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At least 271 records · Page 15

Density and Cavitating Flow Results from a Full-Scale Optical Multiphase Cryogenic Flowmeter

Liquid propulsion systems are hampered by poor flow measurements. The measurement of flow directly impacts safe motor operations, performance parameters as well as providing feedback from ground testing and developmental work. NASA Marshall Space Flight Center, in an effort to improve propulsion sensor technology, has developed an all optical flow meter that directly measures the density of the fluid. The full-scale sensor was tested in a transient, multiphase liquid nitrogen fluid environment. Comparison with traditional density models shows excellent agreement with fluid density with an error of approximately 0.8%. Further evaluation shows the sensor is able to detect cavitation or bubbles in the flow stream and separate out their resulting effects in fluid density.

Korman, Valentin↗

Device-scale CFD study for mass transfer coefficient and effective mass transfer area in packed column

Carbon dioxide (CO 2 ) is a significant contributor of greenhouse gases emissions responsible for global warming. The fossil-fueled power plant is one of the major sources of CO 2 emission worldwide and needs to be mitigated. Post-combustion carbon capture by chemical absorption can be a promising technology to reduce CO 2 emission from power plants. The absorption is carried out via countercurrent flow in the packed columns. Although monoethanolamine (MEA) is a popular solvent, it has also limitations such as high volatility of solvent, corrosivity that leads to product degradation and damage to apparatuses, low CO 2 loading capacity, etc. Therefore, alternate solvents are being explored as prospective materials for carbon capture. A water-lean solvent, CO 2 binding organic liquids (CO2BOL), is currently being developed as a prospective material in carbon capture at the Pacific Northwest National Laboratory. Since the development of the material is at the primitive stage, it needs extensive investigation before industrial deployments. Hydrodynamics and mass transfer phenomena in the packed column using CO 2 BOL is unknown. Computational fluid dynamics (CFD) can be a useful tool to understand these phenomena in the packed column. Before employing the extensive CFD investigations, one needs to carefully validate CFD predictions for accurate flow predictions. This report demonstrates the validation of multiphase flow simulations against the experimental results for both structured and random packed columns. The reactive multiphase flow simulations using volume of fluid method were conducted at a wide range of liquid loads and contacts angles. The effective area is one of the critical factors dictating interphase mass transfer due to chemical reactions. Accordingly, CFD-predicted effective areas were compared with the experimental results of Tsai et al. [1] for Mellapak 250.Y structured packing. Both results matched well at different liquid loads in the presence of fast chemical kinetics using caustic solvents. Further, reactive multiphase flow simulations were also conducted in pall ring random packing to compute effective areas in the presence of fast chemical reactions. The CFD-predicted effective area compared well with correlation developed by Song et al. [2]. With successful validations, the current simulation framework can be further used for prediction of hydrodynamics and mass transfer phenomena using CO 2 BOL solvents in the packed column. Subsequently, it would be helpful in design optimization of a packed column. In addition to validation of the CFD model, this report also explains the mechanism for enhanced liquid side mass transfer for a structured packed column as compared to the wetted wall column.

20 FOSSIL-FUELED POWER PLANTS↗

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗

Modelling Viscoelastic Behaviour of Polymer by A Mixed Velocity, Displacement Formulation - Numerical and Experimental Results

The objective of this work is to model the viscoelastic behaviour of polymer from the solid state to the liquid state. With this objective, we perform experimental tensile tests and compare with simulation results. The chosen polymer is a PMMA whose behaviour depends on its temperature. The computation simulation is based on Navier-Stokes equations where we propose a mixed finite element method with an interpolation P1+/P1 using displacement (or velocity) and pressure as principal variables. The implemented technique uses a mesh composed of triangles (2D) or tetrahedra (3D). The goal of this approach is to model the viscoelastic behaviour of polymers through a fluid-structure coupling technique with a multiphase approach.

