Multiphase Fluid Flow Research Articles

On the Performance of the Node Control Volume Finite Element Method for Modeling Multi-phase Fluid Flow in Heterogeneous Porous Media

In this paper, we critique the performance of the node control volume finite element (NCVFE) method for modeling multi-phase fluid flow in heterogeneous media. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them. Material properties are defined on elements, while transport is simulated on the control volumes. These two meshes are not aligned producing inaccurate results and artificial fluid smearing when modeling multi-phase fluid flow in heterogeneous media. We perform numerical tests to quantify and visualize the extent of this artificial fluid smearing in domains with different material properties. The domains are composed of tetrahedron finite elements. Large artificial fluid smearing is observed in coarse meshes; however, it decreases with the increase in mesh resolution. These findings prompt the use of high-resolution meshes for the method and the need for development of novel numerical methods to address this unphysical flow.

Multi-phase fluid flow simulation by using peridynamic differential operator

The problems of multi-phase fluid flows are often encountered in engineering. In this study, a non-local numerical model of multi-phase fluid flows in the Lagrangian description is developed. Based on the peridynamic theory, a peridynamic differential operator is proposed which can convert any arbitrary order of differentials into their integral form without calculating the peridynamic parameters. Therefore, the Navier-Stokes equations including the surface tension forces are reformulated into their integral form. Subsequently, an updated Lagrangian algorithm for solving the multi-phase fluid flow problems is proposed. Besides, the particle shifting technology and moving least square algorithm are also adopted to avoid the possible tension instability. Finally, several benchmark multi-phase fluid flow problems such as two-phase hydrostatic problem, two-phase Poiseuille flow, and 2D square droplet deformation are solved to validate the proposed non-local model. It can be concluded from the current study that the peridynamic differential operator can be applied as an alternative method for multi-phase fluid flow simulation.

The role of incremental magma chamber growth on ore formation in porphyry copper systems

Porphyry copper deposits are formed by fluids released from felsic magmatic intrusions of batholithic dimensions, which are inferred to have been incrementally built up by a series of sill injections. The growth of the magma chamber is primarily controlled by the volumetric injection rate from deeper-seated magma reservoirs, but can further be influenced by hydrothermal convection and fluid release. To quantify the interplay between magma chamber growth, volatile expulsion and hydrothermal fluid flow during ore formation, we used numerical simulations that can model episodic sill injections in concert with multi-phase fluid flow. To build up a magma chamber that constantly maintains a small region of melt within a period of about 50 kyrs, an injection rate of at least 1.3 x 10−3 km3/y is required. Higher magma influxes of 1.9 to 7.6 x 10−3 km3/y are able to form magma chambers with a thickness of 2 to 3 km. Such an intrusion continuously produces magmatic volatiles which can precipitate a copper ore shell in the host rock about 2 km above the fluid injection location. The steady fluid flux from such an incrementally growing magma chamber maintains a stable magmatic fluid plume, precipitating a copper ore shell in a more confined region and resulting in higher ore grades than the ones generated by an instantaneous emplacement of a voluminous magma chamber. Our simulation results suggest that magma chambers related to porphyry copper deposits form by rapid and episodic injection of magma. Slower magma chamber growth rates more likely result in barren plutonic rocks, although they are geochemically similar to porphyry-hosting plutons. However, these low-frequency sill injection events without a significant magma chamber growth can generate magmatic fluid pulses that can reach the shallow subsurface and are typical for high-sulfidation epithermal deposits.

