Search NASA⌕ Search

SEARCH · Search NASA

Results for “matrix diffusion”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Impact of Radiogenic Heating on the Formation Conditions of Comet 67P/Churyumov–Gerasimenko

Because of the high fraction of refractory material present in comets, the heat produced by the radiogenic decay of elements such as aluminum and iron can be high enough to induce the loss of ultravolatile species such as nitrogen, argon, or carbon monoxide during their accretion phase in the protosolar nebula (PSN). Here, we investigate how heat generated by the radioactive decay of {sup 26}Al and {sup 60}Fe influences the formation of comet 67P/Churyumov–Gerasimenko, as a function of its accretion time and the size of its parent body. We use an existing thermal evolution model that includes various phase transitions, heat transfer in the ice-dust matrix, and gas diffusion throughout the porous material, based on thermodynamic parameters derived from Rosetta observations. Two possibilities are considered: either, to account for its bilobate shape, 67P/Churyumov–Gerasimenko was assembled from two primordial ∼2 km sized planetesimals, or it resulted from the disruption of a larger parent body with a size corresponding to that of comet Hale–Bopp (∼70 km). To fully preserve its volatile content, we find that either 67P/Churyumov–Gerasimenko’s formation was delayed between ∼2.2 and 7.7 Myr after that of Ca–Al-rich Inclusions in the PSN or the comet’s accretion phase took place over the entire time interval, depending on the primordial size of its parent body and the composition of the icy material considered. Our calculations suggest that the formation of 67P/Churyumov–Gerasimenko is consistent with both its accretion from primordial building blocks formed in the nebula or from debris issued from the disruption of a Hale–Bopp-like body.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Structure and ionic conductivity of well-aligned polycrystalline sodium titanogallate grown by reactive diffusion

We prepared the b-axis-oriented polycrystalline Na{sub 0.85}Ti{sub 0.51}Ga{sub 4.37}O{sub 8} (NTGO) embedded in Ga{sub 2}O{sub 3}-doped Na{sub 2}Ti{sub 4}O{sub 9} matrix using the reactive diffusion technique. When the sandwich-type Ga{sub 2}TiO{sub 5}/NaGaO{sub 2}/Ga{sub 2}TiO{sub 5} diffusion couple was heated at 1323 K for 24 h, the NTGO polycrystal was readily formed in the presence of a liquid phase. The resulting polycrystalline material was characterized by X-ray diffractometry, electron microscopy and impedance spectroscopy. We mechanically processed the annealed diffusion couple and obtained the thin-plate electrolyte consisting mostly of the grain-aligned NTGO polycrystal. The ionic conductivity (σ) of the electrolyte along the common b-axis direction steadily increased from 1.3×10{sup −4} to 7.3×10{sup −3} S/cm as the temperature increased from 573 to 1073 K. There was a slope change at ca. 792 K for the Arrhenius plot of σ; the activation energies were 0.39 eV above this temperature and 0.57 eV below it. The NTGO showed the crystal structure (space group C2/m) with substantial positional disordering of one of the two Ga sites. The Na{sup +} ions occupied ca. 43% of the Wyckoff position 4i site, the deficiency of which would contribute to the relatively high ionic conductivity along the b-axis. The reactive diffusion could be widely applicable as the novel technique to the preparation of grain-aligned ceramics of multi-component systems. - Graphical abstract: We have prepared the b-axis-oriented Na{sub 0.85}Ti{sub 0.51}Ga{sub 4.37}O{sub 8} polycrystal embedded in Ga{sub 2}O{sub 3}-doped Na{sub 2}Ti{sub 4}O{sub 9} matrix by the heat treatment of sandwich-type diffusion couple of Ga{sub 2}TiO{sub 5}/NaGaO{sub 2}/Ga{sub 2}TiO{sub 5}. The resulting Na{sub 0.85}Ti{sub 0.51}Ga{sub 4.37}O{sub 8} electrolyte showed the ionic conductivity ranging from 1.3×10{sup −4} S/cm at 573 K to 7.3×10{sup −3} S/cm at 1073 K. - Highlights: • The b-axis-oriented polycrystalline Na{sub 0.85}Ti{sub 0.51}Ga{sub 4.37}O{sub 8} is successfully prepared. • Crystal structure of Na{sub 0.85}Ti{sub 0.51}Ga{sub 4.37}O{sub 8} is determined by single-crystal XRD. • The polycrystal shows relatively high Na{sup +} ion conductivity along the common b-axis. • Reactive diffusion is successfully used for the preparation of grain-aligned ceramics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Oxygen isotope thermometry using quartz inclusions in garnet

