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NASA NTRS2011

Method to Estimate the Dissolved Air Content in Hydraulic Fluid

In order to verify the air content in hydraulic fluid, an instrument was needed to measure the dissolved air content before the fluid was loaded into the system. The instrument also needed to measure the dissolved air content in situ and in real time during the de-aeration process. The current methods used to measure the dissolved air content require the fluid to be drawn from the hydraulic system, and additional offline laboratory processing time is involved. During laboratory processing, there is a potential for contamination to occur, especially when subsaturated fluid is to be analyzed. A new method measures the amount of dissolved air in hydraulic fluid through the use of a dissolved oxygen meter. The device measures the dissolved air content through an in situ, real-time process that requires no additional offline laboratory processing time. The method utilizes an instrument that measures the partial pressure of oxygen in the hydraulic fluid. By using a standardized calculation procedure that relates the oxygen partial pressure to the volume of dissolved air in solution, the dissolved air content is estimated. The technique employs luminescent quenching technology to determine the partial pressure of oxygen in the hydraulic fluid. An estimated Henry s law coefficient for oxygen and nitrogen in hydraulic fluid is calculated using a standard method to estimate the solubility of gases in lubricants. The amount of dissolved oxygen in the hydraulic fluid is estimated using the Henry s solubility coefficient and the measured partial pressure of oxygen in solution. The amount of dissolved nitrogen that is in solution is estimated by assuming that the ratio of dissolved nitrogen to dissolved oxygen is equal to the ratio of the gas solubility of nitrogen to oxygen at atmospheric pressure and temperature. The technique was performed at atmospheric pressure and room temperature. The technique could be theoretically carried out at higher pressures and elevated temperatures.

Hauser, Daniel M.↗

NASA NTRS2016

Generalized Fluid System Simulation Program, Version 6.0

The Generalized Fluid System Simulation Program (GFSSP) is a general purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. Two thermodynamic property programs (GASP/WASP and GASPAK) provide required thermodynamic and thermophysical properties for 36 fluids: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutene, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride, ammonia, hydrogen peroxide, and air. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. The users can also supply property tables for fluids that are not in the library. Twenty-four different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include pipe flow, flow through a restriction, noncircular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, Joule-Thompson device, control valve, heat exchanger core, parallel tube, and compressible orifice. The program has the provision of including additional resistance options through User Subroutines. GFSSP employs a finite volume formulation of mass, momentum, and energy conservation equations in conjunction with the thermodynamic equations of state for real fluids as well as energy conservation equations for the solid. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. The application and verification of the code has been demonstrated through 30 example problems.

Majumdar, A. K.↗

DOE OSTI2016

Heating production fluids in a wellbore

A method for heating a production fluid in a wellbore. The method can include heating, using a packer fluid, a working fluid flowing through a first medium disposed in a first section of the wellbore, where the first medium transfers heat from the packer fluid to the working fluid. The method can also include circulating the working fluid into a second section of the wellbore through a second medium, where the second medium transfers heat from the working fluid to the production fluid. The method can further include returning the working fluid to the first section of the wellbore through the first medium.

02 PETROLEUM↗

DOE OSTI2025

Real-fluid behavior in rapid compression machines: Does it matter?

