Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “complex fluid”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

A reduced set of gyrofluid equations for plasma flow in a diverging magnetic field

Plasmas are often generated in a small diameter source with a strong magnetic field and subsequently flow into a region with greater diameter and smaller field. The magnetic mirror force that accelerates plasma in a diverging magnetic field appears in the gyrofluid equations developed for applications to toroidal devices, but this force is often absent from fluid equations. A set of gyrofluid equations with reduced complexity is developed in which drifts are assumed negligible and the mirror force is retained. The Chew–Goldberger–Low equations of state are used for a simple closure. These reduced gyrofluid equations are applied to plasma equilibrium in a magnetic mirror, to acceleration of plasma in a magnetic nozzle, and to space charge neutralization of an ion beam by electrons in a diverging magnetic field. The results from gyrofluid theory are compared with results from drift kinetic theory to find the accuracy of the gyrofluid approximation in these applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

NdPO 4 solubility and aqueous Neodymium speciation in supercritical fluids: An experimental study at 500–700 °C and 1.7 kbar

A key aspect in the formation of rare earth elements (REE) deposits is the role of REE transport as aqueous REE complexes in supercritical hydrothermal solutions, where the nature of the aqueous complex is controlled by solution composition, temperature and pressure. Despite chloride being considered as one of the most abundant transporting ligands in magmatic-hydrothermal fluids, experimental investigations on the stability of aqueous REE chloride complexes are scarce above 300 °C. In this study, synthetic NdPO 4 crystals were reacted with non-saline and saline (0, 0.05 and 0.5 mNaCl), acidic (0.01 mHCl) aqueous solutions in a series of solubility experiments conducted at 500–700 °C and 1.7 kbar, where the solubilities were determined using a stable Nd isotope ( 145 Nd isotope spike) dilution technique. NdPO 4 solubility ranges between 28 ppm and 10,858 ppm, where solubility increases with both temperature and salinity. At 500 °C, log mNdPO 4 increases from –3.93 to –1.60 and there is a strong correlation between NdPO 4 solubility and NaCl concentrations (slope of 1.2 ± 0.3), indicating stabilization of the Nd chloride aqueous complexes with a stoichiometry corresponding to NdCl 2+ . At 600 °C, this correlation is weaker (slope of 0.4, log mNdPO 4 increases from –2.63 to –1.88) indicating the stabilization of both Nd chloride and hydroxyl species controlling solubility. At 700 °C, NdPO 4 solubility is largely independent of NaCl concentration indicating that solubility is controlled by Nd hydroxyl complexes, where stoichiometry suggests the neutral Nd(OH) 3 0 species is dominant. The solubility product (Ksp) of NdPO4 is derived from experimental data with the relation: log K sp = -41.81 – 0.057T – 20987/T, with T temperature in Kelvin. Comparison of the measured Nd phosphate solubility to thermodynamic predictions using the available Helgeson-Kirkham-Flowers equation of state parameters for aqueous Nd complexes indicate that predictions are up to three orders of magnitude lower compared to experimental observations. This discrepancy is most pronounced in saline solutions, suggesting that thermodynamic properties of the REE chloride species in supercritical fluids require revision. Numerical simulations of fluid-rock interaction between acidic, saline fluids and a Strange Lake felsic mineral assemblage demonstrates that NdPO 4 solubility predictions from models are four to six orders of magnitude lower than those calculated based on empirical fits from experiments, which suggests that acidic, saline fluids may play an important role in mobilizing large amounts of light REE from 450 to 700 °C.

58 GEOSCIENCES↗
DOE OSTI2014

Automated High-Pressure Titration System with In Situ Infrared Spectroscopic Detection