Oxygen isotope ratios of quartz inclusions (QI) within garnet from granulite and amphibolite facies gneisses in the Adirondack Mountains, NY were analysed and used to determine metamorphic temperatures. Primary QI for eight of 12 samples have δ 18 O values significantly lower than matrix quartz (MQ). The primary QI retain δ 18 O values representative of thermal conditions during garnet crystallization, whereas the δ 18 O values of MQ were raised by diffusive exchange with other matrix minerals (e.g. mica and feldspar) during cooling. The δ 18 O differences between QI and MQ show that garnet (a mineral with slow diffusion of oxygen) can armour QI from isotopic exchange with surrounding matrix, even during slow cooling. These differences between δ 18 O in MQ and QI can further be used to test cooling rates by Fast Grain Boundary diffusion modelling. Criteria for identifying QI that preserve primary compositions and are suitable for thermometry were developed based on comparative tests. Relations between δ 18 O and inclusion size, distance of inclusion to host–garnet rim, core–rim zonation of individual inclusions, and presence or absence of petrological features (healed cracks in QI, inclusions in contact with garnet cracks lined by secondary minerals, and secondary minerals along the inclusion grain boundary) were investigated. In this study, 61% of QI preserve primary δ 18 O and 39% were associated with features that were linked to reset δ 18 O values. If δ 18 O in garnet is homogeneous and inclusions are removed, laser-fluorination δ 18 O values of bulk garnet are more precise, more accurate, and best for thermometry. Intragrain δ 18 O(Grt) profiles measured in situ by ion microprobe show no δ 18 O zonation. Almandine–rich garnet (Alm 60–75 ) from each sample was measured by laser-fluorination mass-spectrometry (LF-MS) for δ 18 O and compared with ion microprobe measurements of δ 18 O in QI for thermometry. The Δ 18 OO(Qz–Grt) values for Adirondack samples range from 2.66 to 3.24‰, corresponding to temperatures of 640–740 °C (A[Qz–Alm] = 2.71). Out of 12 samples that were used for thermometry, nine are consistent with previous estimates of peak temperature (625–800 °C) based on petrological and carbon–isotope thermometry for regional granulite and upper amphibolite facies metamorphism. The three samples that disagree with independent thermometry for peak metamorphism are from the anorthosite–mangerite–charnockite–granite suite in the central Adirondacks and yield temperatures of 640–665 °C, ~100 °C lower than previous estimates. Finally, these low temperatures could be interpreted as thermal conditions during late (post-peak) crystallization of garnet on the retrograde path.

58 GEOSCIENCES↗
DOE OSTI2016

Dynamic tensile deformation and damage of B 4 C-reinforced Al composites: Time-resolved imaging with synchrotron x-rays

Dynamic tensile experiments are conducted on 15% and 30% in weight percentage B 4 C/Al composites with a split Hopkinson tension bar, along with high-speed synchrotron x-ray digital image correlation (XDIC) to map strain fields at μ m and μ s scales. As manifested by bulk-scale stress – strain curves, a higher particle content leads to a higher yield strength but lower ductility. Strain field mapping by XDIC demonstrates that tension deformation and tensile fracture, as opposed to shear and shear failure, dominate deformation and failure of the composites. The fractographs of recovered samples show consistent features. The particle-matrix interfaces are nucleation sites for strain localizations, and their propagation and coalescence are diffused by the Al matrix. The reduced spacing between strain localization sites with increasing particle content, facilitates their coalescence and leads to decreased ductility. Furthermore, designing a particle-reinforced, metallic-matrix composite with balanced strength and ductility should consider optimizing the inter-particle distance as a key par

36 MATERIALS SCIENCE↗
DOE OSTI2021

Precipitate growth kinetics under inhomogeneous concentration fields using a phase-field model

