Study on Mathematical Model of Homogenization of Dendritic Segregation

2012 ◽  
Vol 430-432 ◽  
pp. 355-360
Author(s):  
Xin Gang Liu ◽  
Bo Liu ◽  
Huan Guo ◽  
Miao Jin ◽  
Bao Feng Guo

The cosine solution of the Fick-2 Law, which was considered as the mathematical model of homogenization of dendritic segregation, has always been used to analyze high temperature diffusion. Cosine solution can not exactly describe the actual distribution of alloying elements in dendrite, as the slope of cosine curve is quite gentle. Based on segregation ratio SR, a new mathematical model was established by using Gauss solution of the Fick-2 Law. The new model could describe the evolution of homogenization of alloying elements during the process of high temperature, which was proved by some specific examples.

2021 ◽  
Author(s):  
Bin Liu ◽  
Baolin Yue ◽  
Wei Zhang ◽  
Cunliang Chen ◽  
Zhiqiang Zhu ◽  
...  

Abstract Due to the high viscosity of crude oil and high water-oil mobility ratio, water channeling is serious in a Bohai oilfield. Polymer flooding has been carried out in the oilfield, and good results have been achieved. When polymer flooding is implemented in the oilfield, only the wellhead viscosity of polymer is known, but the viscosity of polymer system in the formation is not accurately known. The viscosity of polymer system in the formation is an important parameter for polymer flooding effect and later polymer injection parameter optimization. Due to the lack of data and the difficulty of operation in offshore oilfield, it is urgent to study the viscosity retention of polymer after being sheared from the borehole. The flow of polymer solution is divided into two stages. The first flow stage is that the flow of polymer solution in the wellbore is equivalent to the flow of an equal diameter circular pipe. Assuming that the solution system is incompressible and is one-dimensional stable flow, the mathematical model of apparent viscosity is established by momentum theory and the constitutive equation of pseudo-plastic fluid. Finally, the apparent viscosity and shear rate of the solution system are calculated by the mathematical model, which keep unchanged along the flow direction in the equal diameter circular pipe. The second flow stage is that the flow process of polymer solution through the borehole is equivalent to the flow process of shrinkage and expansion in a variable cross-section pipeline. The viscosity mathematical model of the solution system after the borehole shearing is established. The viscosity retention is calculated by the mathematical model, and the influence of perforation radius and other indexes on formation working viscosity is analyzed. The results show that the viscosity retention of the polymer system is 34.1%∼36.9% by using the new model. Through the analysis of the influencing factors, it is concluded that the consistency coefficient and perforation radius have the greatest influence on the viscosity retention. By applying the calculated viscosity retention obtained by the new model to the numerical simulation, the water cut history fitting of single well is improved. Due to the same concentration injected in the whole oilfield, the effect of polymer flooding in some areas is not obvious. The viscosity of polymer in the formation is calculated by the new model. After concentration optimization and adjustment, the concentration of polymer injection in three wells increases from 800mg/L, 1000mg/L and 1200mg/L to 1500mg/L respectively, and the oil production of the surrounding production wells increases significantly, and the daily oil production increases 105m3. The new technology has been widely used in five wells of other two oilfields in Bohai Oilfield. On the basis of calculating the viscosity retention rate, good results have been achieved by adjusting the injection concentration, and the total oil increase has reached 5×104m3. There are some assumptions in the calculation of this technology. In the future, the fluid flow will be further studied under the condition of removing the assumptions.


2006 ◽  
Vol 524-525 ◽  
pp. 355-360
Author(s):  
O.R. Hachkevych ◽  
V.S. Mykhailyshyn ◽  
A. Ravska-Skotnichna

The mathematical model is developed for description of thermomechanical processes at cooling during high temperature annealing with the known initial temperature distribution (the temperature of holding) and stresses (acquired stresses at the final of a holding). It is taken into account the thermal sensitivity and material hardening at elasto-plastic solid deforming. The methodology based on the finite element method is proposed for solving thermomechanics problems of wide range. The suitable software is developed. At the final stage of annealing a cylindrical solid it is investigated residual stresses being formed on the cooling stage.


