Recovery Curves Research Articles

Repeated γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} irradiation and thermal annealing via built-in thermo-electric coolers of Si avalanche photodiodes

When operating in space, on-board Silicon Geiger-Mode Avalanche Photodiodes (GM-APDs) are exposed to radiation damage that result in an increase in dark count rates. Thermal annealing has been found to mitigate the damage, although prior studies have largely focused on annealing following a single session of proton irradiation. This work reports that thermal annealing can be performed simply with the built-in thermo-electric coolers of the GM-APDs. Annealing was also done in 10 min intervals for a clearer view of the recovery curve. Mitigation of damage from repeated γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} radiation was observed from the: (1) halving of the increase in dark count rates on average and (2) outperformance of room temperature annealing (25∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$25\\,^{\\circ }$$\\end{document}C) by 33%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}. Additionally, we show that heavy doses of γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} radiation (21 krad) have a probability of causing Random Telegraph Signals in GM-APDs that can be suppressed by lowering the operating temperature.

Accelerated 2D radial Look-Locker T1 mapping using a deep learning-based rapid inversion recovery sampling technique.

Efficient abdominal coverage with T1-mapping methods currently available in the clinic is limited by the breath hold period (BHP) and the time needed for T1 recovery. This work develops a T1-mapping framework for efficient abdominal coverage based on rapid T1 recovery curve (T1RC) sampling, slice-selective inversion, optimized slice interleaving, and a convolutional neural network (CNN)-based T1 estimation. The effect of reducing the T1RC sampling was evaluated by comparing T1 estimates from T1RC ranging from 0.63 to 2.0s with reference T1 values obtained from T1RC =2.5-5s. Slice interleaving methodologies were evaluated by comparing the T1 variation in abdominal organs across slices. The repeatability of the proposed framework was demonstrated by performing acquisition on test subjects across imaging sessions. Analysis of in vivo data based on retrospectively shortening the T1RC showed that with the CNN framework, a T1RC =0.84 s yielded T1 estimates without significant changes in mean T1 (p> 0.05) or significant increase in T1 variability (p> 0.48) compared to the reference. Prospectively acquired data using T1RC =0.84 s, an optimized slice interleaving scheme, and the CNN framework enabled 21 slices in a 20 s BHP. Analyses across abdominal organs produced T1 values within 2% of the reference. Repeatability experiments yielded Pearson's correlation, repeatability coefficient, and coefficient of variation of 0.99, 2.5%, and 0.12%, respectively. The proposed T1 mapping framework provides full abdominal coverage within a single BHP.

A framework for post-windstorm functional recovery of non-residential buildings applied to hospitals

This study introduces a framework for recovery-based design in wind engineering. Currently, research is well advanced to implement this approach in earthquake engineering, with the scope of improving the resilience of structures and critical infrastructure, to achieve a durable and re-occupiable built environment after the occurrence of a disaster, and estimating downtimes and quantifying service disruption. The concept of interdependencies between the nonstructural components (building envelope) and a building’s functions is realized using Fault-Tree Analysis (FTA). Using this method allows the construction of fragility curves of systems of components and services using information as weights to reduce epistemic uncertainties, and a hypothetical recovery curve for the functionality of building services based on exposure to the hazard’s impact on the building envelope. The recovery process established here highlights the fundamental importance of accurate estimation of service losses. The methodology is applied to 4 hospitals located in different climatic regions in the United States surveyed using the database of EYP Architecture & Engineering. The analysis showed the importance of building design factors; such as the location of services relative to the envelope, number of stories, and the Window-to-Wall Ratio as significant influences on the risk of service disruption and recovery.