36 MATERIALS SCIENCE↗

Rotational and reflectional equivariant convolutional neural network for data-limited applications: Multiphase flow demonstration

This article deals with approximating steady-state particle-resolved fluid flow around a fixed particle of interest under the influence of randomly distributed stationary particles in a dispersed multiphase setup using convolutional neural network (CNN). The considered problem involves rotational symmetry about the mean velocity (streamwise) direction. Thus, this work enforces this symmetry using SE(3)-equivariant, special Euclidean group of dimension 3, CNN architecture, which is translation and three-dimensional rotation equivariant. This study mainly explores the generalization capabilities and benefits of a SE(3)-equivariant network. Accurate synthetic flow fields for Reynolds number and particle volume fraction combinations spanning over a range of [86.22, 172.96] and [0.11, 0.45], respectively, are produced with careful application of symmetry-aware data-driven approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Pore-scale investigation on stress-dependent characteristics of granular packs and the impact of pore deformation on fluid distribution

Understanding the effect of changing stress conditions on multiphase flow in porous media is of fundamental importance for many subsurface activities including enhanced oil recovery, water drawdown from aquifers, soil confinement, and geologic carbon storage. Geomechanical properties of complex porous systems are dynamically linked to flow conditions, but their feedback relationship is often oversimplified due to the difficulty of representing pore-scale stress deformation and multiphase flow characteristics in high fidelity. In this work, we performed pore-scale experiments of single- and multiphase flow through bead packs at different confining pressure conditions to elucidate compaction-dependent characteristics of granular packs and their impact on fluid flow. A series of drainage and imbibition cycles were conducted on a water-wet, soda-lime glass bead pack under varying confining stress conditions. Simultaneously, X-ray micro-CT was used to visualize and quantify the degree of deformation and fluid distribution corresponding with each stress condition and injection cycle. Micro-CT images were segmented using a gradient-based method to identify fluids (e.g., oil and water), and solid phase redistribution throughout the different experimental stages. Changes in porosity, tortuosity, and specific surface area were quantified as a function of applied confining pressure. Results demonstrate varying degrees of sensitivity of these properties to confining pressure, which suggests that caution must be taken when considering scalability of these properties for practical modeling purposes. Changes in capillary number with confining pressure are attributed to the increase in pore velocity as a result of pore contraction. Furthermore, this increase in pore velocity was found to have a marginal impact on average phase trapping at different confining pressures.

58 GEOSCIENCES↗

A regularized-interface method as a unified formulation for simulations of high-pressure multiphase flows

The injection of multi-species fluids into high-pressure and high-temperature environments beyond the species' critical points is commonly found in engineering applications. At these conditions, for immiscible species, both subcritical interfacial dynamics and supercritical mixing can coexist due to variations in temperature around the mixture critical point. The modeling of these complex transcritical phenomena for large-scale configurations is so far not possible. To address this issue, we propose the Regularized-Interface Method (RIM) as a unified formulation that can describe both sub- and supercritical processes as well as the transition between them. The proposed method is derived via filtering of the nanoscale interface-resolving formulation based on van der Waals' linear gradient theory. Thus, this approach allows for the consistent modeling of interfacial dynamics that vanishes at supercritical conditions, while significantly reducing the temporal and spatial resolution constraints of the original nanoscale formulation. The resulting RIM formulation is examined in interface-capturing simulations of sub-, trans-, and supercritical fuel injection processes, involving droplets and jets. Furthermore, these results highlight the importance of resolving spatio-temporal transitions from subcritical interfacial dynamics to supercritical mixing in high-pressure multiphase simulations, in contrast to commonly employed diffused-interface methods, where interfacial dynamics are often neglected.

Interface capturing↗

The Continued Need for Modeling and Scaled Testing to Advance the Hanford Tank Waste Mission

Hanford tank wastes are chemically complex slurries of liquids and solids that can exhibit changes in rheological behavior during retrieval and processing. The Hanford Waste Treatment and Immobilization Plant (WTP) recently abandoned its planned approach to use computational fluid dynamics (CFD) supported by testing at less than full scale to verify the design of vessels that process these wastes within the plant. The commercial CFD tool selected was deemed too difficult to validate to the degree necessary for use in the design of a nuclear facility. Alternative, but somewhat immature, CFD tools are available that can simulate multiphase flow of non-Newtonian fluids. Yet both CFD and scaled testing can play an important role in advancing the Hanford tank waste mission—in supporting the new verification approach, which is to conduct testing in actual plant vessels; in supporting waste feed delivery, where scaled testing is ongoing; as a fallback approach to design verification if the Full Scale Vessel Testing Program is deemed too costly and time-consuming; to troubleshoot problems during commissioning and operation of the plant; and to evaluate the effects of any proposed changes in operating conditions in the future to optimize plant performance.

