Tangent Distance Research Articles

A novel method to accelerate the three-phase flash calculation of the hydrocarbon-CO2 system

To achieve high computational efficiency and simulation accuracy in the equation-of-state-based compositional simulation, the fast multiphase flash calculation approach is required for the hydrocarbon-CO2 system, allowing for the simultaneous existence of vapour, CO2-lean, and CO2-rich phases. However, the conventional step-by-step method for multiphase flash calculation is associated with a high cost in identifying the three-phase equilibrium, thereby significantly impeding the computation efficiency of compositional simulation when the three-phase equilibrium appears in most grids.To address this challenge, a novel approach to multiphase flash calculation is proposed. In this study, all trial phases exhibiting negative tangent plane distance are employed to identify the three-phase equilibrium, eliminating the need for additional phase stability analysis and two-phase split calculations. Furthermore, this new method incurs minimal computational cost and requires only minor modifications to the existing stepwise procedure. Phase diagram calculations conducted on four cases demonstrate that the newly proposed method dramatically accelerates the identification of the three-phase equilibrium.

Quadratic surface preserving parameterization of unorganized point data

Finding parameterizations of spatial point data is a fundamental step for surface reconstruction in Computer Aided Geometric Design. Especially the case of unstructured point clouds is challenging and not widely studied. In this work, we show how to parameterize a point cloud by using barycentric coordinates in the parameter domain, with the aim of reproducing the parameterizations provided by quadratic triangular Bézier surfaces. To this end, we train an artificial neural network that predicts suitable barycentric parameters for a fixed number of data points. In a subsequent step we improve the parameterization using non-linear optimization methods. We then use a number of local parameterizations to obtain a global parameterization using a new overdetermined barycentric parameterization approach. We study the behavior of our method numerically in the zero-residual case (i.e., data sampled from quadratic polynomial surfaces) and in the non-zero residual case and observe an improvement of the accuracy in comparison to standard methods. We also compare different approaches for non-linear surface fitting such as tangent distance minimization, squared distance minimization and the Levenberg Marquardt algorithm.

Geometric Morphometric Study of Wing Shape in Leva indica (Acrididae: Gomphocerinae) from Different Environmental Sites of Coimbatore, India

A landmark based geometric morphometric study was carried out to describe the variation in wing of male and female Leva indica from different environmental sites of Coimbatore, Tamil Nadu, India. A total of 60 male and 60 female forewings were used in this study. To demonstrate the variation in wing shape, landmark data of each individual was examined through the morphometric softwares namely tps-Util, tps-Dig, tps-Relw, tps-Small and integrated software PAST. In total, 19 landmarks were identified in both male and female wings of L. indica. Based on the landmark coordinates, the first two relative warp analysis showed significant variation within and between the male and female wing shape from different sites. Procrustes vs. tangent space distance showed that the distances were similar within males and females but significant differences appeared between the male and female wings of L. indica. Principal Component Analysis (PCA) between the male and female wings scatter plots also showed clear distinction from the result. The obtained results indicate that each sex of L. indica from different regions displays morphological differences in wing shape. These morphological changes could have occurred as a result of phenotypic plasticity.

Relationship between Horizontal Curve Geometry and Single-Vehicle Crash Occurrence on Rural Secondary Highways

Single-vehicle crashes are overrepresented on rural two-lane highway curves. While prior work investigated the relationship between crash occurrence and aggregate curve characteristics, several important aspects related to curve geometry remain uninvestigated. To this end, research was undertaken to evaluate the safety effects associated with several specific horizontal curve-related geometric characteristics (including curve type, curve direction, tangent distance between curves, and curve design speed) on rural two-lane undivided highways, considering non-animal single-vehicle crashes. Eight years of crash data were obtained for 277 mi and 557 mi of curved state and county highway segments, respectively, within Michigan. Several mixed-effects negative binomial models, with county- and site-specific random intercepts, were developed separately for state and county highways. The model results indicated that several key geometric factors were associated with crash occurrence on rural two-lane highways, including curve type, curve direction, tangent distance approaching the curve, inner-curve tangent distance, and curve design speed. Each of the following geometric characteristics was associated with elevated single-vehicle crash occurrence: (1) compound and reverse curves (compared with simple curves); (2) left-turning curves (compared with right-turning); (3) curves with design speeds lower than the speed limit (compared with curves with higher design speeds); (4) longer tangent distances approaching a simple curve or the initial curve in a series; and (5) shorter inner-curve distances between successive compound or reverse curves. Compound or reverse curves should be avoided in favor of simple curves with an elongated inner-curve distance. Enhanced warning signage should be considered where such curve designs cannot be avoided.