Method for determining reagent optimum volume for acid treatments of carbonate reservoirs based on a pressure build-up curve method

Relevance. The need to increase the efficiency of acid treatments of carbonate reservoirs. Often, the design of treatments does not take into account the actual operating conditions of production wells, which leads to an overestimation or underestimation of the required volume of the reagent. Aim. To propose a method for determining the optimal amount of reagent for carrying out acid treatments of carbonate reservoirs in order to restore the permeability of the rock in the near-well zone, taking into account the actual operating conditions of the well, which allows rationalizing the use of subsoil user resources. Objects. Producing oil wells exploiting oil deposits in carbonate deposits of the Perm region, as well as the results of hydrodynamic studies carried out on these wells. Methods. Theoretical substantiation of the possibility of determining the zone of deteriorated permeability around the well using the pressure recovery curve graph, graphical processing of diagnostic graphs of the pressure recovery curve, mathematical calculation of technological indicators based on hydrodynamic testing data of wells, integration of inflow volumes, analysis of technological data and conditions of applicability of the methodology. Results. The authors have developed the methodology for determining the optimal volume of reagent for acid treatments of carbonate reservoirs based on the pressure recovery curve method. The optimal volume of reagent for 21 production wells was calculated. Using the example of 13 wells, the efficiency of the injected volume of reagent was determined and an overestimated volume of reagent injected into the formation was demonstrated. The authors assessed the subsoil user's costs taking into account the excess consumption of the reagent. The factors influencing the success of the method application depending on the operating conditions of the wells were identified. Criteria inappropriateness of acid treatment were identified.

Machine learning model identifies patient gait speed throughout the episode of care, generating notifications for clinician evaluation

IntroductionThe advent of digital and mobile health innovations, especially use of wearables for passive data collection, allows remote monitoring and creates an abundance of data. For this information to be interpretable, machine learning (ML) processes are necessary. Research questionCan a machine learning model successfully identify patients expected to have low gait speed in the early recovery period following joint replacement surgery? MethodsA commercial database from a smartphone-based care management platform passively collecting mobility data pre- and post-lower limb arthroplasty was used. We sought to create a ML model to predict gait speed recovery curves and identify patients at risk of poor gait speed outcome, a measure associated with range of motion and patient-reported outcomes. Model performance including sensitivity, specificity, precision, and accuracy were determined. Receiver operator curve (ROC) analysis was used to compare true and false positive rates. To benchmark our model, we compared threshold-based notifications based on the patient’s current gait speed. ResultsThe performance of the predictive model was significantly improved compared to baseline of threshold-based exceptions using current gait speed. The ML model currently provides 53 % precision, 88 % accuracy, 36 % sensitivity, and 95 % specificity on the held-out test set. The ROC analysis suggests good clinical performance (AUC=0.81). SignificanceUtilization of ML to predict gait recovery following total joint replacement is feasible and provides results with excellent specificity. This model will allow inclusion of additional data for retraining as patient populations evolve. Clinician feedback regarding notifications, including resulting actions and outcomes, can be used to further inform the model and improve clinical utility.

Staying Ahead of the Curve: The Case for Recovery Curves in Total Knee Arthroplasty

BackgroundSensor technology embedded within the total knee arthroplasty (TKA) implant has the potential to record data that can track recovery and provide diagnostic information. In this study, we introduce the concept of physical function recovery curve analytics, which are created from daily spatial-temporal gait metrics and step counts from a large cohort of TKA patients. MethodsIn our study population, 258 patients underwent a primary TKA with a smart implanted tibial extension between October 4, 2021, and July 15, 2022, by 33 surgeons. The average age was 63 years, with 138 (54%) women. All kinematic data was collected on a Health Insurance Portability and Accountability Act (HIPAA)-compliant cloud data management platform. ResultsSummaries of the gait parameters at 6 weeks are suggestive of differences between people over and under 65 years, with the older patients walking more slowly and having shorter stride lengths. The 6-week percentiles demonstrated a strong, linear correlation to the 12-week percentiles for each gait parameter, with correlation coefficients ranging from 0.87 to 0.92. ConclusionsA novel screening gait test at 6 weeks shows promising results for predicting patients who will likely have poor recovery based on at least 1 gait parameter recovery curve at 12 weeks with high sensitivity and specificity. A future study is needed to validate the screening tool with an independent set of patients.

