Flash Calculation Using Successive Substitution Accelerated by the General Dominant Eigenvalue Method in Reduced-Variable Space: Comparison and New Insights

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 3332-3348
Author(s):  
Haining Zhao ◽  
Hongbin Jing ◽  
Zhengbao Fang ◽  
Hongwei Yu
Keyword(s):  
Stability Analysis ◽  
Phase Stability ◽  
Linear Acceleration ◽  
Phase Region ◽  
Dominant Eigenvalue ◽  
Two Phase ◽  
Eigenvalue Method ◽  
Successive Substitution ◽  
The Stability ◽  
Flash Calculation

Summary On the basis of a previously published reduced-variables method, we demonstrate that using these reduced variables can substantially accelerate the conventional successive-substitution iterations in solving two-phase flash (TPF) problems. By applying the general dominant eigenvalue method (GDEM) to the successive-substitution iterations in terms of the reduced variables, we obtained a highly efficient solution for the TPF problem. We refer to this solution as Reduced-GDEM. The Reduced-GDEM algorithm is then extensively compared with more than 10 linear-acceleration and Newton-Raphson (NR)-type algorithms. The initial equilibrium ratio for flash calculation is generated from reliable phase-stability analysis (PSA). We propose a series of indicators to interpret the PSA results. Two new insights were obtained from the speed comparison among various algorithms and the PSA. First, the speed and robustness of the Reduced-GDEM algorithm are of the same level as that of the reduced-variables NR flash algorithm, which has previously been proved to be the fastest flash algorithm. Second, two-side phase-stability-analysis results indicate that the conventional successive-substitution phase-stability algorithm is time consuming (but robust) at pressures and temperatures near the stability-test limit locus in the single-phase region and near the spinodal in the two-phase region.

Phase Stability of Sigma + Beta Microstructures in the Ternary Nb-Ti-Al System

1990 ◽  
Vol 194 ◽  
Author(s):  
D. T. Hoelzer ◽  
F. Ebrahimi
Keyword(s):  
Phase Stability ◽  
Orthorhombic Phase ◽  
Beta Phase ◽  
Phase Region ◽  
Nominal Composition ◽  
Two Phase ◽  
Σ Phase ◽  
Β Phase ◽  
Heat Treated ◽  
The Stability

AbstractAn alloy with the nominal composition 42Nb-28Ti-30Al (at.%) was heat treated in the sigma + beta phase region. The evolution of σ phase from the metastable β phase and the stability of the two-phase microstructure at various aging temperatures were evaluated using TEM techniques. The results indicate that the β phase in equilibrium with the σ phase at high temperatures decomposes to the orthorhombic phase at temperatures below 1200°C.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

Dynamic Stability Analysis of the Tower Structure of Construction Elevators

2013 ◽  
Vol 459 ◽  
pp. 646-649
Author(s):  
Xian Rong Qin ◽  
Ying Hong ◽  
Peng Yue ◽  
Qing Zhang ◽  
Yuan Tao Sun
Keyword(s):  
Stability Analysis ◽  
Stress Field ◽  
Dynamic Stability ◽  
Transient Analysis ◽  
Stress Effect ◽  
Construction Process ◽  
Moving Loads ◽  
Eigenvalue Method ◽  
Tower Structure ◽  
The Stability

This paper proposed a method of dynamic stability analysis for the tower structure of construction elevators based on dynamic eigenvalue method. The method employed the time frozen formulation to model the problem, and the stress field from transient analysis was utilized to simulate the pre-stress effect of buckling analysis. The proposed method was applied to estimate the dynamic stability of the tower structure of construction elevators under moving loads, and the results suggest that high coefficients of lateral load and inclined tower structure will dramatically reduce the stability of the elevator in the construction process.

The Effect of the Treatment of Localised Friction in Two-Phase Mixtures on the Stability of Parallel Channels

2002 ◽  
Author(s):  
H. N. Abdou ◽  
V. B. Garea ◽  
A. E. Larreteguy
Keyword(s):  
Homogeneous Model ◽  
Stability Boundary ◽  
Density Wave ◽  
Phase Region ◽  
Experimental Results ◽  
Exact Equation ◽  
Two Phase ◽  
Heated Channel ◽  
Phase Mixture ◽  
The Stability