CFD Simulations of Multiphase Flows: Interaction of Miscible Liquids with Different Temperatures

The incorporation of new equations to extend the applicability of open-source computational fluid dynamics (CFD) software according to the user’s needs must be complemented with code verification and validation with a representative case. This paper presents the development and validation of an OpenFOAM®-based solver suitable for simulating multiphase fluid flow considering three fluid phases with different densities and temperatures, i.e., two miscible liquids and air. A benchmark “dam-break” experiment was performed to validate the solver. Ten thermistors measured temperature variations in different locations of the experimental model and the temperature time series were compared against those of numerical probes in analogous locations. The accuracy of the temperature field assessment considered three different turbulence models: (a) zero-equation, (b) k-omega (Reynolds averaged simulation; RAS), and (c) large eddy simulation (LES). The simulations exhibit a maximum time-average relative and absolute errors of 9.3% and 3.1 K, respectively; thus, the validation tests proved to achieve an adequate performance of the numerical model. The solver developed can be applied in the modeling of thermal discharges into water bodies.

Onset dynamics of air-water menisci on rock fracture surfaces

ABSTRACT Information on menisci dynamics and equilibrium contact angles, θe, is needed for modeling multiphase flow of fluids in geologic formations. The wettability of fracture faces is relevant to applications such as waterflooding in enhanced oil recovery and evaluation of caprock integrity for geologic carbon sequestration. We investigated the vertical capillary rise of air-water menisci on exposed fracture faces for a sandstone, a shale, and three granites. The experimental design approximated that employed in the Wilhelmy plate method. Replicate fracture faces were prepared by fracturing cylindrical rock cores using the Brazilian method and splitting the fractured cores apart along their fracture planes. Meniscus onset was imaged from a cross-sectional perspective using dynamic neutron radiography, and quantified with change point analysis. An existing model for meniscus onset fitted the experimental data very well (median R2 = 0.96). Capillary rise was typified by t 2 3 scaling (where t is time), followed by a constant equilibrium height, ze. The average time taken for the menisci to reach ze was 0.39 s, with no differences between rock types. The menisci achieved a greater vertical extent on the fracture faces of the sedimentary rocks as compared to those of the granites. Apparent θe values were calculated from the best fit estimates of ze using the Wilhelmy plate equation for a smooth and planar vertical surface. Despite the fractal roughness of some of the fracture faces, there was a significant linear relationship (R2 = 0.80) between the apparent θe values and intrinsic θe values measured on polished surfaces of the same rocks using the sessile drop method. The regression equation indicated the apparent θe values were consistently greater than the intrinsic values. This overestimation may be due to averaging of pixels at the air-water-solid interface, a required step in the image analysis. Further exploration of the range of applicability and measurement accuracy of this proposed new technique would be valuable.

Design Space Exploration of Turbulent Multiphase Flows Using Machine Learning-Based Surrogate Model

This study focuses on establishing a surrogate model based on machine learning techniques to predict the time-averaged spatially distributed behaviors of vaporizing liquid jets in turbulent air crossflow for momentum flux ratios between 5 and 120. This surrogate model extends a previously developed Gaussian-process-based framework applicable to laminar flows to accommodate turbulent flows and demonstrates that in addition to detailed fields of primitive variables, second-order turbulence statistics can also be predicted using machine learning techniques. The framework proceeds in 3 steps—(1) design of experiment studies to identify training points and conducting high-fidelity calculations to build the training dataset; (2) Gaussian process regression (supervised training) for the range of operating conditions under consideration for gaseous and dispersed phase quantities; and (3) error quantification of the surrogate model by comparing the machine learning predictions with the truth model for test conditions (i.e., conditions not used for training). The framework was trained using data generated by high-fidelity large eddy simulation (LES)-based calculations (also referred to as the truth model), which solves the complete set of conservation equations for mass, momentum, energy, and species in an Eulerian reference frame, coupled with a Lagrangian solver that tracks the dispersed phase. Simulations were conducted for the range of momentum flux ratios between 5 and 120 for liquid water injected into crossflowing air at a pressure of 1 atm and temperature of 600 K. Results from the machine-learned surrogate model, also called emulations, were compared with the truth model under testing conditions identified by momentum flux ratios of 7 and 40. L1 errors for time-averaged field quantities, including velocity magnitudes, pressure, temperature, vapor fraction of the evaporated liquid, and turbulent kinetic energy in the gas phase, and spray penetration and Sauter mean diameters in the dispersed phase are reported. Speedup of 65 was achieved with this emulator when compared against LES simulation of the same test conditions with errors for all quantities below 14%, thus demonstrating the potential benefits of using machine learning techniques for design space exploration of devices that are based on turbulent multiphase fluid flows. This is the first effort of its kind in the literature that demonstrates the application of machine learning techniques on turbulent multiphase flows.

