Nonlinear Convergence for Near-Miscible Problem: A Mystery Unveiled for Natural Variable Simulator

2017 ◽  
Author(s):  
Hui Cao ◽  
Rustem Zaydullin ◽  
Eguono Obi
Keyword(s):  
Natural Variable

scholarly journals Power Series Expansion of the Mie Scattering Phase Function

1983 ◽  
Vol 36 (5) ◽  
pp. 701 ◽  
Author(s):  
Michael A Box
Keyword(s):  
Power Series ◽  
Phase Function ◽  
Power Series Expansion ◽  
Mie Scattering ◽  
Matrix Elements ◽  
Dust Clouds ◽  
Power Series Expansions ◽  
Scattering Phase ◽  
Natural Variable ◽  
Scattering Phase Function

We develop power series expansions for both the Mie theory scattering amplitudes and the scattering phase matrix elements in terms of the variable s = sin2W, where () is the scattering angle. It is easily seen that s is the natural variable for such expansions. These expansions should prove particularly useful whenever the forward diffraction peak, rather than the entire phase function, is of primary interest. Possible applications include the analysis of solar aureole data and the modelling of laser beam propagation in fogs and dust clouds.

scholarly journals Female Entrepreneurship in Perspective: A Methodological Issue

2018 ◽  
Vol 8 (4) ◽  
pp. 67 ◽  
Author(s):  
Paola Paoloni ◽  
Gabriele Serafini
Keyword(s):  
Methodological Approach ◽  
Methodological Issue ◽  
Female Entrepreneurship ◽  
Identification Procedure ◽  
Natural Variable

A methodological approach to the concept of female entrepreneurship concept has not yet been treated: is female entrepreneurship an individual or collective concept? Is it considered a social or natural variable? The purpose of this research is to clear up these alternatives, which are preparatory questions for any research into female entrepreneurship that wishes to measure its features and effects. The article starts with the proposal of an identification procedure, necessary to identifying the variables of female entrepreneurship. It proceeds by classifying the concept of female entrepreneurship into four different modes and discussing their characteristics. The originality of this research consists in its fourfold classification of the concept of female entrepreneurship, intended as a preparatory step prior to the analysis of its characteristics and measures.

A Natural Variable Fully Implicit Compositional Reservoir Simulation

2017 ◽  
Author(s):  
Bruno Ramon Batista Fernandes ◽  
Kamy Sepehrnoori ◽  
Francisco Marcondes
Keyword(s):  
Reservoir Simulation ◽  
Fully Implicit ◽  
Natural Variable

scholarly journals Defining flood risk in a multivariate framework: Application on the Panaro watershed

2016 ◽  
Author(s):  
Eleni Maria Michailidi ◽  
Baldassare Bacchi
Keyword(s):  
Water Level ◽  
Copula Functions ◽  
Initial Water ◽  
Maximum Rainfall ◽  
Lake Water Level ◽  
Flood Peak ◽  
Risk Levels ◽  
Maximum Water Level ◽  
Natural Variable ◽  
Definition Of

Abstract. One of the most important tasks a hydrologist must face is to estimate the hydrological risk (i.e. probability) of a variable exceeding a certain threshold. This risk is often expressed in terms of a Return Period, T, and refers to the failure of the hydraulic structure which controls this variable. Sometimes the "structure" is simply the river embankmentsthe failure of which means their overtopping by the river. The widely adopted definition of T, in a problem regarding the maxima of hydro-logical variables, is "the average time elapsing between two successive occurrences of an event exceeding a given magnitude of the natural variables". Conventional approaches for the estimation of T involve a single natural variable (i.e. flood peak, maximum rainfall intensity, etc.) and its frequency analysis. However, a univariate approach in complex problems ignores the effect of other significant variables leading to different risk levels for each quantity of interest and resulting in an inaccurate estimate of the risk-often wrongfully set equal to the risk of the hydrological event. For example, if one considers the flood inflow in a lake around which establishments are positioned, the variable to be investigated relating to risk assessment is the lake water level. The same water level may occur from very different flood hydrographs, even when the same initial water level and specific spillway characteristics are taken into account. We considered this a result of the interaction of three joint factors: the hydrograph's peak, volume and shape. Consequently, we apply a multivariate distribution framework (using copula functions) in order to find a region where all underlying events are assigned to the same risk- associated here to the maximum water level.

scholarly journals Premature ejaculation - current concepts in the management: A narrative review