A fully automated titration system with infrared detection was developed for investigating interfacial chemistry at high pressures. The apparatus consists of a high-pressure fluid generation and delivery system coupled to a high-pressure cell with infrared optics. A manifold of electronically actuated valves is used to direct pressurized fluids into the cell. Precise reagent additions to the pressurized cell are made with calibrated tubing loops that are filled with reagent and placed in-line with the cell and a syringe pump. The cell’s infrared optics facilitate both transmission and attenuated total reflection (ATR) measurements to monitor bulk-fluid composition and solid-surface phenomena such as adsorption, desorption, complexation, dissolution, and precipitation. Switching between the two measurement modes is accomplished with moveable mirrors that direct radiation from a Fourier transform infrared spectrometer into the cell along transmission or ATR light paths. The versatility of the high-pressure IR titration system is demonstrated with three case studies. First, we titrated water into supercritical CO2 (scCO2) to generate an infrared calibration curve and determine the solubility of water in CO2 at 50 °C and 90 bar. Next, we characterized the partitioning of water between a montmorillonite clay and scCO2 at 50 °C and 90 bar. Transmission-mode spectra were used to quantify changes in the clay’s sorbed water concentration as a function of scCO2 hydration, and ATR measurements provided insights into competitive residency of water and CO2 on the clay surface and in the interlayer. Finally, we demonstrated how time-dependent studies can be conducted with the system by monitoring the carbonation reaction of forsterite (Mg2SiO4) in water-bearing scCO2 at 50 °C and 90 bar. Immediately after water dissolved in the scCO2, a thin film of adsorbed water formed on the mineral surface, and the film thickness increased with time as the forsterite began to dissolve. However, after approximately 2.5 hours, the trend reversed, and a carbonate precipitate began to form on the forsterite surface, exposing dramatic chemical changes in the thin-water film. Collectively, these applications illustrate how the high-pressure IR titration system can provide molecular-level information about the interactions between variably wet scCO2 and minerals relevant to underground storage of CO2 (geologic carbon sequestration). The apparatus could also be utilized to study high-pressure interfacial chemistry in other areas such as catalysis, polymerization, food processing, and oil and gas recovery.

Environmental Molecular Sciences Laboratory↗
NASA NTRSDate not supplied

Time-History Statistics of Soot Formation in A Model Gas Turbine Combustor

Soot formation is a complex dynamic and intermittent process determined by properties of the fuel, combustor design, and combustor operation. Although the major steps in soot formation (i.e., formation of precursors, inception, growth and evolution) are similar for a variety of carbonaceous fuels, applications, and operating conditions, it remains unclear when the temporal transition between these steps occurs. An engineering prediction tool coupled with computational fluid physics (CFD), therefore needs to accurately model all these complex steps. To develop such a model, we propose the time-history concept for understanding the time dependency of soot formation as a function of local properties (i.e., temperature, velocity, local fuel air ratio, etc.). We continue our previous work with modeling the DLR aero-combustor [1] with our updated in-house CFD code, Open National Combustion Code (OpenNCC), that now includes a Multiple Time-Scale Flamelet Progress Variable approach and a the semi-empirical two-equation soot model. We injected massless tracer particles upstream of the injector region of the combustor to collect time-history statistics of the solution variables. The correlations between the collected statistics with respect to the experimental soot volume fraction data showed that time-history effect of certain flow variables, including turbulent kinetic energy (TKE), and multiple species is indeed important for soot formation. We then conducted a time-history based correlation analysis to determine the key species and the concentration ranges critical for soot formation (C6H5-based nucleation, acetylene-based surface growth, and oxidation with OH and O2). Based on the time-history correlation coefficient (THCC) analysis, we propose possible modifications to improve the current two-equation model.

LES↗
DOE OSTI2019

Using Ultrafast X-ray Spectroscopy To Address Questions in Ligand-Field Theory: The Excited State Spin and Structure of [Fe(dcpp) 2 ] 2+

We have employed a range of ultrafast X-ray spectroscopies in an effort to characterize the lowest energy excited state of [Fe(dcpp) 2 ] 2+ (where dcpp is 2,6-(dicarboxypyridyl)pyridine). This compound exhibits an unusually short excited-state lifetime for a low-spin Fe(II) polypyridyl complex of 270 ps in a room-temperature fluid solution, raising questions as to whether the ligand-field strength of dcpp had pushed this system beyond the 5 T 2 / 3 T 1 crossing point and stabilizing the latter as the lowest energy excited state. Kα and Kβ X-ray emission spectroscopies have been used to unambiguously determine the quintet spin multiplicity of the long-lived excited state, thereby establishing the 5 T 2 state as the lowest energy excited state of this compound. Geometric changes associated with the photoinduced ligand-field state conversion have also been monitored with extended X-ray absorption fine structure. The data show the typical average Fe-ligand bond length elongation of ~0.18 Å for a 5 T 2 state and suggest a high anisotropy of the primary coordination sphere around the metal center in the excited 5 T 2 state, in stark contrast to the nearly perfect octahedral symmetry that characterizes the low-spin 1 A 1 ground state structure. This study illustrates how the application of time-resolved X-ray techniques can provide insights into the electronic structures of molecules—in particular, transition metal complexes—that are difficult if not impossible to obtain by other means.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2014

Science Goals and Mission Concept for the Future Exploration of Titan and Enceladus

