Evaluating impacts of CO2 intrusion into an unconsolidated aquifer: II. Modeling results
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Zheng, Liange↗
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Illuminating the geology: Post-injection reservoir characterisation of the CO2CRC Otway site
Proper site characterisation is essential in the planning stages of a CO 2 storage project; but we can also learn a good deal about the reservoir once the injection is underway or has been completed. During CO2CRC Otway Project Stage 2C, sources of valuable information about storage performance have been generated as a consequence of the staged injection of 15,000 t of CO 2 rich gas, as well as observations from time-lapse seismic surveys and well monitoring data. Now that injection has ceased for Stage 2C, the geological model is compared against field observations for the period spanning injection and 23 months after injection ended. The post-injection reservoir characterisation has proven critical to refine the static and dynamic models for future field development and added assurance about the long-term stabilisation of the CO 2 plume. The south-eastern progress of plume development, as seen on the time-lapse seismic data, has led to a review of the structural interpretation and horizon-fault geometry represented in the models. The developing plume has illuminated the extent of splay faults previously unresolved on the baseline seismic data. Saturation profiles interpreted from pulsed-neutron logs at the injection and observation wells show a preference for higher saturations occurring in high permeability distributary channels penetrated by each of the wells. This has reduced the uncertainty in predicting connectivity of this facies between the wells. The pressure data from numerous injection events has been used to refine the characterisation of the average horizontal permeability of the reservoir zone, and the vertical permeability of the intra-formational seal. Furthermore, it has been used to infer near-field bounding conditions of the interior splay fault, which in turn improves our understanding of containment at the site.
58 GEOSCIENCES↗
Geophysical monitoring using active seismic techniques at the Citronelle Alabama CO 2 storage demonstration site
Between August 2012 and September 2014, about 114,000 metric tonnes of CO 2 was captured from the coal-fired Plant Barry Power Station at Bucks Alabama and injected into the Paluxy Formation above the oil pool in the southeast unit of the Citronelle Oilfield. Various monitoring methods were deployed at land surface and in project wells to measure system performance, comply with permit requirements and test new and innovative monitoring tools. The monitoring program relied heavily on active seismic methods for subsurface imaging of geologic structure and time-lapse seismic techniques to track the CO 2 migration in the injection interval. Both conventional geophone/hydrophone and fiber-optic based Distributed Acoustic Sensing (DAS) arrays were deployed and tested, allowing a side by side comparison of the equipment and techniques. Geophysical imaging of the subsurface was successful using DAS in the offset vertical seismic profile (OVSP) survey configuration. A high resolution OVSP image of the subsurface was obtained in 2014 with DAS, which exceeded project expectations in comparison to a lower resolution image obtained in 2012 using a conventional 80-level geophone array. A time-lapse image of the redistribution of CO 2 after injection ended in September 2014 was obtained with two DAS OVSP surveys from June 2014 and December 2015, thus successfully demonstrating its proof-of-concept. Unfortunately, a pre-injection baseline survey with DAS, which was in its initial stage of technology development in 2012, did not have sufficient quality for use, making it difficult to interpret the acquired DAS time-lapse difference. Additional research in this area has since demonstrated the utility of time-lapse DAS OVSP. DAS data were also acquired during a cross-well seismic survey conducted in 2014. Unfortunately, the DAS technique was not success in the cross-well survey configuration because the system noise level was too high in the crosswell frequency output range (100–1200 Hz) of the piezoelectric source (increasing by a factor of ten compared to VSP frequency band). Additionally, the cross-well geometry causes sub-horizontal (broadside) incidence on the vertical DAS fiber cable, which is known to be problematic. Current research is focused on improving the DAS cable response to broadside acoustic energy. Time-lapse seismic surveys using commercially available conventional arrays were also acquired. In contrast to the DAS acquired data, the cross-well seismic results obtained with the conventional array was highly successful and clearly showed the CO 2 remained in zone at the end of injection. Time-lapse differencing of the OSVP surveys acquired with the conventional arrays proved to be inconclusive. Finally, changes in wellbore conditions between surveys and unavoidable changes in equipment (the array used for the baseline survey was retired) affected data quality, making it difficult to interpret the OVSP results.