2021 ◽  
Author(s):  
Arkiath Veettil Raveendran ◽  
Ankur Agarwal
Keyword(s):  
Cognitive Behavioral Therapy ◽  
Pharmacological Treatment ◽  
Premature Ejaculation ◽  
Behavioral Therapy ◽  
Treatment Options ◽  
Sexual Problem ◽  
Sexually Active ◽  
Age Group ◽  
Serotonin Uptake Inhibitors ◽  
Natural Variable

Premature ejaculation (PE; early ejaculation or rapid ejaculation) is a common sexual problem affecting about 20-30% of men in the sexually active age group. PE can be of four types: Primary, secondary, natural variable, and subjective PE. Various non-pharmacological and pharmacological treatment options are available to treat PE including Dapoxetine, which is specifically developed for the treatment of PE. In this review, we discuss the pathophysiology and management aspects of PE. Key words: Premature ejaculation, Cognitive behavioral therapy, Serotonin uptake inhibitors, Dapoxetine.

scholarly journals Surface Area to Volume Ratio: A Natural Variable for Bacterial Morphogenesis

2018 ◽  
Vol 26 (10) ◽  
pp. 815-832 ◽  
Author(s):  
Leigh K. Harris ◽  
Julie A. Theriot
Keyword(s):  
Surface Area ◽  
Volume Ratio ◽  
Natural Variable

scholarly journals Study of compositional multiphase flow formulation using complementarity conditions

2019 ◽  
Vol 74 ◽  
pp. 43 ◽  
Author(s):  
Ibtihel Ben Gharbia ◽  
Eric Flauraud
Keyword(s):  
Phase Transitions ◽  
Multiphase Flow ◽  
Reservoir Simulation ◽  
Flow Problem ◽  
Equations Of State ◽  
Reservoir Engineering ◽  
Petroleum Reservoir ◽  
Complementarity Conditions ◽  
Engineering Problems ◽  
Natural Variable

In this article, two formulations of multiphase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so-called natural variable formulation commonly used in reservoir simulation, the second has been introduced by Lauseret al.and uses the phase pressures, saturations and component fugacities as main unknowns. We will discuss how the Coats and the Lauser approaches can be used to solve a compositional multiphase flow problem with cubic equations of state of Peng and Robinson. Then, we will study the results of several synthetic cases that are representative of petroleum reservoir engineering problems and we will compare their numerical behavior.

A Variable-Switching Method for Mass-Variable-Based Reservoir Simulators

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1469-1495 ◽  
Author(s):  
Faruk O. Alpak ◽  
Jeroen C. Vink
Keyword(s):  
Simulation Models ◽  
Practical Method ◽  
General Purpose ◽  
Local Method ◽  
Complex Processes ◽  
Change Of Variables ◽  
Natural Variable ◽  
Simulation Problem ◽  
Switching Method ◽  
Flow Simulator

Summary Field-scale simulations of complex processes often suffer from long simulation times. One of the main reasons is that the Newton-Raphson (NR) process used to solve each simulation timestep requires many iterations and small timestep sizes to converge. Because the selection of solution variables affects the nonlinearity of the equations, it is attractive to have a practical method to rapidly explore the use of alternative primary variables in general-purpose reservoir simulators. Many reservoir simulators use pressure, saturations, and temperature in each gridblock as the primary solution variables, which are referred to as natural variables. There is also a class of reservoir simulators that uses pressure, total component masses (or moles), and internal energy in each gridblock as primary variables. These simulators are referred to as mass-variable-based reservoir simulators. For a given choice of primary variables, most simulators have dedicated, highly optimized procedures to compute the required derivatives and chain rules required to build the Jacobian matrix. Hence, it is usually not possible to switch between mass and natural variables. In this work, however, we establish a link at the numerical-solution level between natural- and mass-variable formulations and design a novel (nonlinear) block-local method that transforms mass-variable shifts (computed at each NR iteration) into equivalent natural-variable shifts. We demonstrate on a number of simulation models of varying complexity that by use of the proposed approach, a mass-variable-based flow simulator can still effectively use natural variables, where the change of variables can be made locally per gridblock. Results indicate that in some models the total number of NR iterations, linear-solver (LS) iterations, and timestep-size cuts (caused by the nonconvergence of the NR procedure, also known as backups) are reduced when using natural variables instead of mass variables. However, the improvement is relatively modest and not generally observed. Our findings also signify that depending on the specific characteristics of the simulation problem at hand, mass-variable-based simulators may perform comparably or outperform natural-variable-based simulators. The proposed variable-switching method can be used effectively to evaluate the effect of using different primary solution variables on problem nonlinearity and solver efficiency. With this method, the effect of interchanging primary solution variables on problem nonlinearity can be rapidly evaluated.

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