2010 ◽  
Vol 297-301 ◽  
pp. 1475-1480
Author(s):  
Maya Radune ◽  
Alex Radune ◽  
F. Assous ◽  
Michael Zinigrad

A deterministic computational model of high-temperature heterogeneous re- action between metal and oxide melts has been developed. Transport of reagents and products of reaction occur simultaneously both by diusion and by laminar natural con- vection of the melting metal and oxide uxes. The convection-diusion equations have been numerically solved by a nite-dierences time-implicit discretization scheme. The model was implemented by program which had been written in C# language. The com- putations have been performed for desulfurization reaction between liquid steel and slag phases.The computed results agree well with the results which were found by experimen- tal methods.


2008 ◽  
Vol 130 (2) ◽  
Author(s):  
J. Oliveros ◽  
J. L. Alamilla ◽  
E. Astudillo ◽  
O. Flores

The mathematical model to predict failure pressures in corroded pipelines proposed in this work is based on the analysis of the original model by Cronin and Pick. New definitions and interpretations in order to obtain this new model are given. As a consequence of this, the model can be more adequately interpreted and easier to apply under practical conditions. The new model and the finite element method are applied to predict failure pressures for pipelines with corrosion defects of elliptic and irregular geometries, and the predictions are similar. The model is used to predict the failure pressure in actual defects and compared to results of experimental tests and the original model. This study shows that pressures predicted by the model presented here are comparable to those of experimental tests.


2013 ◽  
Vol 470 ◽  
pp. 907-910
Author(s):  
Hua Yuan

In the nature, most phreatic or confined aquifers are of layered distribution. Based on the actual distribution of aquifer and whether there exists transfluence contact between each aquifer, the layered distribution aquifer basically is simplified as multi-aquifer or double aquifer structure. In this paper, all of the aquifer structure models proposed by domestic and foreign scholars are summarized. Furthermore, the mathematical model of each aquifer structure is detailed illustrated.


2020 ◽  
Vol 2020 (1) ◽  
pp. 26-31
Author(s):  
Anatoliy Arhangel'skiy

In this work, a critical analysis of the mathematical model of the Traiber is performed and a new model is developed, based on the concept of "following the leader" and which allows you to take into account the dynamic characteristics of a particular car, its load, road and climatic conditions of operation, as well as more realistic modeling of acceleration processes. braking and stopping the vehicle.


2018 ◽  
Vol 10 (5) ◽  
pp. 1 ◽  
Author(s):  
Thierry Delort

In this article, we propose a new model of dark matter. According to this new model, dark matter is a substance, that is a new physical element not constituted of classical particles, called dark substance and filling the Universe. Assuming some very simple physical properties to this dark substance, we theoretically justify the flat rotation curve of galaxies and the baryonic Tully-Fisher’s law. We then study according to our new theory of dark matter  the different possible distributions of dark matter in galaxies and in galaxy clusters, and the velocities of galaxies in galaxy clusters. Then using the new model of dark matter we are naturally led to propose a new geometrical model of Universe, finite, that is different from all geometrical models proposed by the Standard Cosmological Model (SCM). Despite that our Theory of dark matter is compatible with the SCM, we then expose a new Cosmological model based on this new geometrical form of the Universe and on the interpretation of the CMB Rest Frame (CRF), that has not physical interpretation on the SCM and that we will call local Cosmological frame. We then propose 2 possible mathematical models of expansion inside the new Cosmological model. The 1st mathematical model is based on General Relativity as the SCM and gives the same theoretical predictions of distances and of the Hubble’s constant as the SCM. The 2nd mathematical model of expansion of the Universe is mathematically much simpler than the mathematical model of expansion used in the SCM, but we will see that its theoretical predictions are in agreement with astronomical observations. Moreover, this 2nd mathematical model of expansion does not need to introduce the existence of a dark energy contrary to the mathematical model of expansion of the SCM. To end we study the evolution of the temperature of dark substance in the Universe and we make appear the existence of a dark energy, due to our model of dark matter.


Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.


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