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# Xiang-Zhao Kong Publications Content

## Publications

Underlined names are links to recent or past GEG members

### REFEREED PUBLICATIONS IN JOURNALS

43.
Lima, M., H. Javanmard, D. Vogler, M.O. Saar, and X.-Z. Kong, Flow-through Drying during CO2 Injection into Brine-filled Natural Fractures: A Tale of Effective Normal Stress, International Journal of Greenhouse Gas Control, 109, pp. 103378, 2021. [View Abstract]Injecting supercritical CO2 (scCO2) into brine-filled fracture-dominated reservoirs causes brine displacement and possibly evaporite precipitations that alter the fracture space. Here, we report on isothermal near-field experiments on scCO2-induced flow-through drying in a naturally fractured granodiorite specimen under effective normal stresses of 5-10 MPa, where two drying regimes are identified. A novel approach is developed to delineate the evolution of brine saturation and relative permeability from fluid production and differential pressure measurements. Under higher compressive stresses, the derived relative permeability curves indicate lower mobility of brine and higher mobility of the scCO2 phase. The derived fractional flow curves also suggest an increase in channelling and a decrease in brine displacement efficiencies under higher compressive stresses. Finally, lowering compressive stresses seems to hinder water evaporation. Our experimental results assist in understanding the behaviour of the injectivity of fractures and fracture networks during subsurface applications that involve scCO2 injection into saline formations.

42.
Ma, Y., X.-Z. Kong, C. Zhang, A. Scheuermann, D. Bringemeier, and L. Li, Quantification of natural CO2 emission through faults and fracture zones in coal basins, Geophysical Research Letters, 48, pp. e2021GL092693, 2021. [View Abstract]With the presence of highly permeable pathways, such as faults and fractures zones, coal seam gases, particularly CO2, could potentially migrate upwardly from the coal deposits into the shallow subsurface and then to the atmosphere. This letter reports soil gas mapping and gamma ray survey in coal basin of Hunter River Valley, Australia. The survey facilitated the delineation of fault structures across the sampling regions, where the identified faults were confirmed by an independent drilling investigation later. Furthermore, to evaluate the gas emission fluxes from coalbeds through fault zones, the measured CO2 concentrations, coupled with an inverse modelling, enable the estimation of the width of the fault zone and associated CO2 emission flux in the range of 2×10$^{-5}$-6×10$^{-5}$ mol/m$^{2}$/s at the study site. Our new approach provides a way to determine emissions of gases from deep formations, which may contribute considerably to the greenhouse gases cycles.

41.
Ma, J., M. Ahkami, M.O. Saar, and X.-Z. Kong, Quantification of mineral accessible surface area and flow-dependent fluid-mineral reactivity at the pore scale, Chemical Geology, 563, pp. 120042, 2021. [View Abstract]Accessible surface areas (ASAs) of individual rock-forming minerals exert a fundamental control on the maximum mineral reactivity with formation fluids. Notably, ASA efficiency during fluid-rock reactions can vary by orders of magnitude, depending on the inflow fluid chemistry and the velocity field. Due to the lack of adequate quantification methods, determining the mineral-specific ASAs and their reaction efficiency still remain extremely difficult. Here, we first present a novel joint method that appropriately calculates ASAs of individual minerals in a multi-mineral sandstone. This joint method combines SEM-image processing results and Brunauer-Emmett-Teller (BET) surface area measurements by a Monte-Carlo algorithm to derive scaling factors and ASAs for individual minerals at the resolution of BET measurements. Using these atomic-scale ASAs, we then investigate the impact of flow rate on the ASA efficiency in mineral dissolution reactions during the injection of CO2-enriched brine. This is done by conducting a series of pore-scale reactive transport simulations, using a two-dimensional (2D) scanning electron microscopy (SEM) image of this sandstone. The ASA efficiency is determined employing a domain-averaged dissolution rate and the effective surface area of the most reactive phase in the sandstone (dolomite). As expected, the dolomite reactivity is found to increase with the flow rate, due to the on average high fluid reactivity. The surface efficiency increases slightly with the fluid flow rate, and reaches a relatively stable value of about 1%. The domain averaged method is then compared with the in-out averaged method (i.e the “Black-box” approach), which is often used to analyzed the experimental observations. The in-out averaged method yields a considerable overestimation of the fluid reactivity, a small underestimation of the dolomite reactivity, and a considerable underestimation of the ASA efficiency. The discrepancy between the two methods is becoming smaller when the injection rate increases. Our comparison suggests that the result interpretation of the in-out averaged method should be contemplated, in particular, when the flow rate is small. Nonetheless, our proposed ASA determination method should facilitate accurate calculations of fluid-mineral reactivity in large-scale reactive transport simulations, and we advise that an upscaling of the ASA efficiency needs to be carefully considered, due to the low surface efficiency.

40.
Lima, M., P. Schädle, C. Green, D. Vogler, M.O. Saar, and X.-Z. Kong, Permeability Impairment and Salt Precipitation Patterns during CO2 Injection into Single Natural Brine-filled Fractures, Water Resources Research, 56/8, pp. e2020WR027213, 2020. [View Abstract]Formation dry-out in fracture-dominated geological reservoirs may alter the fracture space, impair rock absolute permeability and cause a significant decrease in well injectivity. In this study, we numerically model the dry-out processes occurring during supercritical CO2 (scCO2) injection into single brine-filled fractures and evaluate the potential for salt precipitation under increasing effective normal stresses in the evaporative regime. We use an open-source, parallel finite-element framework to numerically model two-phase flow through 2-Dimensional fracture planes with aperture fields taken from naturally fractured granite cores at the Grimsel Test Site in Switzerland. Our results reveal a displacement front and a subsequent dry-out front in all simulated scenarios, where higher effective stresses caused more flow channeling, higher rates of water evaporation and larger volumes of salt precipitates. However, despite the larger salt volumes, the permeability impairment was lower at higher effective normal stresses. We conclude that the spatial distribution of the salt, precipitated in fractures with heterogeneous aperture fields, strongly affects the absolute permeability impairment caused by formation dry-out. The numerical simulations assist in understanding the behavior of the injectivity in fractures and fracture networks during subsurface applications that involve scCO2 injection into brine.

39.
Ma, J., L. Querci, B. Hattendorf, M.O. Saar, and X.-Z. Kong, The effect of mineral dissolution on the effective stress law for permeability in a tight sandstone, Geophysical Research Letters, 2020. [View Abstract]We present flow-through experiments to delineate the processes involved in permeability changes driven by effective stress variations and mineral cement dissolution in porous rocks. CO2-enriched brine is injected continuously into a tight sandstone under in-situ reservoir conditions for 455 hours. Due to the dolomite cement dissolution, the bulk permeability of the sandstone specimen significantly increases, and two dissolution passages are identified near the fluid inlet by X-ray CT imaging. Pre- and post-reaction examinations of the effective stress law for permeability suggest that after reaction the bulk permeability is more sensitive to pore pressure changes and less sensitive to effective stress changes. These observations are corroborated by Scanning Electron Microscopy and X-ray CT observations. This study deepens our understanding of the effect of mineral dissolution on the effective stress law for permeability, with implications for characterizing subsurface mass and energy transport, particularly during fluid injection/production into/from geologic reservoirs.

38.
Tutolo, B., A. Luhmann, X.-Z. Kong, B. Bagley, D. Alba-Venero, N. Mitchell, M.O. Saar, and W.E. Seyfried, Contributions of visible and invisible pores to reactive transport in dolomite, Geochemical Perspectives Letters, I4, pp. 42-46, 2020. [View Abstract]Recent technical advances have demonstrated the importance of pore-scale geochemical processes for governing Earth's evolution. However, the contribution of pores at different scales to overall geochemical reactions remains poorly understood. Here, we integrate multiscale characterization and reactive transport modeling to study the contribution of pore-scale geochemical proceses to the hydrogeochemical evolution of dolomite rock samples during CO2-driven dissolution experiments. Our results demonstrate that approximately half of the total pore volume is invisible at the scale of commonly used imaging techniques. Comparison of pre- and post-experiment analyses demonstrate that porosity-increasing, CO2-driven dissolution processes preferentially occur in pores 600 nm – 5 μm in size, but pores <600 nm in size show no change during experimental alteration. This latter observation, combined with the anomalously high rates of trace element release during the experiments, suggests that nanoscale pores are accessible to through-flowing fluids. A three-dimensional simulation performed directly on one of the samples shows that steady-state pore-scale trace element reaction rates must be ~10× faster than that of dolomite in order to match measured effluent concentrations, consistent with the large surface area-to-volume ratio in these pores. Together, these results yield a new conceptual model of pore-scale processes, and urge caution when interpreting the trace element concentrations of ancient carbonate rocks.

37.
Kittilä, A., M.R. Jalali, M.O. Saar, and X.-Z. Kong, Solute tracer test quantification of the effects of hot water injection into hydraulically stimulated crystalline rock, Geothermal Energy, 8/17, 2020. [View Abstract]When water is injected into a fracture-dominated reservoir that is cooler or hotter than the injected water, the reservoir permeability is expected to be altered by the injection-induced thermo-mechanical effects, resulting in the redistribution of fluid flow in the reservoir. These effects are important to be taken into account when evaluating the performance and lifetime particularly of Enhanced Geothermal Systems (EGS). In this paper, we compare the results from two dye tracer tests, conducted before (at ambient temperature of 13 °C) and during the injection of 45 °C hot water into a fractured crystalline rock at the Grimsel Test Site in Switzerland. Conducting a moment analysis on the recovered tracer residence time distribution (RTD) curves, we observe, after hot water injection, a significant decrease in the total tracer recovery. This recovery decrease strongly suggests that fluid flow was redistributed in the studied rock volume and that the majority of the injected water was lost to the far-field. Furthermore, by using temperature measurements, obtained from the same locations as the tracer RTD curves, we conceptualize an approach to estimate the fracture surface area contributing to the heat exchange between the host rock and the circulating fluid. Our moment analysis and simplified estimation of fracture surface area provide insights into the hydraulic properties of the hydraulically active fracture system and the changes in fluid flow. Such insights are important to assess the heat exchange performance of a geothermal formation during fluid circulation and to estimate the lifetime of the geothermal formation, particularly in EGS.

