scholarly journals A New Mathematical Model For Heat Radius of Cyclic Superheated Steam Stimulation with Horizontal Wellbore

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Congge He ◽  
Anzhu Xu ◽  
Zifei Fan ◽  
Lun Zhao ◽  
Bing Bo
Keyword(s):  
Mathematical Model ◽  
Phase Change ◽  
Superheated Steam ◽  
Transformation Method ◽  
Saturated Steam ◽  
Heating Process ◽  
Horizontal Wellbore ◽  
The Mathematical Model ◽  
Laplace Transformation Method ◽  
Steam Stimulation

When superheated steam flows along the horizontal wellbore, it may change to saturated steam at some point of the wellbore. In this paper, to accurately predict the heat radius of cyclic superheated steam stimulation with horizontal wellbore, the distribution of thermophysical properties of superheated steam along the horizontal wellbore is considered. The heating process is divided into 4 stages for superheated steam and 3 stages for saturated steam when the phase change undergoes in the wellbore. On this basis, the mathematical model for heat radius of cyclic superheated steam stimulation with horizontal wellbore was established according to energy conservation principle and Laplace transformation method. The calculation result of the new mathematical model is in good agreement with that of the numerical simulation (CMG STARS) for the same parameters from a specific heavy oil reservoir, which verified the correctness of the new mathematical model. The effect of degree of superheat and the cycle of stimulation are analyzed in detail after the new mathematical model is validated. The results show that the heat radius of superheated zone, steam zone, and hot fluid zone all decrease with horizontal well length and increase with the cycle of stimulation. The higher the degree of superheat is, the farther from the heel of the horizontal wellbore the phase change undergoes. Besides, the radius of superheated zone, steam zone, and hot fluid zone increases with the degree of superheat, but the value increases little at steam zone and hot fluid zone.

Bending of Thermoviscoelastic Functionally Graded Materials Beams

2012 ◽  
Vol 503-504 ◽  
pp. 305-308
Author(s):  
Ming Lu Wang ◽  
Gao Feng Wei
Keyword(s):  
Mathematical Model ◽  
Variational Principle ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Functionally Graded ◽  
Plane Section ◽  
Graded Materials ◽  
Set Up ◽  
The Mathematical Model ◽  
Laplace Transformation Method

According to the constitutive relation of linear thermovisoelasticity, with the help of Laplace transformation method and the introduction of structure functions and thermal functions, the mathematical model and its corresponding variational principle for thermoviscoelastic FGM beams are set up on the basis of the assumption that plane section remains plane and normal to the beam axis. Using Laplace transformation method, the deflection and the stress distribution are discussed.

Superiority of Superheated Steam Flooding in Development of High Water-Cut Heavy Oil Reservoir

2012 ◽  
Vol 616-618 ◽  
pp. 992-995
Author(s):  
An Zhu Xu ◽  
Long Xin Mu ◽  
Xiang Hong Wu ◽  
Zi Fei Fan ◽  
Lun Zhao
Keyword(s):  
Heavy Oil ◽  
Superheated Steam ◽  
High Water ◽  
Viscosity Reduction ◽  
Saturated Steam ◽  
Oil Reservoir ◽  
Heavy Oil Reservoir ◽  
High Water Cut ◽  
Water Cut ◽  
Steam Stimulation

The dryness of superheated steam is 100% and it exists in the form of pure steam whose properties are like ideal gas. When the steam has a large degree of superheat, it may take a relatively long time to cool, during which time the steam is releasing very little energy and transmitted long distances. The heating radius of superheated steam in the formation is 5-10m larger than saturated steam. In the heating area of superheated steam, the comprehensive effects by superheated steam (crude oil viscosity reduction, improved flow environment, changes in rock wettability and improved oil displacement efficiency, etc.) is much higher than that of saturated steam. Superheated steam stimulation in Kenkyak high water cut heavy oil reservoir pilot test results showed that the average daily oil production of single well by superheated steam stimulation was 2-4 times than that of saturated steam stimulation. Superheated steam is more effective to heat water-invaded oil reservoir than saturated steam.