Rapid compression machines (RCMs) have been extensively used to quantify fuel autoignition chemistry and validate chemical kinetic models at high-pressure conditions. Historically, the analyses of experimental and modeling RCM autoignition data have been conducted based on the adiabatic core hypothesis with ideal gas assumption, where real-fluid behavior has been completely overlooked, though this might be significant at common RCM test conditions. Here, this work presents a first-of-its-kind study that addresses two significant but overlooked questions for autoignition studies within RCMs in the fundamental combustion community: (i) experiment-wise, can unaccounted-for real-fluid behavior in RCMs affect the interpretation and analysis of RCM experimental data? and (ii) simulation-wise, can unaccounted-for real-fluid behavior in RCMs affect RCM autoignition modeling and the validation of chemical kinetic models? To this end, theories for real-fluid isentropic change are newly proposed and derived based on high-order Virial EoS, and are further incorporated into an effective-volume real-fluid autoignition modeling framework newly developed for RCMs. With detailed analyses, the strong real-fluid behavior in representative RCM tests is confirmed, which can greatly influence the interpretation of RCM autoignition experiments, particularly the determination of end-of-compression temperature and evolution of the adiabatic core in the reaction chamber. Furthermore, real-fluid RCM modeling results reveal that considerable error can be introduced into simulating RCM autoignition experiments when following the community-wide accepted effective-volume approach by assuming ideal-gas behavior, which can be as high as 64% in the simulated ignition delay time at compressed pressure of 125 bar and lead to contradictory validation results of chemical kinetic models. Therefore, we recommend the community to adopt frameworks with real-fluid behavior fully accounted for (e.g., the one developed in this study) to analyze and simulate past and future RCM experiments, so as to avoid misinterpretation of RCM autoignition experiments and eliminate the potential errors that can be introduced into the simulation results with the existing RCM modeling frameworks.

High-order Virial equation of state↗

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 OSTI2016

Numerical study of effect parameter fluid flow nanofluid Al{sub 2}O{sub 3}-water on heat transfer in corrugated tube

Heating or cooling fluid is a major requirement in the industrial sector, including transport, energy and production needs of the field and the field of electronics. It is known that the thermal properties of the working fluid hold an important role in the development of energy efficiency of heat transfer equipment. The cooling system can be improved either by replacing conventional cooling fluid from the fluid into the fluid of water mixed with nanoparticles (nanofluid). The method of this research is to analyze the calculations and numerical simulations of the nanofluid Al{sub 2}O{sub 3}− Water with the volume fraction of 1% and 3% coolant fluid using CFD Codes. The results of this research show the rate of heat transfer at the increasing velocity of fluid flow, with the velocity of 5 [m/s]. Whereas the 3% nanofluid have greater value than the 1% nanofluid and water, as well as for the velocity of 10 [m/s] which has almost the same pattern. Shown that the concentration of nanofluid has a value effective for improving heat release along the fluid flow rate.

42 ENGINEERING↗

DOE OSTI2025

A Comprehensive Review of Working Fluids for High-Temperature Heat Pumps: History, Selection, and Evaluation

High-temperature heat pumps (HTHPs) are essential for enhancing energy efficiency across various industrial applications, especially in terms of integrating with renewable energy sources and recovering waste heat. This article thoroughly investigates suitable working fluids for HTHPs, highlighting the evolution from traditional refrigerants to contemporary alternatives with low global warming potential (GWP). It proposes comprehensive selection criteria for these working fluids, pre-selects low-GWP working fluids, and outlines a screening methodology. The pre-selected low-GWP working fluids are evaluated for applications in three typical industrial scenarios involving HTHPs. Furthermore, this study demonstrates that regulatory compliance and environmental impacts significantly influence the development of next-generation refrigerants. The choice of working fluids is closely linked to the types of vapor compression cycles, tailored to the specific industrial applications for HTHPs. This study emphasizes areas for future research, including the development of innovative working fluids; integrated strategies that account for performance, safety, and regulatory standards; alignment of HTHP components; exploration of natural working fluids; and broadening the applications of existing working fluids.

Compression↗

DOE OSTI2015

Global chaotization of fluid particle trajectories in a sheared two-layer two-vortex flow

In a two-layer quasi-geostrophic approximation, we study the irregular dynamics of fluid particles arising due to two interacting point vortices embedded in a deformation flow consisting of shear and rotational components. The two vortices are arranged within the bottom layer, but an emphasis is on the upper-layer fluid particle motion. Vortices moving in one layer induce stirring of passive scalars in the other layer. This is of interest since point vortices induce singular velocity fields in the layer they belong to; however, in the other layer, they induce regular velocity fields that generally result in a change in passive particle stirring. If the vortices are located at stagnation points, there are three different types of the fluid flow. We examine how properties of each flow configuration are modified if the vortices are displaced from the stagnation points and thus circulate in the immediate vicinity of these points. To that end, an analysis of the steady-state configurations is presented with an emphasis on the frequencies of fluid particle oscillations about the elliptic stagnation points. Asymptotic relations for the vortex and fluid particle zero–oscillation frequencies are derived in the vicinity of the corresponding elliptic points. By comparing the frequencies of fluid particles with the ones of the vortices, relations between the parameters that lead to enhanced stirring of fluid particles are established. It is also demonstrated that, if the central critical point is elliptic, then the fluid particle trajectories in its immediate vicinity are mostly stable making it harder for the vortex perturbation to induce stirring. Change in the type of the central point to a hyperbolic one enhances drastically the size of the chaotic dynamics region. Conditions on the type of the central critical point also ensue from the derived asymptotic relations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Working Fluid Characterization and Performance Assessment of Subcritical Organic Rankine Cycles Based on the Lee–Kesler Approach for Energy Recovery