Saturn׳s moons, Titan and Enceladus, are two of the Solar System׳s most enigmatic bodies and are prime targets for future space exploration. Titan provides an analogue for many processes relevant to the Earth, more generally to outer Solar System bodies, and a growing host of newly discovered icy exoplanets. Processes represented include atmospheric dynamics, complex organic chemistry, meteorological cycles (with methane as a working fluid), astrobiology, surface liquids and lakes, geology, fluvial and aeolian erosion, and interactions with an external plasma environment. In addition, exploring Enceladus over multiple targeted flybys will give us a unique opportunity to further study the most active icy moon in our Solar System as revealed by Cassini and to analyse in situ its active plume with highly capable instrumentation addressing its complex chemistry and dynamics. Enceladus׳ plume likely represents the most accessible samples from an extra-terrestrial liquid water environment in the Solar system, which has far reaching implications for many areas of planetary and biological science. Titan with its massive atmosphere and Enceladus with its active plume are prime planetary objects in the Outer Solar System to perform in situ investigations. In the present paper, we describe the science goals and key measurements to be performed by a future exploration mission involving a Saturn-Titan orbiter and a Titan balloon, which was proposed to ESA in response to the call for definition of the science themes of the next Large-class mission in 2013. The mission scenario is built around three complementary science goals: (A) Titan as an Earth-like system; (B) Enceladus as an active cryovolcanic moon; and (C) Chemistry of Titan and Enceladus - clues for the origin of life. The proposed measurements would provide a step change in our understanding of planetary processes and evolution, with many orders of magnitude improvement in temporal, spatial, and chemical resolution over that which is possible with Cassini-Huygens. This mission concept builds upon the successes of Cassini-Huygens and takes advantage of previous mission heritage in both remote sensing and in situ measurement technologies.

future missions↗
NASA NTRS1959

Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array

The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Sparrow, E. M.↗
NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗
DOE OSTI2023

A Review of Physics-Informed Machine Learning in Fluid Mechanics

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

42 ENGINEERING↗
DOE OSTI2016

Consistent Fluid Property Evaluation in RELAP5-3D

Previous investigations have developed and tested a methodology to improve the consistency between used to determine the fluid property derivatives used in the numerical solution scheme and the solution scheme itself. Within a bounding rectangle of the fluid property table for a fluid state point, linear interpolants for both fluid property values and their derivatives are calculated. A weighted average between these interpolants the analytical approximations of the fluid properties and derivatives is formed with a weighting factor between 0.0 and 1.0. This average has shown potential to reduce mass error relating to the fluid properties in RELAP5-3D. This linear interpolation and weighted averaging methodology has been implemented in RELAP5-3D with two additional options that adjust the weighting factor in the average according to the location within the bounding rectangle. The first calculates the weighting factor based only on the position between the left and right internal energy endpoints. The second also factors the position between the upper and lower pressure grid points into the calculation of the weighting factor. The new coding passes verification testing and expanded testing of the various options. Graphs are presented from three kinds of test cases, a two volume basic model, Edward’s O’Brien blowdown, and typical PWR. Some trends of the effect of crossing fluid property table pressure and internal energy grid line are identified and discussed for the simple and Edwards test cases. Preliminary results show that it the consistent fluid methodology can reduce mass error in simple cases, but in more complex input models, there is no clear best.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Modeling supercritical CO2 injection induced rupture of a minor fault embedded in a poroelastic layered reservoir-caprock system

CO2 injection for geologic carbon sequestration involves hydromechanical processes that lead to changes in fluid pressure and stresses that can activate existing faults. This paper presents a new method and workflow of modeling fault activation considering more complex three-dimensional geometry of natural faults using the TOUGH-FLAC multiphase fluid flow and geomechanical simulator. In this method and workflow, FLAC3D mechanical interfaces and TOUGH3 finite volume elements are discretized using computer aided design and gridding software along with a tailored mesh translation routine. The method and workflow are demonstrated with a model of a curved minor fault embedded in a poro-elastic layered reservoir-caprock system. The model is used for a comprehensive sensitivity analysis of fault responses to fault length, injection mass rate, injection schedule, well-fault distance, and well locations versus fault location. Four metrics (CO2 plume, shear state of fault, pressure and stress path at fault monitoring points) are selected to assess CO2 migration, pressure change, and the reactivation of faults. The results reveal that CO2 can bypass around the tip of the minor impermeable fault, building up pressure and poro-elastic stress on both sides that tends to impede fault rupture. Our study shows the benefit of carefully designing the injection to achieve the targeted final storage volume, starting at a relatively low rate for considerable time, and then ramping up the injection rate to the full rate of injection. The initial low injection has two distinct benefits: (1) it allows for the formation of an extensive CO2 plume with a much higher mobility through a low viscosity that will result in a lower pressure for a given injection rate, and (2) it allows for gradual build-up of horizontal poro-elastic stress within the reservoir that will tend to impede activation of steeply dipping faults. The injection scenario starting at a low injection rate, denoted here as conservative injection, can significantly reduce the risk of fault activation as high fluid mobility and reservoir strengthening poro-elastic stress has been established long before reaching the peak injection rates. Moreover, simultaneous injection in two injection wells on both sides of fault can provide further reservoir strengthening through poro-elastic stress buildup acting on a fault under normal faulting stress regime. The findings presented in the paper can provide practical and effective guidance on long-term, safe, and reliable geological CO2 storage.