36.
Jia, Y., W. Wu, and X.-Z. Kong, Injection-induced slip heterogeneity on faults in shale reservoirs, International Journal of Rock Mechanics and Mining Sciences, 131, pp. 1-6, 2020. [View Abstract]Managing fluid stimulation protocols is an effective means to mitigate the risk of injection-induced earthquakes during shale gas development. The success of these protocols is dependent on our understanding of fluid pressure heterogeneity and the associated inhomogeneous slip on critically stressed faults. Here we show the evolution of velocity-weakening zone on a simulated fault, derived from fluid injection and velocity stepped experiments, and the corresponding non-uniform fluid pressure distribution, recovered from coupled hydro-mechanical simulations. Our results indicate that the sharp extension of velocity-weakening zone occurs before the nucleation of fault rupture, which could be an indicator to avoid the reactivation of other fault patches beyond the stimulated zone. The dynamic rupture is estimated to extend much faster than the maximum speed of the velocity-weakening zone front. We infer that the velocity-weakening zone may further expand and fully control the fault behavior after multiple slip events.

35.
Kittilä, A., M.R. Jalali, M. Somogyvári, K.F. Evans, M.O. Saar, and X.-Z. Kong, Characterization of the effects of hydraulic stimulation with tracer-based temporal moment analysis and tomographic inversion, Geothermics, 86/101820, 2020. [View Abstract]Tracer tests were conducted as part of decameter-scale in-situ hydraulic stimulation experiments at the Grimsel Test Site to investigate the hydraulic properties of a stimulated crystalline rock volume and to study the stimulation-induced hydrodynamic changes. Temporal moment analysis yielded an increase in tracer swept pore volume with prominent flow channeling. Post-stimulation tomographic inversion of the hydraulic conductivity, K, distribution indicated an increase in the geometric mean of logK and a decrease in the Dykstra-Parsons heterogeneity index. These results indicate that new flow path connections were created by the stimulation programs, enabling the tracers to sweep larger volumes, while accessing flow paths with larger hydraulic conductivities.

34.
Ahkami, M., A. Parmigiani, P.R. Di Palma, M.O. Saar, and X.-Z. Kong, A lattice-Boltzmann study of permeability-porosity relationships and mineral precipitation patterns in fractured porous media, Computational Geosciences, 2020. [View Abstract]Mineral precipitation can drastically alter a reservoir’s ability to transmit mass and energy during various engineering/natural subsurface processes, such as geothermal energy extraction and geological carbon dioxide sequestration. However, it is still challenging to explain the relationships among permeability, porosity, and precipitation patterns in reservoirs, particularly in fracture-dominated reservoirs. Here, we investigate the pore-scale behavior of single-species mineral precipitation reactions in a fractured porous medium, using a phase field lattice-Boltzmann method. Parallel to the main flow direction, the medium is divided into two halves, one with a low-permeability matrix and one with a high-permeability matrix. Each matrix contains one flow-through and one dead-end fracture. A wide range of species diffusivity and reaction rates is explored to cover regimes from advection- to diffusion-dominated, and from transport- to reaction-limited. By employing the ratio of the Damköhler (Da) and the Peclet (Pe) number, four distinct precipitation patterns can be identified, namely (1) no precipitation (Da/Pe < 1), (2) near-inlet clogging (Da/Pe > 100), (3) fracture isolation (1 < Da/Pe < 100 and Pe > 1), and (4) diffusive precipitation (1 < Da/Pe < 100 and Pe < 0.1). Using moment analyses, we discuss in detail the development of the species (i.e., reactant) concentration and mineral precipitation fields for various species transport regimes. Finally, we establish a general relationship among mineral precipitation pattern, porosity, and permeability. Our study provides insights into the feedback loop of fluid flow, species transport, mineral precipitation, pore space geometry changes, and permeability in fractured porous media.

33.
Ahkami, M., T. Roesgen, M.O. Saar, and X.-Z. Kong, High-resolution temporo-ensemble PIV to resolve pore-scale flow in 3D-printed fractured porous media, Transport in Porous Media, 129/2, pp. 467-483, 2019. [View Abstract]Fractures are conduits that can enable fast advective transfer of (fluid, solute, reactant, particle, etc.) mass and energy. Such fast transfer can significantly affect pore-scale physico-chemical processes, which can in turn affect macroscopic mass and energy transport characteristics. Here, flooding experiments are conducted in a well-characterized fractured porous medium, manufactured by 3D printing. Given steady-state flow conditions, the micro-structure of the two-dimensional (2D) pore fluid flow field is delineated to resolve fluid velocities on the order of a sub-millimeter per second. We demonstrate the capabilities of a new temporo-ensemble Particle Image Velocimetry (PIV) method by maximizing its spatial resolution, employing in-line illumination. This method is advantageous as it is capable of minimizing the number of pixels, required for velocity determinations, down to one pixel, thereby enabling resolving high spatial resolutions of velocity vectors in a large field of view (FOV). While the main goal of this study is to introduce a novel experimental and velocimetry framework, this new method is then applied to specifically improve the understanding of fluid flow through fractured porous media. Histograms of measured velocities indicate log-normal and Gaussian-type distributions of longitudinal and lateral velocities in fractures, respectively. The magnitudes of fluid velocities in fractures and the flow interactions between fractures and matrices are shown to be influenced by the permeability of the background matrix and the orientation of the fractures.

32.
Parmigiani, A., P.R. Di Palma, S. Leclaire, F. Habib, and X.-Z. Kong, Characterization of transport-enhanced phase separation in porous media using a lattice-Boltzmann method, Geofluids, 2019, 2019. [View Abstract]Phase separation of formation fluids in subsurface introduces hydrodynamic perturbations which are critical for mass and energy transport of geofluids. Here, we present pore-scale lattice-Boltzmann simulations to investigate the hydrodynamical response of a porous-system to the emergence of non-wetting droplets under background hydraulic gradients. A wide parameter space of capillary number and fluid saturation is explored to characterize the droplet evolution, the droplet size and shape distribution, and the capillary-clogging patterns. We find that clogging is favored by high capillary stress; nonetheless clogging occurs at high non-wetting saturation (larger than 0.3), denoting the importance of convective transport on droplet-growth and permeability. Moreover, droplets are more sheared at low capillary number, however solid matrix plays a key role on droplet's volume-to-surface ratio.

31.
Romano, E., J. Jimenez-Martinez, A. Parmigiani, X.-Z. Kong, and I. Battiato, Contribution of Pore-Scale Approach to Macroscale Geofluids Modelling in Porous Media, Geofluids, 2019, 2019. [View Abstract]Understanding the fundamental mechanisms of fluid flows and reactive transport in natural systems is a major challenge for several fields of Earth sciences (e.g. hydrology, soil science, volcanology) and Geo/Environmental-engineering (CO2 sequestration, NAPLS contamination, geothermal energy, oil&gas reservoir exploitation). The hierarchical structures of natural system (e.g. heterogeneity of geological formations) as well as the different behaviour of single and multi-phase fluids at the pore-scale coupled with the nonlinearity of underlying reactive processes necessitate investigating these aspects at the scale at which they physically occur, the scale of pore and fractures. Recent improvements in pore-scale computational modelling, together with the development of non- invasive microscopic imaging technology and the latest microfluidics technics are allowing the vast field of porous & fractured media research to benefit of major advances due to: 1) an improved understanding and description of pore-scale mechanisms and 2) the ability of thinking in terms of coupled processes. The contributions collected in this Special Issue, although far from constituting a comprehensive picture of the “pore-scale world”, however offer a good example of the potentialities of such an approach to investigate a wide range of processes usually observed at macro-scale, but whose underlying physical and chemical processes take place at micro-scale.

30.
Ma, J., L. Querci, B. Hattendorf, M.O. Saar, and X.-Z. Kong, Toward a Spatiotemporal Understanding of Dolomite Dissolution in Sandstone by CO2‑Enriched Brine Circulation, Environmental Science & Technology, 2019. [View Abstract]In this study, we introduce a stochastic method to delineate the mineral effective surface area (ESA) evolution during a re-cycling reactive flow-through transport experiment on a sandstone under geologic reservoir conditions, with a focus on the dissolution of its dolomite cement, Ca$_{1.05}$Mg$_{0.75}$Fe$_{0.2}$(CO$_3$)$_2$. CO$_2$-enriched brine was circulated through this sandstone specimen for 137 cycles ($\sim$270 hours) to examine the evolution of in-situ hydraulic properties and CO$_2$-enriched brine-dolomite geochemical reactions. The bulk permeability of the sandstone specimen decreased from 356 mD before the reaction to 139 mD after the reaction, while porosity increased from 21.9\% to 23.2\% due to a solid volume loss of 0.25 ml. Chemical analyses on experimental effluents during the first cycle yielded a dolomite reactivity of $\sim$2.45 mmol~m$^{-3}$~s$^{-1}$, a corresponding sample-averaged ESA of $\sim$8.86$\times 10^{-4}$~m$^2$/g, and an ESA coefficient of 1.36$\times 10^{-2}$, indicating limited participation of the physically exposed mineral surface area. As the dissolution reaction progressed, the ESA is observed to first increase, then decrease. This change in ESA can be qualitatively reproduced employing SEM-image-based stochastic analyses on dolomite dissolution. These results provide a new approach to analyze and upscale the ESA during geochemical reactions, which are involved in a wide range of geo-engineering operations.