Micro-Sweep Characteristics of CO2 Flooding

In this paper a micro multi-phase flow equation is built based on the mechanism of a multi-phase fluid flow in porous media. The authors consider the impact of convection diffusion and the improved component mixing rule. In order to accurately evaluate the fluid flow in a low permeability reservoir, two models are established to simulate simple pore throat structure and complex pore throat structure. The predicted residual oil distribution characteristics of CO2 flooding in low permeability reservoir, calculated by finite element microsimulation, have been further verified by experiment. Furthermore, we analyze the effect of different wettability on microflow characteristics of CO2 flooding. The results show that CO2 flooding improving microsweep volume by convective diffusion is more evident in low permeability reservoirs than in high permeability reservoirs. The residual oil is mainly distributed following a pattern of prismatic, wedge-shape, or membrane microstructure. With decrease in the wetting angle on the fluid-rock boundary, the efficiency of oil displacement is further improved.

Melting and Flowing Behavior of Mold Flux in a Continuous Casting Billet Mold for Ultra-High Speed

High casting speed coincides with the development trend of billet continuous casting, which significantly changes the casting characteristics. A mathematical model of the billet mold, which includes multiphase fluid flow, transient heat transfer, and solidification during ultra-high speed of the casting process was developed. The model is first applied to investigate the flow field of molten steel in the mold, studying the influence of steel flow upon the melting and flowing behavior of mold flux. The temperature and velocity distributions of the flux pool that formed above the molten steel surface are described. A parametric study on the melting temperature and viscosity of mold flux on liquid flux thickness and flow velocity is then carried out. Finally, the model is used to derive the relationship between interfacial tension and level fluctuations. The predictions provide an improved understanding of the melting and flowing behavior of mold flux in the billet mold and give the guidance for the design and optimization of mold flux for ultra-high speed of billet casting.

A 6M digital twin for modeling and simulation in subsurface reservoirs

A 6M digital twin for modeling and simulation in subsurface reservoirs

Changes of Multiphase Flow Patterns during Steel Tapping with Simultaneous Argon Bottom Stirring in the Ladle

Changes of unsteady multiphase fluid flow patterns of liquid steel during electric arc furnace-ladle tapping operations, with simultaneous argon bottom injection, are simulated using interfacial tracking computing techniques. The impinging steel jet interacts with the argon bubbling plume, suffering mutual bending effects, and imparting non-symmetric flows of liquid steel during the whole ladle filling time. At low bath levels, radial recirculating flows are generated and at high bath levels, these flows are substituted by vertical long flows generated by the permanent interaction between the impinging jet and the argon plume. Turbulence intensity increases as the bath level rises. Low bath levels are suitable for pre-melting and preheating ferroalloy particles. High bath levels of steel in the ladle, close to total ladle filling, are the most suitable conditions for thermal and chemical homogenizations. Argon gas forms an intermittent blanket over the air–liquid steel mix due to its higher density than air during the whole ladle filling time.

Using Unsupervised Machine Learning to Characterize Capillary Flow and Residual Trapping