Phase equilibria of “syngas” components, aiming for separation by flash distillation

Syngas is a mixture containing methane, hydrogen, carbon dioxide, and carbon monoxide, and it is generated in various processes, such as gasification or methane production via steam reforming. It is desired to separate the syngas to its components in order to create a reliable clean source of energy from methane and hydrogen and to reduce emissions by capturing carbon dioxide. As for today, there is no available data on phase equilibrium of syngas in the literature, which is essential for developing separation processes by distillation. The composition of the syngas depends on its source; therefore, the method for calculating the phase equilibrium shall support any initial composition of the syngas. In the current research, we perform phase stability analysis, using tangent plane distance function and minimizing Helmholtz free energy of the system using two mixing rules: van der Waals and Wong and Sandler. The main strength of the suggested method is its ability to predict any number of phases, avoiding the need for prior knowledge. The current manuscript presents an analysis of binary mixtures of the syngas components, CH4 + CO2, CH4 + CO, CH4 + H2, CO2 + CO, CO2 + H2, and CO + H2, in order to fit the model's parameters to experimental data from the literature, at various temperatures. The aim of this research is to determine which mixing rule shall be further used and to determine the temperature dependent parameters. The parameters fitting is done by minimizing the sum of square errors using “steepest decent” and Fibonacci search method.

A successive substitution approach with embedded phase stability for simultaneous chemical and phase equilibrium calculations

We propose a nested Gibbs energy minimization method for simultaneous chemical and phase equilibrium calculations, relying on a new formulation of the Lagrange multiplier based inner sub-problem with fixed activity coefficients. Using a sufficient condition for global optimality with fixed activity coefficients equivalent in this case to the tangent plane distance criterion, we describe two equivalent algorithms, a combinatorial and a complementarity based one, allowing to robustly solve this new sub-problem always incorporating all phases. The outer-loop of the global successive substitution reactive flash then only consists in updating the values of the activity coefficients from the non necessarily normalized species fractions for all phases calculated by the inner sub-problem. Numerical experiments from the literature illustrate the correct behavior of the proposed approach.

Five-Fraction Radiotherapy for Breast Cancer: Which are the Most Suitable Patients?

<h3>Purpose/Objective(s)</h3> FAST-Forward trial reported that five-fraction radiotherapy (5fx-RT) schedule with 26 Gy in adjuvant setting after breast-conserving surgery for early-breast cancer (BC) was non-inferior to the standard hypo-fx (SHfx) schedule with 40 Gy in 15fx in terms of local tumor control. Since the COVID-19 pandemic started RT expert groups encouraged professionals to implement hypo-fx schedules in order to decrease visits of patients to hospitals. The aim of this study is to help radiation oncologists choose the most suitable patients for 5fx-RT schedule according to anatomical features. <h3>Materials/Methods</h3> Between March 2020 and December 2021, 239 patients suitable for 5fx-RT schedule were referred to our department. Prescribed RT dose was 26 Gy in 5fx to the whole breast plus a simultaneously integrated boost (SIB) up to 29 Gy to tumor bed if indicated. Patients were divided into 3 groups: Group A: Patients treated with 5fx-RT schedule that met all the FAST-Forward constraints for normal tissues; Group B: Patients treated with 5fx-RT schedule that slightly did not meet all constraints, Group C: Patients switched to SHfx schedule as they did not meet constraints in an acceptable way. For each patient, we draw an imaginary straight line connecting the medial and lateral borders of PTV in the axial slice of simulation CT where the longest anteroposterior diameter was found. From midpoint of this line, we measured the tangent distance to PTV margin and collected the data as medial-to-lateral tangent (MELT). Data was analyzed using statistical software. <h3>Results</h3> 150 patients were included in group A, 75 in group B and 14 in group C. The median MELT distance was: 1.91cm, 2.48cm and 3cm respectively. We found that the increase in MELT distance was significantly associated with a poorer compliance of normal tissue constraints (p<0.0001). Patient´s distribution among 3 groups for MELT distance intervals are shown in table 1. Median V8 for ipsilateral lung was: 13.1, 15.46 and 20.49% for groups A, B and C respectively. For the heart, median mean dose was: 1.06, 1.8 and 2.25 Gy for left breast cancer patients and 0.28, 0.33 and 0.48 Gy for right breast cancer patients for groups A, B and C respectively. We found a moderate positive correlation between MELT distance and dosimetric parameters assessed above (r=0.545, 0.475 and 0.418 respectively). According to laterality, for a higher MELT distance the % of left BC patients increased significantly (p=0.039). <h3>Conclusion</h3> MELT distance is an easy tool that helps radiation oncologists predict which BC patients are the most suitable for 5fx-RT before RT planning begins. This could avoid delays in starting RT for patients with a high MELT distance directly planning them with the SHfx schedule.