29.
Lima, M.M., D. Vogler, L. Querci, C. Madonna, B. Hattendorf, M.O. Saar, and X.-Z. Kong, Thermally driven fracture aperture variation in naturally fractured granites, Geothermal Energy Journal, 7/1, pp. 1-23, 2019. [View Abstract]Temperature variations often trigger coupled thermal, hydrological, mechanical, and chemical (THMC) processes that can significantly alter the permeability/impedance of fracture-dominated deep geological reservoirs. It is thus necessary to quantitatively explore the associated phenomena during fracture opening and closure as a result of temperature change. In this work, we report near-field experimental results of the effect of temperature on the hydraulic properties of natural fractures under stressed conditions (effective normal stresses of 5-25 MPa). Two specimens of naturally fractured granodiorite cores from the Grimsel Test Site in Switzerland were subjected to flow-through experiments with a temperature variation of 25-140 °C to characterize the evolution of fracture aperture/permeability. The fracture surfaces of the studied specimens were morphologically characterized using photogrammetry scanning. Periodic measurements of the efflux of dissolved minerals yield the net removal mass, which is correlated to the observed rates of fracture closure. Changes measured in hydraulic aperture are significant, exhibiting reductions of 20-75 % over the heating/cooling cycles. Under higher confining stresses, the effects in fracture permeability are irreversible and notably time-dependent. Thermally driven fracture aperture variation was more pronounced in the specimen with the largest mean aperture width and spatial correlation length. Gradual fracture compaction is likely controlled by thermal dilation, mechanical grinding, and pressure dissolution due to increased thermal stresses exerted over the contacting asperities, as confirmed by the analyses of hydraulic properties and efflux mass.

28.
Kittilä, A., M.R. Jalali, K.F. Evans, M. Willmann, M.O. Saar, and X.-Z. Kong, Field Comparison of DNA-Labeled Nanoparticle and Solute Tracer Transport in a Fractured Crystalline Rock, Water Resources Research, 2019.

27.
Kong, X.-Z., C. Deuber, A. Kittilä, M. Somogyvari, G. Mikutis, P. Bayer, W.J. Stark, and M.O. Saar, Tomographic reservoir imaging with DNA-labeled silica nanotracers: The first field validation, Environmental Science &Technology, 52/23, pp. 13681-13689, 2018. [View Abstract]This study presents the first field validation of using DNA-labeled silica nanoparticles as tracers to image subsurface reservoirs by travel time based tomography. During a field campaign in Switzerland, we performed short-pulse tracer tests under a forced hydraulic head gradient to conduct a multisource−multireceiver tracer test and tomographic inversion, determining the two-dimensional hydraulic conductivity field between two vertical wells. Together with three traditional solute dye tracers, we injected spherical silica nanotracers, encoded with synthetic DNA molecules, which are protected by a silica layer against damage due to chemicals, microorganisms, and enzymes. Temporal moment analyses of the recorded tracer concentration breakthrough curves (BTCs) indicate higher mass recovery, less mean residence time, and smaller dispersion of the DNA-labeled nanotracers, compared to solute dye tracers. Importantly, travel time based tomography, using nanotracer BTCs, yields a satisfactory hydraulic conductivity tomogram, validated by the dye tracer results and previous field investigations. These advantages of DNA-labeled nanotracers, in comparison to traditional solute dye tracers, make them well-suited for tomographic reservoir characterizations in fields such as hydrogeology, petroleum engineering, and geothermal energy, particularly with respect to resolving preferential flow paths or the heterogeneity of contact surfaces or by enabling source zone characterizations of dense nonaqueous phase liquids.

26.
Xia, T., E. Dontsov, Z. Chen, F. Zhang, and X.-Z. Kong, Fluid Flow in Unconventional Gas Reservoirs, Geofluids, 2018, 2018. [View Abstract]Unconventional gas (including tight, shale, and coal seam gas) production has led to a drastic change of global energy landscape. The fundamental understanding of gas flow behaviours in unconventional gas reservoirs is essential to elevate the potential gas resource recovery. The behaviours of gas flow follow a chain of physicochemical processes in unconventional gas reservoirs, which can be labeled as “coupled processes” implying that one process affects the initiation and progress of another. This process chain is linked together through different disciplines, including geoscience, rock mechanics, multiphase flow, engineering chemistry, and thermodynamics, among others. Although progress on evaluation of migration, control, and recovery of unconventional gas has been achieved using mathematical models and physical experiments, the role of different fluids (eg, CH4 and other hydrocarbons, CO2, and water) in unconventional gas flow is not well understood. Filling this knowledge gap is likely to play a critical impact on raising the potential of unconventional gas resource recovery and on reducing the environmental risks.

25.
Galindo-Torres, S.A., T. Molebatsi, X.Z. Kong, A. Scheuermann, D. Bringemeier, and L. Li, Scaling solutions for connectivity and conductivity of continuous random networks, Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 92/4, pp. 041001, 2015. [View Abstract]Connectivity and conductivity of two-dimensional fracture networks (FNs), as an important type of continuous random networks, are examined systematically through Monte Carlo simulations under a variety of conditions, including different power law distributions of the fracture lengths and domain sizes. The simulation results are analyzed using analogies of the percolation theory for discrete random networks. With a characteristic length scale and conductivity scale introduced, we show that the connectivity and conductivity of FNs can be well described by universal scaling solutions. These solutions shed light on previous observations of scale-dependent FN behavior and provide a powerful method for quantifying effective bulk properties of continuous random networks.

24.
Ma, Y., X. -Z. Kong, A. Scheuermann, S. A. Galindo-Torres, D. Bringemeier, and L. Li, Microbubble transport in water-saturated porous media, Water Resources Research, 51/6, pp. 4359-4373, 2015. [View Abstract]Laboratory experiments were conducted to investigate flow of discrete microbubbles through a water-saturated porous medium. During the experiments, bubbles, released from a diffuser, moved upward through a quasi-2-D flume filled with transparent water-based gelbeads and formed a distinct plume that could be well registered by a calibrated camera. Outflowing bubbles were collected on the top of the flume using volumetric burettes for flux measurements. We quantified the scaling behaviors between the gas (bubble) release rates and various characteristic parameters of the bubble plume, including plume tip velocity, plume width, and breakthrough time of the plume front. The experiments also revealed circulations of ambient pore water induced by the bubble flow. Based on a simple momentum exchange model, we showed that the relationship between the mean pore water velocity and gas release rate is consistent with the scaling solution for the bubble plume. These findings have important implications for studies of natural gas emission and air sparging, as well as fundamental research on bubble transport in porous media.

23.
Tutolo, B.M., A.J. Luhmann, X.-Z. Kong, M.O. Saar, and W.E. Seyfried Jr., CO2 sequestration in feldspar-rich sandstone: Coupled evolution of fluid chemistry, mineral reaction rates, and hydrogeochemical properties, Geochimica Et Cosmochimica Acta, 160, pp. 132-154, 2015. [View Abstract]To investigate CO2 Capture, Utilization, and Storage (CCUS) in sandstones, we performed three 150 °C flow-through experiments on K-feldspar-rich cores from the Eau Claire formation. By characterizing fluid and solid samples from these experiments using a suite of analytical techniques, we explored the coupled evolution of fluid chemistry, mineral reaction rates, and hydrogeochemical properties during CO2 sequestration in feldspar-rich sandstone. Overall, our results confirm predictions that the heightened acidity resulting from supercritical CO2 injection into feldspar-rich sandstone will dissolve primary feldspars and precipitate secondary aluminum minerals. A core through which CO2-rich deionized water was recycled for 52 days decreased in bulk permeability, exhibited generally low porosity associated with high surface area in post-experiment core sub-samples, and produced an Al hydroxide secondary mineral, such as boehmite. However, two samples subjected to ?3 day single-pass experiments run with CO2-rich, 0.94 mol/kg NaCl brines decreased in bulk permeability, showed generally elevated porosity associated with elevated surface area in post-experiment core sub-samples, and produced a phase with kaolinite-like stoichiometry. CO2-induced metal mobilization during the experiments was relatively minor and likely related to Ca mineral dissolution. Based on the relatively rapid approach to equilibrium, the relatively slow near-equilibrium reaction rates, and the minor magnitudes of permeability changes in these experiments, we conclude that CCUS systems with projected lifetimes of several decades are geochemically feasible in the feldspar-rich sandstone end-member examined here. Additionally, the observation that K-feldspar dissolution rates calculated from our whole-rock experiments are in good agreement with literature parameterizations suggests that the latter can be utilized to model CCUS in K-feldspar-rich sandstone. Finally, by performing a number of reactive transport modeling experiments to explore processes occurring during the flow-through experiments, we have found that the overall progress of feldspar hydrolysis is negligibly affected by quartz dissolution, but significantly impacted by the rates of secondary mineral precipitation and their effect on feldspar saturation state. The observations produced here are critical to the development of models of CCUS operations, yet more work, particularly in the quantification of coupled dissolution and precipitation processes, will be required in order to produce models that can accurately predict the behavior of these systems.

