and two-phase flow coreflood experiments with varying salinity of the injected solution. The effluent was analysed for salinity, pH and particle concentration. The laboratory data was treated using a mathematical model that accounts for permeability impairment during low-salinity waterflooding due to fines detachment, migration and capture in small pore throats. The parameters of the model were used to predict the impact of formation damage on the water relative permeability during two-phase flow. The mathematical model matched the laboratory data for pressure drop and particle concentration in the outlet with great accuracy. A methodology to predict the impact of formation damage in two-phase flow using one-phase flow data was proposed. A good agreement between the predicted and the measured water relative permeabilities was obtained. The forecasted water relative permeability curve was able to reproduce the non-monotonic behaviour of water relative permeability due to low-salinity water injection.

Flow near porous media boundaries including inertia and slip: A one-domain approach

This work addresses the macroscopic modeling of flow near porous media boundaries. This includes the vicinity with a fluid channel (i.e., a fracture), another rigid porous medium, or an impervious non-deformable solid. The analysis is carried out for one-phase, steady, incompressible, inertial, and isothermal flow of a Newtonian fluid, considering slip effects at the solid–fluid interfaces. A one-domain approach is proposed, employing a simplified version of the volume averaging method, while conceiving the system as two homogeneous regions separated by an inter-region. The upscaling procedure yields a closed macroscopic model including a divergence-free average (filtration) velocity for the mass balance equation and a unique momentum equation having a Darcy structure. The latter involves apparent permeability tensors that are constant in the homogeneous regions and position-dependent in the inter-region. All the permeability tensors are determined from the solution of coupled closure problems that are part of the developments. The derived model is validated by comparisons with direct numerical simulations in several two-dimensional configurations, namely, two porous media of contrasted properties in direct contact or separated by a fracture, the boundaries being either flat or wavy and a porous medium in contact with a flat or corrugated solid wall or separated from the latter by a fluid layer. The simplicity and versatility of the derived model make it an interesting alternative to existing one- and two-domain approaches developed so far.

High-Order Hybridizable Discontinuous Galerkin Formulation for One-Phase Flow Through Porous Media

We present a stable high-order hybridizable discontinuous Galerkin (HDG) formulation coupled with high-order diagonal implicit Runge–Kuta (DIRK) schemes to simulate slightly compressible one-phase flow through porous media. The HDG stability depends on the selection of a single parameter and its definition is crucial to ensure the stability and to achieve the high-order properties of the method. Thus, we extend the work of Nguyen et al. in J Comput Phys 228, 8841–8855, 2009 to deduce an analytical expression for the stabilization parameter using the material parameters of the problem and the Engquist-Osher monotone flux scheme. The formulation is high-order accurate for the pressure, the flux and the velocity with the same convergence rate of P+1, being P the polynomial degree of the approximation. This is important because high-order methods have the potential to reduce the computational cost while obtaining more accurate solutions with less dissipation and dispersion errors than low order methods. The formulation can use unstructured meshes to capture the heterogeneous properties of the reservoir. In addition, it is conservative at the element level, which is important when solving PDE’s in conservative form. Moreover, a hybridization procedure can be applied to reduce the size of the global linear system. To keep these advantages, we use DIRK schemes to perform the time integration. DIRK schemes are high-order accurate and have a low memory footprint. We show numerical evidence of the optimal convergence rates obtained with the proposed formulation. Finally, we present several examples to illustrate the capabilities of the formulation.

Modeling, multi-objective optimization and comparison of fire and water tube heat recovery steam generators for gas engine cogeneration plants

An innovative modeling and optimizing of fire and water tube heat recovery steam generators (HRSG) for gas engine cogeneration plant are performed here. In modeling section, the equations of ɛ-NTU, LMTD and heat transfer coefficients for one-phase flow and two-phase flow are organized to form a nonlinear system of equations. Furthermore, in the next step, two pairs of objective functions (annual expenses—exergy destruction rate and annual expenses—thermal effectiveness) are selected for multi-objective optimization of HRSG by the use of genetic algorithm for one, two and three MW gas engine cogeneration plants. Results for a 2 MW gas engine (as an example) show that the fire tube HRSG total expenses are 50% lower than that for water tube HRSG. In this situation, for water and fire tube boilers, the effectiveness and cost are 0.9, 40,000 ($/year) and 0.9, 20,000 ($/year), respectively. Furthermore, the exergy destruction rates are close and equal to 1373.45 kW and 1366.2 kW for water tube and fire tube boilers, respectively. Moreover, for each gas engine, six equations with thirty constant coefficients are obtained to explain the behavior of HRSG outlet exhaust gas temperature, pinch temperature difference, steam generation mass flow rate, working pressure, thermal effectiveness and exergy destruction rate at partial load.