Classification Based on Machine Learning Methods for Identification of Image Matching Achievements

Classification is one method in image processing. Image processing to search for similar images or with similarity ownership is called image matching or image matching. In the measurement of image matching, the original and fake logo objects are used. Identification of similarity manually with the help of human vision is not necessarily precise and it is difficult to obtain accurate results. Based on this, the identification of image matching of the original and fake logos automatically requires an application, in order to obtain precise and more accurate results. Identification of image suitability is determined through the image segmentation process, and feature extraction is based on the statistics of Red-Green-Blue (RGB), Hue-Saturation-Value (HSV), feature extraction of area, perimeter, eccentricity, and tangent distance measurements. The purpose of this study includes the identification of the achievement of image-matching logo images with comparisons of accuracy between various machine learning methods. The use of machine learning methods in this study includes the k-Nearest Neighbor (kNN), Random Forest (RF), and Multilayer Perceptron (MLP) methods. The use of the dataset includes eighteen training data and eight logo image testing data, divided into genuine and fake classes. The results of the measurement of the accuracy value obtained a value of seventy-five percent with the kNN method or the RF method, while the MLP method obtained an accuracy value of eighty-seven point five percent. Based on these results, it can be concluded that the MLP method with the highest accuracy value was chosen as a classification model from machine learning to identify the achievement of image matching on the original and fake logos. For further development, the system can be developed using other methods or a combination of different methods, in order to obtain better accurate results.

Vapour–liquid–liquid and vapour–liquid equilibrium of paraffinic aromatic synthetic naphtha/water blends: Prediction of the number of phases

AbstractBitumen is extracted from oil sands using warm water and additives. The resulting bitumen froth is diluted with naphtha in a froth treatment process. Residual naphtha in the aqueous tailings of the froth treatment unit is recovered in a naphtha recovery unit (NRU). It is imperative to maximize the naphtha recovery process to minimize the plant's environmental and economic impact. It is, in this respect, that NRU vapour–liquid–liquid equilibrium data is of significant value. In this work, a paraffinic‐aromatic synthetic naphtha (PASN) with a true boiling point (TBP) similar to that of froth treatment naphtha is used. Water/PASN mixtures are studied using the Soave‐Redlich‐Kwong equation of state with a Kabadi‐Danner modification. The tangent plane distance (TPD) is evaluated as a possible criterion to calculate the number of phases, with its significant shortcomings being established. As well, experimental data obtained in a CREC‐VL‐Cell is observed to display higher solubilities of PASN in water than the ones obtained by HYSYS‐Aspen Plus V9 simulation. To address these issues, a machine learning (ML)‐based phase classification methodology was considered, predicting the number of phases with a 99% recall. This anticipates that ML will be of significant value for faster convergence of the flash split calculations for the naphtha hydrocarbon‐water systems under consideration.

SGTPy: A Python Code for Calculating the Interfacial Properties of Fluids Based on the Square Gradient Theory Using the SAFT-VR Mie Equation of State.