Cao, Meng↗
NASA NTRS2017

Robonaut 2 and You: Specifying and Executing Complex Operations

Crew time is a precious resource due to the expense of trained human operators in space. Efficient caretaker robots could lessen the manual labor load required by frequent vehicular and life support maintenance tasks, freeing astronaut time for scientific mission objectives. Humanoid robots can fluidly exist alongside human counterparts due to their form, but they are complex and high-dimensional platforms. This paper describes a system that human operators can use to maneuver Robonaut 2 (R2), a dexterous humanoid robot developed by NASA to research co-robotic applications. The system includes a specification of constraints used to describe operations, and the supporting planning framework that solves constrained problems on R2 at interactive speeds. The paper is developed in reference to an illustrative, typical example of an operation R2 performs to highlight the challenges inherent to the problems R2 must face. Finally, the interface and planner is validated through a case-study using the guiding example on the physical robot in a simulated microgravity environment. This work reveals the complexity of employing humanoid caretaker robots and suggest solutions that are broadly applicable.

Baker, William↗
DOE OSTI2023

Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach

Multiphase Computational Fluid Dynamics (MCFD) based on the two-fluid model is considered a promising tool to model complex two-phase flow systems. MCFD simulation can predict local flow features without resolving interfacial information. As a result, the MCFD solver relies on closure relations to describe the interaction between the two phases. Those empirical or semi-mechanistic closure relations constitute a major source of uncertainty for MCFD predictions. In this paper, we leverage a physics-informed uncertainty quantification (UQ) approach to inversely quantify the closure relations’ model form uncertainty in a physically consistent manner. This proposed approach considers the model form uncertainty terms as stochastic fields that are additive to the closure relation outputs. Combining dimensionality reduction and Gaussian processes, the posterior distribution of the stochastic fields can be effectively quantified within the Bayesian framework with the support of experimental measurements. As this UQ approach is fully integrated into the MCFD solving process, the physical constraints of the system can be naturally preserved in the UQ results. Here, in a case study of adiabatic bubbly flow, we demonstrate that this UQ approach can quantify the model form uncertainty of the MCFD interfacial force closure relations, thus effectively improving the simulation results with relatively sparse data support.

42 ENGINEERING↗
DOE OSTI2024

Computational Methods for Multi-Physics Simulation of Melting in Steelmaking

Iron and steel production accounts for approximately 8% of global carbon dioxide (CO) emissions. Pathways to decarbonize include replacing fossil fuels in iron ore reduction and electrifying other steelmaking processes. Iron pellets produced by hydrogen, called Hydrogen Direct Reduced Iron (HDRI), have property differences from those produced using conventional DRI processes. These differences may impact melting in electric arc furnaces (EAF) and other downstream processes. The physical properties of iron pellets vary significantly with temperature during heating, complicating predictions of their behavior. In this project, we seek to develop an integrated simulation, including the fluid flow and convective thermal transport around the pellet particle. We also examine conduction and phase changes within the particle as they impact the melting process. We use adaptive mesh refinement (AMR) to resolve both the changing size of the particle and the complex physics of the interaction between the pellet and the surrounding fluid. We base our simulations on the AMReX-incflo module, which allows large-scale Navier-Stokes simulation while resolving the changing particle size during melting. As we advance our numerical tools, we anticipate an improved understanding of the dynamics of HDRI melting, which will, in turn, accelerate the adoption of low-carbon technologies in the steelmaking industry.

AMReX↗
NASA NTRS1995

Progress in Integrated Fluid/Structure/Controls Computations Using High Fidelity Equations

Aeroelasticity that involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of aircraft which can experience complex flow/structure interactions. Supersonic transports can experience vortex induced aeroelastic oscillations whereas subsonic transports can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Using these high fidelity methods, design quantities such as structural stresses can be directly computed. Computations using these high fidelity equations require state-of-the-art large computational resources. This paper will describe the transition from potential equations to Euler/Navier-Stokes equations for fluids and from modal equations to finite element equations for structures. Complexities associated with grids for moving control surfaces will be discussed. All contents of the paper will be limited to those already presented at domestic conferences within U.S. such as those sponsored by AIAA. It will not include any materials related to HPCCP computational work.