Fluid Dynamics↗

Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios

Lattice Boltzmann models for simulating multiphase flows are relatively new, and much work remains to be done to demonstrate their ability to solve fundamental test cases before they are considered for engineering problems. From this perspective, a hydrodynamic lattice Boltzmann model for simulating immiscible multiphase flows with high density and high viscosity ratios, up to O(1000) and O(100) respectively, is presented and validated against analytical solutions. The method is based on a two phase flow model with operators extended to handle N immiscible fluids. The current approach is O(N) in computational complexity for the number of different gradient approximations. This is a major improvement, considering the O(N{sup 2}) complexity found in most works. A sequence of systematic and essential tests have been conducted to establish milestones that need to be met by the proposed approach (as well as by other methods). First, the method is validated qualitatively by demonstrating its ability to address the spinodal decomposition of immiscible fluids. Second, the model is quantitatively verified for the case of multilayered planar interfaces. Third, the multiphase Laplace law is studied for the case of three fluids. Fourth, a quality index is developed for the three-phase Laplace–Young’s law, which concerns the position of the interfaces between the fluids resulting from the different surface tensions. The current model is compatible with the analytical solution, and is shown to be first order accurate in terms of this quality index. Finally, the multilayered Couette’s flow is studied. In this study, numerical results can recover the analytical solutions for all the selected test cases, as long as unit density ratios are considered. For high density and high viscosity ratios, the analytical solution is recovered for all tests, except that of the multilayered Couette’s flow. Numerical results and a discussion are presented for this unsuccessful test case. It is believed that other LB models may have the same problem in addressing the simulation of multiphase flows with variable density ratios.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Review of Physical and Numerical Approaches for the Study of Gas Stirring in Ladle Metallurgy

This article presents a review of the research into gas stirring in ladle metallurgy carried out over the past few decades. Herein, the physical modeling experiments are divided into four major areas: (1) mixing and homogenization in the ladle; (2) gas bubble formation, transformation, and interactions in the plume zone; (3) inclusion behavior at the steel–slag interface and in the molten steel; and (4) open eye formation. Several industrial trials have also been carried out to optimize gas stirring and open eye formation. Approaches for selecting criteria for scaling to guarantee flow similarity between industrial trials and physical modeling experiments are discussed. To describe the bubble behavior and two-phase plume structure, four main mathematical models have been used in different research fields: (1) the quasi-single-phase model, (2) the volume of fluid (VOF) model, (3) the Eulerian multiphase (E–E) model, and (4) the Eulerian–Lagrangian (E–L) model. In recent years, the E–E model has been used to predict gas stirring conditions in the ladle, and specific models in commercial packages, as well as research codes, have been developed gradually to describe the complex physical and chemical phenomena. Furthermore, the coupling of turbulence models with multiphase models is also discussed. For physical modeling, some general empirical rules have not been analyzed sufficiently. Based on a comparison with the available experimental results, it is found that the mathematical models focusing on the mass transfer phenomenon and inclusion behaviors at the steel-slag interface, vacuum degassing at the gas–liquid interface, dissolution rate of the solid alloy at the liquid–solid interface, and the combination of fluid dynamics and thermodynamics need to be improved further. To describe industrial conditions using mathematical methods and improve numerical modeling, the results of physical modeling experiments and industrial trials must offer satisfactory validations for the improvement of numerical modeling.

