Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Multiphase flows”

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 775 records · Page 43

Artificial Neural Network Representation of Dynamic Criticality Excursion Experiment Data

This paper outlines time dependent considerations in applying the artificial neural network (ANN) paradigm to dynamic nuclear criticality excursion experiment data. The ANN amongst a variety of uses, can apply to function fitting of multiple input-multiple output data sets, pattern recognition, cluster analysis, and time series prediction. The ANN is a component of Machine Learning (ML) data analysis. The practical application of ML to criticality safety has been funded through the Y-12 Plant Directed Research and Demonstration (PDRD) program to support criticality safety and emergency planning efforts. The initial effort considered function fitting of criticality excursion data. Recent efforts successfully extended the ANN to criticality safety code validation. The initial ANN work applied to criticality excursions centered around multivariate function fitting of static (tabular) data taken from the French Consequences Radiologiques d'un Accident de Criticite (CRAC) and SILENE reactor campaigns. The former report (LeCorche) summarized important tabular data for the first 44 CRAC experiments. The initial ANN was trained to specific time-independent inputs, then applied to predict peak fission rate and total fissions for a wide variety of fissile solutions process conditions. This work extends that effort to apply the ANN paradigm to dynamic prediction of time-dependent criticality excursion experiment data. A dynamic criticality excursion in fissile solution represents a complex multiphysics phenomenon. Factors include among other things, coupled neutronic, multiphase fluid flow, temperature, pressure, acoustic shock, boiling heat transfer, reactivity feedback, and radiolytic gas considerations. There have been many efforts to model (over time) as coupled ordinary and (space) as partial differential equations (ODE, PDE). The ANN representation noted here does not rely on solving explicit ODE or PDEs. Rather the intent is to demonstrate that as a time series, the criticality excursion can be predicted by training specific ANN architectures to experimental input and output time series exclusively. The rationale for extending this work to the time-dependent regime is important in developing a 'criticality excursion emulator' solely on the basis of learning characteristics from experiment dynamic data. An emulator is different than a computer code simulator driven by the solution of ODEs and PDEs given select 'tuning parameters' that match outputs to experiments. A criticality excursion emulator, derived exclusively from an ANN or ML, could predict most likely excursion characteristics, trained from historic dynamic experiment data, presented with input values within the range of those experiments. The work noted shows that generic time-series ANN architectures can be satisfactorily applied to the prediction of dynamic, extremely chaotic criticality excursion power given an initial time dependent input series. In reality, an excursion emulator could be driven by user-supplied initial (t=0), time independent or constant values to generate time dependent outputs. Thus ongoing work includes developing a custom ANN such that initial dynamic conditions would be predicted. Those results then serve as inputs to a customized ANN architecture currently in development. (author)

42 ENGINEERING↗

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↗

Evaluation of CFD Methods for Simulation of Two-Phase Boiling Flow Phenomena in a Helical Coil Steam Generator

The U.S. Department of Energy, Office of Nuclear Energy charges participants in the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program with the development of advanced modeling and simulation capabilities that can be used to address design, performance and safety challenges in the development and deployment of advanced reactor technology. The NEAMS has established a high impact problem (HIP) team to demonstrate the applicability of these tools to identification and mitigation of sources of steam generator flow induced vibration (SGFIV). The SGFIV HIP team is working to evaluate vibration sources in an advanced helical coil steam generator using computational fluid dynamics (CFD) simulations of the turbulent primary coolant flow over the outside of the tubes and CFD simulations of the turbulent multiphase boiling secondary coolant flow inside the tubes integrated with high resolution finite element method assessments of the tubes and their associated structural supports. This report summarizes the demonstration of a methodology for the multiphase boiling flow analysis inside the helical coil steam generator tube. A helical coil steam generator configuration has been defined based on the experiments completed by Polytecnico di Milano in the SIET helical coil steam generator tube facility. Simulations of the defined problem have been completed using the Eulerian-Eulerian multi-fluid modeling capabilities of the commercial CFD code STAR-CCM+. Simulations suggest that the two phases will quickly stratify in the slightly inclined pipe of the helical coil steam generator. These results have been successfully benchmarked against both empirical correlations for pressure drop and simulations using an alternate CFD methodology, the dispersed phase mixture modeling capabilities of the open source CFD code Nek5000.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Capillary Pressure to Relative Permeability: Task 7.3.4 Relative Permeability Analysis Final Report