We investigate precipitation dynamics in the presence of a local solute gradient using phase-field simulations. During the homogenization heat treatment of the solidified Inconel 718 alloy, high Nb concentration within the Laves phases or at the core of the secondary arms results in Nb diffusion into the γ matrix. The volume fraction and spatial distribution of precipitation during subsequent annealing can be controlled by tailoring the Nb concentration gradient in the matrix during homogenization. We use a surrogate Ni-Fe-Nb alloy for Inconel 718 to explore the growth dynamics of δ precipitates related to the local Nb concentration levels. The simulations indicate that in the presence of a Nb concentration gradient the growth rate of δ precipitates is higher than in a matrix of uniform average Nb concentration. The higher growth rate is a result of the higher local thermodynamic driving force at the interface between the solute-rich matrix and the δ interface. Here, we propose a phenomenological model to describe the diffusion-controlled growth kinetics of the δ phase under a solute concentration gradient.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Morphology Evolution in Self-Healing Liquid-Gallium-Based Mg-Ion Battery Anode

Conventional solid battery anodes suffer from dendrite growth and volume changes, resulting in poor cycling performances. Self-healing electrodes made of liquid metals and alloys can overcome these issues by reversibly undergoing liquid–solid phase transformations during (dis)charging. Just recently, we achieved 1000 cycles in Mg-ion battery anodes using liquid Ga as the active material, which reversibly transformed into solid Mg 2 Ga 5 during (de)magnesiation. However, the fundamental mechanism behind this liquid–solid phase transformation remains unclear. In this follow-up work, cryogenic focused ion beam electron microscopy is used to elucidate the morphology evolution when liquid Ga embedded in a carbon-binder matrix transforms into solid Mg 2 Ga 5 during cycling. We found that liquid Ga gradually diffuses into the surrounding matrix, increasing the contact area between active material and electrolyte, facilitating the charge transfer process. These new insights will help understand the performance of alkali- and alkaline-earth-metal batteries based on liquid anodes.

25 ENERGY STORAGE↗
DOE OSTI2025

Developing the Science Basis for Understanding Polymer Encapsulant Degradation Mechanisms: DuraMAT 2.0 Final Project Report

Polymeric encapsulants are essential materials in photovoltaic modules, protecting sensitive electronics from the environment while providing mechanical integrity to the multilayered assembly. However, these polymeric materials are susceptible to degradation processes driven by the ingress of environmental species, ultraviolet radiation, thermal stresses, and mechanical loading. In this study, we employ a combined atomistic simulation and accelerated aging experimental approach to study the molecular-scale mechanisms of encapsulant degradation. Classical molecular dynamics simulations quantify the diffusion of environmental and degradation species through the polymer matrix, producing composition-specific diffusion coefficients. Reactive simulations characterize activation energy barriers and reaction rate constants for key chemical pathways. In parallel, thermal-desorption analyses coupled with mass spectrometry monitor the emergence and concentration profiles of degradation products under controlled stressor conditions. By integrating simulation and experiment, we establish quantitative correlations between polymer composition, species diffusivity, and chemical reactivity. We anticipate that these relations and quantitative values could serve as high-fidelity inputs to reaction-diffusion models, enabling physics-informed lifetime predictions and guiding the design of more durable encapsulant materials for solar energy applications.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Investigating the stability of second phase particles in Zr-Nb alloys under irradiation

The stability of the β-Nb Second Phase Particles (SPPs) in two types of Zr–Nb alloys (recrystallised Zr-1.0Nb and Zr-2.5Nb) was studied by in-situ heavy ion irradiation in a transmission electron microscope (TEM), combined with ex-situ analysis by energy dispersive x-ray spectroscopy (EDX). TEM thin foils were irradiated by 1 MeV Kr + ions at four different temperatures from 50 K to 873 K, and by 350 keV Kr + ions at different doses up to 39dpa. The change in size of individual β-Nb SPPs has been measured quantitatively, and the degradation mechanisms under irradiation at different temperatures discussed. It has been shown that the Nb redistribution between the SPPs and the Zr matrix is governed both by radiation induced mixing and local diffusion in the surrounding Zr matrix. Finally, under the radiation conditions reported in this study, the β-Nb SPPs have shown remarkably stability against irradiation, and the extent of Nb redistribution between the SPPs and Zr matrix is very limited under all experimental conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Evolution of intermetallic phases in an Al–Si–Ti alloy during solution treatment