22.
Tutolo, B.M., X.-Z. Kong, W.E. Seyfried Jr., and M.O. Saar, High performance reactive transport simulations examining the effects of thermal, hydraulic, and chemical (THC) gradients on fluid injectivity at carbonate CCUS reservoir scales, International Journal of Greenhouse Gas Control, 39, pp. 285-301, 2015. [View Abstract]Carbonate minerals and CO2 are both considerably more soluble at low temperatures than they are at elevated temperatures. This inverse solubility has led a number of researchers to hypothesize that injecting low-temperature (i.e., less than the background reservoir temperature) CO2 into deep, saline reservoirs for CO2 Capture, Utilization, and Storage (CCUS) will dissolve CO2 and carbonate minerals near the injection well and subsequently exsolve and re-precipitate these phases as the fluids flow into the geothermally warm portion of the reservoir. In this study, we utilize high performance computing to examine the coupled effects of cool CO2 injection and background hydraulic head gradients on reservoir-scale mineral volume changes. We employ the fully coupled reactive transport simulator PFLOTRAN with calculations distributed over up to 800 processors to test 21 scenarios designed to represent a range of reservoir depths, hydraulic head gradients, and CO2 injection rates and temperatures. In the default simulations, 50 °C CO2 is injected at a rate of 50 kg/s into a 200 bar, 100 °C calcite or dolomite reservoir. By comparing these simulations with others run at varying conditions, we show that the effect of cool CO2 injection on reservoir-scale mineral volume changes tends to be relatively minor. We conclude that the low heat capacity of CO2 effectively prevents low-temperature CO2 injection from decreasing the temperature across large portions of the simulated carbonate reservoirs. This small thermal perturbation, combined with the low relative permeability of brine within the supercritical CO2 plume, yields limited dissolution and precipitation effects directly attributable to cool CO2 injection. Finally, we calculate that relatively high water-to-rock ratios, which may occur over much longer CCUS reservoir lifetimes or in materials with sufficiently high brine relative permeability within the supercritical CO2 plume, would be required to substantially affect injectivity through thermally-induced mineral dissolution and precipitation. Importantly, this study shows the utility of reservoir scale-reactive transport simulators for testing hypotheses and placing laboratory-scale observations into a CCUS reservoir-scale context.

21.
Tutolo, B.M., X.-Z. Kong, W.E. Seyfried Jr., and M.O. Saar, Internal consistency in aqueous geochemical data revisited: Applications to the aluminum system, Geochimica et Cosmochimica Acta, 133, pp. 216-234, 2014. [View Abstract]Internal consistency of thermodynamic data has long been considered vital for confident calculations of aqueous geochemical processes. However, an internally consistent mineral thermodynamic data set is not necessarily consistent with calculations of aqueous species thermodynamic properties due, potentially, to improper or inconsistent constraints used in the derivation process. In this study, we attempt to accommodate the need for a mineral thermodynamic data set that is internally consistent with respect to aqueous species thermodynamic properties by adapting the least squares optimization methods of Powell and Holland (1985). This adapted method allows for both the derivation of mineral thermodynamic properties from fluid chemistry measurements of solutions in equilibrium with mineral assemblages, as well as estimates of the uncertainty on the derived results. Using a large number of phase equilibria, solubility, and calorimetric measurements, we have developed a thermodynamic data set of 12 key aluminum-bearing mineral phases. These data are derived to be consistent with Na+ and K+ speciation data presented by Shock and Helgeson (1988), H4SiO4(aq) data presented by Stefánsson (2001), and the Al speciation data set presented by Tagirov and Schott (2001). Many of the constraining phase equilibrium measurements are exactly the same as those used to develop other thermodynamic data, yet our derived values tend to be quite different than some of the others’ due to our choices of reference data. The differing values of mineral thermodynamic properties have implications for calculations of Al mineral solubilities; specifically, kaolinite solubilities calculated with the developed data set are as much as 6.75 times lower and 73% greater than those calculated with Helgeson et al. (1978) and Holland and Powell (2011) data, respectively. Where possible, calculations and experimental data are compared at low T, and the disagreement between the two sources reiterates the common assertion that low-T measurements of phase equilibria and mineral solubilities in the aluminum system rarely represent equilibrium between water and well-crystallized, aluminum-bearing minerals. As an ancillary benefit of the derived data, we show that it may be combined with high precision measurements of aqueous complex association constants to derive neutral species activity coefficients in supercritical fluids. Although this contribution is specific to the aluminum system, the methods and concepts developed here can help to improve the calculation of water–rock interactions in a broad range of earth systems.

20.
Luhmann, A.J., X.-Z. Kong, B.M. Tutolo, N. Garapati, B.C. Bagley, M.O. Saar, and W.E. Seyfried Jr., Experimental dissolution of dolomite by CO2-charged brine at 100oC and 150 bar: Evolution of porosity, permeability, and reactive surface area, Chemical Geology, 380, pp. 145-160, 2014. [View Abstract]Hydrothermal flow experiments of single-pass injection of CO2-charged brine were conducted on nine dolomite cores to examine fluid–rock reactions in dolomite reservoirs under geologic carbon sequestration conditions. Post-experimental X-ray computed tomography (XRCT) analysis illustrates a range of dissolution patterns, and significant increases in core bulk permeability were measured as the dolomite dissolved. Outflow fluids were below dolomite saturation, and cation concentrations decreased with time due to reductions in reactive surface area with reaction progress. To determine changes in reactive surface area, we employ a power-law relationship between reactive surface area and porosity (Luquot and Gouze, 2009). The exponent in this relationship is interpreted to be a geometrical parameter that controls the degree of surface area change per change in core porosity. Combined with XRCT reconstructions of dissolution patterns, we demonstrate that this exponent is inversely related to both the flow path diameter and tortuosity of the dissolution channel. Even though XRCT reconstructions illustrate dissolution at selected regions within each core, relatively high Ba and Mn recoveries in fluid samples suggest that dissolution occurred along the core's entire length and width. Analysis of porosity–permeability data indicates an increase in the rate of permeability enhancement per increase in porosity with reaction progress as dissolution channels lengthen along the core. Finally, we incorporate the surface area–porosity model of Luquot and Gouze (2009) with our experimentally fit parameters into TOUGHREACT to simulate experimental observations.

19.
Tutolo, B.M., A.J. Luhmann, X.-Z. Kong, M.O. Saar, and W.E. Seyfried Jr., Experimental observation of permeability changes in dolomite at CO2 sequestration conditions, Environmental Science and Technology, 48/4, pp. 2445-2452, 2014. [View Abstract]Injection of cool CO2 into geothermally warm carbonate reservoirs for storage or geothermal energy production may lower near-well temperature and lead to mass transfer along flow paths leading away from the well. To investigate this process, a dolomite core was subjected to a 650 h, high pressure, CO2 saturated, flow-through experiment. Permeability increased from 10–15.9 to 10–15.2 m2 over the initial 216 h at 21 °C, decreased to 10–16.2 m2 over 289 h at 50 °C, largely due to thermally driven CO2 exsolution, and reached a final value of 10–16.4 m2 after 145 h at 100 °C due to continued exsolution and the onset of dolomite precipitation. Theoretical calculations show that CO2 exsolution results in a maximum pore space CO2 saturation of 0.5, and steady state relative permeabilities of CO2 and water on the order of 0.0065 and 0.1, respectively. Post-experiment imagery reveals matrix dissolution at low temperatures, and subsequent filling-in of flow passages at elevated temperature. Geochemical calculations indicate that reservoir fluids subjected to a thermal gradient may exsolve and precipitate up to 200 cm3 CO2 and 1.5 cm3 dolomite per kg of water, respectively, resulting in substantial porosity and permeability redistribution.

18.
Ma, Y., A. Scheuermann, D. Bringemeier, X.-Z. Kong, and L. Li, Size distribution measurement for densely binding bubbles via image analysis, Experiments in Fluids, 55/1860, 2014. [View Abstract]For densely binding bubble clusters, conventional image analysis methods are unable to provide an accurate measurement of the bubble size distribution because of the difficulties with clearly identifying the outline edges of individual bubbles. In contrast, the bright centroids of individual bubbles can be distinctly defined and thus accurately measured. By taking this advantage, we developed a new measurement method based on a linear relationship between the bubble radius and the radius of its bright centroid so to avoid the need to identify the bubble outline edges. The linear relationship and method were thoroughly tested for 2D bubble clusters in a highly binding condition and found to be effective and robust for measuring the bubble sizes.

17.
Kong, X.-Z., and M.O. Saar, Numerical study of the effects of permeability heterogeneity on density-driven convective mixing during CO2 dissolution storage, Int. J. Greenhouse Gas Control, 19, pp. 160-173, 2013. [View Abstract]Permanence and security of carbon dioxide (CO2) in geologic formations requires dissolution of CO2 into brine, which slightly increases the brine density. Previous studies have shown that this small increase in brine density induces convective currents, which greatly enhances the mixing efficiency and thus CO2 storage capacity and rate in the brine. Density-driven convection, in turn, is known to be largely dominated by permeability heterogeneity. This study explores the relationship between the process of density-driven convection and the permeability heterogeneity of an aquifer during CO2 dissolution storage, using high-resolution numerical simulations. While the porosity is kept constant, the heterogeneity of the aquifer is introduced through a spatially varying permeability field, characterized by the Dykstra-Parsons coefficient and the correlation length. Depending on the concentration profile of dissolved CO2, we classify the convective finger patterns as dispersive, preferential, and unbiased fingering. Our results indicate that the transition between unbiased and both preferential and dispersive fingering is mainly governed by the Dykstra-Parsons coefficient, whereas the transition between preferential and dispersive fingering is controlled by the permeability correlation length. Furthermore, we find that the CO2 dissolution flux at the top boundary will reach a time-independent steady state. Although this flux strongly correlates with permeability distribution, it generally increases with the permeability heterogeneity when the correlation length is less than the system size.