58 GEOSCIENCES↗
Pressure falloff testing to characterize CO 2 plume and dry-out zone during CO 2 injection in saline aquifers
The fluid mobilities and the lateral extent of the CO 2 plume and the dry-out zone are among important unknowns required to effectively manage CO 2 storage in saline aquifers projects. These unknowns can be derived from pressure falloff testing which has been widely used to characterize the subsurface. This paper provides a three-region analytical solution for falloff pressure during the infinite-acting period of CO 2 injection in saline aquifers. The solution is derived using Laplace transformation technique of the governing diffusivity equations and the accompanying initial and boundary conditions. The exact solution is validated against numerical results obtained from a black-oil reservoir simulator for two cases. The solution is approximated into simple forms in real-time domain considering different time periods. Then, a graphical semi-log analysis technique based on the approximate solutions is provided as an interpretation tool of falloff tests where the fluid mobilities and the extents of dry-out zone and CO 2 plume can be inferred. The interpretation technique is applied to synthetic falloff test data to investigate its potential and reliability.
02 PETROLEUM↗
A comprehensive analysis of transient pressure and rate data from CO 2 storage projects in a depleted pinnacle reef oil field complex, Michigan, USA
Pressure and rate data are commonly recorded as part of a basic monitoring program in CCS projects. This paper discusses the application of multiple analytical techniques to interpret pressure and rate transient data from CO 2 injection and storage operations. The techniques of interest, i.e., injection-falloff analysis, injectivity/productivity index analysis and pressure pulse arrival time analysis, are commonly used in the oil and gas industry to assess reservoir properties, but not well known in the CCS literature (especially the last two). Injection-falloff analysis involves log-log pressure derivative plotting for the falloff data and history-matching of the entire injection-falloff sequence to determine permeability. In the injectivity/productivity index analysis, rate-normalized pressure buildup is plotted against material balance time or ratio of cumulative injection to injection rate to determine the injectivity index (ratio of injection rate to stabilized pressure buildup) which can be related to the permeability-thickness product. The arrival time analysis identifies the arrival of a pressure disturbance (~0.1 psi change from ambient) to determine the hydraulic diffusivity from which permeability can be estimated. The applicability of these techniques is demonstrated via illustrative examples from multiple wells in different pinnacle carbonate reefs undergoing CO 2 -EOR in Northern Michigan. The paper ends with a discussion of the relative merits of each interpretive technique, as well as recommendations that could be useful for other field projects.
42 ENGINEERING↗
Machine learning to discover mineral trapping signatures due to CO 2 injection
Mineral trapping is pursued as a geological CO 2 sequestration (GCS) mechanism because it permanently stores CO 2 in solid phases or minerals. However, CO 2 mineral-trapping mechanisms are poorly understood due to (1) lack of sufficient field and laboratory data characterizing these complex processes, and (2) challenges to develop site-specific reactive-transport models coupling fluid flow and geochemical reactions occurring at various temporal (from milliseconds to years) and spatial (from pore (millimeters) to field (kilometers)) scales. Reactive transport with additional complexities such as heterogeneity can make the simulation outputs even more difficult to interpret because of complex nonlinearity and multi-scale interdependencies. Furthermore, the values of model outputs such as concentrations can vary by several orders of magnitude, making it harder to correlate and characterize the impact of the variables via traditional data interpretation techniques such as exploratory data analyses. Recently, machine learning (ML) has shown promise in feature discovery and in highlighting hidden mechanisms that cannot be obtained by existing data-analytics and statistical methods. In this study, we applied an unsupervised ML approach, non-negative matrix factorization with custom -means clustering (NMF) to the data generated by reactive-transport simulations of GCS. The reactive-transport data consisted of 19 attributes, including four physio-chemical variables (pH, porosity, aqueous CO 2 , and sequestered CO 2 ), six chemical species (K + , Na + , HCO, Ca 2+ , Mg 2+ , Fe 2+ ), and four carbonate minerals (calcite, dolomite, siderite, and ankerite), a feldspar mineral (albite), and four clay minerals (illite, clinochlore, kaolinite, and smectite) over a period of 200 years of simulation time. Furthermore, the simulation data used was for Morrow B sandstone at the Farnsworth hydrocarbon unit in Texas. Data are sampled at two locations within the model domain: (1) at the injection well and (2) 200 m west of the injection well. The injection was performed for a period of 10 years. Using NMF, we estimated the temporal interdependencies among the 19 attributes over a span of 200 years. We found that NMF was able to identify four reaction stages and their dominant attributes; these cannot be directly discerned through traditional visualization (e.g., line plots, Pareto analysis, Glyph-based visualization methods) or exploratory data analysis tools of the simulation data. The four stages were: reactions in the injection phase followed by short-, mid-, and long-term reactions. The NMF analysis also revealed that 10 among the 19 attributes are dominant. These dominant attributes for mineral trapping include calcite, dolomite at injection well, siderite at 200 m away from the injection well, clinochlore, kaolinite, Na + , K + , Ca 2+ , Mg 2+ , pH, and aqeuous CO 2 . Finally, at late times (65–200 years), our results showed that calcite plays a major role in mineral trapping with insignificant contribution from siderite, ankerite, and clay minerals. These findings make the proposed unsupervised ML-model attractive for reactive-transport sensing towards real-time GCS monitoring.
