Using Direct Numerical Simulation of Pore-Level Events to Improve Pore-Network Models for Prediction of Residual Trapping of CO2

Direct numerical simulation and pore-network modeling are common approaches to study the physics of two-phase flow through natural rocks. For assessment of the long-term performance of geological sequestration of CO2, it is important to model the full drainage-imbibition cycle to provide an accurate estimate of the trapped CO2. While direct numerical simulation using pore geometry from micro-CT rock images accurately models two-phase flow physics, it is computationally prohibitive for large rock volumes. On the other hand, pore-network modeling on networks extracted from micro-CT rock images is computationally efficient but utilizes simplified physics in idealized geometric pore elements. This study uses the lattice-Boltzmann method for direct numerical simulation of CO2-brine flow in idealized pore elements to develop a new set of pore-level flow models for the pore-body filling and snap-off events in pore-network modeling of imbibition. Lattice-Boltzmann simulations are conducted on typical idealized pore-network configurations, and the interface evolution and local capillary pressure are evaluated to develop modified equations of local threshold capillary pressure of pore elements as a function of shape factor and other geometrical parameters. The modified equations are then incorporated into a quasi-static pore-network flow solver. The modified model is applied on extracted pore-network of sandstone samples, and saturation of residual trapped CO2 is computed for a drainage-imbibition cycle. The modified model yields different statistics of pore-level events compared with the original model; in particular, the occurrence of snap-off in pore-throats is reduced resulting in a more frontal displacement pattern along the main injection direction. Compared to the original model, the modified model is in closer agreement with the residual trapped CO2 obtained from core flow experiments and direct numerical simulation.

Petrographic Composition of the Coal Within the Benue Trough, Nigeria, With a Consideration of the Paleodepositional Setting

The petrographic composition of coals hosted in the Benue Trough, Nigeria are presented and discussed in terms of paleodepositional setting that influenced the coal-bearing formations. The Benue Trough is a failed arm of the triple ‘RRr’ junction of an inland sedimentary basin that extends in a NE-SW direction from the Gulf of Guinea in the south, to the Chad Basin in the north. A total of twenty-nine (29) coal samples were obtained from 19 coal localities in the Upper (UBT), Middle (MBT), and Lower Benue Trough (LBT). The proximate data indicates the coal samples have a high volatile matter content, low ash yield, and high calorific value (24.82 MJ/Kg, on average). The sulphur values are generally low (average of 0.94 %). The coal samples are generally high in vitrinite, with an average of 59.3% by volume (mineral-matter free). Variation was noted in the inertinite content for the three sub-region samples. Liptinite macerals were not commonly observed in the studied samples and are absent in the MBT samples. The MBT coal samples reported a higher gelification index than the UBT and the LBT samples. Comparison of the array of coal facies models show the MBT samples are different from the UBT and LBT samples, concurring with the characterisation data. In view of the modified equations and the plots used, interpreting depositional environment accurately from just a single model is quite challenging.

A General Model for Describing the Ovate Leaf Shape

Many plant species produce ovate leaves, but there is no general parametric model for describing this shape. Here, we used two empirical nonlinear equations, the beta and Lobry–Rosso–Flandrois (LRF) equations, and their modified forms (referred to as the Mbeta and MLRF equations for convenience), to generate bilaterally symmetrical curves along the x-axis to form ovate leaf shapes. In order to evaluate which of these four equations best describes the ovate leaf shape, we used 14 leaves from 7 Neocinnamomum species (Lauraceae) and 72 leaves from Chimonanthus praecox (Calycanthaceae). Using the AIC and adjusted root mean square error to compare the fitted results, the modified equations fitted the leaf shapes better than the unmodified equations. However, the MLRF equation provided the best overall fit. As the parameters of the MLRF equation represent leaf length, maximum leaf width, and the distance from leaf apex to the point associated with the maximum leaf width along the leaf length axis, these findings are potentially valuable for studying the influence of environmental factors on leaf shape, differences in leaf shape among closely related plant species with ovate leaf shapes, and the extent to which leaves are bilaterally symmetrical. This is the first work in which temperature-dependent developmental equations to describe the ovate leaf shape have been employed, as previous studies lacked similar leaf shape models. In addition, prior work seldom attempted to describe real ovate leaf shapes. Our work bridges the gap between theoretical leaf shape models and empirical leaf shape indices that cannot predict leaf shape profiles.