36 MATERIALS SCIENCE↗

Quantitative Characterization of Impacts of Coupled Geomechanics and Flow on Safe and Permanent Geological Storage of CO 2 in Fractured Aquifers

This is the final scientific report for the award DE-FE0023305, entitled “Quantitative Characterization of Impacts of Coupled Geomechanics and Flow on Safe and Permanent Geological Storage of CO 2 in Fractured Aquifers.” The work has been divided into six tasks. In Task 2, we characterized rock properties, which are important when developing a quantitative approach for understanding and predicting geomechanical effects on large-scale CO 2 injection and long-term storage in the subsurface. Rock properties of interest for this characterization include porosity, permeability, elastic constants, strength, and heat capacity. We measured rock properties for three different rock types: concrete, sandstone and shale. These properties were obtained from the acoustic measurement, permeability and porosity measurement, Brazilian test, the uniaxial compressive test, and heat capacity measurement. Then, using the Brazilian technique to fracture samples, we measured their permeability under brine injection for varying effective stresses, followed by similar measurements of permeability under sc-CO 2 injection. Permeability to brine and sc-CO 2 decreased as the effective stress increased. The apparent permeability to sc-CO 2 was an order of magnitude less than that for brine, a consequence of CO 2 being the non-wetting fluid. In Task 3, we developed understandings and correlations for CO 2 injection pressure induced fracturing. We initially fractured four eight inch cubes of concrete with brine to establish a standard test procedure. Then, additional concrete samples were fractured using brine. Confining stresses were exerted on the samples and brine was injected at a constant rate into a borehole that was previously drilled into the concrete cube. The borehole pressure was measured and fracture initiation was identified as a peak in the pressure profile. That was followed by fracture propagation, which was identified as a plateau in the pressure profile, and finally the fracture reached the sample surface. The sample surfaces were photographed before and after fracturing, which enabled determination of where the fracture reached the sample surface. Afterwards, aqueous food dye solution was injected into the fractured concrete samples to color the fracture planes. The borehole was filled with food dye solution in advance, a gas pulse was transmitted to the borehole, and the borehole was then shut in to allow the food dye to be driven into existing fractures. Then, the concrete samples were broken down by high-pressure gas injection to reveal the geometry and morphology of the hydraulic fractures. In addition, acoustic measurements were conducted on multiple locations on each face of the concrete samples before and after injection for comparison. This comparison was used to confirm changes in the internal structure of the concrete sample, namely the formation of fractures. There were six concrete samples fractured with brine. Afterwards, concrete samples were fracture using sc-CO 2 . The main change in experimental procedure was the inclusion of temperature control, since in the field, we mostly encounter temperature and pressure conditions above the supercritical point of CO 2 . The concrete samples were pre-heated in an oven to elevate their temperature, and thermal tape was used to heat the CO 2 to a temperature above its supercritical temperature. Two concrete samples were fractured using liquid CO 2 , four concrete samples were fractured using gaseous CO 2 , and twenty two concrete samples were fractured using sc-CO 2 . For the concrete samples fractured using sc-CO 2 , three had pre-existing hydraulic fractures on the surface near the wellbore, and two were water saturated (as opposed to containing only air). Two concrete samples were composite samples, with a high permeability ball in the center, in order to represent CO 2 injection into a high permeability zone surrounded by a low permeability sealing formation. Later, we fractured five shale samples, obtained from the Niobrara shale outcrop, with sc-CO 2 . The injection rate was constant, confining stresses were applied, the shale samples were pre-heated in an oven to the desired temperature, and the sample was then fractured. An analysis of the failure type was done for many of the concrete samples, based on the predicted break down pressure for tensile and shear failure, and it was found that most samples fractured due to shear failure. Also, the presence of induced fractures has little to no effect on the fracture initiation pressure, but significantly changes the fracture morphology. The CO 2 fracturing in water saturated samples behaved much similar to brine induced fracturing. There was a significant difference of breakdown pressure for injection of CO 2 and brine, where the breakdown pressure for CO 2 induced fracturing is generally around the minimum horizontal stress and that for brine is much higher. Finally, the fracture orientation for most samples with large confining stress differential was perpendicular to the minimum horizontal stress. When the stress differential, especially the difference between the two directions with the smallest stresses was small, the fracture orientation was determined