16.
Kong, X.-Z., and M.O. Saar, DBCreate: A SUPCRT92-based program for producing EQ3/6, TOUGHREACT, and GWB thermodynamic databases at user-defined T and P, Computers and Geosciences, 51, pp. 415-417, 2013. [View Abstract]SUPCRT92 is a widely used software package for calculating the standard thermodynamic properties of minerals, gases, aqueous species, and reactions. However, it is labor-intensive and error-prone to use it directly to produce databases for geochemical modeling programs such as EQ3/6, the Geochemist's Workbench, and TOUGHREACT. DBCreate is a SUPCRT92-based software program written in FORTRAN90/95 and was developed in order to produce the required databases for these programs in a rapid and convenient way. This paper describes the overall structure of the program and provides detailed usage instructions.

15.
Luhmann, A.J., X.-Z. Kong, B.M. Tutolo, K. Ding, M.O. Saar, and W.E. Seyfried Jr., Permeability reduction produced by grain reorganization and accumulation of exsolved CO2 during geologic carbon sequestration: A new CO2 trapping mechanism, Environmental Science and Technlogy, 47/1, pp. 242-251, 2013. [View Abstract]Carbon sequestration experiments were conducted on uncemented sediment and lithified rock from the Eau Claire Formation, which consisted primarily of K-feldspar and quartz. Cores were heated to accentuate reactivity between fluid and mineral grains and to force CO2 exsolution. Measured permeability of one sediment core ultimately reduced by 4 orders of magnitude as it was incrementally heated from 21 to 150 °C. Water-rock interaction produced some alteration, yielding sub-?m clay precipitation on K-feldspar grains in the core’s upstream end. Experimental results also revealed abundant newly formed pore space in regions of the core, and in some cases pores that were several times larger than the average grain size of the sediment. These large pores likely formed from elevated localized pressure caused by rapid CO2 exsolution within the core and/or an accumulating CO2 phase capable of pushing out surrounding sediment. CO2 filled the pores and blocked flow pathways. Comparison with a similar experiment using a solid arkose core indicates that CO2 accumulation and grain reorganization mainly contributed to permeability reduction during the heated sediment core experiment. This suggests that CO2 injection into sediments may store more CO2 and cause additional permeability reduction than is possible in lithified rock due to grain reorganization.

14.
Kong, X.-Z., M. Holzner, F. Stauffer, and W. Kinzelbach, Time-resolved 3D visualization of air injection in a liquidsaturated refractive-index-matched porous medium, Exp. Fluids, 50, pp. 1659-1670, 2011. [View Abstract]The main goal of this work is to implement and validate a visualization method with a given temporal/spatial resolution to obtain the dynamic three-dimensional (3D) structure of an air plume injected into a deformable liquid-saturated porous medium. The air plume develops via continuous air injection through an orifice at the bottom of a loose packing of crushed silica grains. The packing is saturated by a glycerin-water solution having the same refractive index and placed in a rectangular glass container. By using high-speed image acquisition through laser scanning, the dynamic air plume is recorded by sequential tomographic imaging. Due to the overlap between adjacent laser sheets and the light reflection, air bubbles are multiply exposed in the imaging along the scanning direction. Four image processing methods are presented for the removal of these redundant pixels arising from multiple exposure. The respective results are discussed by comparing the reconstructed air plume volume with the injected one and by evaluating the morphological consistency of the obtained air plume. After processing, a 3D dynamic air flow pattern can be obtained, allowing a quantitative analysis of the air flow dynamics on pore-scale. In the present experimental configuration, the temporal resolution is 0.1 s and the spatial resolution is 0.17 mm in plane and about 1 mm out of plane of the laser sheet.

13.
Kong, X.-Z., W. Kinzelbach, and F. Stauffer, Compaction and size segregation in a liquid-saturated grain packing due to pulsation effect during air injection, Chem.Eng.Sci., 65, pp. 2680-2688, 2010. [View Abstract]Injecting air into two-dimensional vertical liquid-saturated assemblies of grains causes a rearrangement of the grains. The interaction of the air flow injected at the bottom with the grains and the liquid leads to a mobilization of the grains, in which air channels migrate and grain clusters undergo shearing. The channel migration comes to a stop after some time, leaving one thin and stable preferential channel for air flow. Furthermore, the grain packing is compacted due to a rearrangement process caused by the pulsating movement of air channels. The compaction process is found to obey a slow exponential growth law. Additionally, the pulsation introduces size segregation in the packing. This is visualized by a set of tracing experiments showing that the coarser grains tend to accumulate at the downstream end of the preferential air pathway. However, the pulsating strength decreases sharply as the grain size increases. Therefore no segregation was observed in the coarse packing. A stabilization process of the preferential air channel can be described by a lower bound of critical channel size assuming the validity of Hagen–Poiseuille air flow inside the channel. Nevertheless, the channel size could not exceed an upper size which is determined by the capillary instability, assuming a quasi-static equilibrium of the dilating process of the air channel.

12.
Kong, X.-Z., W. Kinzelbach, and F. Stauffer, Morphodynamics during air injection into water-saturated movable spherical granulates, Chem.Eng.Sci., 65, pp. 4652-4660, 2010. [View Abstract]Laboratory air injection experiments in a two-dimensional vertically placed cell filled with a water-saturated packing of spherical glass beads show a particular transition of air flow patterns at different length scales, tree-like fingering with pore-scale drainage, a local fluidization of beads with finger-scale channeled air flow, and an oscillating irregular channel with finger-scale air flow, where the channel is formed by pushing beads aside. The tree-like pattern shows a parabola-like growth with vertical height, while both the top and the bottom lateral width of the pattern increase linearly for the small injection rate, then stay more or less constant for further increasing injection rates. By tracing the vertical position of maximum advance of the fluidized pattern with time, the evolution of the fluidized pattern is characterized by two dynamic regimes, the pattern not reaching or reaching the injection orifice, respectively, using small and medium injection rates. As the injection rate increases further, the fluidized pattern shows up immediately after air is injected. Via physical conceptual models using local forces or pressure gradient balances, we derive a series of characteristics that describe the width of the tree-like air plume, the width of a single channel, and the starting vertical position of the fluidized pattern.

11.
Kong, X.-Z., W. Kinzelbach, and F. Stauffer, Migration of air channels: an instability of air flow in mobile saturated porous media, Chem.Eng.Sci., 64, pp. 1528-1535, 2009. [View Abstract]A set of two-dimensional laboratory visualization experiments reveals a previously unrecognized gas-flow instability in a porous medium saturated with a glycerine–water solution. The medium is a non-fixed vertically placed packing of grains of crushed fused silica glass. The interaction of the injected air flow and the medium structure leads to mobilization of the medium and an instability, which causes the air channel to migrate. This instability is dominated by a dimensionless number α, which can be interpreted as a normalization of a critical velocity with a dipole velocity for saturated conditions. The channel migration appears as a sequence of previous channels collapsing and new channels opening. The channel migration comes to a stop after some time, leaving one thin and stable channel. The process is studied by calculating the cumulated lateral movement distance of a channel and the lateral width of the area affected by the migration, both scaled by α with an empirical power of 0.25. Another dimensionless number f is defined to qualify the migration under different grain size, height of bed, and air flow rate.

10.
Stauffer, F., X.-Z. Kong, and W. Kinzelbach, A stochastic model for air injection into saturated porous media, Water Resour, 32, pp. 1180-1186, 2009. [View Abstract]Air injection into porous media is investigated by laboratory experiments and numerical modelling. Typical applications of air injection into a granular bed are aerated bio-filters and air sparging of aquifers. The first stage of the dynamic process consists of air injection into a fixed or a quasi-fixed water-saturated granular bed. Later stages could include stages of movable beds as well, but are not further investigated here. A series of laboratory experiments were conducted in a two-dimensional box of the size 60 cm × 38 cm × 0.55 cm consisting of glass walls and using glass beads of diameter 0.4–0.6 mm as granular material. The development of the air flow pattern was optically observed and registered using a digital video camera. The resulting transient air flow pattern can be characterized as channelled flow in a fixed porous medium with dynamic tree-like evolution behaviour. Attempts are undertaken to model the air injection process. Multiphase pore-scale modelling is currently disregarded since it is restricted to very small scales. Invasion percolation models taking into account gravity effects are usually restricted to slow processes. On the other hand a continuum-type two-phase flow modelling approach is not able to simulate the observed air flow pattern. Instead a stochastic continuum-type approach is discussed here, which incorporates pore-scale features on a subscale, relevant for the immiscible processes involved. Consequently, the physical process can be modelled in a stochastic manner only, where the single experiment represents one of many possible realizations. However, the present procedure retains realistic water and air saturation patterns and therefore produces similar finger lengths and widths as observed in the experiments. Monte Carlo type modelling leads to ensemble mean water saturation and the related variance.

9.
Wang, W.-J., X.-Z. Kong, and Z.-G. Zhu, Friction and relative energy dissipation in sheared granular materials, Phys.Rev. E, 75/041302, 2007. [View Abstract]The oscillating cylinder of a low-frequency inverted torsion pendulum is immersed into layers of noncohesive granular materials, including fine sand and glass beads. The relative energy dissipation and relative modulus of the granular system versus the amplitude and immersed depth of the oscillating cylinder are measured. A rheological model based on a mesoscopic picture is presented. The experimental results and rheological model indicate that small slides in the inhomogeneous force chains are responsible for the energy dissipation of the system, and the friction of the grains plays two different roles in the mechanical response of sheared granular material: damping the energy and enhancing the elasticity.