In this work, we showcase SGTPy, a Python open-source code developed to calculate interfacial properties (interfacial concentration profiles and interfacial or surface tension) for pure fluids and fluid mixtures. SGTPy employs the Square Gradient Theory (SGT) coupled to the Statistical Associating Fluid Theory of Variable Range employing a Mie potential (SAFT-VR-Mie). SGTPy uses standard Python numerical packages (i.e., NumPy, SciPy) and can be used under Jupyter notebooks. Its features are the calculation of phase stability, phase equilibria, interfacial properties, and the optimization of the SGT and SAFT parameters for vapor-liquid, liquid-liquid and vapor-liquid-liquid equilibria for pure fluids and multicomponent mixtures. Phase equilibrium calculations include two-phase and multiphase flash, bubble and dew points, and the tangent plane distance. For the computation of interfacial properties, SGTPy incorporates several options to solve the interfacial concentration, such as the path technique, an auxiliary time function, and orthogonal collocation. Additionally, the SGTPy code allows the inclusion of subroutines from other languages (e.g., Fortran, and C++) through Cython and f2py Python tools, which opens the possibility for future extensions or recycling tested and optimized subroutines from other codes. Supporting Information includes a review of the theoretical expressions required to couple SAFT-VR-Mie equation of state with the SGT. The use and capabilities of SGTPy are illustrated through step by step examples written on Jupyter notebooks for the cases of pure fluids and binary and ternary mixtures in bi- and three- phasic equilibria. The SGTPy code can be downloaded from https://github.com/gustavochm/SGTPy.

Phase equilibrium modelling for multi-component mixtures using highly accurate Helmholtz energy equation of state

Phase stability of a mixture at given conditions is studied. The modelling of equilibrium phase compositions is considered when the original phase of the mixture is unstable. The tangent plane distance criterion is used for stability analysis and the Gibbs energy minimisation is employed for phase equilibrium calculation when the successive substitution does not work well. With the Helmholtz free energy equation of state, thermodynamic properties in single phase and two-phase equilibrium were calculated for methane-ethane mixtures. Phase envelopes were also calculated.

Phase equilibrium modelling for multi-component mixtures using highly accurate Helmholtz energy equation of state

Phase stability of a mixture at given conditions is studied. The modelling of equilibrium phase compositions is considered when the original phase of the mixture is unstable. The tangent plane distance criterion is used for stability analysis and the Gibbs energy minimisation is employed for phase equilibrium calculation when the successive substitution does not work well. With the Helmholtz free energy equation of state, thermodynamic properties in single phase and two-phase equilibrium were calculated for methane-ethane mixtures. Phase envelopes were also calculated.

Phase equilibrium calculations in shale gas reservoirs

Compositional multiphase flow in subsurface porous media is becoming increasingly attractive due to issues related with enhanced oil recovery, CO 2 sequestration and the urgent need for development in unconventional oil/gas reservoirs. One key effort to construct the mathematical model governing the compositional flow is to determine the phase compositions of the fluid mixture, and then calculate other related physical properties. In this paper, recent progress on phase equilibrium calculations in unconventional reservoirs has been reviewed and concluded with authors’ own analysis, especially focusing on the special mechanisms involved. Phase equilibrium calculation is the main approach to investigate phase behaviors, which could be conducted using different variable specifications, such as the NPT flash and NVT flash. Recently, diffuse interface models, which have been proved to possess a high consistency with thermodynamic laws, have been introduced in the phase equilibrium calculation, incorporating the realistic equation of state (EOS), e.g. Peng-Robinson EOS. In the NVT flash, the Helmholtz free energy is minimized instead of the Gibbs free energy used in NPT flash, and this thermodynamic state function is decomposed into two terms using the convex-concave splitting technique. A semi-implicit numerical scheme is applied to the dynamic model, which ensures the thermodynamic stability and then preserves the fast convergence property. A positive definite coefficient matrix is designed to meet the Onsager reciprocal principle so as to keep the entropy increasing property in the presence of capillary pressure, which is required by the second law of thermodynamics. The robustness of the proposed algorithm is demonstrated by using two numerical examples, one of which has up to seven components. In the complex fluid mixture, special phenomena could be captured from the global minimum of tangent plane distance functions and the phase envelope. It can be found that the boundary between the single-phase and vapor-liquid two phase regions shifts in the presence of capillary pressure, and then the area of each region changes accordingly. Furthermore, the effect of the nanopore size distribution on the phase behavior has been analyzed and a multi-scale scheme is presented based on literature reviews. Fluid properties including swelling factor, criticality, bubble point and volumetrics have been investigated thoroughly by comparing with the bulk fluid flow in a free channel. Cited as : Zhang, T., Li, Y., Sun, S. Phase equilibrium calculations in shale gas reservoirs. Capillarity, 2019, 2(1): 8-16, doi: 10.26804/capi.2019.01.02