not only by the minimum stress direction, but also the magnitude of the confining stress, the tensile strength of the rock, and the breakdown pressure. In Task 4, we modified our coupled flow-geomechanical models to model fracture growth and propagation in storage formations and caprocks. These flow-geomechanical models are TOUGH2-CSM and TOUGH2-FLAC. The TOUGH2-CSM fluid and heat flow formulation is based on the TOUGH2 formulation of mass and energy conservation equations that govern fluid and heat flow in general multiphase, multicomponent, multi-porosity systems. The TOUGH2-CSM simplified geomechanical formulation is based on the linear theory of elasticity applied to multi-porosity non-isothermal (thermo-multi-poroelastic) media. We previously derived, from the fundamental relations of the linear theory of elasticity, an equation relating mean stress, pore pressures, temperatures, and body force (the Mean Stress equation) that we added to the TOUGH2-CSM fluid and heat flow equations. We extended the TOUGH2-CSM simplified geomechanical formulation to calculate the entire stress tensor by deriving equations for stress tensor components from derivatives of the Cartesian thermo-multi-poroelastic Navier equation components. In addition, we derived equations for stress tensor components in rz-coordinates. We solved these geomechanical equations using the integral finite difference method. This method utilizes momentum fluxes obtained by “factoring” a divergence operator out of each geomechanical equation. In Task 5, we did a literature survey to determine suitable correlations for fracture initiation, growth, and propagation. After surveying numerous papers, we modified TOUGH2-CSM to model stress dependent fracture initiation and growth using the Mohr-Coulomb criterion for shear failure in faults and caprock and the condition of negative minimum effective stress for tensile failure. Tensile failure results in a fracture whose width depends on the difference between fracture pressure and minimum stress and whose propagation is based on the difference between the stress intensity factor at the fracture tip and the rock toughness. The TOUGH-FLAC model is based on the FLAC3D ubiquitous joint model, extended for the modeling of permeability changes induced by changes in effective normal stress across fractures as well permeability changes caused by shearing along fractures. In Task 6, we validated our coupled flow-geomechanical models using analytical solutions and problems from the literature. We validated the TOUGH2-CSM modifications using analytical solutions to the displacement from a uniform load on a semi-infinite elastic medium and the two-dimensional Mandel-Cryer effect. Those were followed by a sample problem to test our stress tensor calculations, which was for injection into a single-phase reservoir with constant properties. Comparisons of our simulator to published results were done on for the depletion of a single-phase reservoir with stress dependent porosity, two examples from the In Salah gas project, an axisymmetric baserock–reservoir–caprock system with a normal faulting stress regime that had thermally induced shear stresses, simulations of CO 2 leakage through caprock in a two-dimensional reservoir in Cartesian coordinates, and predictions of caprock failure from CO 2 injection into an axisymmetric reservoir. Finally, we simulated CO 2 injection pressure-induced fracturing from one of our laboratory studies, Sample 39, and obtained a fracture profile. We also validated the TOUGH2-FLAC model for fluid driven fracture growth against solutions based on the KGD model and a case with an inclined fracture that was loaded from the boundaries to achieve wing-crack propagation. The strain softening tensile behavior and softening of modulus considering a simple damage approach was verified by a simulation representing hydraulic fracturing stress measurement around a vertical well. Finally, the model was validated against deep fracture zone opening and surface uplift at In Salah with inverses analysis used to improve the match of simulation with field data. In Task 7, we developed a scheme based on inverse modeling that can be used to identify caprock leakage. Injection of fluid into a reservoir results in a time varying pressure profile that depends on the properties of the rock and the fluid. The presence of significant caprock leakage would effect this pressure profile and we used inverse modeling, namely the Levenberg-Marquardt method, to determine the leakage location from the pressure profile. A two-dimensional and a three-dimensional example based on published data were presented. The published simulation was run and its results were considered as “field” data. In the two-dimensional example, a simulation of CO 2 injection into a two-dimensional aquifer-caprock system, the caprock had a vertical fault through which leakage could occur. The location of this leakage was obtained from our inverse modeling scheme. In the three-dimensional example, the simulation domain had four geological layers, one of which was the injection zone that contained a horizontal injection well. We simulated fractures as high permeability gridblocks, introduced a fracture that spanned the caprock depth, and ran a simulation to obtain “field” data. Then, using our inverse modeling scheme, we obtained the location of that fracture.