8.
Kong, X.-Z., M.-B. Hu, Q.-S. Wu, and Y.-H. Wu, Kinetic energy sandpile model for conical sandpile development by evolving rivers, Phys. Lett A, 348, pp. 77-81, 2006. [View Abstract]In this Letter, a kinetic energy sandpile model, taking into account of grain inertia and the moving directions of the toppling grain, is developed and used to study the behaviour of sandpiles. In our model, the inertial effects are based on the toppling kinetic energy. The phenomenon of sandpile formation by revolving rivers is reproduced with the model, revolving velocity ω∼t^{−2/3} and ∼h^{−3/2}, where t is the simulation time and h is the height of the sandpile.

7.
Kong, X.-Z., M.-B. Hu, Q.-S. Wu, and Y.-H. Wu, Effects of bottleneck on granular convection cells and segregation, Granular Matter, 8, pp. 119-124, 2006. [View Abstract]Dry glass granular material confined to a 2D-chamber convects when it is subjected to vertical sinusoidal vibrations of sufficient intensity. Effects of the container geometry on convection pattern and segregation process are studied experimentally. Here we introduce a bottleneck into the ordinary rectangular chamber, with one sidewall bended inward, characterized by λ being the ratio of the length of the bottleneck to the length of the chamber’s base. The convection roll and segregation pattern are significantly affected by λ. For λ = 0.9, two different stabilized patterns co-exist, depending on initial granular distribution. The sloping angle of the free surface to the horizontal increases with increasing λ, and reaches its saturation at λ = 0.9. The angle of the interface of the segregation region to the horizontal also increases with increasing λ.

6.
Kong, X.-Z., M.-B. Hu, Q.-S. Wu, and Y.-H. Wu, Effects of vibration frequency on intruders’ position in granular bed, Phys. Lett A, 356, pp. 267-271, 2006. [View Abstract]In this Letter, we study the motion of multiple intruders in a vertically vibrated granular bed. From molecular dynamics simulations, it is found that the mean vertical position of the intruders, relative to the base of the container, is governed primarily by the vibration frequency for a fixed vibration acceleration. The intruders stay in the upper layer of the granular bed at low frequency, then sink into the granular bed at a certain depth as the frequency increases, but rise up again at high frequency. This implies that the mean position of the intruders in the granular bed can be controlled by decreasing or increasing the vibration frequency. A subsequent theoretical analysis is also conducted to explore the mechanism behind the phenomenon.

5.
Hu, M.-B., Q.-S. Wu, X.-Z. Kong, and Y.-H. Wu, Discharge oscillation of particles from a vertical Pipe with capillary outlet, Chinese Science Bulletin, 50, pp. 1076-1078, 2005. [View Abstract]A new style of discharge process from a vertical open-top pipe with capillary outlet is reported. The outflux fluctuates greatly with time and the bulk condensed granular flow in the pipe shows stop-and-go motion when the filling height is above a threshold. When the filling height falls towards the threshold, led by a transitional stage, the outflux and the bulk movement become much stable. The upper surface dropping velocity variation is measured. A heuristic theory is proposed to understand the stop- and-go motion and the transitional behavior.

4.
Kong, X.-Z., M.-B. Hu, Q.-S. Wu, and Y.-H. Wu, Ring-like size segregation in vibrated cylinder with a bottleneck, Phys. Lett A, 341, pp. 278-284, 2005. [View Abstract]In this Letter, a ring-like segregation pattern of bi-dispersed granular material in a vibrated bottleneck-cylinder is presented. The driving frequency can greatly affect the strength and structure of the convection roll and segregation pattern. The position and height of the ring (cluster of big beads) can be adjusted by altering the vibration frequency. And a heuristic theory is developed to interpret the ring's position dependence on driving frequency.

3.
Hu, M.-B., X.-Z. Kong, Q.-S. Wu, and Y.-H. Wu, Granular segregation in a multi-bottleneck container: Mobility effect, Int. J. Mod. Phys. B, 19, pp. 1793-1800, 2005. [View Abstract]We investigate experimentally and via computer simulations the segregation pattern of binary granular mixtures in a vibrated container with bottlenecks. During the vibration the granular motion is more violent at the bottlenecks than at the bellies. Particles with more mobility congregate to the necks, while those with less mobility congregate to the bellies. We use discrete element simulations to reproduce the main characteristics of the experimental observations.

2.
Hu, M.-B., X.-Z. Kong, Q.-S. Wu, and Y.-H. Wu, Effects of container geometry on granular segregation pattern, Chinese Physics, 14, pp. 1793-1800, 2005. [View Abstract]In a set of vibrating quasi-two-dimensional containers with the right-hand sidewall bent inward, three new segregation patterns have been identified experimentally including a Two-Side segregation Pattern, a Left-hand Side segregation Pattern and a pattern where big particles aggregate to the upper left part of the container. In a container with small bending degree, either the two-side segregation pattern or the left-hand side segregation pattern is stable, which is determined by the initial distribution of particles.

1.
Hu, M.-B., X.-Z. Kong, Q.-S. Wu, and Z.-G. Zhu, Experimental study of energy absorption properties of granular materials under low frequency vibrations, Int. J. Mod. Phys. B., 18, pp. 2708-2712, 2004. [View Abstract]The low frequency vibration energy absorption properties of granular materials have been investigated on an Invert Torsion Pendulum (ITP). The energy absorption rate of granular material changes nonlinearly with amplitude under low frequency vibration. The frequency of ITP system increases a little with granular materials in the holding cup. The vibration frequency of ITP system does not change with time.

### PROCEEDINGS REFEREED

4.
Lima, M., P. Schädle, D. Vogler, M. Saar, and X.-Z. Kong, A Numerical Model for Formation Dry-out During CO2 Injection in Fractured Reservoirs Using the MOOSE Framework: Implications for CO2-based Geothermal Energy Extraction, Proceedings of the World Geothermal Congress 2020, Reykjavík, Iceland, (in press). [View Abstract]Injection of supercritical carbon dioxide (scCO2) into geological reservoirs is involved in Carbon Capture, Utilization, and Storage (CCUS), such as geological CO2 storage, and Enhanced Geothermal Systems (EGS). The potential physico-chemical interactions between the dry scCO2, the reservoir fluid, and rocks may cause formation dry-out, where mineral precipitates due to continuous evaporation of water into the scCO2 stream. This salt precipitation may impair the rock bulk permeability and cause a significant decrease in the well injectivity. Formation dry-out and the associated salt precipitation during scCO2 injection into porous media have been investigated in previous studies by means of numerical simulations and laboratory experiments. However, few studies have focused on the dry-out effects in fractured rocks in particular, where the mass transport is strongly influenced by the fracture aperture distribution. In this study, we numerically model the dry-out processes occurring during scCO2 injection into brine-saturated single fractures and evaluate the potential of salt precipitation. Fracture aperture fields are photogrammetrically determined with fracture geometries of naturally fractured granite cores from the Deep Underground Geothermal (DUG) Lab at the Grimsel Test Site (GTS), in Switzerland. We use an open-source, parallel finite element framework to numerically model two-phase flow through a 2D fracture plane. Under in-situ reservoir conditions, the brine is displaced by dry scCO2 and also evaporates into the CO2 stream. The fracture permeability is calculated with the local cubic law. Additionally, we extend the numerical model by the Young-Laplace equation to determine the aperture-based capillary pressure. Finally, as future work, the precipitation of salt will be modelled by employing a uniform mineral growth approach, where the local aperture uniformly decreases with the increase in precipitated mineral volume. The numerical simulations assist in understanding the long-term behaviour of reservoir injectivity during subsurface applications that involve scCO2 injection, including CO2-based geothermal energy extraction.

3.
Lima, M.M., P. Schädle, D. Vogler, M.O. Saar, and X.-Z. Kong, Impact of Effective Normal Stress on Capillary Pressure in a Single Natural Fracture, European Geothermal Congress 2019, pp. 1-9, 2019. [View Abstract]Multiphase fluid flow through rock fractures occurs in many reservoir applications such as geological CO2 storage, Enhanced Geothermal Systems (EGS), nuclear waste disposal, and oil and gas production. However, constitutional relations of capillary pressure versus fluid saturation, particularly considering the change of fracture aperture distributions under various stress conditions, are poorly understood. In this study, we use fracture geometries of naturally-fractured granodiorite cores as input for numerical simulations of two-phase brine displacement by super critical CO 2 under various effective normal stress conditions. The aperture fields are first mapped via photogrammetry, and the effective normal stresses are applied by means of a Fast Fourier Transform (FFT)-based convolution numerical method. Throughout the simulations, the capillary pressure is evaluated from the local aperture. Two approaches to obtain the capillary pressure are used for comparison: either directly using the Young-Laplace equation, or the van Genuchten equation fitted from capillary pressure-saturation relations generated using the pore-occupancy model. Analyses of the resulting CO2 injection patterns and the breakthrough times enable investigation of the relationships between the effective normal stress, flow channelling and aperture-based capillary pressures. The obtained results assist the evaluation of two-phase flow through fractures in the context of various subsurface applications.

2.
Ma, J., M.O. Saar, and X.-Z. Kong, Estimation of Effective Surface Area: A Study on Dolomite Cement Dissolution in Sandstones, Proceedings World Geothermal Congress 2020, 2019.