SWAN/SOHO Lyman‐α Mapping: The Hydrogen Geocorona Extends Well Beyond the Moon

AbstractThe Earth's hydrogen exosphere Lyman‐α radiation was mapped with the Solar Wind Anisotropies/Solar and Heliospheric Observatory (SWAN/SOHO) instrument in January 1996, 1997, and 1998 (low solar activity). The use of a hydrogen absorption cell allowed to disentangle the interplanetary emission from the geocoronal one and to assign the absorbed signal almost entirely to the geocorona. The geocorona was found to extend at least up to 100 Earth radii (RE) with an intensity of 5 Rayleigh, an unprecedented distance well exceeding the recent results of Lyman Alpha Imaging Camera (LAICA) imager (∼50 RE), and encompassing the orbit of the Moon (∼60 RE). We developed a numerical kinetic model of the hydrogen atoms distribution in the exosphere, which includes the solar Lyman‐α radiation pressure and the ionization. The radiation pressure compresses the H exosphere on the dayside, producing a bulge of H density between 3 and 20 RE, which fits observed intensities very well. The SWAN Lyman‐α distribution of intensity was compared both to LAICA (2015) and to Orbiting Geophysical Observatory number 5 (1968) measurements. Integrated H densities of SWAN at a tangent distance of 7 RE are larger than LAICA/Orbiting Geophysical Observatory number 5 by factors 1.1–2.5, while we should expect a stronger effect of the radiation pressure at solar max. We discuss the possible role of H atoms in satellite orbits to explain this apparent contradiction. An onion‐peeling technique is used to retrieve hydrogen number density in the exosphere for the three SWAN observations. They show an excess of density versus models at large distances, which is likely due to nonthermal atoms (not in the model).

An improved LLE-based cluster security approach for nonlinear system fault diagnosis

This paper proposes a novel improved LLE-based (local linear embedding) approach (TLLE) for solving the fault diagnosis problem of the nonlinear system. Firstly, tangent space distance is introduced to LLE approach, which can satisfy the local linearity of LLE and better preserve the local manifold features of the original data simultaneously. Then, to solve the problem of inner dimension in LLE approach is hard to estimate, the method of intrinsic dimension estimation based on fractal dimension is employed in the approach by means of linear fitting. Furthermore, a fault diagnosis scheme is presented based on the TLLE approach. We combine fault state with special distribution to complete the fault diagnosis, which can simplify the computation obviously and improve the real-time capability of the approach. Finally, numerical simulations of the TE process data are performed to illustrate the effectiveness of the proposed fault diagnosis scheme.

Volume-based phase stability testing at pressure and temperature specifications

Conventional phase equilibrium calculations at temperature and pressure specifications require the resolution of the equation of state (EoS). In volume-based calculations, the EoS must not be solved for volume, which is a primary variable. The tangent plane distance (TPD) function can be expressed in terms of mole numbers and volume or of component molar densities. The stationary points of the TPD function, as well as the location of the stability test limit locus (STLL) are different for the two formulations. A modified TPD function in terms of mole numbers and volume is proposed here. Using the block structure of the Hessian matrix, it is shown that Newton iterations in volume-based stability are inherently slower than those in the conventional PT stability, since the Hessian matrix is evaluated at a lower implicitness level. The minimization of several TPD functions (in volume-based and conventional stability testing) is analyzed using various sets of independent variables and scaling procedures. A modified Cholesky factorization and a two-stage line search procedure ensure a sequence of decreasing TPD functions in all cases. The proposed methods are tested for several mixtures, with emphasis on the vicinities of singularities (STLL and spinodal). With proper scaling, the modified Newton iterations are robust and converge very fast for most conditions and reasonably fast for very difficult conditions. The proposed algorithm is not model-dependent; any pressure explicit EoS can be used, provided the required partial derivatives are available.