54 ENVIRONMENTAL SCIENCES↗
Joint impedance and facies inversion of time-lapse seismic data for improving monitoring of CO 2 incidentally stored from CO 2 EOR
Time-lapse seismic monitoring is an effective and proven technology for mapping the distribution of CO 2 in a subsurface reservoir. When injected CO 2 displaces other reservoir fluids, porous-medium properties are changed and thus the seismic impedance changes, causing time-lapse seismic amplitude differences in the injection zones. The analysis and interpretation of images created from these amplitude differences can provide information about reservoir architecture and the CO 2 migration within the reservoir. Incorporating seismic inversion and rock physics into the interpretation of time-lapse seismic data can considerably improve the modeling and monitoring to detect and assess the location of CO 2 over time. The joint inversion method presented in this paper has an integral representation of the geology in the inversion algorithm using elastic facies, which provides information about the spatial distribution of the geologic heterogeneities controlling the movement of fluids in the reservoir. The method was successfully applied to time-lapse seismic data from a mature oil field undergoing CO 2 enhanced oil recovery. The estimated seismic acoustic impedances and facies reflect the characteristics of individual geologic facies and fluid conditions of the reservoir subject to CO 2 injection. Finally, the probabilities estimated by the joint impedance and facies inversion for the reservoir's litho-fluid facies can be used for forecasting CO 2 saturation and pressure changes within the target reservoir.
4D seismic↗
Development towards stable chlorine isotope measurements of astromaterials using the modified Middleton source of an accelerator mass spectrometer
The volatile element Cl can be lost during the formation and evolution of planetary bodies, leading to fractionation of its two stable isotopes 35 Cl and 37 Cl. Chlorine isotope variations (reported as δ 37 Cl in parts per thousand (‰) relative to Standard Mean Ocean Chloride, SMOC) are documented to exceed 80‰ between different lunar rock samples and have been variably interpreted as the fingerprint of degassing during accretion, magma ocean, or volcanic portions of lunar history. The large intersample and intrasample variations observed by both bulk isotope ratio mass spectrometry (IRMS) and in-situ secondary ion mass spectrometry (SIMS) methods are difficult to interpret in part because of a paucity of bulk Cl isotope measurements. This lack of high-precision bulk data is due to the relative rarity of IRMS laboratories capable of making these high precision measurements on small samples of precious planetary materials such as those returned by human or robotic exploration. Here we present a new method for performing high precision δ 37 Cl measurements using the modified Middleton ion source of an existing accelerator mass spectrometer. For samples with as little as 1 μg Cl–the equivalent of 2–4 mm 3 of a typical lunar rock sample–the average cathode accuracy is ~1‰. Finally, cathode reproducibility is typically ~1‰ (2σ) for samples with at least 10 μg of Cl, increasing to ~3–6‰ for aliquots with ~1–2 μg Cl, similar to published SIMS results and sufficient to study astromaterials from the Moon, Mars, or 4 Vesta, which have tens of ‰ observed variations.
