Numerical Simulation Of Multiphase Flow Research Articles

An encoder-decoder ConvLSTM surrogate model for simulating geological CO2 sequestration with dynamic well controls

In Geological Carbon Sequestration (GCS), effectively managing the project requires predicting state variables such as pressure and saturation. However, numerical simulation of multiphase flow in subsurface porous media involves solving large linear algebra systems, resulting in a substantial computational burden. This can make it impractical for real-time history matching or optimization. Meanwhile, deep learning-based surrogate models are emerging as fast and accurate approximators. This study delves into the application of the Encoder-Decoder Convolutional Long Short-Term Memory (ED-ConvLSTM) neural network for predicting the complex evolution of state variables under dynamic CO2 injection schemes. Inception blocks enhanced with light-weighted attention modules are introduced in the encoder to extract high-dimensional input features. ConvLSTM is employed to propagate spatial temporal information in the low-dimensional latent space. Further, progressive upsampling blocks are used to reconstruct the latent features for the desired output. Instead of taking discrete time steps as an input feature, the proposed network captures the dynamic dependencies with the inherent ConvLSTM cell. The network has access to data at only portion of the initial time steps during training stage, while it is used to predict the state variables at unseen time steps during testing stage. Results show that the network can produce excellent predictions for both pressure and saturation, even at unseen future time steps. The remarkable generalizability to different geological permeability fields is also evaluated. ED-ConvLSTM outperforms the standard U-Net by far, especially when predicting beyond the training time period. These numerical experiments demonstrate the advantages of ED-ConvLSTM in terms of prediction accuracy, extrapolability and generalizability. This study highlights the importance of incorporating recurrent connections into the deep neural networks for simulating time-dependent multiphase flow problems. The proposed methodology has great potential in GCS surrogate modeling and offers a possible approach for real-time optimization of CO2 injection.

Three dimensional interface normal prediction for Volume-of-Fluid method using artificial neural network

In the numerical simulations of multi-phase flow using Volume-of-Fluid (VOF) method, the calculation of the interface normal is a crucial point. In this paper, a machine learning method is used to develop an artificial neural network (ANN) model to make more accurate prediction of the local normal vector from neighboring volume fractions. Spherical surfaces with different radii are intersected with a structural background grid to generate 84328 groups of data: 3×3×3 neighboring volume fractions are used as input, and normal vector as output. Using 90% data as training dataset, the ANN model is well trained by optimizing the number of hidden layers and the number of neurons on each layer. Using the remaining 10% data, normal predictions are made using ANN-VOF and the most used YOUNG and HEIGHT-FUNCTION methods. The RMSE of the ANN-VOF/YOUNG/ HEIGHT-FUNCTION methods are 0.008/0.022/0.045 respectively. In the reconstruction of a sinusoidal surface, the MSE of the ANN-VOF/YOUNG/ HEIGHT-FUNCTION methods are 0.008/0.018/0.041. It is demonstrated that the ANN-VOF method has better performance for interface normal prediction. The proposed method has a simple computational logic and does not need to deal with complex geometric topology, which lays the foundation for application in other more complex grids.

Development of the concept of a multiphase flowmeter

In a number of industries: oil and gas, chemical and nuclear industries, the task of controlling multiphase flow regimes arises. In the nuclear and chemical industries, the flow regime directly affects the nature of technological processes and their safety. In the oil and gas industry, the products extracted from wells are usually a mixture of oil, water and gas, and the task of monitoring the flow regime is related to compliance with the permissible parameters of pumping and control equipment. When using multiphase flowmeters of the flow type, the algorithms for calculating phase flow rates in a multiphase flow are very sensitive to a violation of the uniformity and homogeneity of the measured flow. Excessive noise of the signal of pressure sensors, volume content and flow caused by projectile, cork or stratified modes can negatively affect the accuracy of measurements. As a rule, flow mode maps are used when determining the current mode. This approach is based on the calculation of a number of dimensionless flow parameters (Froude number, Lockhart–Martinelli parameter, etc.). In the case of a dynamically changing flow, this approach may not be suitable. For a more accurate and reliable determination of flow modes, it is proposed to use a direct method of analyzing the spatial distribution of phases in the flow and recognizing the type of flow using artificial convolutional neural networks. This approach allows you to get rid of classification errors and get more accurate information about the flow. The aim of the study is to develop a technique for neural network analysis of images of a multiphase flow with subsequent determination of its type. In the course of the work, approaches to the formation of a training sample are considered, the search for the optimal structure of the neural network is carried out and an accuracy assessment is given for the classification of multiphase flow modes by a convolutional neural network. The study was carried out on two types of data: 1) synthetic images obtained using numerical simulation of multiphase flows, and 2) experimentally obtained flow images on a multiphase flow stand.

Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data

Numerical simulations of multiphase flows are crucial in numerous engineering applications, but are often limited by the computationally demanding solution of the Navier–Stokes (NS) equations. The development of surrogate models relies on involved algebra and several assumptions. Here, we present a data-driven workflow where a handful of detailed NS simulation data are leveraged into a reduced-order model for a prototypical vertically falling liquid film. We develop a physics-agnostic model for the film thickness, achieving a far better agreement with the NS solutions than the asymptotic Kuramoto–Sivashinsky (KS) equation. We also develop two variants of physics-infused models providing a form of calibration of a low-fidelity model (i.e. the KS) against a few high-fidelity NS data. Finally, predictive models for missing data are developed, for either the amplitude, or the full-field velocity and even the flow parameter from partial information. This is achieved with the so-called ‘gappy diffusion maps’, which we compare favourably to its linear counterpart, gappy POD.

Diffuse-Interface Blended Method for Imposing Physical Boundaries in Two-Fluid Flows.

Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are generally defined by a conformal unstructured mesh which, depending on the complexity of the physical system, results in time-consuming mesh generation which frequently requires user-intervention. Furthermore, the resulting conformal unstructured mesh could potentially contain a large number of skewed elements, which is undesirable for numerical stability and accuracy. The diffuse-interface approach allows for the use of a simple structured meshes to be used while still capturing the desired physical (e.g., solid-fluid) boundaries. In this work, a novel diffuse-interface method for the imposition of physical boundaries is developed for the incompressible two-fluid multiphase flow model. This model is appropriate for dispersed multiphase flows which are pervasive in chemical engineering processes, in that this flow regime results in high levels of mass and energy transfer between phases. A diffuse interface is used to define the physical boundaries and boundary conditions are imposed by blending the conservation equations from the two-fluid model with that of the nondeformable solid. The results from the diffuse-interface method are compared with results from a conformal unstructured mesh for different interface functions and widths. For small interface widths, the accuracy of the flow profile is unaffected by the choice of interface function and the phase fraction distribution and flow behavior are within 3% compared to those from a conformal mesh. As the interface width increases, the diffuse-interface solution deviates from the conformal mesh solution in both the localized gas fraction and the overall gas hold-up, resulting in a difference up to 30%. In the case of flow past a cylinder, where the solid interacts with the flow, the presence of the diffuse interface extends the thickness of the solid boundary and results in a deviation from the conformal mesh solution as time increases.

Numerical simulation of multiphase flow and co-gasification of biomass and coal for a new test reactor

Numerical simulation of multiphase flow and co-gasification of biomass and coal for a new test reactor

Pore-scale modeling of two-phase flow: A comparison of the generalized network model to direct numerical simulation.