Offline Fault Localization Technique on HVDC Submarine Cable via Time–Frequency Domain Reflectometry

Fault localization is one of the most significant aspects in the maintenance of high-voltage direct current (HVdc) submarine cables that have unconventional installation characteristics, such as long cable lengths and underwater installation locations. In order to protect and diagnose the cable, an improved fault localization technique, that is, time–frequency domain reflectometry (TFDR) and tangent distance pattern recognition are proposed in this paper. The fault location information of the HVdc submarine cables can be obtained from the tangent distance, to support the results of TFDR. To verify the performance of the proposed method, a commercial HVdc submarine cable is used in the experiments. A test bed is constructed for creating a similar environment with that of the submarine cable and filled with sea water. Both low- and high-impedance faults are emulated in this experiment by local insulation faults with iron, sea water, and air. The theoretical concepts and experimental results of the proposed method are presented. It is expected that the proposed method can improve the reliability of real-world HVdc power systems.

Fast and robust phase stability testing at isothermal-isochoric conditions

In this paper, a robust and efficient phase stability testing procedure at isotherm-isochoric conditions is proposed. The tangent plane distance function is expressed in terms of component molar densities. Convergence behavior using various sets of independent variables is analyzed and it is shown that the choice of independent variables is very important for both robustness and computational speed. A particular attention is paid for conditions in which the Hessian matrix is notoriously ill-conditioned, that is, in the vicinity of the stability test limit locus (STLL) and of the spinodal, where the convergence is slow and problematic. It is found that poor conditioning occurs also at certain conditions in the two-phase region at low temperatures and towards high densities. A modified Cholesky factorization (to ensure a descent direction) and a line search procedure are used in Newton iterations. The equation of state (EoS) must not be solved for volume and any pressure explicit EoS can be used; only expressions of pressure, fugacity and their partial derivatives with respect to mole numbers are required. The proposed method is tested on several examples from the literature, using a refined grid in the temperature-molar density plane. The variables obtained by scaling the ideal part of the Hessian matrix lead by far to the most robust formulation, with no failure observed for the investigated mixtures, and much faster than previous methods, with a low average number of iterations required for convergence for all mixtures.

Calculation of multicomponent vapor–liquid critical point using the Dividing Rectangles global optimization algorithm

ABSTRACTIn this paper, the Dividing Rectangles (D.R.) global optimization technique is used to predict the critical temperature and pressure for multicomponent systems. The D.R. optimization algorithm is a fast and reliable optimization method without any need for adjustable parameters, initial guesses or objective function derivation. For calculating the critical point the tangent plane distance (TPD) in terms of the Helmholtz energy is selected. The Peng Robinson (PR) equation of state is applied for determining thermodynamic relations. The procedure of the critical point calculation by means of global optimization is described stepwise in order to clarify the concept and method of programing. The D.R.-based computer program is tested for some multicomponent systems and the results are compared with the Simulated Annealing (SA) global optimization method and with experimental data. The results indicated that the number of the objective function calls (the main parameter that increases the speed and efficiency of an optimization algorithm) is reduced to one twentieth with almost the same accuracy.

Clustering of architectural floor plans: A comparison of shape representations

Abstract Generative design methods are able to produce a large number of potential solutions of architectural floor plans, which may be overwhelming for the decision-maker to cope with. Therefore, it is important to develop tools which organise the generated data in a meaningful manner. In this study, a comparative analysis of four architectural shape representations for the task of unsupervised clustering is presented. Three of the four shape representations are the Point Distance, Turning Function, and Grid-Based model approaches, which are based on known descriptors. The fourth proposed representation, Tangent Distance, calculates the distances of the contour's tangents to the shape's geometric centre. A hierarchical agglomerative clustering algorithm is used to cluster a synthetic dataset of 72 floor plans. When compared to a reference clustering, despite good perceptual results with the use of the Point Distance and Turning Function representations, the Tangent Distance descriptor (Rand index of 0.873) provides the best results. The Grid-Based descriptor presents the worst results.