A one-dimensional analytical model has been developed to be used for the linear analysis of density-wave oscillations in a parallel heated channel. The heated channel is divided into a single-phase and a two-phase region. The two-phase region is represented by the homogeneous model. The localised friction at the channel exit is treated considering the two-phase mixture. The exact equation for the total channel pressure drop is perturbed around the steady state. The stability characteristics of the heated channel are investigated using the Nyquist criterion. The marginal stability boundary (MSB) is determined in the two-dimensional thermodynamic equilibrium space parameters, the subcooled boiling number and the phase change number. The predictions of the model are compared with experimental results published in open literature. The results indicate a more stable system with (1) low system pressure, (2) high inlet restriction, (3) low outlet restriction, and (4) high inlet velocity. The results show that the model agrees well with the available experimental data. In particular, the results show the significance of correcting the localised friction due to the presence of the two-phase mixture in the two-phase region: explicit inclusion of the two-phase localised friction improves the agreement with experimental results. This effect is more important for high heating power and high inlet subcooling.

scholarly journals An improved reduction method for phase stability testing in the single-phase region

2020 ◽  
Vol 18 (1) ◽  
pp. 1316-1322
Author(s):  
Dan Vladimir Nichita ◽  
Catinca Secuianu
Keyword(s):  
Phase Stability ◽  
Reduction Method ◽  
Phase Region ◽  
Binary Interaction ◽  
Stability Testing ◽  
Number Of Components ◽  
Mixture Phase ◽  
Residual Functions ◽  
Binary Interaction Parameters ◽  
The Stability

AbstractA new reduction method for mixture phase stability testing is proposed, consisting in Newton iterations with a particular set of independent variables and residual functions. The dimension of the problem does not depend on the number of components but on the number of components with nonzero binary interaction parameters in the equation of state. Numerical experiments show an improved convergence behavior, mainly for the domain located outside the stability test limit locus in the pressure–temperature plane, recommending the proposed method for any applications in which the problematic domain is crossed a very large number of times during simulations.

The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media

1981 ◽  
Vol 21 (02) ◽  
pp. 249-258 ◽  
Author(s):  
Ekwere J. Peters ◽  
Donald L. Flock
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Stability Theory ◽  
Critical Value ◽  
Immiscible Displacement ◽  
Dimensionless Number ◽  
Two Phase ◽  
Displacement Front ◽  
The Stability ◽  
Scaling Group

Abstract This paper presents a dimensionless number and its critical value for predicting the onset of instability during immiscible displacement in porous media. The critical dimensionless number obtained from a stability theory for a cylindrical system successfully predicted the onset of instability in laboratory floods. Therefore, this number can be used to classify the stability of two-phase incompressible displacements in homogeneous porous media. Introduction When a fluid displaces a more viscous fluid, the displacement front may become unstable, resulting in viscous fingering. This phenomenon raises both practical and theoretical concerns. Apart from further reducing the displacement efficiency of an already inefficient displacement arrangement, instability may invalidate the usual method of simulating immiscible displacement performance based on relative permeability and capillary pressure concepts. Also, it introduces an additional scaling requirement for using model tests to forecast prototype displacement results. Therefore, it would be most beneficial to predict the onset of instability, so as to avoid viscous fingering, or, where it is unavoidable, to be able to recognize it as a factor in the displacement.The onset of instability call be predicted by a stability analysis of the displacement. The objective of such an analysis is to determine the conditions under which small disturbances or perturbations of the displacement front will grow to become viscous fingers. Ideally, the analysis should give a universal dimensionless scaling group together with its critical value above which instability will occur. The stability classification then would entail no more than the calculation of one dimensionless number in a manner analogous to the calculation of a Reynolds number to distinguish between laminar and turbulent flow.Several stability studies of immiscible displacement have been reported in the literature. Collectively, they show that these variables are pertinent to the stability problem:mobility (or viscosity) ratio,displacement velocity, system geometry and dimensions,capillary and gravitational forces, andsystem permeability and wettability. However, none of the previous studies have combined these variables into one dimensionless number that can be used to quantify the stability classification.The objective of this study was to obtain, by means of a stability analysis, a universal dimensionless scaling group and its critical value for predicting the onset of instability during immiscible displacement in porous media. This paper shows how the stability theory of Chuoke et al. was extended to achieve this objective and presents the results of laboratory floods that confirm the predicted onset of instability in cylindrical cores. Theory The pertinent dimensionless number for predicting the onset of instability was obtained by extending the stability theory of Chuoke et al. Their theory was based on a piston-like unperturbed displacement model in which the oil and water zones are separated by a planar interface. Details of the theory and our extension of it are presented in the following sections. SPEJ P. 249^