Mathematical Model of Multi-Layer Wall with Phase Change Material and its Use in Optimal Design

2013 ◽  
Vol 649 ◽  
pp. 295-298
Author(s):  
Lubomir Klimes ◽  
Pavel Charvát ◽  
Josef Stetina
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Phase Change ◽  
Phase Change Material ◽  
Control Volume ◽  
Operational Conditions ◽  
Volume Method ◽  
The Mathematical Model ◽  
Change Material

The paper deals with the mathematical model of the multi-layer wall containing the phase change material (PCM). The model utilizes the effective heat capacity method for modeling the latent heat of phase change and the control volume method is used for the discretization of the model. The utilization of the model is then demonstrated on the problem of the optimal design of the multi-layer wall with the PCM. The TMY2 data for the city of Brno were used in simulations as operational conditions. The main attention is aimed at the determination of the optimal thickness of the PCM layer for the multi-layer wall design with various thicknesses of the masonry.

A Theoretical Investigation into Phase Change Clothing Benefits for Firefighters under Extreme Conditions

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Geoffry N. Mercer ◽  
Harvinder S Sidhu
Keyword(s):  
Mathematical Model ◽  
Thermal Properties ◽  
Phase Change ◽  
Protective Clothing ◽  
The Body ◽  
Extreme Conditions ◽  
Heat Absorption ◽  
Fire Exposure ◽  
Subcutaneous Layer ◽  
The Mathematical Model

We investigate the thermal performance of protective clothing that has an embedded phase change layer. Heat absorption due to phase change within the material is used to limit the thermal penetration of heat into the material and hence to the firefighter. The distribution of temperature within the fabric and skin during the exposure to an extreme firefighting situation is determined. To determine the protective nature of the clothing, we also include a model of the skin as three layers with differing thermal properties namely the epidermis, dermis and the subcutaneous layer. In our model, we have also incorporated the air gap between the garment and the body. The mathematical model is used to predict the duration of fire exposure during which the garment is able to protect the firefighter from getting first and second degree burns.

scholarly journals The Solution of a Mathematical Model for Dengue Fever Transmission Using Differential Transformation Method

2019 ◽  
pp. 82-87
Author(s):  
Felix Yakubu Eguda ◽  
Andrawus James ◽  
Sunday Babuba
Keyword(s):  
Mathematical Model ◽  
Dengue Fever ◽  
Transformation Method ◽  
Vital Role ◽  
Differential Transformation Method ◽  
Linear Ordinary Differential Equations ◽  
Differential Transformation ◽  
Long Term Behavior ◽  
The Mathematical Model

Differential Transformation Method (DTM) is a very effective tool for solving linear and non-linear ordinary differential equations. This paper uses DTM to solve the mathematical model for the dynamics of Dengue fever in a population. The graphical profiles for human population are obtained using Maple software. The solution profiles give the long term behavior of Dengue fever model which shows that treatment plays a vital role in reducing the disease burden in a population.

scholarly journals Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

2020 ◽  
Author(s):  
A. John Christopher ◽  
N. Magesh ◽  
G. Tamil Preethi
Keyword(s):  
Mathematical Model ◽  
Preventive Measures ◽  
Control Strategies ◽  
Transformation Method ◽  
Dynamical Analysis ◽  
Transform Method ◽  
Potential Control ◽  
Corona Virus ◽  
Differential Transform ◽  
The Mathematical Model

Abstract The aim of this paper is applying the Differential Transformation Method (DTM) to analyze and find the solution for the mathematical model described by the system of nonlinear ordinary differential equations which describe the epidemiology of the most threatening virus called Corona-virus later labelled as COVID-19. The behaviour of the outcomes is presented in terms of plots. Finally, the present study may help you to examine the wild class of real world models and also aid to predict their behaviour with respect to parameters considered in the model. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

scholarly journals Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
A. Harir ◽  
S. Melliani ◽  
H. El Harfi ◽  
L. S. Chadli
Keyword(s):  
Mathematical Model ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Differential Transformation ◽  
Variational Iteration ◽  
The Mathematical Model

The aim of the present study is to analyze and find a solution for the model of nonlinear ordinary differential equations (ODEs) describing the so-called coronavirus (COVID-19), a deadly and most parlous virus. The mathematical model based on four nonlinear ODEs is presented, and the corresponding numerical results are studied by applying the variational iteration method (VIM) and differential transformation method (DTM).