Despite recent advances in pore-scale modeling of two-phase flow through porous media, the relative strengths and limitations of various modeling approaches have been largely unexplored. In this work, two-phase flow simulations from the generalized network model (GNM) [Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312; Phys. Rev. E 97, 023308 (2018)2470-004510.1103/PhysRevE.97.023308] are compared with a recently developed lattice-Boltzmann model (LBM) [Adv. Water Resour. 116, 56 (2018)0309-170810.1016/j.advwatres.2018.03.014; J. Colloid Interface Sci. 576, 486 (2020)0021-979710.1016/j.jcis.2020.03.074] for drainage and waterflooding in two samples-a synthetic beadpack and a micro-CT imaged Bentheimer sandstone-under water-wet, mixed-wet, and oil-wet conditions. Macroscopic capillary pressure analysis reveals good agreement between the two models, and with experiments, at intermediate saturations but shows large discrepancy at the end-points. At a resolution of 10 grid blocks per average throat, the LBM is unable to capture the effect of layer flow which manifests as abnormally large initial water and residual oil saturations. Critically, pore-by-pore analysis shows that the absence of layer flow limits displacement to invasion-percolation in mixed-wet systems. The GNM is able to capture the effect of layers, and exhibits predictions closer to experimental observations in water and mixed-wet Bentheimer sandstones. Overall, a workflow for the comparison of pore-network models with direct numerical simulation of multiphase flow is presented. The GNM is shown to be an attractive option for cost and time-effective predictions of two-phase flow, and the importance of small-scale flow features in the accurate representation of pore-scale physics is highlighted.

Efficient dissipation-based nonlinear solver for multiphase flow in discrete fractured media

Solving nonlinear equation systems resulting from the Fully Implicit Method (FIM) remains a challenge for numerical simulation of multiphase flow in subsurface fractured media. The Courant numbers can vary orders of magnitude across discrete fracture-matrix (DFM) models because of the high contrasts in the permeability and length-scale between matrix and fracture. The standard Newton solver is usually unable to converge for big timestep sizes.Limited research has been conducted on nonlinear solver techniques for multiphase flow and transport in fractured media. We make an extension of a new dissipation-based continuation (DBC) method to DFM models. Our goal is to prevent timestep cuts and maintain efficient time-stepping for FIM. The DBC algorithm builds a homotopy of the discretized conservation equations through the addition of numerical dissipation terms. We introduce a continuation parameter for controlling the dissipation and ensuring that accuracy of the computed solution will not be reduced. Under the nonlinear framework of DBC, general dissipation operators and adaptive strategies are developed to provide the optimal dissipation matrix for the multiphase hyperbolic system.We assess the new nonlinear solver using multiple numerical examples. Results reveal that the damped-Newton solver suffers from serious restrictions on timestep sizes and wasted iterations. In contrast, the DBC solver provides excellent computational performance. The dissipation operators are able to successfully resolve main convergence difficulties. We also investigate the impact of star-delta transformation which removes the small cells at fracture intersections. Moreover, we demonstrate that an aggressive time-stepping does not affect the solution accuracy.

Case Studies and Operation Features of Long Horizontal Wells in Bazhenov Formation

Summary In this study, unique field data analysis and modeling of operating wells with an extended horizontal wellbore (HW) and multistage hydraulic fracturing (MHF) in the Bazhenov formation were conducted. Moreover, a large amount of long horizontal well data obtained from the Bazhenov formation field was used. Wells with extended HW drilling and MHF are necessary for commercial oil production in the Bazhenov formation. Problems can occur in such wells when operating in the flowing mode and using an artificial lift at low flow rates. This study aimed to describe the field experiences of low-rate wells with extended HWs and MHF and the uniqueness of well operations and complexities. It was also focused on modeling various operation modes of such wells using specialized software and accordingly selecting the optimal downhole parameters and analyzing the sensitivity of fluid properties and well parameters to the well flow. The flow rates in wells with extended HW and MHF decrease in the first year by 70–80% when oil is produced from ultralow-permeability formations. Drainage occurs in a nonstationary mode in the entire life of a well, leading to complexities in operation. A comprehensive analysis of field data [downhole and wellhead pressure gauges, electric submersible pump (ESP) operation parameters, and phases’ flow rate measurements] and fluid sample laboratory studies was conducted to identify the difficulties in various operating modes. For an accurate description of the physical processes, various approaches were used for the numerical simulation of multiphase flows in a wellbore, considering the change in the inflow from the reservoir. The complexities that may arise during the operation of wells were demonstrated by analyzing the field data and the numerical simulation results. The formation of a slug flow in low flow rates in a wellbore was caused by a rapid decline in the production rate, a decrease in the water cut, and an increase in the gas/oil ratio (GOR) over time. Based on the results, proppant particles can be carried into the HW and thereby reduce the effective section of the well in case of high drawdowns in the initial period of well operation. Consequently, the pressure drops along the wellbore increased, and the drawdown on the formation decreased. Other difficulties were determined to be associated with the consequences and technologies of hydraulic fracturing (HF). These effects were shown based on the field data and the numerical simulation results of the flow processes in wells. In addition, corrective measures were established to address various complexities, and the applications of these recommendations in the field were conducted.