58 GEOSCIENCES↗

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Impact of drilling fluid rheology and wellbore pressure on rock cuttings removal performance: numerical investigation

Drilling fluids exhibit non-Newtonian behavior which is generally described in the literature by two rheological models: Power Law and Herschel-Bulkley models. We have used Eulerian- Eulerian multiphase flow model to evaluate the drilling fluid flow patterns and filter cake formation patterns for both models for ultra-deep drilling conditions. Simulated drilling fluid flow patterns clearly show that the Herschel - Bulkley model exhibits fewer vortices around the drilling pipe, indicating better rock cuttings removal performance. In addition to mud rheology, we have analyzed the pressure drop variation with the filter cake formation on the wellbore during ultradeep drilling process. We have shown that filter cake thickness at the wall linearly increases with differential pressure between the well and formation. This implies that the differential pressure needs to be optimized. Very thin filter cake may lead to excessive fluid seepage into the permeable subterranean vertical zone resulting in a loss of fluid circulation and hence in a loss of rock cuttings removal. Yet, very thick filter cake reduces the effective diameter of the hole which may lead to a poor rock cuttings removal performance and stuck pipe. The mathematical model presented here needs to be experimentally validated when filter cake thickness data in deep drilling conditions become available. The model could be useful to provide drilling engineers insight on the filter cake formation, drilling fluid flow pattern, and give guide-line to optimize the filter cake as field experimental data are scarce.

02 PETROLEUM↗

An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes

Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. Additionally, an adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.

42 ENGINEERING↗

Slugging Flow of Water Draining from the Bottom of a Non-Vented Container

Experiments were run to observe the behavior of water exiting through an orifice at the bottom of an non-vented container. Initially, the container is nearly full of water with a small air space on top. Once the orifice was uncovered, the slugging rate and the drain rate of the water leaving the container were measured. Upon initially opening the orifice, water drains out until the air pressure above the water reduces enough that the air pressure drop from inside to outside of the container supports the water column and the water stops flowing. Air then enters the container through the orifice forming a bubble, which grows until it detaches and bubbles through the water to reach the air space. Once the bubble enters, this added air increases the pressure in the air space enough to allow the water to start flowing out again. This cycle of flow out, flow stoppage, air inflow, and bubble breakoff continues over and over until the hole is closed or the container empties. This is referred to as the “slugging cycle.” A mechanism is proposed to describe the slugging cycle which is modeled analytically. This paper presents the description of the experiments, data obtained, the mechanistic model, and comparison of the model to the experimental data. The model predicts outflow rates close to experimental values. Flow rates from non-vented containers are more than 10 to 20 less than vented containers. The bubbles which must enter the container periodically to increase the internal air pressure stop the water flow momentarily so are responsible for this large decrease in flow rate. Swirl induced in the non-vented container causes the flow rates to increase by a factor of two. The flow rate out of a non-vented container is independent of water height which is in direct contrast to a vented container where the flow rate is proportional to the square root of the water height. The constant rate is due to the container pressure. The higher the water level, the lower the air pressure is in the container. This analytical model requires input of the bubble size. The volume recommended is the volume of a cylinder with the base of the orifice area and length of 3.3 cm. Slugging rate varies only a small amount falling in the range to 2 to 4 cycles/sec. Preliminary work with other containers indicates larger containers, larger orifices and nozzle exit shapes produce higher specific flow rates. The standard multiphase flow equations could not be used to analyze this situation because the two phases are not interpenetrating. Instead one phase must fully stop before the other can flow. Interpenetrating phases allow can pass one another each affecting the other with friction and virtual mass. An interesting observation: The negative air pressure in the container is observable. It equals the water height.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