Improvements of Superheated Steam Stimulation in Secondary Development of Heavy Oil Reservoir

2012 ◽  
Vol 524-527 ◽  
pp. 1450-1455
Author(s):  
An Zhu Xu ◽  
Xiang Hong Wu ◽  
Zi Fei Fan ◽  
Lun Zhao ◽  
Cheng Gang Wang
Keyword(s):  
Heavy Oil ◽  
Superheated Steam ◽  
Oil Production ◽  
Saturated Steam ◽  
Oil Reservoir ◽  
Displacement Efficiency ◽  
Oil Displacement ◽  
Oil Displacement Efficiency ◽  
Heavy Oil Reservoir ◽  
Steam Stimulation

With superheated steam, there is no direct relationship between temperature and pressure, Therefore, at a particular pressure it is possible for superheated steam to exist at a wide range of temperatures higher than that of its saturated steam. The heat transfer coefficient is 1/150-1/250 as much as that of saturated steam during heat transferring, and it takes a relatively long time to cool, during which time the steam is releasing very little energy and transmitted long distances. The mechanisms of superheated steam stimulation are mainly pointed to the performance of crude oil viscosity reduced, flow environment improved, rock wettability changed, oil displacement efficiency improved. Physical simulation shows that oil displacement efficiency by superheated steam is 6-12% higher than that of saturated steam at the same temperature, and under the condition of carrying the same heat, superheated steam enlarged the heating radius by about 10m, oil steam ratio increased by 0.7. Superheated steam stimulation was put into Kazakstan’s heavy oil reservoir after two cycles of saturated steam stimulation. The average daily oil production was 2-4 times that of saturated steam stimulation, which improved heavy oil production effectively. The secondary heavy oil thermal recovery by superheated steam stimulation applied in marginal heavy oil reservoirs achieved satisfactory effect.

Effect of Continuous Heating on Grain Growth in Fe-40Ni-Ti Alloy

2014 ◽  
Vol 988 ◽  
pp. 151-155
Author(s):  
Shao Qiang Yuan ◽  
Yue Hui Yang ◽  
Zhen Liang Wang
Keyword(s):  
Mathematical Model ◽  
Grain Size ◽  
Grain Growth ◽  
Experimental Results ◽  
Continuous Heating ◽  
Heating Process ◽  
Ti Alloy ◽  
Size Growth ◽  
Metallographic Observation ◽  
The Mathematical Model

The grain growth of Fe-40Ni-Ti alloy was investigated by means of metallographic observation during continuous heating. The experimental results indicate that: the microstructures consist of multi-polygon austenite. No transformation happens of tested alloy during heating only the grain size increases gradually. The size of grain grows steadily below 1160°C until 1200°C, the grain size growth unusually. The process of grain growth has relations with the dissolving of TiN particles. Finally, the mathematical model of grain growth in continuous heating process was obtained for the tested alloy.

scholarly journals The Effect of Functionally Graded Materials on Temperature during Frictional Heating: Under Uniform Sliding

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4285
Author(s):  
Aleksander Yevtushenko ◽  
Katarzyna Topczewska ◽  
Przemysław Zamojski
Keyword(s):  
Mathematical Model ◽  
Functionally Graded Materials ◽  
Frictional Heating ◽  
Ceramic Materials ◽  
Functionally Graded ◽  
Heating Process ◽  
Spatial Distributions ◽  
Graded Materials ◽  
Exponential Change ◽  
The Mathematical Model

The mathematical model of heating process for a friction system made of functionally graded materials (FGMs) was proposed. For this purpose, the boundary-value problem of heat conduction was formulated for two semi-spaces under uniform sliding taking into consideration heating due to friction. Assuming an exponential change in thermal conductivities of the materials, the exact, as well as asymptotic (for small values of time), solutions to this problem were obtained. A numerical analysis was performed for two elements made of ZrO2–Ti-6Al-4V and Al3O2–TiC composites. The influence of the gradient parameters of both materials on the evolution and spatial distributions of the temperature were investigated. The temperatures of the elements made of FGMs were compared with the temperatures found for the homogeneous ceramic materials.

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