Numerical Simulation of Multiphase Flow in Subsurface Reservoirs: Existing Challenges and New Treatments

Numerical Simulation of Multiphase Flow in Subsurface Reservoirs: Existing Challenges and New Treatments

Multiscale multiphase flow simulations using interface capturing and Lagrangian particle tracking

Numerical simulations of multiphase flows with both interfaces and discrete particles are challenging because they possess a wide range of length and time scales. Meanwhile, the volume of fluid (VOF) method is suitable for resolving the interface, while the discrete particle model (DPM) under the Lagrangian frame better simulates unresolvable particles; a multiscale VOF–DPM combined model is urgently needed for multiscale multiphase flows. The present work implements a VOF–DPM solver that includes a two-way transition algorithm to model the transformation between discrete and continuous phases for bubbles or droplets using OpenFOAM. The interface-capturing scheme in the solver is based on the interIsoFoam solver, which supports the geometric reconstruction of the interface and adaptive mesh refinement. A connected component labeling approach is used for particle detection and VOF-to-DPM transition for discrete bubbles or droplets produced by interface breakup. Conversely, a DPM-to-VOF transition algorithm for particles touching the interface is incorporated to achieve a two-way transition. In addition, phase change modeling between continuous phases and bubble dynamic modeling for cavitating flow cases are also implemented in the solver. Test simulations are performed for validation, including the gas–liquid two-phase dam break and cavitating flow in a convergent–divergent test section. The results demonstrate that the solver is reasonably accurate and can adequately represent the complex phase structure, including the interface and discrete particles.

Numerical Simulation of Multiphase Flow in Steel Continuous Casting Mold Using a Novel Euler–Euler–Lagrange Method

Herein, a new Euler–Euler–Lagrange hybrid method is used to simulate the liquid–solid–gas three‐phase flow in a continuous casting mold. In the used method, bubble coalescence and breakup, inclusion aggregation, bubble–inclusion interaction, and complex force balance of bubbles near the solidification front are simultaneously considered. The predicted inclusion size distribution is in good agreement with previous industrial test results. With the application of this method, inclusions can be tracked even if they are collected by bubbles. This characteristic is useful in the study of harmful phenomena in that bubbles are captured by the solidification front after collecting numerous inclusions. Herein, the effects of various simulation factors on results are studied. The descending order of importance of the simulation factors is as follows: bubble–inclusion interaction, bubble coalescence and breakup, and inclusion aggregation. Ignoring any of these factors underestimates the inclusion removal rate and increases the prediction deviation of the inclusion size distribution. Although inclusion aggregation has little effect on the overall removal fraction, it is the most important way to remove small inclusions with a maximum size of 14.14 μm under the conditions of this research.

U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we present U-FNO, a novel neural network architecture for solving multiphase flow problems with superior accuracy, speed, and data efficiency. U-FNO is designed based on the newly proposed Fourier neural operator (FNO), which has shown excellent performance in single-phase flows. We extend the FNO-based architecture to a highly complex CO2-water multiphase problem with wide ranges of permeability and porosity heterogeneity, anisotropy, reservoir conditions, injection configurations, flow rates, and multiphase flow properties. The U-FNO architecture is more accurate in gas saturation and pressure buildup predictions than the original FNO and a state-of-the-art convolutional neural network (CNN) benchmark. Meanwhile, it has superior data utilization efficiency, requiring only a third of the training data to achieve the equivalent accuracy as CNN. U-FNO provides superior performance in highly heterogeneous geological formations and critically important applications such as gas saturation and pressure buildup “fronts” determination. The trained model can serve as a general-purpose alternative to routine numerical simulations of 2D-radial CO2 injection problems with significant speed-ups than traditional simulators.