AbstractRecent research has highlighted the impact mesoscale heterogeneity can have on larger‐scale multiphase fluid flow properties. However, currently, there is no consensus on how to quickly and reliably analyze coreflooding experimental data to gain insights into mesoscale capillary‐dominated flow behaviors and how rock petrophysical properties affect such behaviors. In this study, we combine a machine learning‐based clustering method with physics‐based hypothesis testing to analyze multistage steady‐state coreflooding experimental data. By examining five different sets of coreflooding data, we have found that under capillary‐dominated flow regimes, voxel‐level CO2 saturation fields are much more heterogeneous as capillary equilibrium is approached. CO2 saturation time series behaviors are distinctively different between high and low permeability voxels. However, the effect of mesoscale permeability greatly diminishes under viscous‐dominated flow regimes. By computing the maximum and optimal number of clusters on the CO2 saturation time series data, we are able to differentiate between these two flow regimes. Through this analysis method, it is now also possible to identify regions within a sandstone core with capillary heterogeneity trapping behaviors. It is confirmed that capillary heterogeneity trapping indeed occurs upstream of capillary barriers. Furthermore, we have discovered a new type of capillary heterogeneity trapping—one that occurs within the capillary barrier itself, which can cause parts of the core to achieve residual CO2 saturations much higher than expected based on existing models of residual gas trapping.

Review of measurement techniques for void fraction of two-phase flow through annulus

This paper presents a state of the art measurement and imaging systems used to determine the Gas Void Fraction (GVF) of two-phase flow through annuli. Several research works were conducted for GVF measurement of two and three-phase fluids flowing through full circular pipelines but only few of them targeted the annuli. The highly restricted access and the low volume within which the multiphase fluid flows through in annuli make the instrumentation design challenging. This is especially true if non-intrusive sensors are required to not disturb the flow, which is the case, for instance, if an accurate CFD modeling of annulus flow is sought out of these measurements. Motivated by the numerous industrial applications of annuli, several researchers have suggested various corresponding non-invasive GVF measurement devices to better understand the behavior of the annulus flow and also to determine the production rate. Many of these techniques are based on electrical conductivity measurements using one or several pairs of electrodes. Various configurations of the electrodes were suggested and this paper highlights that none of them can cope with all kinds of flow patterns. Imaging techniques using wire mesh and electrical resistance tomography were also suggested and the initial corresponding results were very encouraging. This paper provides a critical review of each of these techniques and highlights the advantages, disadvantages, and limitations of each one. Hence, it can be a valuable research reference for either new scientists in the area of instrumentation to design a sensor targeting annulus flow or to experienced engineers and researchers to keep in touch with the most recent research advances in the area.

Information-theoretic sensor planning for large-scale production surveillance via deep reinforcement learning

Production surveillance is the task of monitoring oil and gas production from every well in a hydrocarbon field. Accurate surveillance is a basic necessity for several reasons that include improved resource management, better equipment health monitoring, reduced operational cost, and ultimately optimal hydrocarbon production. A key challenge in this task, especially for large fields with many wells, is the measurement of multiphase fluid flow using a limited number of noisy sensors of varying characteristics. Current surveillance practices are based on fixed utilization schedules of such flow sensors, which rarely change over time. Such a passive mode of sensing is completely agnostic to surveillance performance and thus often fails to achieve a desired accuracy. Here we propose an active surveillance approach, underpinned by the concept of value of information-based sensing. Borrowing some well-known concepts from Markov decision processes, reinforcement learning and artificial neural networks, we demonstrate that a practical active surveillance strategy can be devised, which can not only improve surveillance performance significantly, but also reduce usage of flow sensors.

Semi-implicit method to solve compressible multiphase fluid flows without acoustic time step restrictions

A new 3D multiphase numerical capability is presented here for simulating multiphase flow regimes at all Mach numbers (M). The new method is a semi-implicit extension of the finite volume discrete equation method (DEM) of Chinnaya et al. (2004), which originally used explicit time-stepping. The capability is also developed to work with another extension of the DEM to moving grids for arbitrary Lagrangian-Eularian (ALE) methods detailed in Dunn (2011). Rather than solving all phase equations simultaneously, the DEM reduces the equations to a system of single-phase Riemann solves, where each phase has its own velocity and thermodynamic state. Exchanges between the phases are modeled through source terms accounting for the phase interactions. Since the original multiphase scheme uses an explicit time-advancement scheme, it has time step restrictions dictated by the speed of sound, which limits the model's ability to simulate weakly compressible flows which typically need to be integrated for longer time periods. Here, we extend the current multiphase formulation by implementing a pressure-correcting step to enable implicit calculations and remove acoustic time step limitations. The new semi-implicit algorithm allows use of relatively large time steps compared to an explicit method. Validation and benefits of the new implicit time-step method are illustrated using several examples including weakly compressible flows and strong shock waves. The scheme presented here is general and may be used for a variety of applications which require capabilities for handling multiphase flow at a wide range of Mach numbers. However, the goal of this research is to simulate all stages of high energy explosions, including the shock formation (high Mach numbers) and evolution of the buoyant cloud (low Mach numbers).