Surface tension affects all aspects of fluid flow in porous media. Through measurements of surface tension interaction under multiphase conditions, a relative permeability relationship can be determined. Relative permeability is a numerical description of the interplay between two or more fluids and the porous media they flow through. It is a critical parameter for various tools used to characterized subsurface multiphase flow systems, such as numerical simulation for oil and gas development, carbon sequestration, and groundwater contamination remediation. Therefore, it is critical to get a good statistic distribution of relative permeability in the porous media under study. Empirical relationships for determining relative permeability from capillary pressure are already well established but do not provide the needed flexibility required to match laboratory derive relative permeability relationships. By expanding the existing methods for calculating relative permeability from capillary pressure data, it is possible to create both two and three-phase relative permeability relationships. Existing laboratory-measured relative permeability data along with mercury intrusion capillary (MICP) data coupled with interfacial tension and contact angle measurements were used to determine the efficacy of this approach to relative permeability curve creation. The relative permeability relationships determined with this method were fit to existing laboratory data to elucidate common fitting parameters that were then used to create relative permeability relationships from MICP data that does not have an associated laboratory-measured relative permeability relationship.

58 GEOSCIENCES↗

Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections

This panel presentation focuses on multiphase radial distribution networks with wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase power flow models are developed to facilitate the integration of delta-connected loads or generation resources in the OPF problem. The first model is referred to as the extended branch flow model (EBFM). The second model leverages a linear relationship between phase-to-ground power injections and delta connections that holds under a balanced voltage approximation (BVA). Based on these models, pertinent OPF problems are formulated and relaxed to semidefinite programs (SDPs). Numerical studies on IEEE test feeders show that the proposed SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidence also indicates that solving the resultant SDP under BVA is faster than under EBFM. Moreover, both SDP solutions are numerically exact with respect to voltages and branch flows. It is further shown that the SDP solution under BVA has a small optimality gap, and the BVA model is accurate in the sense that it reproduces actual system voltages.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A QCQP Approach for OPF in Multiphase Radial Networks with Wye and Delta Connections: Preprint

This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated using two unbalanced multiphase distribution feeders with both wye and delta connections.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

High-Speed Synchrotron X-ray Imaging Studies of the Ultrasound Shockwave and Enhanced Flow during Metal Solidification Processes

The highly dynamic behavior of ultrasonic bubble implosion in liquid metal, the multiphase liquid metal flow containing bubbles and particles, and the interaction between ultrasonic waves and semisolid phases during solidification of metal were studied in situ using the complementary ultrafast and high-speed synchrotron X-ray imaging facilities housed, respectively, at the Advanced Photon Source, Argonne National Laboratory, US, and Diamond Light Source, UK. Real-time ultrafast X-ray imaging of 135,780 frames per second revealed that ultrasonic bubble implosion in a liquid Bi-8 wt pctZn alloy can occur in a single wave period (30 kHz), and the effective region affected by the shockwave at implosion was 3.5 times the original bubble diameter. Furthermore, ultrasound bubbles in liquid metal move faster than the primary particles, and the velocity of bubbles is 70 similar to 100 pct higher than that of the primary particles present in the same locations close to the sonotrode. Ultrasound waves can very effectively create a strong swirling flow in a semisolid melt in less than one second. The energetic flow can detach solid particles from the liquid-solid interface and redistribute them back into the bulk liquid very effectively.

Tan, Dongyue↗

TOUGH-RFPA: Coupled thermal-hydraulic-mechanical Rock Failure Process Analysis with application to deep geothermal wells

This paper presents a coupled thermal-hydraulic-mechanical (THM) model for simulating failure processes in geological media. The coupling between stress/strain and heat transfer describing how thermal expansion affects stress is based on the theory of thermo-elasticity. Additionally, the coupling between stress/strain and fluid flow describing how pore-pressure affects stress is governed by Biot's consolidation theory. Stress/strain-dependent porosity/permeability/capillary-pressure defines the influence of stress on fluid flow and thermal fields. The THM model is implemented in the solver module that links the multiphase, multicomponent fluid flow simulator TOUGH2 with the geomechanical simulator RFPA (Rock Failure Process Analysis), which is based on the concept that heterogeneity leads to non-linearity and progressive failure behavior. Capability of TOUGH-RFPA simulator was verified by two benchmark problems related to hydraulic-mechanical and thermal-mechanical response in a hollow cylinder. Then the applicability of TOUGH-RFPA was demonstrated for modeling cooling-induced damage around a very deep geothermal well with mesoscopic heterogeneous properties, which showed complex damage evolution and fracturing during well cooling and fluid pressurization.