Here, a generalized model using the Lee–Kesler approach based on the corresponding states principle is developed to assess the performance of subcritical Organic Rankine Cycles operating with different working fluids. Each fluid is characterized by five parameters: the acentric factor, critical temperature, critical pressure, molar mass, and the ideal-gas ratio of specific heats at the critical temperature. The model was developed using the compressibility factor modified version of the Benedict–Webb–Rubin equation proposed by Lee and Kesler and the enthalpy and entropy functions to calculate thermodynamic state properties. The model was validated by comparing the results calculated with the model and working fluid thermodynamic properties obtained with the CoolProp database. This comparison was conducted for 91 working fluids, obtaining a relative error below 5% for 88 out of the 91 fluids (∼97%). A generalized parametric study was conducted to determine the influence of the pinch point and each fluid parameter on the performance of Organic Rankine Cycle (ORC) systems. It was found that efficiency increases with critical temperature, ideal-gas ratio of specific heats at the critical temperature, and acentric factor, reaching up to 13%. The developed model enables the evaluation of ORC system performance for existing working fluids. It also allows the formulation and evaluation of new fluids to enhance the performance of the ORC while retrieving energy from any kind of source; and likewise, the methodology can be applied to other power generation cycles.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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↗

NASA NTRS2013

Microgravity Fluids for Biology, Workshop

Microgravity Fluids for Biology represents an intersection of biology and fluid physics that present exciting research challenges to the Space Life and Physical Sciences Division. Solving and managing the transport processes and fluid mechanics in physiological and biological systems and processes are essential for future space exploration and colonization of space by humans. Adequate understanding of the underlying fluid physics and transport mechanisms will provide new, necessary insights and technologies for analyzing and designing biological systems critical to NASAs mission. To enable this mission, the fluid physics discipline needs to work to enhance the understanding of the influence of gravity on the scales and types of fluids (i.e., non-Newtonian) important to biology and life sciences. In turn, biomimetic, bio-inspired and synthetic biology applications based on physiology and biology can enrich the fluid mechanics and transport phenomena capabilities of the microgravity fluid physics community.

biology↗

NASA NTRS2023

Intravenous Fluid Generation Mini (IVGEN Mini) Summary and Related Research

This paper assists the ongoing effort to support NASA Glenn’s mission and its Human Research Program (HRP) core competency by investigating a technology demonstration to mitigate human health and performance risks during space exploration. Crew health and performance are critical to successful human exploration beyond low Earth orbit. Four hundred forty-two medical conditions have been identified and may present and require treatment during long-duration space exploration missions. One hundred fifteen out of four hundred forty-two identified medical conditions would require medical fluid treatment, generating a need for an on-demand or continuous supply of medical fluid. Intravenous Fluid Generation Mini (IVGEN Mini) is a technology demonstration designed to demonstrate a water purification and pharmaceutical mixing system that can make intravenous (IV) fluid in microgravity and builds on the success of the original Intravenous Fluid Generation for Exploration Missions (IVGEN) experiment, which flew on the ISS in March 2010. IVGEN Mini seeks to increase the Technology Readiness Level (TRL) and the overall function of the original IVGEN experiment to reduce the dependence of a needed medical consumable and streamline the size of the device and process to generate IV fluid IVGEN Mini is funded by the Advanced Exploration Systems (AES) directorate via the Exploration Medical Integrated Product Team (XMIPT) as a part of their mission to advance exploration medical technologies to benefit the overall health and safety of crews for beyond low Earth orbit space missions. This paper discusses a collection of related research topics such as microgravity fluid mixing and studying past efforts of IV fluid usage in extreme environments to aid IVGEN Mini project scientists in developing the IVGEN Mini technology.