A novel one-domain approach for modeling flow in a fluid-porous system including inertia and slip effects

A new one-domain approach is developed in this work yielding an operational average description of one-phase flow in the classical Beavers and Joseph configuration including a porous medium topped by a fluid channel. The model is derived by considering three distinct regions: the homogeneous part of the porous domain, the inter-region, and the free fluid region. The development is carried out including inertial flow and slip effects at the solid–fluid interfaces. Applying an averaging procedure to the pore-scale equations, a unified macroscopic momentum equation, applicable everywhere in the system and having a Darcy form, is derived. The position-dependent apparent permeability tensor in this model is predicted from the solution of two coupled closure problems in the inter-region and in the homogeneous part of the porous medium. The performance of the model is assessed through in silico validations in different flow situations showing excellent agreement between the average flow fields obtained from direct numerical simulations of the pore-scale equations in the entire system and the prediction of the one-domain approach. Furthermore, validation with experimental data is also presented for creeping flow under no-slip conditions. In addition to the fact that the model is general from the point of view of the flow situations it encompasses, it is also simple and novel, hence providing a practical and interesting alternative to models proposed so far using one- or two-domain approaches.

Validation of the Moody and Henry–Fauske Critical Flow Models in apros Against Marviken Critical Flow Experiments

Abstract The Moody and Henry–Fauske critical flow models implemented in Advanced Process Simulation Software (apros) have been validated against Marviken critical flow experiments and compared with other available simulations of the same experiments. Both models in combination with discharge coefficient 0.75 (suggested for best estimate calculations) produce results close to the experimental data for two-phase flows, while one-phase flow of subcooled water is underpredicted. Using discharge coefficient 1.0 for subcooled water leads to a good match with the experimental results, while two-phase flows become overpredicted.

Performance numerical analysis of thermoelectric generator sizing for integration into a high temperature proton exchange membrane fuel cell

This paper presents a three-dimensional finite element analysis that couples the high temperature proton exchange membrane fuel cell (HT-PEMFC) and thermoelectric generator into a single model. The proposed model is aimed to accurately simulate this hybrid system by implementing the laminar one-phase flow, concentrated species, ideal gas law physics, electrochemical dynamics of the HT-PEMFC, and the thermoelectric effect of the thermoelectric generator. Furthermore, the thermoelectric generator size, characterized by the number of thermocouple legs, has also been varied to additionally analyze how this parameter will influence the thermoelectric generator and HT-PEMFC’s performances under an identical 353.15 K temperature boundary condition that is representative of domestic hot water. Results show that, for a 7.5 cm by 3 cm fuel cell, increasing the thermoelectric generator size would also increase the current density, heat generated and the output power of the fuel cell. However, higher cathode water and hydrogen concentrations by around 25% and 7% respectively were also found from using a larger thermoelectric generator, which is not favorable from the lifetime perspective. Moreover, adopting a smaller thermoelectric generator size such as the one with 2 pairs of thermocouples increased the thermoelectric generator’s output efficiency to around 1.2%.

Hp-discontinuous Galerkin Finite Element Method for Incompressible Miscible Displacement in Porous Media

We used (hp-DGFEM) for solving the coupled system of incompressible miscible displacement problem in porous media. Flow and transport equations are solved by hp-symmetric interior penalty Discontinuous Galerkin (hp-SIPG) method. We prove the error analysis in the energy norm to the coupled system of incompressible one-phase flow problem.

A new and consistent well model for one-phase flow in anisotropic porous media using a distributed source model

A new well model for one-phase flow in anisotropic porous media is introduced, where the mass exchange between well and a porous medium is modeled by spatially distributed source terms over a small neighborhood region. To this end, we first present a compact derivation of the exact analytical solution for an arbitrarily oriented, infinite well cylinder in an infinite porous medium with anisotropic permeability tensor in R3, for constant well pressure and a given injection rate, using a conformal map. The analytical solution motivates the choice of a kernel function to distribute the sources. The presented model is independent from the discretization method and the choice of computational grids. It can be applied to porous media with full anisotropic permeability tensors. In numerical experiments, the new well model is shown to be consistent and robust with respect to rotation of the well axis, rotation of the permeability tensor, and different anisotropy ratios. Finally, a comparison with a Peaceman-type well model suggests that the new scheme leads to an increased accuracy for injection (and production) rates for arbitrarily-oriented pressure-controlled wells.