Numerical Simulation of Multiphase Flow in a Biaxial Agitator for Cyclopentane Hydrate Formation

Numerical Simulation of Multiphase Flow in a Biaxial Agitator for Cyclopentane Hydrate Formation

Development and Validation of a Computational Fluid Dynamics Model for the Optimization of a Sink-Float Separator for Plastics Recycling

The Circular Economy Action Plan, in the context of the European Green deal, introduces new policies which promote a more sustainable use of plastics. These policies also prioritize the optimization of plastics recycling processes by increasing both the amount and quality of plastic recyclates produced, which is to a large extend defined by the purity and yield achieved by state-of-the-art plastic sorting processes. Therefore, the presented research focuses on developing a Computational Fluid Dynamics (CFD) based model to predict and obtain better insights in the separation performance of sink float separators, more specifically Dense Medium Drum (DMD) separators. The flow inside the drum is simulated by adopting an Euler-Lagrangian approach, a widely employed model for the numerical simulation of multi-phase flows including solid particles. To validate the simulations, a transparent lab-scale sink float separator, using the principle of a rotating drum, is constructed. In all experiments, water is used as medium. The separation objects represent a single polymer type which is fed to the drum. For the present work these are Polypropylene (PP), Polystyrene (PS), High Density Polyethylene (HDPE) Acrylonitrilic Butadiene Styrene (ABS), Polycarbonate Acrylonitrile Butadiene Styrene (PC/ABS) grains with a length scale of 3 mm and High Density Polyethylene grains of 4 mm. The separation number is easily expressed as the ratio of objects leaving the sink or float outlet depending on the type of the polymer density to the total amount of separation objects. It was found that the separation numbers computed by the numerical model for all separated objects agree with the measured ones within a maximum error of 7%. When comparing the hydrophilic ABS to the hydrophobic PS, which have similar densities, it is shown that air bubbles have a large influence on the separation efficiency. With the validated CFD model, essential insights are gained on the physics of the flow field inside the separator which help in further optimizing these devices to achieve higher separation efficiencies.

The impact of sub-resolution porosity on numerical simulations of multiphase flow

Sub-resolution porosity (SRP) is a ubiquitous, yet often ignored, feature in Digital Rock Physics. It embodies the trade-off between image resolution and field-of-view, and it is a direct result of choosing an imaging resolution that is larger than the smallest pores in a heterogeneous rock sample. In this study, we investigate the impacts of SRP on multiphase flow in porous rocks. To do so, we use our newly developed Multiphase Micro-Continuum model to perform first-of-a-kind direct numerical simulations of two-phase flow in porous samples containing SRP. We show that SRP properties (porosity, permeability, wettability) can impact predicted absolute permeabilities, fluid breakthrough times, residual saturations, and relative permeabilities by factors of 2, 1.5, 3, and 20, respectively. In particular, our results reveal that SRP can function as a persistent connector preventing the formation of isolated wetting fluid domains during drainage, thus dramatically increasing relative permeabilities to both fluids at low saturations. Overall, our study confirms previous evidence that flow within the SRP cannot be disregarded without incurring significant errors in numerical predictions or experimental analyses of multiphase flow in heterogeneous porous media.

Improved well-balanced free-energy lattice Boltzmann model for two-phase flow with high Reynolds number and large viscosity ratio

Spurious velocities and inaccurate density properties arising from the imbalance of discretized forces at discrete level are frequently observed in numerical simulation of multiphase flows based on lattice Boltzmann equation (LBE) models. In this paper, an improved well-balanced free-energy LBE model is proposed for two phase flows with high Reynolds numbers and large viscosity differences based on the well-balanced LBE [Guo et al., Phys. Fluids 33, 031709 (2021)]. To this end, a free parameter associated with the shear rate is introduced into the equilibrium distribution function. This results in a fluid viscosity that is dependent not only on the relaxation time but also on the introduced parameter. The relaxation time can be chosen to improve the numerical stability and accuracy, while the viscosity is mainly determined by the new parameter. To test the capability of the present model in capturing discrete equilibrium states, both one-dimensional flat interface and two-dimensional stationary droplet are simulated. Numerical results show that the present model is capable of eliminating spurious velocities and maintaining a constant chemical potential when the system reaches an equilibrium state. To further validate the performance of the present LBE for dynamic problems, both binary droplet collision and single bubble rising are performed, which demonstrates that the present model has the capability to deal with two phase flows with high Reynolds number and large viscosity ratio.