iv generation↗

DOE OSTI2017

On the micromechanics of slip events in sheared, fluid-saturated fault gouge

We used a three-dimensional discrete element method coupled with computational fluid dynamics to study the poromechanical properties of dry and fluid-saturated granular fault gouge. The granular layer was sheared under dry conditions to establish a steady state condition of stick-slip dynamic failure, and then fluid was introduced to study its effect on subsequent failure events. The fluid-saturated case showed increased stick-slip recurrence time and larger slip events compared to the dry case. Particle motion induces fluid flow with local pressure variation, which in turn leads to high particle kinetic energy during slip due to increased drag forces from fluid on particles. The presence of fluid during the stick phase of loading promotes a more stable configuration evidenced by higher particle coordination number. Our coupled fluid-particle simulations provide grain-scale information that improves understanding of slip instabilities and illuminates details of phenomenological, macroscale observations.

58 GEOSCIENCES↗

DOE OSTI2022

Non-equilibrium molecular dynamics simulation to evaluate the effect of confinement on fluid flow in silica nanopores

The flow of fluids in nano-confinement has applications in separations, water purification, medical systems and in the recovery of fluids in petroleum systems. It is believed that fluids do not obey continuum laws when flowing in nanopores (or in confinement). This paper attempts to shed light on various nano confinement effects such as fluid-wall interactions, pore size and molecular geometry, using molecular dynamic simulation. Here, water, hexane, and methanol flow behaviors were simulated for pore diameters ranging from 1 to 8 nm. In addition to the density analysis of the confined fluids, the fluid flows in saturated nanopores were simulated by the sectional flow method. Water and methanol molecules were completely stabilized in the 1 nm pore. Hexane molecules could not enter the 1 nm pore, due to geometric considerations. For the 2 – 8 nm pores, all fluids showed reduced flow rate compared to the Hagen–Poiseuille flow, due to an interfacial molecular layer stabilized at the pore surface. Flow reduction observed in these studies is contrary to significant flow enhancements observed for fluid flow in carbon nanotubes of similar dimensions. Water flow showed almost constant stick length for all the pore sizes. Methanol flow had the largest stick length. Hexane flow was reduced because of overcrowding of molecules at the pore surface. The effect of confinement diminished with an increase in pore diameter.

42 ENGINEERING↗

DOE OSTI2023

Effect of initial water saturation on the performance of fracturing fluids with and without polyallylamine under simulated EGS conditions

