scholarly journals Two-dimensional three-phase mathematical model of forest fires

2017 ◽  
pp. 1-12 ◽  
Author(s):  
Andrey Aleksandrovich Kuleshov ◽  
Elena Evgenievna Myshetskaya ◽  
Sergey Evgenievich Yakush
Keyword(s):  
Mathematical Model ◽  
Forest Fires ◽  
Two Dimensional ◽  
Three Phase

scholarly journals Simulation of forest fires based on a two-dimensional three-phase model

2019 ◽  
Vol 1336 ◽  
pp. 012002 ◽  
Author(s):  
A A Kuleshov ◽  
E E Myshetskaya ◽  
S E Yakush
Keyword(s):  
Forest Fires ◽  
Phase Model ◽  
Two Dimensional ◽  
Three Phase

Numerical, Three-Phase Simulation of the Linear Steamflood Process

1969 ◽  
Vol 9 (02) ◽  
pp. 232-246 ◽  
Author(s):  
N.D. Shutler
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Heat Conduction ◽  
One Dimension ◽  
Two Dimensional ◽  
Gas Composition ◽  
Water Steam ◽  
Three Phase ◽  
Process Mechanics

Abstract This paper describes a numerical mathematical model of the steamflood process that depends on fewer restrictive assumptions than models previously reported. The solution, however, is previously reported. The solution, however, is obtained economically. Example calculations are presented that on comparison with experimental presented that on comparison with experimental results, tend to validate the model. Results that expose certain process mechanics are discussed. The model describes the simultaneous flow of three phases oil, water and gas in one dimension. It includes the effects of three-phase relative permeabilities, capillary pressure, and temperature- and pressure-dependent fluid properties. Interphase mass transfer of water-steam properties. Interphase mass transfer of water-steam is allowed, but the oil is assumed nonvolatile and the hydrocarbon gas insoluble in the liquid phases. The model allows heat convection in one dimension and two-dimensional heat conduction in a vertical cross-section spanning the oil sand and adjacent strata. The hydrocarbon-steam gas composition is tracked, but the effect of gas composition on water-steam phase behavior is neglected. The model is soloed numerically in three separate stages. The three-phase mass balances are solved simultaneously using Newtonian iteration on nonlinearities occurring in the accumulation terms. The energy balance is solved separately by noniterative application of the alternating-direction implicit procedure. Separate solution of the composition balance is accomplished by straight-forward solution of the finite difference equations. The method of effecting nonsimultaneous, stable solution of the mass and energy balances is the key to the success of the model. Introduction Mathematical tools as well as laboratory and field experiments are necessary to help us understand the complex steamflood process. A mathematical model can expose process mechanics and show the relative importance of process variables, but this ability is often limited by restrictive assumptions. Most known models of steam processes, with the exception of the model of Gottfried, are "simplified" in that they involve analytic approximations and require many restrictive assumptions. The primary utility of these methods lies in the routine use as an aid in engineering design. By contrast, the comprehensive model presented here is numerical and requires far fewer restrictive assumptions. It finds its primary utility as a research tool. It serves as an aid in understanding the nature of the process, in interpreting laboratory experiments and in evaluating and developing simpler mathematical models for engineering design. The major reason why previously presented models have been confined to the "simplified" class is evidenced by the one published exception. In 1965, Gottfried presented a numerical model for the combustion process of which the steam process is a subset. The result is a comprehensive tool (though it neglects capillarity and two-dimensional heat conduction) that is troubled with convergence problems and that requires 2 to 3 hours of IBM 7094 problems and that requires 2 to 3 hours of IBM 7094 time to complete a calculation. Though our present model does not simulate combustion, it does consider capillarity and two-dimensional heat conduction and it overcomes the convergence and computer-time problems. MATHEMATICAL DESCRIPTION OF STEAMFLOODING FLUID FLOW The equations employed to describe three-phase fluid flow are of a familiar form. SPEJ P. 232

MODELING SYSTEMS DIRECT TORQUE CONTROL USING А THREE-PHASE MATHEMATICAL MODEL

2016 ◽  
Vol 22 (98) ◽  
pp. 56-61
Author(s):  
Vladislav A. Kosenko ◽  
◽  
Valeriy O. Kvashnin ◽  
Keyword(s):  
Mathematical Model ◽  
Direct Torque Control ◽  
Torque Control ◽  
Modeling Systems ◽  
Three Phase

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

2009 ◽  
Vol 30 (4) ◽  
pp. 455-462
Author(s):  
Gai-ping Zhao ◽  
Er-yun Chen ◽  
Jie Wu ◽  
Shi-xiong Xu ◽  
M. W. Collins ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Discrete Mathematical Model

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

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