07 ISOTOPE AND RADIATION SOURCES↗
Mechanical specific energy versus depth of cut in rock cutting and drilling
The relationship between Mechanical Specific Energy (MSE) and the Rate of Penetration (ROP), or equivalently the depth of cut per revolution, provides an important measure for strategizing a drilling operation. This study explores how MSE evolves with depth of cut, and presents a concerted effort that encompasses analytical, computational and experimental approaches. A simple model for the relationship between MSE and cutting depth is first derived with consideration of the wear progression of a circular cutter. This is an extension of Detournay and Defourny's phenomenological cutting model. Wear is modeled as a flat contact area at the bottom of a cutter referred to as a wear flat, and that wear flat in the past is often considered to be fixed during cutting. But during a drilling operation by a full bit that consists of multiple circular cutters, the wear flat length may increase because of various wear mechanisms involved. The wear progression of cutters generally results in reduced efficiency with either increased MSE or decreased ROP. Also, an accurate estimate of removed rock volume is found important for the evaluation of MSE. The derived model is compared with experiment results from a single circular cutter, for cutting soft rock under ambient pressure with actual depth measured through a micrometer, and for cutting high strength rock under high pressure with actual cutting area measured by a confocal microscope. Lastly, the model is employed to interpret the evolution of MSE with depth of cut for a full drilling bit under confining pressure. The general form of equation of the developed model is found to describe well the experiment data and can be applied to interpret the drilling data for a full bit.
42 ENGINEERING↗
Interobserver Variability in Target Definition for Hepatocellular Carcinoma With and Without Portal Vein Thrombus: Radiation Therapy Oncology Group Consensus Guidelines
Purpose: Defining hepatocellular carcinoma (HCC) gross tumor volume (GTV) requires multimodal imaging, acquired in different perfusion phases. The purposes of this study were to evaluate the variability in contouring and to establish guidelines and educational recommendations for reproducible HCC contouring for treatment planning. Methods and Materials: Anonymous, multiphasic planning computed tomography scans obtained from 3 patients with HCC were identified and distributed to a panel of 11 gastrointestinal radiation oncologists. Panelists were asked the number of HCC cases they treated in the past year. Case 1 had no vascular involvement, case 2 had extensive portal vein involvement, and case 3 had minor branched portal vein involvement. The agreement between the contoured total GTVs (primary + vascular GTV) was assessed using the generalized kappa statistic. Agreement interpretation was evaluated using Landis and Koch's interpretation of strength of agreement. The S95 contour, defined using the simultaneous truth and performance level estimation (STAPLE) algorithm consensus at the 95% confidence level, was created for each case. Results: Of the 11 panelists, 3 had treated >25 cases in the past year, 2 had treated 10 to 25 cases, 2 had treated 5 to 10 cases, 2 had treated 1 to 5 cases, 1 had treated 0 cases, and 1 did not respond. Near perfect agreement was seen for case 1, and substantial agreement was seen for cases 2 and 3. For case 2, there was significant heterogeneity in the volume identified as tumor thrombus (range 0.58-40.45 cc). For case 3, 2 panelists did not include the branched portal vein thrombus, and 7 panelists contoured thrombus separately from the primary tumor, also showing significant heterogeneity in volume of tumor thrombus (range 4.52-34.27 cc). Conclusions: In a group of experts, excellent agreement was seen in contouring total GTV. Heterogeneity exists in the definition of portal vein thrombus that may impact treatment planning, especially if differential dosing is contemplated. Guidelines for HCC GTV contouring are recommended.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
Thermal Pretreatment of a High Lignin SSF Digester Residue to Increase its Softening Point
Residues high in lignin and ash generated from the simultaneous saccharification and fermentation of corn stover were thermally pretreated in an inert (N2) atmosphere to study the effect of time and temperature on its softening point. These residues are difficult to feed into gasifiers due to premature thermal degradation and formation of reactive liquids in the feed lines, leading to plugging. The untreated and treated residues were characterized by proximate and ultimate analysis, and then analyzed via TGA, DSC, 13C NMR, Py-GC-MS, CHNO/S, and TMA. Interpretation of the compositional analysis indicates that the weight loss observed during pretreatment is mainly due to the thermal decomposition and volatilization of the hemicelluloses and amorphous cellulose fractions. Fixed carbon increases in the pretreated material, mostly due to a concentration effect rather than the formation of new poly-aromatic material. The optimal processing time and temperature to minimize the production of carbonyl groups in the pretreated samples was 300°C at a time of 30 minutes. Results showed that the softening point of the material could be increased from 187°C to 250°C, and that pretreatment temperature plays a more important role than time. The increase in softening point was mainly due to the formation of covalent bonds in the lignin structures and the removal of low molecular weight volatile intermediates.