A cast Al–Si–Ti alloy was solution treated at 540 °C for different periods between 0 and 72 h to understand the evolution of intermetallic phases. Only an (Al,Si) 3 Ti intermetallic phase with a low Si content was found in the as-cast alloy. The (Al,Si) 3 Ti particles were converted partly into a lamellar structure, a eutectoid phase, consisting of a Si-rich phase and an Al phase during solution treatment. The amount of the lamellar structure increased with the solution treatment time, but the composition of either constitute was kept almost unchanged regardless of the solution treatment times. The lamellar Si-rich phase is (Al,Si) 2 Ti (τ 2 ) with a TiSi 2 (C49-type) structure based on thermodynamic calculations and high-resolution TEM analyses. FCC Al phase is the product residing between the τ 2 lamellae after the completion of transformation from (Al,Si) 3 Ti to τ 2 phase. A near-rational orientation relationship (OR) between the Al and τ 2 phases is determined as Al [110]//τ 2 [100], Al ()//τ 2 [060]. The phase transformation from (Al,Si) 3 Ti to τ 2 being a result of the diffusion of Ti and Si within the original (Al,Si) 3 Ti particulates as well as the Si diffusion from the Al matrix during solution treatment is proposed. The formation of the lamellar structure in the microstructure is attributed mainly to the limited diffusivity of Ti element.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The impact of nanoparticle softness on its tracer diffusion coefficient in all polymer nanocomposites

The diffusion of nanoparticles in a polymer matrix is an area of current interest. However, a complete understanding is still limited as it is often difficult to quantify the much slower motion of nanoparticles in a polymer matrix. To combat this problem, we have developed a protocol to measure the diffusion coefficient of soft nanoparticles in a linear polymer matrix. Recently developed synthetic control over soft nanoparticle structures combined with this protocol provides a pathway to separately elucidate the effects of the molecular weight and nanoparticle softness on its diffusive behavior. These results indicate that the nanoparticle softness and deformability dictate its motion. Increasing the cross-linking density of the nanoparticle for all molecular weights increases its hardness and suppresses its motion in the linear matrix. Additionally, the nanoparticle molecular weight dependence deviates from the exponential dependence for star polymers suggesting that these nanoparticles benefit from the cooperative motion of the matrix to open pathways for the nanoparticle. Finally, comparison of these experimentally determined values to the Stokes–Einstein theory demonstrates that the nanoparticles diffuse much slower than a hard sphere. This is interpreted to indicate that there exist additional interactions between the nanoparticle and polymer matrix that are not captured by Stokes–Einstein, including threading or entanglement of the linear chain with the nanoparticle.

Rostom, Sahar↗
DOE OSTI2016

Mesoscale Polymer Dissolution Probed by Raman Spectroscopy and Molecular Simulations

The diffusion of various solvents into a polystyrene (PS) matrix was probed experimentally by monitoring the temporal profiles of the Raman spectra and theoretically from molecular dynamics (MD) simulations of the binary system. The simulation results assist in providing a fundamental, molecular level connection between the mixing/dissolution processes and the difference = solvent – PS in the values of the Hildebrand parameter () between the two components of the binary systems: solvents having similar values of with PS (small ) exhibit fast diffusion into the polymer matrix, whereas the diffusion slows down considerably when the ’s are different (large ). To this end, the Hildebrand parameter was identified as a useful descriptor that governs the process of mixing in polymer – solvent binary systems. The experiments also provide insight into further refinements of the models specific to non-Fickian diffusion phenomena that need to be used in the simulations.

Chang, Tsun-Mei↗
DOE OSTI2017

Comparison of Thermal Diffusivity Degradation of Irradiated Zirlo and SiC-SiC Composite

