scholarly journals METHOD OF SEQUENTIAL CHANGINGOF STATIONARY STATES FOR ONE-DIMENSIONAL FILTRATION PROBLEM WITH LIMITING GRADIENT OF PRESSURE

2017 ◽  
Vol 20 (7) ◽  
pp. 75-84
Author(s):  
O.V. Belova ◽  
V.Sh. Shagapov
Keyword(s):  
Pressure Gradient ◽  
Nonlinear Effects ◽  
Approximate Solutions ◽  
Darcy Law ◽  
Nonlinear Filtration ◽  
Stationary States ◽  
Filtration Problem ◽  
One Dimensional ◽  
Well Production ◽  
Sequential Change

Taking into account nonlinear effects observed in experiments with low-per- meability layers, at low pressure gradients (e.g., about 105 Pa/m), refinement of Darcy law is proposed. On the basis of this model, by means of method of sequential change of stationary states and the problem of one-dimensional filter- ing is numerically solved. It is established that approximate solutions received by the method of sequential change of stationary states, for the description of distribution of pressure in layer and a well production, will be agreed with the numerical solution of the equation of a filtration in full statement. The analysis of influence of pressure gradient q and limiting exponent defining the rate of yield of the nonlinear filtration law to the linear Darcy’s law with increasing pressure gradient γ, on the features of hydrodynamic fields and well production is carried out.

Inverse Problem For A Linear Filtration Function

2020 ◽  
pp. 64-68
Keyword(s):  
Porous Medium ◽  
Least Squares Method ◽  
Macroscopic Model ◽  
Asymptotic Formulas ◽  
Model Parameters ◽  
Nonlinear Filtration ◽  
Unknown Parameters ◽  
Filtration Problem ◽  
One Dimensional ◽  
Linear Filtration

The article is devoted to an important task of underground hydro-mechanics-filtration of suspension in a porous medium. One-dimensional long-term deep filtration of a monodisperse suspension in a homogeneous porous medium is considered. For a one-dimensional macroscopic model with a linear filtration function, an asymptotic solution is constructed near the concentration front of suspended and retained particles. On the basis of explicit asymptotic formulas, the inverse filtration problem is studied : finding the filtration function for a given concentration of suspended particles at the outlet of a porous medium. It is revealed that the least squares method is an effective way to determine the model parameters. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the numerical solution. The proposed numerical - asymptotic method makes it possible to calculate the linear filtration function using laboratory experiments and adjust the model to specific field conditions. It is concluded that the next stage in solving the inverse filtration problem is to determine unknown parameters of a nonlinear filtration function that depends on three or more constants. To do this, it is needed to modify the methods presented in this paper.

scholarly journals Capillary Impregnation with Non-Linear Filtration Laws

2020 ◽  
Vol 131 (6) ◽  
pp. 24-27
Author(s):  
A. M. Svalov ◽  
Keyword(s):  
Pressure Gradient ◽  
Oil And Gas ◽  
Practical Interest ◽  
Zero Point ◽  
Darcy Law ◽  
Low Permeability ◽  
Nonlinear Filtration ◽  
Capillary Impregnation ◽  
Non Linear ◽  
Linear Filtration

In connection with the increasing share of low-permeability oil and gas reservoirs, of particular scientific and practical interest is the study of the characteristics of the flow of filtration processes in reservoirs characterized by non-linear filtration laws. The article presents the results of an analytical study of the features of capillary impregnation of low-permeability reservoirs characterized by non-linear filtration laws. Mathematical modeling of the impregnation processes was carried out under the assumption that the dependence of the filtration rate on the pressure gradient modulus near the zero point can be represented by a power function. It was established that, in contrast to capillary impregnation processes under the traditional linear Darcy law, the intensity of impregnation of low-permeability layers of a productive formation in a nonlinear case depends on the longitudinal pressure gradient in the formation - the larger this gradient, the higher the intensity of impregnation. It was also shown that for nonlinear filtration laws, the capillary impregnation front in a porous medium with a fluid at rest can propagate at a finite speed, which is impossible with linear filtration laws.

scholarly journals Markov chain approximation of one-dimensional sticky diffusions

2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang
Keyword(s):  
Markov Chain ◽  
Approximate Solutions ◽  
Price Model ◽  
One Dimensional ◽  
Markov Chain Approximation ◽  
Alternative Approaches ◽  
Second Order Convergence ◽  
Chain Approximation ◽  
Matrix Exponentials ◽  
Interior Points

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

scholarly journals Nonlinear processes in the bunched electron beams of high-power klystrons and the limits of analytical and one-dimensional numerical models applicability for their analysis.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
V.Y. Rodyakin ◽  
◽  
V.M. Pikunov ◽  
V.N. Aksenov ◽  
◽  
...  
Keyword(s):  
Electron Beam ◽  
High Power ◽  
Numerical Models ◽  
Nonlinear Effects ◽  
Analytical Models ◽  
Modulation Amplitude ◽  
Two Dimensional ◽  
One Dimensional ◽  
Charge Parameter ◽  
Program Data

We present the results of a comparative theoretical analysis of the electron beam bunching in a single-stage klystron amplifier using analytical models, a one-dimensional disk program, and a two-dimensional program. Data on the influence of various one-dimensional and two-dimensional nonlinear effects on the efficiency of electron beam bunching at different values of the space charge parameter and the modulation amplitude are presented. The limits of applicability of analytical and one-dimensional numerical models for electron beam bunching analysis in high-power klystron amplifiers are found.

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberta Massabò
Keyword(s):  
Crack Length ◽  
Lower Bounds ◽  
Beam Theory ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
One Dimensional ◽  
Limit Value ◽  
Elastic Mismatch ◽  
Fracture Specimens

Abstract Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

NONLINEAR EFFECTS FOR FLOW IN PERIODICALLY CONSTRICTED CHANNEL CAUSED BY HIGH INJECTION RATE

1998 ◽  
Vol 08 (03) ◽  
pp. 379-405 ◽  
Author(s):  
ALAIN BOURGEAT ◽  
EDUARD MARUSIC-PALOKA
Keyword(s):  
Taylor Expansion ◽  
Nonlinear Effects ◽  
Injection Rate ◽  
Nonlinear Filtration ◽  
Well Posedness ◽  
Viscous Incompressible Flow ◽  
High Injection ◽  
Flow Through ◽  
Strong Injection ◽  
Constricted Channel

We consider a stationary viscous incompressible flow through a periodically constricted channel with the period and thickness ∊, governed by a strong injection of order ∊-1. We prove the well-posedness of the homogenized problem and the convergence of the homogenization process. We obtain a nonlinear filtration law and we give the Taylor expansion of the filtration velocity as a function of the pressure gradient.

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