Predicting Sand Production Rate in High-Pressure, High-Temperature Wells in the Tarim Basin

Summary Sand production has been a very serious concern for the high-pressure, high-temperature (HPHT) gas wells in the Tarim Basin. However, the possible reasons and mechanisms remain unclear because there is no sufficient model to predict both onset of sanding and sand-production rate. The objective of this study is to develop a three-dimensional (3D) numerical sand production-prediction model and apply it to these HPHT gas wells to determine the main mechanisms for sand production and to propose completion designs to minimize sand production. This paper presents the development of a fully coupled 3D, poro-elasto-plastic sand-production model and the simulation results for two key wells that are prone to sanding. The sand-production model was used to model the different completion designs and flowback strategies that were used in the field. The model couples multiphase fluid flow and elasto-plasticity to simulate pressure transient behavior and rock deformation during production. The sanding criterion is a combination of both mechanical failure (shear/tensile/compressive failure) and fluid erosion. A novel cell-removal algorithm has been implemented to predict the dynamic (time dependent) sand-production process. In addition, the complex geometry of the wells and perforations are explicitly modeled to show cavity propagation around hole/perforations during sand production. For this case study, triaxial tests on core samples were conducted, and the stress-strain curves under different confining stresses are analyzed to obtain rock properties for both the preyield and post-yield period. The wells were categorized into ones that had massive sand production and ones that showed much less sand production. Operational and mechanical factors that were empirically found to result in sand production were identified. The sand-production model was run to verify the role played by different factors. It is shown that completion design, rock strength, and post-failure behavior of the rock are key factors responsible for the observed sanding in these wells. In addition, the drawdown strategy and the associated bottomhole pressure (BHP) change and the extent of depletion play an important role in the sanding rate. Several strategies for minimizing sand production are suggested for these wells. These include drawdown management, completion, and perforation design. In this study, we show for the first time that data from HPHT gas wells that have severe sand-production problems can be analyzed quantitatively with the developed model to determine the mechanisms of sand production. This allows us to make operational recommendations to minimize sanding risk in these wells.

A macroelement stabilization for mixed finite element/finite volume discretizations of multiphase poromechanics

Strong coupling between geomechanical deformation and multiphase fluid flow appears in a variety of geoscience applications. A common discretization strategy for these problems is a continuous Galerkin finite element scheme for the momentum balance equation and a finite volume scheme for the mass balance equations. When applied within a fully implicit solution strategy, however, this discretization is not intrinsically stable. In the limit of small time steps or low permeabilities, spurious oscillations in the piecewise-constant pressure field, i.e., checkerboarding, may be observed. Further, eigenvalues associated with the spurious modes will control the conditioning of the matrices and can dramatically degrade the convergence rate of iterative linear solvers. Here, we propose a stabilization technique in which the mass balance equations are supplemented with stabilizing flux terms on a macroelement basis. The additional stabilization terms are dependent on a stabilization parameter. We identify an optimal value for this parameter using an analysis of the eigenvalue distribution of the macroelement Schur complement matrix. The resulting method is simple to implement and preserves the underlying sparsity pattern of the original discretization. Another appealing feature of the method is that mass is exactly conserved on macroelements, despite the addition of artificial fluxes. The efficacy of the proposed technique is demonstrated with several numerical examples.