1.
Wu, Q.-S., M.-B. Hu, X.-Z. Kong, and Y.-H. Wu, Particle Discharge Process from a Capillary Pipe, Traffic and Granular Flow’05, pp. 193-202, 2007. [View Abstract]The particle discharge process from a vertical open-top pipe with a capillary outlet reveals some exceptions to the common belief that the outflux oscillation results solely from dynamic arching of beads at the orifice and that the outflux is not sensitive to the filling height. With beads of a particular size range, the outflux fluctuates greatly with time and the bulk dense granular flow in the pipe shows stop-and-go motion when the filling height is above a threshold. When the filling height falls to the threshold, led by a transitional stage, the outflux and the bulk movement become stable. The dropping velocity variation of the upper surface is measured to study the bulk motion in the pipe. With a heuristic theory, we find that the granular compaction and interstitial air pressure effect are responsible for the stop-and-go oscillation and the transitional behavior.

Kong, X.-Z., Experimental investigation of air injection in saturated unconsolidated porous media, Dissertation, ETH Zurich, 128 pp., 2010. [View Abstract]The work described in this thesis is primarily concerned with the construction and study of laboratory scale models for the process of air injection into liquid-saturated grain packing. Experiments, both in two-dimensional (2D) and three-dimensional (3D) setups, were carried out using water-saturated packings of glass beads and/or packings of crashed fused silica glass grains saturated with a glycerin-water solution. High resolution digital images of the invasion patterns were recorded and analyzed. During air injection into a vertically-placed 2D glass bead packing saturated with water, three stages were identified, a tree-like pattern, a fluidized pattern, and a migrating single-channel pattern. The expansion of the tree-like pattern behaves in a diffusion-like manner as the air branches advance upward randomly, and finally reach a more or less constant width. The starting position of the fluidized pattern was quantitatively estimated via balancing the pressure forces between the effective stress due to the weight of the grains and the pressure resistance on the displaced fluid combined with the capillary pressure. Four dynamic regimes were distinguished: regime (i) where the fluidization stops somewhere between the top of the packing and the injection orifice, a transition regime (ii), regime (iii) where the fluidization reaches the injection orifice, and regime (iv) where the deformation of the packing appears as soon as the air is injected. A critical injection rate $Q_{f}$ is defined to identify the transition regime. The value of $Q_{f}$ can be determined via $Q_{a}$, where $Q_{a}$ is calculated as averaged flux per channel. The regime (iv) is characterized by a characteristic injection rate $Q_{c}$, which is estimated by balancing the pressure gradient of the air flow and the overburden pressure gradient of the medium. The phenomenon of the migrating channel is measured quantitatively in two parts, before and after breakthrough. Before breakthrough, the characteristic measurements concern maximum vertical advance, maximum horizontal advance, air volumetric fraction, ratio of total surface area to volume, specific surface area of the air phase, and box-counting dimension. After breakthrough, the characteristic measurements focus on mean horizontal position of air channel, horizontal shifting distance, lateral movement distance, and lateral movement width. Before breakthrough, the maximum vertical height of the air structure approximately advances linearly with time. The maximum horizontal advance reaches a maximum value and then levels off for the rest of the time. Air volumetric fraction decreases monotonically with time, and finally levels off asymptotically to an approximate constant. In all cases, the air volumetric fraction for packings of small grains is larger than that for packings of large grains. The ratio of total surface area to volume varies in time similarly to the air volumetric fraction. However, the ratio of total surface area to volume can clearly be grouped according to the grain size, which is also true for the specific surface area of the air phase. Both can be scaled with the Bond number with a power of -0.5. After breakthrough, the migration process is studied by analyzing the mean horizontal position, horizontal shifting distance, lateral movement distance, and lateral movement width of the air channel. The results indicate that over 99% of the horizontal shifting distance is less than 10 mm. Furthermore, the its probability density function indicates that the air channel oscillates more frequently in the packing of small grains than in the packing of large grains. The interaction of the air flow with the grains and the liquid leads to a mobilization of the grains, in which air channels migrate and grain clusters undergo shearing. The channel migration comes to a stop after some time, leaving one thin and stable preferential channel for air flow. Assuming Hagen-Poiseuille’s formula to be applicable, the size of the preferential channel should exceed a lower threshold $D_{ch}$ so that a mechanical equilibrium at the channel interface is maintained, but it should stay below an upper threshold $D_{max}$ so that a stable air channel is sustained. A rearrangement of the grains is observed which is caused by a pulsation effect. It induces a compaction process, in which the individual grains are disassembled from the region of non-zero shear rate and then reassembled into the compacted clusters of the region of zero shear rate. It also induces a size segregation process, in which smaller grains move into the spaces beneath larger grains. By using high-speed image acquisition through laser scanning, the 3D dynamic air plume is recorded by sequential tomographic imaging. Due to the overlap between adjacent laser sheets and the light reflection, air bubbles are multiply exposed in the imaging along the scanning direction. A “curvature” method, based on a threshold on the curvature of grey-value in scanning direction, is proposed to remove the redundant pixels. The respective results are discussed by comparing the reconstructed air plume volume with the injected one and by evaluating the morphological consistency of the obtained air plume. The reconstructed air plume is further investigated with respect to its growth characteristics, such as breakthrough, air volume fraction, and air channel migration.
Kong, X.-Z., Investigation on some dynamical characteristics of granular material, MSc Thesis, University of Science and Technology of China, 60 pp., 2006. [View Abstract]This paper presents experimental and theoretical studies on segregation of granular media subjected to external vertical sinusoidal vibration, vibration energy absorption properties of granular materials, dynamic behaviors of sandpile formation, and the stop-and-go motion in vertical pipe flow. Results of our studies not only extend the knowledge of non-linear properties of granular media under some dynamical conditions, such as vibrating, shearing, and flowing etc, but also is a theoretical instruction in the processing, storing and transporting of granular media in applied engineering. In the experiments with vertical sinusoidal vibration of granular material in containers with bottleneck(s), new segregation patterns and convection properties were found: (1)Under the condition of two-dimensional containers with one bottleneck, with the variation of the width of bottleneck, big and small particles show Two Side segregation Pattern", Left Side segregation Pattern" and a pattern that big particles segregate to the upper-left part of the container. Furthermore, the angle of segregation interface and the angle of free-surface of granular bed follow a determinate rule, and the convection rolls of granular bed turn relatively and regularly. (2)Under the condition of three-dimensional container with one bottleneck, big particles aggregate and form a Ring-like Segregation" pattern, and the position and length of big particle cluster can be adjusted by changing the vibration frequency. And mechanism of segregation is proposed. (3)Under the condition of three-dimensional container with a series of bottlenecks along its vertical axis, according to the differences of Mobility" of each particle, particles will segregate alternantly. The simulation results of discrete element method (DEM) are in agreement with the experimental observations. The discovering of these new segregation patterns are of theoretical significance to studying the complex dynamical properties of granular materials, which also would be the engineering instruction for avoiding or enhancing segregation in the processing and transporting of granular materials. A DEM simulation of particle segregation patterns controlled by vibration frequency is carried out. It was found that: at low vibration frequency, large particles clustered on the top of the granular bed; as the frequency raised, large particles sinked into the granular assembly; at very high vibration frequency, large particles went up again. The mechanism of the transition of large particles clustering on the top---sinking---rising is studied in detail. The relation within inputted energy, void fraction and the effective restitution coefficient are found out. A Cellular Automata (CA) simulation of dynamic of sandpile formation is performed. A kinetic energy sandpile model, taking into account of grain inertia and the moving directions of the toppling grain, is developed and used to study the behaviour of sandpiles. In this model, the inertial effects are based on the toppling kinetic energy. The CA model reproduces the phenomenon of sandpile formation by revolving rivers which was found in previous experimental study in literature, and the relation between anglar speed and the height of sandpile is obtained. The simulation resluts reveal the non-symmetry of the sandpile formation and the selectivity of motion path of sand. The concepts and measuring method of internal friction are successfully applied to the measurement of low frequency vibration energy absorption properties of granular materials. An Invert Torsion Pendulum is designed to measure the energy absorption properties of granular materials under low frequency vibration using the free-attenuation mode. The vibration energy absorption of granular material decreases non-linearly with the increment of vibration amplitude under low frequency vibration. These results here can provide evidence for the understanding of some granular collective behaviors. When particles discharge from an open-top capillary pipe, it was found that, with particles of a particular size range, the outflux fluctuates greatly with time and the bulk dense granular flow in the pipe shows stop-and-go motion when the filling height is much larger than a threshold. When the filling height reduces towards the threshold, undergoing a transitional stage, the outflux and the bulk movement become much more stable. A heuristic theory taking into account of the granular compaction and interstitial air pressure effect is proposed to explain the appearing and disappearing of the stop-and-go motion. Finally, the conclusion of this paper and the prospect of further work are presented.


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• S Das Gupta

Articles written in Pramana – Journal of Physics

• The canonical and grand canonical models for nuclear multifragmentation

Many observables seen in intermediate energy heavy-ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble, canonical ensemble or grand canonical ensemble. This paper deals with calculations with canonical and grand canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in nuclear matter.

• Nuclear multifragmentation: Basic concepts

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different $Z_{\text{bound}}$, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined.

• # Pramana – Journal of Physics

Current Issue
Volume 92 | Issue 6
June 2019

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In the process of ‘leveling up’ as a programmer, I have started trying to implement some lightweight, basic software engineering concepts. This post serves as a way for me to organize my own thoughts as I learn. It focuses primarily on open-source methodologies, but of course the core lessons themselves apply in any environment.

Community implementations

When implementing engineering guidelines in community-developed projects (such as open source software), we have to take a few steps. GitHub will show a link to a contributor guide on all issue and pull request pages. The guidelines document should explain the process, as well as any other considerations (such as licensing and coding standards).