Guruswamy, Guru P.↗
DOE OSTI2019

New approach to electron microscopy imaging of gel nanocomposites in situ

We present that characterization of Au-nanocomposites is routinely done with scattering techniques where the structure and ordering of nanoparticles can be analyzed. Imaging of Poloxamer gel-based Au-nanocomposites is usually limited to cryo-TEM imaging of cryo-microtomed thin sections of the specimen. While this approach is applicable for imaging of the individual nanoparticles and gauging their size distribution, it requires altering the state of the specimen and is prone to artifacts associated with preparation protocols. Use of Scanning Transmission Electron Microscopy (S/TEM) with fluid cell in situ provides an opportunity to analysis of these complex materials in their hydrated state with nanometer resolution, yet dispensing dense gel-based samples onto electron-transparent substrates remains challenging. Here, we show that Poloxamer gel-based Au nanocomposites exhibiting thermoreversible behavior can be imaged in a fully hydrated state using a commercially available fluid cell holder, and we describe a specimen preparation method for depositing femtoliter amounts of gel-based nanocomposites directly onto the 50 nm-thick SiN window membranes. Ultimately, fluid cell S/TEM in situ imaging approach offers a pathway to visualization of individual nanoparticles within a thick gel media while maintaining the hydrated state of the carrier polymeric matrix.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Sensing of fluid viscoelasticity from piezoelectric actuation of cantilever flexural vibration

An experimental method is proposed to measure the rheological properties of fluids. The effects of fluids on the vibration actuated by piezoelectric patches were analyzed and used in measuring viscoelastic properties. Fluid-structure interactions induced changes in the beam vibration properties and frequency-dependent variations of the complex wavenumber of the beam structure were used in monitoring these changes. To account for the effects of fluid-structure interaction, fluids were modelled as a simple viscoelastic support at one end of the beam. The measured properties were the fluid’s dynamic shear modulus and loss tangent. Using the proposed method, the rheological properties of various non-Newtonian fluids were measured. The frequency range for which reliable viscoelasticity results could be obtained was 10–400 Hz. Viscosity standard fluids were tested to verify the accuracy of the proposed method, and the results agreed well with the manufacturer’s reported values. The simple proposed laboratory setup for measurements was flexible so that the frequency ranges of data acquisition were adjustable by changing the beam’s mechanical properties.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Computational Modeling of Hydraulic Properties of a Sheared Single Rock Fracture

Flow through a single mechanically sheared Marcellus shale fracture was investigated computationally and experimentally. To provide a better understanding of the variation of hydraulic and geometrical characteristics of a fracture subjected to shearing, coupled shear flow tests on the fracture for four shearing displacement steps under constant normal stress were performed. At the end of each shearing step, computed tomography (CT) scans with resolution 26.8 μm were obtained and the corresponding fracture geometries were evaluated. The CT images were used to generate full aperture maps of the fracture configuration. In addition, average aperture maps were also created by averaging the full-resolution data over 10 × 10 pixels, smoothing out fine structural details. Computational modeling of water flow through the fractures at different shearing steps was performed using a modified local cubic law approach and the 3D full Navier–Stokes equations with the use of the ANSYS-Fluent software. Both the average aperture maps and full maps were used in these simulations. The experimental pressure drops of the fracture at shearing step 1, which has very small apertures, poorly matched the numerical results, quite likely because the fracture structure was inadequately captured by the scanning resolution. Shearing typically increased the aperture height of the fracture, whose features were then better captured by the CT scan. Good agreement between the experimental data and the numerical results of the full map for shearing step 2 was observed. The simulations were performed for both full and average aperture maps, and the effects of scan resolution and surface roughness on the accuracy of the results were studied. The modified local cubic law and full Navier–Stokes simulations of the averaged map fracture were found to be in good agreement. It was conjectured that this was because the nonlinear losses were insignificant for the smoothed out averaged map fracture. Similar comparisons with those of the full map showed agreement in trends, but there were some quantitative differences. The averaged fracture map simulations also predicted lower pressure drops compared to the full map, particularly for high flow rates. These differences were due to the fine-scale geometrical complexity (surface roughness) of fracture geometry that affects the fluid flow in the fracture. In conclusion, an improved cubic law model was also proposed, and its accuracy was verified by comparing its predictions with those of the Navier–Stokes simulations.

58 GEOSCIENCES↗