Muscle Mitochondrial Capacity Is Impaired Immediately Following Maximal Exercise.

This study measured the time course mVO2max following both maximal and submaximal exercise. Healthy male and female participants were tested (n = 12 maximal and n = 8 submaximal exercise). A NIRS device was placed on the left medial gastrocnemius. Participants performed either one minute of maximal, rapid (~2 Hz), or submaximal (~0.37 Hz) plantar flexion exercise on a custom pneumatic ergometer. mVO2max was measured before and immediately after exercise. mVO2max measurements consisted of four incomplete recovery curves of muscle metabolism taken after 30 seconds of electrical muscle stimulation except in the first post-exercise trial. The four recovery curves were collected 50-, 156-, 260-, and 366-seconds post-exercise, each producing a mVO2max rate constant. After maximal exercise muscle acceleration decreased to 52 + 18% (p = 0.001) of pre-values. mVO2max was reduced from the pre-exercise mean at the first post-trial (2.16 + 0.44 min-1 to 1.21 + 0.52 min -1, p < 0.001). The fourth trial showed recovery from the first (2.2 + 0.46 min-1 vs 1.21 + 0.52 min-1, p < 0.001) and was not significantly different from pre-exercise values (2.2 + 0.46 min-1 vs 2.16 + 0.44 min-1, p = 0.41). No change in acceleration or mVO2max was seen after submaximal exercise (p > 0.05). The 56.7% reduction in mVO2max supports the hypothesis that in young, healthy individuals a minute of maximal exercise transiently impairs mVO2max which then recovers within six minutes. The NIRS method shows promise in tracking time course changes in mVO2max and warrants further investigation of the transient effects of exercise on mVO2max.

DYSPLASTIC HIPS THAT ARE TOO LATE FOR PERIACETABULAR OSTEOTOMY ARE NOT TOO EARLY FOR TOTAL HIP ARTHROPLASTY

Total hip arthroplasty (THA) is often performed in symptomatic patients with developmental dysplasia of the hip (DDH) who do not qualify for periacetabular osteotomy (PAO). The impact of osteoarthritis (OA) severity on postoperative outcomes in DDH patients who undergo THA is not well described. We hypothesized that DDH patients who undergo THA with mild OA have slower initial recovery postoperatively, but similar one-year patient reported outcome measures (PROMs) when compared to DDH patients with severe OA.We performed a retrospective review at a single academic institution over a six-year period of patients with DDH who underwent primary THA and compared them to patients without DDH who underwent THA. Within the DDH cohort, we compared PROMs stratified by DDH severity and OA severity. Diagnosis of DDH was verified using radiographic lateral center edge angle (LCEA). Minimum one-year follow-up was required. PROMs were collected through one-year postoperatively. Logistic and linear regression models were used adjusting for age, sex, body mass index, and Charlson Comorbidity Index.263 patients with DDH were compared to 1,225 THA patients without DDH. No significant differences were found in postoperative PROMs or revision rates (p=0.49). When stratified by DDH severity, patients with LCEA&lt;10° had worse preoperative pain (p=0.01), mental health (p&lt;0.01) and physical function (p=0.03) scores but no significant difference in postoperative PROMs. Within the DDH group, when stratified by OA severity, patients with Grade 3 Tonnis score had worse preoperative pain (p=0.04) but no significant difference in postoperative PROMs. Recovery curves in DDH patients based upon severity of DDH and OA were not significantly different at 2-weeks, 6-weeks and 1-year.DDH patients who have mild OA have similar recovery curves compared to those with severe OA. THA is reasonable in symptomatic DDH patients who have mild arthritis and do not qualify for PAO.