Gasification, Lignin rich feedstocks, high lignin ↗
Cell concentrations and metabolites enhance the SIP response to biofilm matrix components
Here we investigated the relative effect of different bacterial biofilm components to influence spectral induced polarization (SIP) signals and Cole-Cole model parameters (i.e. normalized chargeability (S m –1 ) and relaxation time ($τ$)) in order to reduce the ambiguity associated with interpretation of SIP signatures in biostimulated environments. SIP measurements were collected over a frequency range, (i.e. 0.1 Hz –1 kHz) from experimental columns containing Pseudomonas aeruginosa PAO1 (non-mucoid bacterial strain) cell suspensions alone and cell suspensions mixed with different molecules associated with P. aeruginosa biofilm matrix (alginate, DNA and phenazine). Results from SIP measurements of cell density investigations suggest an increase in phase (~ 200%), imaginary conductivity (σ" S m –1 ), and normalized chargeability (S m –1 ) values as cell densities increase (1.50–5.55 × 10 9 CFUml –1 ), yet no significant change in the real conductivity (σ' S m –1 ) or relaxation time was observed. The addition of alginate resulted in a suppression of phase (φ mrads), imaginary conductivity (σ" S m –1 ), and normalized chargeability (S m –1 ) response. However, a mixture of cells and alginate increased all parameters but with no significant changes in real conductivity (σ' S m –1 ) or relaxation time. Similar trend was observed in the DNA treatments; increasing concentrations of DNA reduced the imaginary conductivity (σ" S m –1 ), phase (φ mrads), and normalized chargeability (S m –1 ) response. In contrast, the addition of phenazine, a secondary metabolite of P. aeruginosa, resulted in a significant increase in both imaginary conductivity (σ" S m –1 ), phase (φ mrads), and normalized chargeability (S m –1 ) values especially at larger concentrations (>50 mM). Our work suggests that cell density and metabolites are significant factors increasing the polarization response in biofilms and advances the interpretation of electrical signals associated with biofilms in the subsurface.
58 GEOSCIENCES↗
Recommendations for improving rigor and reproducibility in site specific characterization
Heterogeneous catalysis is driven by the interaction of reactant molecules and the catalyst surface. The locus of this interaction as well as the surrounding ensemble of atoms is referred to as the catalyst active site. Active site characterization attempts to distinguish active catalytic sites from inactive surface sites, to elucidate the structural and chemical nature of active sites, and to quantify active site concentration. Numerous techniques have been demonstrated to provide compositional and structural information about the active sites within a catalyst. However, each technique has its own limitations and experimental pitfalls that can lead to data misinterpretation or irreproducible results. Further, this work aims to provide an overview of the types of data that can be collected, to outline common experimental challenges and how to avoid them, and to assemble relevant references for the most used active site characterization techniques. More broadly, we aim to outline best practices for researchers to collect, interpret, and report active site characterization data in a way that provides the most benefit to the broader catalysis community. Increasing the rigor and reproducibility of active site characterization offers a strategy to better link properties with catalytic performance and to enable the community to develop consensus concerning these relationships.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Disordered interfaces of alkaline aluminate salt hydrates provide glimpses of Al 3+ coordination changes
Hypothesis: The precipitation and dissolution of aluminum-bearing mineral phases in aqueous systems often proceed via changes in both aluminum coordination number and connectivity, complicating molecular-scale interpretation of the transformation mechanism. Here, the thermally induced transformation of crystalline sodium aluminum salt hydrate, a phase comprised of monomeric octahedrally coordinated aluminate which is of relevance to industrial aluminum processing, has been studied. Because intermediate aluminum coordination states during melting have not previously been detected, it is hypothesized that the transition to lower coordinated aluminum ions occurs within a highly disordered quasi-two-dimensional phase at the solid-solution interface. Experiments and simulations: In this work, in situ X-ray diffraction (XRD), Raman and 27 Al nuclear magnetic resonance (NMR) spectroscopy were used to monitor the melting transition of nonasodium aluminate hydrate (NSA, Na 9 [Al(OH) 6 ] 2 ·3(OH)·6H 2 O). A mechanistic interpretation was developed based on complementary classical molecular dynamics (CMD) simulations including enhanced sampling. A reactive forcefield was developed to bridge speciation in the solution and in the solid phase. Findings: In contrast to classical dissolution, aluminum coordination change proceeds through a dynamically stabilized ensemble of intermediate