Objectives/Scope: StimuFrac (US Patents 9,873,828 B2 and 9,447,315 B2), a CO 2 - reactive polymer aqueous solution [polyallylamine (PAA) 1wt% in water] combined with CO 2 , can be used as a potentially less water-intensive fracturing fluid for enhanced geothermal systems (EGS). Our previous results show that in hot dry rock (HDR), PAA/CO 2 fracturing fluids outperformed other fluids such as water, CO 2 , and CO 2 /water in generating large fractures with less fluid consumed. The objective of this work is to investigate the effect of initial water saturation on the performance of StimuFrac by conducting hydraulic fracturing tests with ½ foot cubic rock samples held under representative EGS stress/temperature conditions and by using cyclic injection strategies (under constant injection rate). The resulting fracture hydraulic conductivities, breakdown pressures, and volumes of fluids required are compared. Methods/Procedures/Process: To simulate geothermal reservoir conditions, in all tests, the rock sample was held under triaxial confinement and at 200 °C, and different volumes of water were initially injected into the rock sample before any fracturing processes were initiated. For the single-cycle PAA (or water) alternating CO 2 (PAG or WAG) injection fracturing experiments, one complete cycle consisted of two steps: (1) injecting a PAA slug (or water slug) followed by (2) injecting CO 2 to initiate and propagate the fracture. For experiments involving multiple injection cycles, the CO 2 injection pressure is increased until it peaks and begins to decline (indicating fracture initiation at this moment), and then continued being injected for another 30 seconds to propagate the fracture. Then, these two-step cycles [injection of PAA (or water) followed by CO 2 injection (up to 2-4 mL/min)] are repeated. Applications/Significance/Novelty: The results of this study suggest that water saturation significantly affects the fracturing fluid transmission into the rock pore space, thus affecting the fracture initiation and propagation. In this study, fracturing tests via a single injection cycle or multiple injection cycles were performed. Splitting the rock samples in half after testing reveals that fracture propagation is significantly limited under high water saturation conditions (three-day initial water injection) compared to stimulation experiments performed in hot dry rock. The fractures propagate less than 1/3 of the distance from the wellbore to the outer rock surface, and in some cases, no fracture is generated. This may be caused by leak-off dominating the fracturing process and the fluid injection rate is insufficient to overcome leak-off, even under high injection rate conditions. Additionally, CO 2 could be leaking off into the wellbore annulus and this may be making it more difficult to generate sufficiently high-pressure gradients away from the near-wellbore region. Under low water saturation conditions (dry rock or after 1-day initial water injection), PAA/CO 2 consistently generated significantly larger fractures compared with the other fluids. CO 2 generated large fractures only in the hot dry rock and only when using high injection rates, though data variability is high.

58 GEOSCIENCES↗

DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Shale-fluid interactions during forced lmbibition and flow-back

One way to minimize the need for disposal of flow-back waters produced during the hydraulic fracturing of unconventional reservoirs is, potentially, to recycle these fluids by recovering and re-injecting them during hydraulic fracturing of nearby new wells. These flow-back waters contain, however, large concentrations of dissolved salts. During hydraulic fracturing of unconventional reservoirs, a well may undergo extended shut-in periods, following the initial hydraulic-fracture stimulation. The concern here, therefore, is that the salts dissolved in the re-injected flow-back waters may precipitate in the subsurface, thus promoting scale formation; or alternately, because of their high salinity, these same fluids may cause the dissolution of various minerals present in the subsurface. Large divalent cations (e.g., Ca²⁺, Ba²⁺ and Sr²⁺) and anions (e.g., CO3²⁻ and SO4²) may chemically interact with and cause the swelling of clay fractions, thus blocking pores in certain pore size ranges. All these phenomena (i.e., scale formation, clay swelling, minerals dissolution) can influence the petrophysical properties of the formation, including its permeability, porosity, contact angle, etc. One way to potentially overcome some of these technical challenges, is to pre-treat these flow-back waters, prior to re-injection (e.g., via chemical precipitation, followed by membrane filtration) in order to remove unwanted salts. However, such pre-treatment is costly, and the degree of salt removal needed to prevent formation damage is important in determining the economic viability of flow-back water recycle via re-injection. A key focus of this work, therefore, is to study the impact that the injection of flow-back waters, that have undergone varying degrees of pre-treatment and clean-up, will have on the flow-through characteristics of a tight-gas reservoir, particularly of the Marcellus Shale formation. To do so, we have carried-out forced-imbibition experiments with shale samples from various depths in the Marcellus formation, whose properties span high to low ranges of TOC, clay content and matrix permeabilities. We have studied the forced-imbibition characteristics, at an injection pressure of 24,233 kPa (3500 psig), of various flow-back fluids into shale cores saturated with methane at a pore pressure of 17,338 kPa (2500 psig) and a confining stress of 27,680 kPa (4000 psig). Following the forced imbibition experiments, we analyzed the cores for potential changes in permeability and porosity. Quantification of the ion content of the injected and recovered fluids was also performed using Ion Chromatography (IC). The IC analysis of the recovered fluids indicates substantial interactions and geochemical reactions between the invading fluids and the shale cores. The injection of flow-back fluids shows significant impact on the flow-through characteristics, with untreated flow-back fluids, which have the highest cation and anion content, also exhibiting the highest observable reductions in permeability (>90%).

defects, mechanical behavior, carbon sequestration↗