Use of the essential oil of Thymus vulgaris (thyme) and its nanoemulsion as an anesthetic during the cultivation of tambaqui (Colossoma macropomum): anesthesia induction and recovery curve, physiology, performance, and feed consumption

Use of the essential oil of Thymus vulgaris (thyme) and its nanoemulsion as an anesthetic during the cultivation of tambaqui (Colossoma macropomum): anesthesia induction and recovery curve, physiology, performance, and feed consumption

A practical method for functional recovery analysis based on seismic resilience assessment of city building portfolios

Enhancing the seismic resilience of city building portfolios represents a pivotal strategy for mitigating the adverse effects of earthquakes. A practical method for functional recovery analysis is proposed to quantitatively assess the seismic resilience of city building portfolios. The proposed method involves quantifying delay time and developing repair scheduling schemes. The delay time considers the dependencies of normal functioning buildings on infrastructure service availability and road accessibility. It emphasizes the varying demands of buildings for critical versus general infrastructure services. The repair scheduling scheme, conducted in two steps, employs a rational repair priority index that integrates the post-earthquake residual functionality, service capacity, and relative importance of buildings. This scheme prioritizes the repair of life-rescue-related buildings, distinguishes the repair sequence for different occupancy types of buildings, and reflects the principles of local governments in repair decision-making. The effectiveness of this practical method is demonstrated through a case study. Recovery curves are compared under different earthquake scenarios and levels of labor force constraints. The concept of normalized time is introduced to allow for a comparative assessment of seismic resilience across different recovery scenarios in a more practical manner. The results can provide valuable guidance for formulating pre-earthquake risk reduction strategies, developing post-earthquake functional recovery schemes, and constructing more resilient cities.

Exploring the restoration stability of abandoned open-pit mines by vegetation resilience indicator based on the LandTrendr algorithm

Open-pit mining causes serious damage to the ground surface and vegetation. Remote sensing technology helps assess and monitor the effectiveness of ecological restoration in abandoned open-pit mines, offering vital information for exploring the ecosystem recovery process. However, previous studies have mostly focused on changes in characteristics and lack quantitative characterization of restoration stability and its dynamics. In this study, we applied the vegetation resilience indicator based on the LandTrendr algorithm, which can combine vegetation disturbance and recovery characteristics for abandoned open-pit mines. Eighteen abandoned open-pit mines around Dongting Lake in China were taken as the research areas. Google Earth Engine and all available Landsat remote sensing images for June-September 1984–2022 were utilized. The effectiveness of mine restoration was determined according to the vegetation resilience indicator and recovery magnitude. The results showed that eighteen abandoned open-pit mines had a range of vegetation resilience between 5.06 and 9.45, indicating that the overall open-pit mines around Dongting Lake were well-restored. The recovery curves of the abandoned open-pit mines had an “inverted S-shape” and “S-shape,” indicating that the overall recovery characteristics of the different types of abandoned open-pit mines before and after the implementation of ecological restoration measures differed. Mine type and restoration measures affect the restoration stability of open-pit mines. The average values of vegetation resilience of the three types of mines were 7.73, 6.91, and 5.79, respectively, indicating that the resilience of the abandoned open-pit mines with serious damage was lower, and at the same time, the restoration was more dependent on the degree of input of artificial restoration. This study provides a reference for the selection of measures and the determination of restoration costs in the future ecological restoration of abandoned open-pit mines.

Improved Amott Method to Determine Oil Recovery Dynamics from Water-Wet Limestone Using GEV Statistics