states in a disordered layer at the solid-solution interface. In both melting and dissolution of NSA, octahedral, monomeric aluminum transition through an intermediate of pentahedral coordination. The intermediate dehydroxylates to form tetrahedral aluminate (Al(OH)$_4^–$) in the liquid phase. This coordination change is concomitant with a breaking of the ionic aluminate-sodium ion linkages. The solution phase Al(OH)$_4^–$ ions subsequently polymerize into polynuclear aluminate ions. However, there are some differences between bulk melting and interfacial dissolution, with the onset of the surface-controlled process occurring at a lower temperature (~30 °C) and the coordination change taking place more gradually as a function of temperature. This work to determine the local structure and dynamics of aluminum in the disordered layer provides a new basis to understand mechanisms controlling aluminum phase transformations in highly alkaline solutions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Contaminant point source localization error estimates as functions of data quantity and model quality
We develop empirically-grounded error envelopes for localization of a point contamination release event in the saturated zone of a previously uncharacterized heterogeneous aquifer into which a number of plume-intercepting wells have been drilled. We assume that flow direction in the aquifer is known exactly and velocity is known to within a factor of two of our best guess from well observations prior to source identification. Other aquifer and source parameters must be estimated by interpretation of well breakthrough data via the advection-dispersion equation. We employ high performance computing to generate numerous random realizations of aquifer parameters and well locations, simulate well breakthrough data, and then employ unsupervised machine optimization techniques to estimate the most likely spatial (or space-time) location of the source. Tabulating the accuracy of these estimates from the multiple realizations, we relate the size of 90% and 95% confidence envelopes to the data quantity (number of wells) and model quality (fidelity of ADE interpretation model to actual concentrations in a heterogeneous aquifer with channelized flow). We find that for purely spatial localization of the contaminant source, increased data quantities can make up for reduced model quality. For space-time localization, we find similar qualitative behavior, but significantly degraded spatial localization reliability and less improvement from extra data collection. Since the space-time source localization problem is much more challenging, we also tried a multiple-initial-guess optimization strategy. Furthermore, this greatly enhanced performance, but gains from additional data collection remained limited.
54 ENVIRONMENTAL SCIENCES↗
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Efficient hybrid explicit-implicit learning for multiscale problems
Splitting method is a powerful method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretization. Here, in this paper, our goal is to use temporal splitting concepts in designing machine learning algorithms and, at the same time, help splitting algorithms by incorporating data and speeding them up. We propose a machine learning assisted splitting scheme which improves the efficiency of the scheme meanwhile preserves the accuracy. We consider a recently introduced multiscale splitting algorithms, where the multiscale problem is solved on a coarse grid. To approximate the dynamics, only a few degrees of freedom are solved implicitly, while others explicitly. This splitting concept allows identifying degrees of freedom that need implicit treatment. In this paper, we use this splitting concept in machine learning and propose several strategies. First, the implicit part of the solution can be learned as it is more difficult to solve, while the explicit part can be computed. This provides a speed-up and data incorporation for splitting approaches. Secondly, one can design a hybrid neural network architecture because handling explicit parts requires much fewer communications among neurons and can be done efficiently. Thirdly, one can solve the coarse grid component via PDEs or other approximation methods and construct simpler neural networks for the explicit part of the solutions. We discuss these options and implement one of them by interpreting it as a machine translation task. This interpretation of the splitting scheme successfully enables us using the Transformer since it can perform model reduction for multiple time series and learn the connection between them. We also find that the splitting scheme is a great platform to predict the coarse solution with insufficient information of the target model: the target problem is partially given and we need to solve it through a known problem which approximates the target. Our machine learning model can incorporate and encode the given information from two different problems and then solve the target problems. We conduct four numerical examples and the results show that our method is stable and accurate.
97 MATHEMATICS AND COMPUTING↗