Dynamic Simulation of High-Speed Induction Motor

In the drives of high-speed devices, such as a blood centrifuge, dynamic states also play an important role in terms of the time and quality of the tests performed. The article presents the application of modified equations resulting from the mathematical model of an induction motor to model dynamic phenomena during motor start-up, both with mains supply and with frequency start-up. The applied solution considers the phenomenon of current displacement in the rotor bar and the phenomenon of saturation. The comparison of the obtained results with the experiment shows that the method is sufficiently accurate. The obtained results can also be extended to higher power machines and to modeling other dynamic states.

Stability theory for some scalar finite difference schemes: validity of the modified equations approach

In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial differential equations. We show that the infinite series obtained by Fourier transform of the modified equation is not always convergent and that in the case of divergence, it becomes unrelated to the scheme. Based on these results, we explain when the stability analysis of a given truncation of a modified equation may yield a reasonable estimation of a stability condition for the associated scheme. We illustrate our analysis by some examples of schemes namely for the heat equation and the transport equation.

Scenario of accelerated universe expansion under exposure to entropic forces related to with the entropies of Barrow and Tsallis−Cirto

In the work within the framework of "entropic cosmology", the scenario of the cosmological accelerated expansion of a flat, homogeneous and isotropic Universe under the influence of entropic forces is considered without the concept of dark energy a hypothetical medium with negative pressure. Assuming that the horizon of the Universe has its own temperature and entropy, which arises during the holographic storage of information on the screen of the horizon surface, the entropy models of the Universe associated with the BekensteinHawking entropy and the non-extensive Barrow and Tsallis–Cirto entropies are considered. The modified equations of acceleration and continuity of Friedman with governing power terms having an entropic nature are derived both within the framework of Einstein's general theory of relativity and on the basis of a thermodynamic approach that allows modeling the non-adiabatic evolution of the Universe. At the same time, models based on nonextensive entropies predict the existence of both a decelerating and accelerating Universe.

Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics

The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz andMontijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are usedto demonstrate the similarity between them, in particular the distance of Hausdorff. The results show that these equations are similar fromthe mathematical point of view and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It isconcluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe thegrowth kinetics of unperturbed tumors.

Modification of the Electron Entropy Production in a Plasma

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments hr1…rm(m) by means of the irreducible tensorial Hermite polynomials.

Modified Pooled Cohort Atherosclerotic Cardiovascular Disease Risk Prediction Equations in American Indians

American Indians (AI) have a high prevalence of diabetes, obesity, cardiovascular disease (CVD), and chronic kidney disease. Inclusion of kidney function and other population-specific characteristics in equations used to predict atherosclerotic CVD (ASCVD) risk may help define risk more accurately in populations with these chronic diseases. We used data from the Strong Heart Study (SHS), a population-based longitudinal cohort study of AI, to modify the American College of Cardiology/American Heart Association (ACC/AHA) Pooled Cohort ASCVD risk equations and then explored the performance of the new equations in predicting ASCVD in AI. The study included baseline SHS exam data from 4213 individuals between 45 and 75 years of age, collected in 13 communities from 3 geographic areas in the United States and spanning a wide range of tribal backgrounds, with continuous follow-up data from 1989 to 2015. Using SHS data for blood pressure, diabetes, cholesterol, smoking, and renal function, Cox proportional hazard models were developed to predict ASCVD-free time for AI men and women. ASCVD risk in AI calculated using the SHS-modified equations were compared to risk calculated using the ACC/AHA pooled cohort equations for African Americans (AAs) and Whites. Goodness-of-fit measures for ASCVD risk prediction showed that the SHS-modified equations fit the data from the SHS better than the ACC/AHA equations for AAs and Whites. Adjusting risk prediction equations using population data from the SHS and including measures of renal function significantly improved ASCVD risk prediction in our AI cohort.