Counter-current spontaneous imbibition of water is a critical oil recovery mechanism. In the laboratory, the Amott test is a commonly used method to assess the efficacy of brine imbibition into oil-saturated core plugs. The classic Amott-cell experiment estimates ultimate oil recovery, but not the recovery dynamics that hold fundamental information about the imbibition mechanisms. Retention of oil droplets at the outer core surface and initial production delay are the two key artifacts of the classic Amott experiment. This retention, referred to here as the “external-surface oil holdup effect” or simply “oil holdup effect”, often results in stepwise recovery curves that obscure the true dynamics of spontaneous imbibition. To address these holdup drawbacks of the classic Amott method, we modified the Amott cell and experimental procedure. For the first time, using water-wet Indiana limestone cores saturated with brine and mineral oil, we showed that our improvements of the Amott method enabled accurate and reproducible measurements of oil recovery dynamics. Also for the first time, we used the generalized extreme value (GEV) statistics to describe oil production histories from water-wet heterogeneous limestone cores with finite initial water saturations. We demonstrated that our four-parameter GEV model accurately described the recovery dynamics, and that optimal GEV parameter values systematically reflected the key characteristics of the oil–rock system, such as oil viscosity and rock permeability. These findings gave us a more fundamental understanding of spontaneous, counter-current imbibition mechanisms and insights into what constitutes a predictive model of counter-current water imbibition into oil-saturated rocks with finite initial water saturation.

Development and characterization of ZIF-8/WS2 composites for NH3 detection at room temperature

This study successfully synthesized zeolitic imidazolate frameworks-8 (ZIF-8) particles and tungsten disulfide (WS2) nanosheets, forming ZIF-8/WS2 composites via a layer-by-layer filtration adsorption method. The morphological and structural characterization results revealed that ZIF-8 particles and WS2 nanosheets effectively combine under filtration to form a hierarchical film structure. Room temperature ammonia (NH3) detection results indicated that the ZIF-8/WS2 composites-based gas sensor, due to the high specific surface area (1458 m2/g) and strong gas adsorption capability of ZIF-8, exhibits response intensity to NH3 that is 4.98 times higher than that of pure WS2 nanosheets. Additionally, it demonstrated stable response and recovery curves with short response/recovery times (113.5 ± 3.9 s/115.0 ± 1.9 s). This work provides valuable insights and inspiration for the construction of composite materials involving 2D TMDs and the enhancement of their room-temperature gas sensing performance.

Functional clustering of NPLs recovery curves

The recovery performance of a portfolio of Non-Performing Loans can be measured in terms of recovery rate and liquidation time jointly through a “recovery curve” representative of recovery rates over time. When portfolio heterogeneity is very high, it is informative to estimate more than just one curve by dividing the portfolio into several homogeneous subsets, i.e. clusters, and calculating a recovery curve for each of them. The aim of this work is to estimate the optimal portfolio partition and the smoothed recovery curves of each cluster by means of non-parametric statistical learning techniques.

Cross-correlated relaxation in the NMR of near-equivalent spin pairs: Longitudinal relaxation and long-lived singlet order.

The evolution of nuclear spin state populations is investigated for the case of a 13C2-labeled triyne in solution, for which the near-equivalent coupled pairs of 13C nuclei experience cross-correlated relaxation mechanisms. Inversion-recovery experiments reveal different recovery curves for the main peak amplitudes, especially when the conversion of population imbalances to observable coherences is induced by a radio frequency pulse with a small flip angle. Measurements are performed over a range of magnetic fields by using a sample shuttle apparatus. In some cases, the time constant TS for decay of nuclear singlet order is more than 100 times larger than the time constant T1 for the equilibration of longitudinal magnetization. The results are interpreted by a theoretical model incorporating cross-correlated relaxation mechanisms, anisotropic rotational diffusion, and an external random magnetic field. A Lindbladian formalism is used to describe the dissipative dynamics of the spin system in an environment of finite temperature. Good agreement is achieved between theory and experiment.

Position dependence of recovery coefficients in 177Lu-SPECT/CT reconstructions – phantom simulations and measurements