Numerical simulation of multiphase flows using an enhanced Volume-of-Fluid (VOF) method

The main objective of the present work is to enhance the stability and accuracy of Volume-of-Fluid (VOF) method for simulating multiphase flow problems with large density ratios and moving interfaces. In order to accomplish this, a novel high-order TVD flux-limiter scheme is developed and applied to approximate the convective fluxes in the momentum, energy and volume fraction equations. Moreover, the classical implicit non-iterative PISO algorithm is modified according to SIMPLER algorithm and the combined model (PISOR) is then employed to handle the pressure-velocity coupling. Furthermore, the piecewise linear interface calculation (PLIC) based on the Efficient Least Squares Volume-of-Fluid Interface Reconstruction Algorithm (ELVIRA) is adopted for the treatment of the interface and curvature estimation. The robustness and consistency of the proposed modifications in handling violent free-surface flows involving interface rupture and coalescence are verified via simulation of several canonical test cases including: dam break over the dry and wet beds, rotating square patch of fluid and Rayleigh-Taylor Instability (RTI). The results show that, the proposed flux-limiter scheme can significantly suppress false-diffusion errors and maintain interface sharpness while preserving the boundedness and positivity of the volume fraction field. Moreover, it is found that the proposed PISOR model has robust convergence behavior in strongly coupled multiphysics problems and provides more stable and consistent results than the standard PISO and SIMPLER algorithms. The performance and efficiency of proposed models are further verified, for single phase flow, through analysis of transient entropy generation due to natural convection heat transfer in differentially heated cavity.

Numerical simulation of multiphase flow in a full coal-direct chemical looping combustion process

Chemical looping combustion (CLC) is a promising clean combustion technology alternative to conventional oxy-combustion, yet the full loop flow details are not well understood. In this work, a multi-fluid model based on the Eulerian-Eulerian framework is used to study the gas-solid hydrodynamics in a full-loop Coal-direct chemical looping (CDCL) combustion unit with a unique moving-bed fuel reactor. The unique fluidization states are described throughout the full-loop system. Then, the influences of several operating conditions on the solid circulation rate and pressure distribution are investigated. It is shown that the solids circulation rate is dominantly controlled by the gas flow rate on the standpipe of the L-valve. Meanwhile, a higher combustor gas velocity reduces the pressure of the whole system and an increased L-valve gas velocity influences the pressure distribution slightly but increases the local pressure at the L-valve. This work provides a cost-effective tool for understanding and optimizing the CDCL process.

Development of singular value decomposition based solution scheme for a numerical simulation of multiphase flow

This paper presents an innovative solution scheme that may resolve the numerical challenges of simulating the phase appearance and disappearance phenomena in multiphase flow. In this study, a least square problem for the mass and internal energy conservation equations is reviewed, and its inherent ill-posedness, originating from the rank deficiency of the coefficient matrix, in the inverse problem is introduced. Since building mathematically well-conditioned matrices is essential to avoiding the numerical instability as well as the singularity of matrices, first of all, a new solution scheme for the mass and internal energy conservation equations for the simulation of multiphase flow in which phase can appear and disappear under various flow conditions is derived based on a truncated Singular Value Decomposition (SVD)-based low rank approximation. The truncated SVD-based low rank approximation is then used to solve the mass and internal energy conservation equations by computing the pseudo inverse of the low rank approximation matrix. The field equations and closure relations currently being developed by introducing arbitrary values, which replace an extremely low volume fraction of fluids, are redefined in this study. As such, the physical phenomena themselves are directly considered without any modifications to the mathematical equations to compute phase transitions. The characteristics of phase transition are classified into convection, vaporization, and condensation over a wide range of fluid conditions, and the verification of the proposed solution method is completed through simulations of the 3 phase transition mechanisms. The SVD-based low rank approximation method improves computations of phase transition as simulation results indicate that the proposed solution scheme describes the physics better than the conventional one.