42 ENGINEERING↗

A general peridynamics model for multiphase transport of non-Newtonian compressible fluids in porous media

Herein a general state-based peridynamics model is developed to simulate transport of fluids in an arbitrary heterogeneous porous medium. The generality encompasses modeling of multiphase, multi-component flow of non-Newtonian and compressible fluids, which is often encountered in but not limited to subsurface reservoirs. Peridynamic model is especially useful for solving non-local problems, such as crack propagation, since it does not assume spatial continuity of field variables. Thus, the formulation presented here, combined with peridynamics-based damage model, can be used to simulate hydraulic fracturing with complex fluids. To demonstrate its capability to simulate multi-phase flow in porous media, the derived model is verified against the analytical Buckley-Leverett solution for immiscible Newtonian two-phase flow. Further, the non-Newtonian two-phase fluid flow in porous media is verified by simulating the polymer flood process involving immiscible displacement of a Newtonian fluid by a non-Newtonian fluid against a generalized solution obtained by Wu et al. The non-local solutions are shown to be consistent with the corresponding local solutions in limiting cases. Moreover, mass conservation of all the phases is satisfied, irrespective of discretization and extent of non-locality.

42 ENGINEERING↗

Pore scale study of multiphase multicomponent reactive transport during CO 2 dissolution trapping

Solubility trapping is crucial for permanent CO 2 sequestration in deep saline aquifers. For the first time, a pore-scale numerical method is developed to investigate coupled scCO 2 -water two-phase flow, multicomponent (CO 2 (aq), H + , HCO 3 – , CO 3 2 – and OH – ) mass transport, heterogeneous interfacial dissolution reaction, and homogeneous dissociation reactions. Pore-scale details of evolutions of multiphase distributions and concentration fields are presented and discussed. Time evolutions of several variables including averaged CO 2 (aq) concentration, scCO 2 saturation, and pH value are analyzed. Specific interfacial length, an important variable which cannot be determined but is required by continuum models, is investigated in detail. Mass transport coefficient or efficient dissolution rate is also evaluated. The pore-scale results show strong non-equilibrium characteristics during solubility trapping due to non-uniform distributions of multiphase as well as slow mass transport process. Complicated coupling mechanisms between multiphase flow, mass transport and chemical reactions are also revealed. Lastly, effects of wettability are also studied. The pore-scale studies provide deep understanding of non-linear non-equilibrium multiple physicochemical processes during CO 2 solubility trapping processes, and also allow to quantitatively predict some important empirical relationships, such as saturation-interfacial surface area, for continuum models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computational Study of Droplet Dynamics in Dispersed Flow Film Boiling Regime in PWR Geometries

Dispersed flow film boiling (DFFB) regime is exhibited during low-flooding rate conditions following the postulated Loss-of-Coolant Accident (LOCA) in nuclear reactor flow channels. LOCA is a type of design-basis accident scenario, which is crucial for reactor design and licensing. Accurate models to predict the heat transfer in DFFB regime is critical for the reactor to maintain safety limits. The nominal operating linear heat rate is also set based on the maximum linear heat rate determined for a LOCA transient. It is understood that the behavior of entrained droplets in DFFB regime greatly affects the heat transfer by evaporating and desuperheating the surrounding steam. Furthermore, interaction with flow structures also aids in increasing the evaporation rate of entrained droplets. In order to quantify this enhancement in heat transfer, the size of droplets downstream of flow structures (Spacer Grids and Mixing Vanes) is of crucial importance. Thermal hydraulic analysis codes like COBRA-TF, CATHARE-3 and adopt a three-field equation model that allows them to model the droplet field separately. However, to ensure the accuracy of these field equations, various correlations and physical models are required. This paper proposes a method for characterizing the mean Sauter Diameter of droplets across spacer-grids and mixing vanes in PWR sub-channels using PHASTA - a high fidelity flow solver with multiphase capabilities using the level-set method. The PHASTA code is a finite element based computational fluid dynamics code designed for solving compressible and incompressible turbulent flows. It has been demonstrated to be massively scalable (up to 786,432 cores), which is crucial for simulating large realistic domains. The code incorporates the level-set method for interface tracking of the gas-liquid interface.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Chen, Yen-Sen↗

Flow-Driven Branching in a Frangible Porous Medium

Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium. We provide a simple theoretical framework that embodies this feedback mechanism in a multiphase model for flow through a frangible porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. Furthermore, this allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.