BackgroundAlthough the importance of quantitative SPECT has increased tremendously due to newly developed therapeutic radiopharmaceuticals, there are still no accreditation programs to harmonize SPECT imaging. Work is currently underway to develop an accreditation for quantitative 177Lu SPECT/CT. The aim of this study is to verify whether the positioning of the spheres within the phantom has an influence on the recovery and thus needs to be considered in SPECT harmonization. In addition, the effects of these recovery coefficients on a potential partial volume correction as well as absorbed-dose estimates are investigated.MethodsUsing a low-dose CT of a SPECT/CT acquisition, a computerized version of the NEMA body phantom was created using a semi-automatic threshold-based method. Based on the mass-density map, the detector orbit, and the sphere centers, realistic SPECT acquisitions of all possible 720 sphere configurations of both the PET and the SPECT versions of the NEMA Body Phantom were generated using Monte Carlo simulations. SPECT reconstructions with different numbers of updates were performed without (CASToR) and with resolution modeling (STIR). Recovery coefficients were calculated for all permutations, reconstruction methods, and phantoms, and their dependence on the sphere positioning was investigated. Finally, the simulation-based findings were validated using SPECT/CT acquisitions of six different sphere configurations.ResultsOur analysis shows that sphere positioning has a significant impact on the recovery for both of the reconstruction methods and the phantom type. Although resolution modeling resulted in significantly higher recovery, the relative variation in recovery within the 720 permutations was even larger. When examining the extreme values of the recovery, reconstructions without resolution modeling were influenced primarily by the sphere position, while with resolution modeling the volume of the two adjacent spheres had a larger influence. The SPECT measurements confirmed these observations, and the recovery curves showed good overall agreement with the simulated data.ConclusionOur study shows that sphere positioning has a significant impact on the recovery obtained in NEMA sphere phantom measurements and should therefore be considered in a future SPECT accreditation. Furthermore, the single-measurement method normally performed for PVC should be reconsidered to account for the position dependency.

Diffusion Mapping with Diffractive Optical Elements for Periodically Patterned Photobleaching.

Fourier transform-fluorescence recovery after photobleaching (FT-FRAP) using a diffractive optical element (DOE) is shown to support distance-dependent diffusion analysis in biologically relevant media. Integration of DOEs enables patterning of a dot array for parallel acquisition of point-bleach FRAP measurements at multiple locations across the field of view. In homogeneous media, the spatial harmonics of the dot array analyzed in the spatial Fourier transform domain yield diffusion recovery curves evaluated over specific well-defined distances. Relative distances for diffusive recovery in the spatial Fourier transform domain are directly connected to the 2D (h,k) Miller indices of the corresponding lattice lines. The distribution of the photobleach power across the entire field of view using a multidot array pattern greatly increases the overall signal power in the spatial FT-domain for signal-to-noise improvements. Derivations are presented for the mathematical underpinnings of FT-FRAP performed with 2D periodicity in the photobleach patterns. Retrofitting of FT-FRAP into instrumentation for high-throughput FRAP analysis (Formulatrix) supports automated analysis of robotically prepared 96-well plates for precise quantification of molecular mobility. Figures of merit are evaluated for FT-FRAP in analysis for both slow diffusion of fluorescent dyes in glassy polymer matrices spanning several days and model proteins and monoclonal antibodies within aqueous solutions recovering in matters of seconds.

Changes in blink reflex after simultaneous supraorbital and mental nerve stimulations in healthy subjects.

In this study, we investigated the blink reflex (BR) after simultaneous and asynchronous stimulation of two trigeminal nerve branches. The objective was to characterize the physiology of trigeminal and facial circuits. We performed three sets of experiments: recording BR response i. after supraorbital nerve stimulation (SON), after mental nerve stimulation (MN), and after simultaneous SON and MN stimulation (SON+MN) in 18 healthy individuals; ii. after MN (at an intensity eliciting BR response) preceding SON at various interstimulus intervals (ISIs) in seven healthy subjects; iii after MN (at sensory threshold) preceding SON at various ISIs. We compared the magnitudes of early and late responses. The R1 amplitude after simultaneous SON+MN stimulation was greater than responses after single stimulation of the same branches. After simultaneous stimulations, the R2 and R2c areas under the curve (AUC) were smaller than the arithmetic sums of R2 and R2c AUC obtained after single stimulations. The second experiment provided a recovery excitability curve. In the third step, we obtained facilitation of R1 and inhibition of late responses. The SON+MN stimulation caused an increased R1 circuit excitability compared to the arithmetic sum of the single stimulations; however, magnitudes of late responses did not potentiate. Thus, we have provided evidence for R1 circuit enhancement by simultaneous stimulation in humans, whereas modulation of late responses exhibited a recovery curve similar to that shown for paired SON stimulation.