Thermo-hydrodynamic analytical model, numerical solution and experimental validation of a radial heat pipe with internally finned condenser applied for building heat recovery units

Heat pipes have been extensively applied in the domain of energy conversion and heat recovery application. A novel radial heat pipe with internally finned condenser has been proposed to recover waste heat from air conditioning units. Full mathematical description and computational fluid dynamics model were developed to predict the loop flow and thermal performance in a single radial heat pipe, respectively. The research focuses mainly on the effects of input power, filling ratio, pipe diameter, and velocity of the cooling water on the thermal performance and entropy generation rate of this novel heat pipe. Numerical results illustrate that average reductions in total thermal resistance with utilization of fins approximately achieved 8.69% and 14.78% for fins nf = 4 and nf = 8, respectively. Similarly, entropy generation rate shows an average decrease of 19.4% and 37.5% for identical operations. Additionally, the effect of internally finned condenser on the multiphase fluid flow has been comprehensively analyzed, including the break of the condensed film, generation of bubbles and nucleation boiling. The results further indicate that incorporation of internal fins has a significant influence on enhancing thermal homogenization and waste thermal recovery efficiency of a radial heat pipe. Case results agreed well with experimental data within average deviation being no more than 10%.

DARCY-AND PORE-SCALE ISSUES ASSOCIATED WITH MULTI-PHASE FLUID FLOW THROUGH A PETROLEUM RESERVOIR

This manuscript primarily focuses on the constraints associated with the extended version of Darcy’s law that is used to describe the multiphase flow through a porous media; and in particular, a petroleum reservoir. This manuscript clearly brings out the basics associated with the usage of Darcy’s law, and reasons out the inapplicability of the Navier-Stokes Equation in order to describe the momentum conservation in a typical petroleum reservoir. Further, this work highlights the essence of continuum-based Darcy’s macroscopic-scale equation with that of Navier-Stokes’s microscopic-scale equation. Further, the absence of capillary forces in original Darcy’s equation and extending the same by considering the concept of ‘capillary pressure’ in order to accommodate the multi-phase flow has several critical constraints associated with it. In this manuscript, all these constraints or limitations have been posed in the form of a list of basic queries that need to be addressed or at least to be understood with clarity, when applying the multi-phase fluid flow equations associated with a petroleum reservoir. This study is limited to an oil-water two-phase system.

A study on temperature–stress model of pre-cooling for re-condenser in LNG receiving station

Pre-cooling in a re-condenser is one of the key tasks for the smooth operation in a liquefied natural gas receiving station. It should be conducted economically and efficiently to ensure operation safety so that the re-condenser material damage caused by the thermal stress can be avoided. In this paper, a pre-cooling temperature model based on the computational fluid dynamics technology has been established to complete the large-grid calculation in the re-condenser. Combined with the component transport equation and volume of fluid multi-phase flow model, a theoretical system has been built which can be applied to both the gas phase pre-cooling model and the liquid phase pre-cooling model. The fast and stable calculation of the multi-component multiphase and large-scale has been realized through controlling the grid optimization, dynamic relaxation factor, and phase change model selection. To realize the coupling between the temperature model and the stress model and analyze the thermal stress caused by the temperature change in the pre-cooling real time, a pre-cooling stress model has been constructed and a temperature difference algorithm has been proposed. After analyzing the overall and local model of the re-condenser, the thermal deformation and thermal stress during the pre-cooling of the re-condenser can be comprehensively analyzed, and the detailed analysis of the stress and fatigue life at the peak stress region (e.g., the nozzle) can be achieved. The prediction accuracy of the pre-cooling temperature–stress model has been verified by the on-site measured data. They have great popularizing and applying values. The two models can provide scientific support in pre-cooling scheme design, optimization, pre-cooling flow, and structural safety, and when applied to engineering, they can lead to significant economic and safety benefits.

Flow in porous media with low dimensional fractures by employing enriched Galerkin method

This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.