Zirlo (Zircaloy cladding material from Westinghouse) has been widely used as the fuel cladding material in Light Water Reactors because of its high melting point, low susceptibility to corrosion, good thermal and mechanical shock resistance, and low degradation of mechanical properties under irradiation. But as Zirlo reacts with water at high temperature, which can trigger serious accidents, efforts have been made to explore better candidates to replace Zirlo in the water-cooled reactors. SiC-SiC composite is considered as one of the most viable options due to its comparable mechanical performances and corrosion resistance. However, one of the most important properties, thermal diffusivities of both Zirlo and SiC-SiC composite, and their degradation after irradiation, are not well known yet. Ion-irradiated samples are used to study the thermal property degradation caused by irradiation instead of the neutron-irradiated ones due to the significantly lower radioactivity. The microstructural damage is estimated from the software simulation SRIM/TRIM based on the energy and fluence of the ion, and the target material, and represented by DPA (displacement by atom). Different from neutron-irradiated samples, the damaged layer of ion-irradiated samples is only a few to a few tens of micrometers thick, and the damage is depth dependent. It is impossible to directly measure the bulk property change, and a microscale measurement technique is necessary. Laser-based photothermal reflectance technique is one of the ideal methods to measure local thermal conductivity and diffusivity with high spatial resolution. The main principle of this technique is to heat the solid sample using an intensity-modulated laser, and scan the sample with a constant intensity continuous-wave (CW) laser to detect the thermal wave propagation. On bulk, isotropic material, if the heating laser intensity is modulated as a sine wave, thermal diffusivity of the sample can be derived from the phase lag of the thermal wave, scan distance and modulation frequency in a straight forward manner. By using more specific analytical models, thermal conductivity and diffusivity in complicated cases, such as layered structure materials, composite materials, and/or anisotropic materials, are measurable as well. In this work, thermal diffusivity of the light damage layer of the post-irradiation Zirlo and SiC-SiC composite are measured and compared. The Zirlo sample is irradiated by Ni{sup 9+} ion, and SiC-SiC composite material is irradiated by Si{sup 7+} ion. The peak DPA of both sample is similar as ∼10. For ion-irradiated materials, DPA is known to increase with depth before it reaches the peak, and then sharply drop to zero. In term of light damage layer in this manuscript, we mean by the layer with a DPA smaller than 5% maximum value. In this layer DPA increases slowly and smoothly with depth, and the structure and thus thermal properties are more spatially uniform. For the SiC-SiC composite, the measurements are separately conducted on fibers along radial or axial direction, and on the matrix. Our measurement results show that with similar microstructural damage, thermal diffusivity of matrix SiC reduces more significantly than that of Zirlo. For fiber SiC that has a much lower thermal diffusivity than the matrix SiC before irradiation, the post-irradiation effect on thermal diffusivity is not obvious.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

MODELING AND ANALYSIS OF FISSION PRODUCT TRANSPORT IN THE AGR-3/4 EXPERIMENT

In this work we describe the ongoing modeling and analysis efforts in support of the AGR-3/4 experiment. AGR-3/4 is intended to provide data to assess fission product retention and transport (e.g., diffusion coefficients) in fuel matrix and graphite materials. We describe a set of pre-test predictions that incorporate the results of detailed thermal and fission product release models into a coupled 1D radial diffusion model of the experiment, using diffusion coefficients reported in the literature for Ag, Cs, and Sr. We make some comparisons of the predicted Cs profiles to preliminary measured data for Cs and find these to be reasonable, in most cases within an order of magnitude. Our ultimate objective is to refine the diffusion coefficients using AGR-3/4 data, so we identify an analytical method for doing so and demonstrate its efficacy via a series of numerical experiments using the model predictions. Finally, we discuss development of a post-irradiation examination plan informed by the modeling effort and simulate some of the heating tests that are tentatively planned.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Modeling and analysis of fission product transport in the AGR-3/4 experiment - 18693

In this work we describe the ongoing modeling and analysis efforts in support of the AGR-3/4 experiment. AGR-3/4 is intended to provide data to assess fission product retention and transport (e.g., diffusion coefficients) in fuel matrix and graphite materials. We describe a set of pre-test predictions that incorporate the results of detailed thermal and fission product release models into a coupled 1D radial diffusion model of the experiment, using diffusion coefficients reported in the literature for Ag, Cs, and Sr. We make some comparisons of the predicted Cs profiles to preliminary measured data and find these to be reasonable, in most cases within an order of magnitude. Our ultimate objective is to refine the diffusion coefficients using AGR-3/4 data, so we develop an analytical method for doing so and demonstrate its efficacy via a series of numerical experiments using the model predictions. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Utilisation of steel furnace slag coarse aggregate in a low calcium fly ash geopolymer concrete