36 MATERIALS SCIENCE↗

Multiphase computational fluid dynamics modeling of reacting flows in absorption columns for carbon capture

First-principles derived computational fluid dynamics (CFD) simulations have been proposed as a fundamental tool for investigating solvent-based CO 2 absorption in packed columns due to their ability to accurately represent the underlying nonlinear, multiscale dynamics. Numerous studies have previously utilized such CFD simulations to investigate hydrodynamics of columns with structured and random packings by assessing the key hydrodynamic metrics such as the interfacial and wetted areas. While mapping such metrics for different conditions is essential to the optimization of absorption columns, it is not sufficient, as the CO 2 capture rate depends also on the coupled, nonlinear dynamics from the underlying chemical reaction kinetics, thermodynamics, and heat-transfer rates. In this work, we present detailed CFD simulation results augmented by incorporating the effects of interfacial physical mass transfer of CO 2 , heat release from chemical reaction kinetics, and thermophysical property variations from resulting temperature gradients. We demonstrate the applicability of the proposed approach in numerically assessing the performance of packed columns by evaluating key hydrodynamic quantities, CO 2 absorption rates, and temperature rise in a reference column with packings that are structurally similar to the Sulzer Mellapak™ 250.Y packing, for different solvent inflow velocities and temperatures. Predictions from simulation results are found to be consistent with the trends in experimental observations from the literature, suggesting that the predictive capabilities of the simulation framework can be leveraged to guide the future development of absorber-column designs and optimized process flowsheets.

Absorption columns↗

A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]

A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM + -up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. The resulting method is significantly less expensive in regions where otherwise the Riemann solver would be invoked. A transformation from conservative variables to primitive variables is presented and the primitive variables are then solved in the implicit method in order for the current finite volume method to be able to solve, effectively and efficiently, low Mach number flows in traditional multiphase applications, which otherwise is a great challenge for the standard density-based algorithms. Here, a number of benchmark test cases are presented to assess the performance and robustness of the developed finite volume method for both inviscid and viscous two-phase flow problems. The numerical results indicate that the current density-based method provides an attractive and viable alternative to its pressure-based counterpart for compressible two-phase flows at all speeds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

An extension of Darcy’s law incorporating dynamic length scales

We propose a physics-based, macroscale formulation of multiphase porous-media flows that both honors the validity of Darcy’s law in steady or near-steady flows and accommodates the effects of heterogeneities and nonlinearities in unsteady flows. The new formulation recognizes that parameters characterizing the system operate at different length-scales. In particular, the use of Darcy’s law, predicated on the assumption of near-steady flows, requires dynamic length scales, owing to the possibility of rapid fluctuations in rock properties and fluid saturations attributable to heterogeneity and nonlinearity. We accommodate these dynamic length-scales through dynamic spatial averaging. The length and position of the averaging window are characterized by the length of the mixing zone and the direction of propagation of information in the transport process. Here, we validate the proposed formulation by comparing highly accurate,two dimensional numerical solutions against core-scale displacement experiments. The proposed paradigm is consistent with the classical multiphase Darcy formulation, in the sense that the latter also represents the results of an averaging approach.

42 ENGINEERING↗

Radiation/convection coupling in rocket motor and plume analysis

A method for describing radiation/convection coupling to a flow field analysis was developed for rocket motors and plumes. The three commonly used propellant systems (H2/O2, RP-1/O2, and solid propellants) radiate primarily as: molecular emitters, non-scattering small particles (soot), and scattering larger particles (Al2O3), respectively. For the required solution, the divergence of the radiation heat flux was included in the energy equation, and the local, volume averaged intensity was determined by a solution to the radiative transfer equation. A rigorous solution to this problem is intractable, therefore, solution methods which use the ordinary and improved differential approximation were developed. This radiation model was being incorporated into the FDNS code, a Navier-Stokes flowfield solver for multiphase, turbulent combusting flows.

Saladino, A. J.↗