The Role of Core Sample Geometry on Countercurrent Spontaneous Imbibition: Mathematical Foundation, Examples, and Experiments Accounting for Realistic Geometries

Summary Countercurrent spontaneous imbibition (SI) experiments are among the most common multiphase experiments performed on porous rock samples. Although the samples rarely are designed to give linear flow, they are often modeled and interpreted using mathematical descriptions assuming linear flow. In this work, the goal is to derive general understanding of how imbibition into different sample geometries behaves compared with linear (1D) imbibition. Using the mathematical theory of N-volume spheres (N being the dimension), we consider core samples as N-spherical and quantify their geometry by a dimension N and length scale L. For the special cases, N=1,2,3, we obtain linear, radial, and spherical flow; however, we treat the dimension as an arbitrary real number for cases not adhering to either of these regimes. Particularly, for rectangular or cylindrical core plugs, a continuous range of dimensions is produced. Theoretical calculations of N and L of arbitrary sample shapes are derived based on relations with area per volume and derivative of area with respect to volume. They correctly produce limit cases and physically meaningful values for symmetrical, cylindrical, and rectangular geometries. The differential equation for countercurrent imbibition in N-dimensions is derived and solved with numerical examples. Also, a simplified analytical solution assuming piston-like displacement is derived to get illustrative relations between system parameters (including dimension) and recovery and front position. Predicted recovery profiles of the N-dimensional (N-D) solution overlap consistently with numerical simulations (by an alternative simulator) into cylindrical geometries with a wide range of height/diameter ratios and viscosity ratios. At early time, the saturation profiles are self-similar (look the same plotted against position divided by square root of time) and identical regardless of dimension. As long as the profiles are self-similar near the open boundary, recovery is proportional to the square root of time. For N=1, this lasts long after the front has reached the closed boundary, while for N &amp;gt;1, it can happen long before the boundary has been reached. The same time scale was applicable for all geometries, stating especially that doubling the length scale increased the time of the entire recovery profile by a factor 4. As long as recovery is proportional to square root of time, at a given time, it is also proportional to dimension over length, NL, and the time needed to reach same level of recovery is proportional to LN2. Permeability anisotropy (lower vertical than horizontal permeability) could effectively be modeled using an effective increased height, which further was captured by the dimension and length scale. Literature and in-house experimental data were matched by the model and used to validate model predictions such as the variation in time, shape of recovery curves with changes in dimension, and the importance of accounting for the dimension (geometry) during data interpretation. The model is valid for all wetting states but assumes negligible gravity and compressibility effects.

A probabilistic framework to evaluate seismic resilience of substations based on three-stage uncertainty

Electrical substation systems exhibit vulnerability after an earthquake. It results in significant economic losses because of the uncertainty of the functional state and recovery process. To quantitatively assess the uncertainty of substations, this paper proposes a probability-based seismic resilience assessment framework. This framework considers uncertainty in three stages: functional state, functional recovery, and resource constraints. Based on the functional characteristics of substation systems, a directed acyclic graph was constructed, and the Monte Carlo algorithm was used to obtain the functional state matrix, thereby establishing a probability-based functional state model. Moreover, a dynamic post-earthquake functional recovery analysis framework was built based on recovery efficiency metrics, and functional recovery paths were obtained through iterative simulations. A stepped functional recovery curve was developed based on resource constraints. Three-stage uncertainty parameters were transformed into resilience features for quantitative assessment. By analysing seismic resilience of a typical 220 kV step-down substation, probability distributions of functional recovery curves and confidence intervals for seismic resilience metrics were obtained. Notably, mutual constraint relationships among resource conditions were identified.