This paper evaluates the performance of steel furnace slag (SFS) coarse aggregate in blended slag and low calcium fly ash geopolymer concrete (GPC). The geopolymer binder is composed of 90% of low calcium fly ash and 10% of ground granulated blast furnace slag (GGBFS). Mechanical and physical properties, shrinkage, and detailed microstructure analysis were carried out. The results showed that geopolymer concrete with SFS aggregate offered higher compressive strength, surface resistivity and pulse velocity than that of GPC with traditional aggregate. The shrinkage results showed no expansion or swelling due to delayed calcium oxide (CaO) hydration after 320 days. No traditional porous interfacial transition zone (ITZ) was detected using scanning electron microscopy, indicating a better bond between SFS aggregate and geopolymer matrix. Energy dispersive spectroscopy results further revealed calcium (Ca) diffusion at the vicinity of ITZ. Raman spectroscopy results showed no new crystalline phase formed due to Ca diffusion. X-ray fluorescence result showed Mg diffusion from SFS aggregate towards geopolymer matrix. The incorporation of Ca and Mg into the geopolymer structure and better bond between SFS aggregate and geopolymer matrix are the most likely reasons for the higher compressive strength observed in GPC with SFS aggregate.

36 MATERIALS SCIENCE↗
DOE OSTI2022

High-temperature and/or high pressure gas enclosure

A gas enclosure can include a refractory metal liner; a ceramic matrix composite cladding; and a diffusion barrier layer. The refractory metal liner is adapted to surround and enclose a gas to be contained within the gas enclosure. The diffusion barrier layer is disposed between the refractory metal liner and the ceramic matrix composite cladding.

Miao, Yinbin↗
DOE OSTI2022

Sodium diffusion in heterogeneous porous media: Connecting laboratory experiments and simulations

Sodium has been suggested as a tracer for brine in reservoir formations where a significant amount of sodium ion is found mainly in the aqueous phase. Fortunately, the most abundant sodium isotope, 23 Na, is Nuclear Magnetic Resonance (NMR) active, making it possible to study the structure and dynamical properties of both bulk and pore confined fluid systems. We investigated the diffusion of key dissolved sodium species in bulk solution and porous media as a function of composition, ionic strength, and permeability of the carbonate samples using NMR relaxometry and pulsed-field gradient (PFG) NMR techniques. We use Indiana limestone as an example of natural porous media and water as a freely diffusible tracer and carrier. We demonstrate apparent diffusion measurement of sodium based on changes in spin–spin relaxation time (T 2 ) signal in pore confinement. The diffusion rate of sodium decreases with increasing counter-ion size. This effect is greater at higher ionic strengths and lower chemical potentials in porous media. The reactive transport code, CrunchFlow, was used to complement the NMR experiments to simulate diffusion behavior in porous media. Combining these two methods provides a powerful approach to estimating effective diffusion coefficients in heterogeneous matrices. The modeling considers the influence of physical properties (porosity and tortuosity) and chemical properties (geochemical composition and chemical gradients). The results presented in this work highlight the advantage of measuring apparent diffusivity using NMR T 2 relaxometry in conjunction with numerical simulation to derive effective diffusivity and the corresponding matrix properties (i.e., tortuosity) of the system.

58 GEOSCIENCES↗
DOE OSTI2019

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

Numerous analytical solutions have been developed for modeling thermal perturbations to underground formations caused by deep-well injection of fluids. Each solution has been derived for a specific boundary value problem and a simplified flow network with one set of parallel fractures. In this paper, new generalized solutions G*( x, s ) are developed using (existing) global transfer functions G$^*_0(x,s)$ and a new memory function g*( s ), where x and s are the space and Laplace variable. The memory function represents the solutions of conductive heat exchange between fractures and matrix blocks and between fractured aquifers and unfractured aquitards. The memory function is developed to account for multirate exchange induced by different shapes, sizes, properties, and volumetric fractions of matrix blocks bounded by multiple sets of orthogonal fractures with different spacing. The global transfer functions represent the fundamental solutions to convective, convective-conductive, and convective-dispersive heat transport in fractures (or aquifers) without exchange and are available for various (1-D linear, 1-D radial, 2-D dipole, and single-well injection-withdrawal) flow fields. The new solutions with exchange are developed using $G^*(x,s) = B^*(s)G^*_0{x, s[1 + Θg^*(s)]}$, thereby greatly simplifying solution development in a novel way, where Θ and B*( s ) are a fracture-matrix scaling factor and the boundary condition function. As a result, the new solutions are applied to several example problems, showing that heat transport in fractured aquifers is significantly impacted by (1) thermal dispersion in fractures that is rarely considered, (2) multirate heat exchange with a wide range of size and anisotropy of rectangular matrix blocks, and (3) heat exchange between aquifers and aquitards.

58 GEOSCIENCES↗