Basic flow

I’ve used the Github Flow for quite a while for lots of things (recently including even this blog). But this mostly applies to processes that use continuous deployment, like GitHub itself. It can also work pretty well for documentation and other similar projects that don’t need the concept of “releases”.

For projects with staged releases, we need a few more bits. The git branching model documented by Vincent Driessen has become quite popular lately. I think it really just shows how to use git for implementing a very common model we’ve used for a long time. (I recall using this basic approach twenty years ago when our source code collaboration just relied on using a whiteboard to document who had which file checked out. That sucked as hard as it sounds.)

This model uses two primary branches: master, which must always be deployable and represents the current release, and development, which contains the currently-accepted features and bug fixes for the next release. Hot fixes for production-affecting bugs can be merged directly into both of these, but otherwise everything goes through development before going to master.

Code quality

The smart folks over at Yelp have a fun tool called pre-commit. This tool uses git hooks to run a few scripts before committing code, even locally. This primarily should include code linters, although in some projects some level of testing may also run here.

For an example, take a look at the pre-commit configuration file for Maltrieve. This runs a few scripts to format my code according to PEP8, check any JSON and YAML files, etc. While slavish adherence to PEP8 can create problems, in general it will result in more readable and standard code when used judiciously. Other languages have similar tools and linters available, so pre-commit should work even for projects coded in some other language like C.

Tools like Landscape can also run these sorts of linters and style checkers (among other things) to generate code quality metrics. For open-source projects, this can work well in conjunction with pre-commit because it can look at code in PRs from outside contributors.

Testing

I remember trying test-driven development a decade ago, and for whatever reason the lesson didn’t take. (Probably because I wrote all my code in Perl at the time, carrying with it a whole slew of issues for me.) However, I’ve committed to improving code quality by writing tests, if not going to full TDD just yet. Rather than use the standard unittest in Python, going with pytest allows a developer to get started much more quickly. I just create an additional Python module with a set of functions that start with test (e.g. _test_data_load()_) and assert that results from functions in my production code meet certain expectations. It uses simple decorators for setup and teardown. While larger projects might need more complex testing environments, everything I currently write fits easily into this tool. Friends have told me that it has changed writing tests so that they have fun writing them now.

Continuous Integration

Projects with tests can start implementing continuous integration. For my projects, this means I have automated testing running that gives me a result before merging it back to master (or even development). GitHub has great support for CI tools. Popular hosted choices include Travis CI and CircleCI, while projects that want to run their own could look at Jenkins. In both cases, developers can log into the tools with their GitHub accounts and specify which repositories to check. CircleCI has some basic support for getting started automatically, but taking proper advantage of either tool will require a small, straightforward configuration file written in YAML.

After testing both extensively, I chose to stick with CircleCI. Both offer free testing for open-source projects (by which they seem to mean “public repositories”), but CircleCI has a little lower pricing than Travis CI for private repositories or closed-source projects. I also liked how the UI integrates a little more with GitHub, making it easy to check on a pull request, branch, or commit right from its interface. Both provide solid options, though, and for many people Travis CI may actually be the right choice.

CI can do a lot more than run tests, of course, including providing some level of automation for continuous deployment. That has applications for projects that provide services or do other stuff with data, for example.

Test Coverage

Getting those green check marks when all tests pass gives a great feeling. But if the tests only handle a small amount of code, then the probability increases that things have broken and nobody knows it. Code coverage tools measure how much code actually gets exercised by tests. (Note the distinction between that and how much code gets tested well.) For py.test, the pytest-cov plugin outputs a data table after the tests run:

-------------------- coverage: platform linux2, python 2.6.4-final-0 ---------------------
Name                 Stmts   Miss  Cover
----------------------------------------
myproj/__init__          2      0   100%
myproj/myproj          257     13    94%
myproj/feature4286      94      7    92%
----------------------------------------
TOTAL                  353     20    94%

Percentages on my projects have not climbed to where I would like them, but they’ve increased from 0%.

For seeing automated results, Coveralls integrates well with both of the CI tools listed above. In CircleCI, just add some environment variables so that API keys don’t have to go into a public repository. (In this area, Travis CI probably integrates a little better with Coveralls.)

Releases

Eventually, software has to be released. GitHub allows project maintainers to create releases. This applies a lightweight tag and also allows a download of the code as a snapshot. GitHub also will serve binaries (e.g. compiled code). At one time, I used a nonstandard sequential system like “beta1” and “beta2”. However, semantic versioning allows for more granularity and works well with different sorts of tools like PyPI.

Kanban

The Kanban approach, originally developed for manufacturing processes, can apply to task management too. I’ve used a version of it for personal productivity in past jobs, including offline versions (a white board with actual sticky notes). Waffle provides a very lightweight interface to GitHub issues, including synchronizing state and comments with issue and pull requests plus filters on milestones and such. Trello is probably better-known for general Kanban usage, but by itself doesn’t directly integrate with GitHub to my knowledge. A number of other add-ons can help with this, such as connecting them with IFTTT or Zapier. For a similar tool that doesn’t use the Kanban methodology, I’ve heard great things about Asana.

Conclusion

For a long time, I have been a “hacker” and even “coder” but not a “software engineer”. My code is a house of cards and I just try not to topple it with an errant breath. But software engineering can go much deeper. Projects such as code that needs to meet life safety requirements really do require much more. But applying extra polish and quality can benefit just about any project, and the tools & methodologies here represent huge improvements over what I have used for the last couple of decades.


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# Find the partial correlation coefficient $r_{1p.2468}.$

Suppose all the simple correlations between $x_i$ and $x_j$ are $r$ for all $i,j=1,2,\dots,p, i\neq j.p>8$. Find the partial correlation coefficient $r_{1p.2468}.$

By definition, $$r_{1p.2468}=\frac{cov(e_{1.2468},e_{p.2468})}{\sqrt{var(e_{1.2468})}\sqrt{var(e_{p.2468})}}$$ how can I find $cov(e_{1.2468},e_{p.2468}),var(e_{1.2468}),var(e_{p.2468})$ in terms of $r$?

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# angular frequency and angular velocity in UCM and SHM

by al_famky
Tags: angular, frequency, velocity
 P: 29 this is another conceptual question, so sorry for not following the template. I thought that angular frequency and angular velocity shouldn't be the same thing, but after going through some of the forum threads, there was the idea: "the only difference between angular frequency and angular velocity is ---the former is a scalar and the latter is a vector. They have the same magnitudes. " which got me quite confused, because in general simple harmonic motion, angular frequency is constant and angular velocity is a varible...as in a pendulum or other motions. so i was wondering if someone could enlighten me on the matter? Thank you.
 HW Helper P: 3,339 These words can have different meanings, which is why it can be confusing at times. You are correct that the speed of a pendulum in the angular direction changes with time. And now, angular frequency, well it depends how you define it. If you define it as 2PI/T then yes, you are correct that for SHM, the angular frequency will be a constant. But if you define it as the speed in the angular direction, divided by the length of the pendulum, you can see that it is a variable. So I think that you have the concepts correct. It is where people are using different definitions for the same word which has confused you. This does happen quite a bit in physics unfortunately. So you just need to be careful which definition is being used. And when you get really comfortable with a subject, you can often guess which definition a person is using, even though they don't explicitly state it.
 HW Helper P: 508 In an ideal SHM nothing rotates or circulates. The motion of the particle is in straight line, to and fro about the equilibrium position. As the motion is periodic and the displacement, velocity and acceleration are sinusoidal functions of time, we can represent this motion as the projection of circular motion of a (imaginary) particle on a straight line. Thus every simple harmonic motion can be referred as projection of circular motion of an imaginary particle called reference particle. Angular velocity of this reference particle is called angular frequency. It has noting to do with the angular velocity of the pendulum bob. If we consider oscillations of a spring mass system these are simple harmonic. It will have angular frequency equal to sq.rt (k/m) but there is nothing like angular velocity.
P: 29

## angular frequency and angular velocity in UCM and SHM

Thank you very much, BruceW and mukundpa, it was really enlightening reading your explanations!

 Related Discussions Introductory Physics Homework 1 Introductory Physics Homework 2 Classical Physics 5 General Physics 2 Introductory Physics Homework 3


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# Springer Action on Centre of Parabolic Category O (after Brundan)

I recently learned of a result of Brundan describing the centre of the regular block of parabolic category $\mathcal{O}$ for $\mathfrak{gl}_{n}$ as the cohomology of a corresponding Springer fibre (available here); this is an isomorphism at the level of $\mathbb{C}$-algebras. However, we also have an action of the symmetric group on these cohomology algebras.

Question: Is there a way to define an $S_{n}$-action on the centre of (parabolic) category $\mathcal{O}$ for $\mathfrak{gl}_{n}$, and in such a way that Brundan's isomorphism becomes a morphism of graded $S_{n}$-modules?

Of course, I can simply transport the $S_{n}$-action in the obvious way but I was looking for a more intrinsic action on the centre that arises from (parabolic) category $\mathcal{O}$ itself. Also, I've had a look at Brundan's paper but it doesn't appear to be discussed there (if I'm being blind then please let me know!)

• Category O for any group carries an action of the corresponding Artin braid group by autoequivalences. This comes from an action on the full category of representations with given generalized infinitesimal character commuting with the action of $G$. This gives an action on the Hochschild cohomology (or center) (though maybe more naturally on Hochschild homology, or cocenter), which I expect gives the Springer action you're looking for. – David Ben-Zvi Apr 13 '13 at 3:40


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Category:Additive Group of Real Numbers is Not Isomorphic to Multiplicative Group of Real Numbers

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