Stability Analysis of Chaotic Wavy Stratified Fluid-Fluid Flow With the 1D Fixed-Flux Two-Fluid Model

2016 ◽  
Author(s):  
Avinash Vaidheeswaran ◽  
William D. Fullmer ◽  
Krishna Chetty ◽  
Raul G. Marino ◽  
Martin Lopez de Bertodano
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Two Phase Flow ◽  
Chaotic Behavior ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Two Fluid Model ◽  
The Stability ◽  
Two Fluid

The one-dimensional fixed-flux two-fluid model (TFM) is used to analyze the stability of the wavy interface in a slightly inclined pipe geometry. The model is reduced from the complete 1-D TFM, assuming a constant total volumetric flux, which resembles the equations of shallow water theory (SWT). From the point of view of two-phase flow physics, the Kelvin-Helmholtz instability, resulting from the relative motion between the phases, is still preserved after the simplification. Hence, the numerical fixed-flux TFM proves to be an effective tool to analyze local features of two-phase flow, in particular the chaotic behavior of the interface. Experiments on smooth- and wavy-stratified flows with water and gasoline were performed to understand the interface dynamics. The mathematical behavior concerning the well-posedness and stability of the fixed-flux TFM is first addressed using linear stability theory. The findings from the linear stability analysis are also important in developing the eigenvalue based donoring flux-limiter scheme used in the numerical simulations. The stability analysis is extended past the linear theory using nonlinear simulations to estimate the Largest Lyapunov Exponent which confirms the non-linear boundedness of the fixed-flux TFM. Furthermore, the numerical model is shown to be convergent using the power spectra in Fourier space. The nonlinear results are validated with the experimental data. The chaotic behavior of the interface from the numerical predictions is similar to the results from the experiments.

Effect of substituents with different valences on antiferroelectric stability of antiferroelectric lead zirconate ceramics

1999 ◽  
Vol 14 (11) ◽  
pp. 4251-4258 ◽  
Author(s):  
Qi Tan ◽  
Z. Xu ◽  
Dwight Viehland
Keyword(s):  
Electron Diffraction ◽  
Phase Stability ◽  
Dielectric Spectroscopy ◽  
Ferroelectric Phase ◽  
Lead Zirconate ◽  
Phase Region ◽  
Effect Of Substituents ◽  
Antiferroelectric Phase ◽  
Ionic Size ◽  
The Stability

The effect of lower valent substituents on the stability of the antiferroelectric phase of lead zirconate was studied by dielectric spectroscopy, Sawyer–Tower polarization methods, and electron diffraction techniques. The stability of an intermediate ferroelectric phase region was found to be enhanced with increasing lower valent substitution concentration. The influences of substituents of different ionic size and valence on the stabilization of the intermediate ferroelectric phase were differentiated. In general, lower valent substituents, such as K+ and Fe3+ affected antiferroelectric phase stability more significantly than higher valent ones.

Stability analysis of a two-phase suspension between rotating porous cylinder with the radial flow

2015 ◽  
Vol 29 (05) ◽  
pp. 1550014
Author(s):  
Feng-Hui Wang ◽  
Yu-Chuan Zhu ◽  
Zhan-Hong Wan ◽  
Song He
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Hydrodynamic Stability ◽  
Stability Problem ◽  
Radial Flow ◽  
Wave Number ◽  
Porous Cylinder ◽  
Two Phase ◽  
Stabilizing Effect ◽  
The Stability

The hydrodynamic stability analysis of viscous flow between rotating porous cylinder has been researched for a long time by many researchers. But little works have been carried out about the linear stability analysis of the two-phase suspension. When the radial flow is present, the linear hydrodynamic stability analysis of suspension has been carried out between rotating porous cylinder. We know that the continuous and Stokes equations cannot only solve the stability problem of the continuous fluid phase, but also solving the stability problem of the discontinuous particle phase. The stability equations from an eigenvalue problem that was solved by a numerical technique based on Wan's method. The results reveal that the radial Reynolds number have a great effect on the critical Taylor number in the suspension. In this paper, we also researched on how the critical Taylor number changes as the radius ratio η, the axial wave number k, the particle concentration and the circumferential direction wave number happen to change with the radial Reynolds number increasing range from -5 to 5. Thus, our research discovered the radial inflow and outflow have a stabilizing effect on the two-phase suspension and the circumferential direction wave number also has a stabilizing effect.

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