A fractal network model with tunable fractal dimension

Author(s):  
Lei Yang ◽  
Wenjiang Pei ◽  
Tao Li ◽  
Yanfei Cao ◽  
Yi Shen ◽  
...  
1991 ◽  
Vol 113 (3) ◽  
pp. 516-525 ◽  
Author(s):  
A. Majumdar ◽  
C. L. Tien

The topography of rough surfaces strongly influences the conduction of heat and electricity between two surfaces in contact. Roughness measurements on a variety of surfaces have shown that their structure follows a fractal geometry whereby similar images of the surface appear under repeated magnification. Such a structure is characterized by the fractal dimension D, which lies between 2 and 3 for a surface and between 1 and 2 for a surface profile. This paper uses the fractal characterization of surface roughness to develop a new network model for analyzing heat conduction between two contacting rough surfaces. The analysis yields the simple result that the contact conductance h and the real area of contact At are related as h ~ AtD/2 where D is the fractal dimension of the surface profile. Contact mechanics of fractal surfaces has shown that At varies with the load F as At ~ Fη where η ranges from 1 to 1.33 depending on the value of D. This proves that the conductance and load are related as h ~ FηD/2 and resolves the anomaly in previous investigations, which theoretically and experimentally obtained different values for the load exponent. The analytical results agreed well with previous experiments although there is a tendency for overprediction.


2013 ◽  
Vol 716 ◽  
pp. 409-412
Author(s):  
Jie Fan ◽  
Lian Ying Zhao ◽  
Chong Qi Ma ◽  
Yong Liu

The effect of the nanoscale fractal tree-shaped network on the fluid permeation in wool fiber driven by capillary force was investigated in this paper. The fluid permeation obeys murrays law, and the permeation efficiency highly depends on the fractal dimension of the channel length. A better understanding of the mechanism of structural effect on the tree-shaped flow in the nanoscale fractal network of wool fiber could help the further design of bio-mimetic artificial fiber and functional fabric.


1991 ◽  
Vol 6 (8) ◽  
pp. 1680-1684 ◽  
Author(s):  
T. Carrière ◽  
C. Ortiz ◽  
G. Fuchs

This work presents the first experimental evidence of the formation of a fractal network of crystalline clusters in the first stage of the amorphous-crystal transformation. Although this transformation has been extensively studied, such an intermediate stage between amorphous and crystalline phases has never been experimentally revealed before. This fractal network was obtained by laser irradiation of an amorphous Te–Se–Br alloy. The irradiation conditions have been determined in order to be in a regime of limited diffusion, which is the basis of fractal formation. Moreover, the fractal dimension has been determined to be 1.55, which corresponds to the theoretical value obtained for fractal growth by a process of cluster-cluster aggregation with some structural readjustment.


Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Juhua Li ◽  
Chen Chen

Darcy’s law is not suit for describing high velocity flow in the near wellbore region of gas reservoirs. The non-Darcy coefficient β of the Forchheimer’s equation is a main parameter for the evaluation of seepage capacity in gas reservoirs. The paper presented a new method to calculate β by performing gas and con-water flow simulations with random 3D micropore network model. Firstly, a network model is established by random fractal method. Secondly, based on the network simulation method of non-Darcy flow in the literature of Thauvin and Mohanty, a modified model is developed to describe gas non-Darcy flow with irreducible water in the porous medium. The model was verified by our experimental measurements. Then, we investigated the influence of different factors on the non-Darcy coefficient, including micropore structure (pore radius and fractal dimension), irreducible water saturation ( S wi ), tortuosity, and other reservoir characteristics. The simulation results showed that the value of the non-Darcy coefficient decreases with the increase in all: the average pore radius, fractal dimension, irreducible water saturation, and tortuosity. The non-Darcy coefficients obtained by the fractal method of microparameters are estimated more precisely than the conventional methods. The method provides theoretical support for the productivity prediction of non-Darcy flow in gas reservoirs.


1998 ◽  
Vol 34 (15) ◽  
pp. 1443 ◽  
Author(s):  
C. Borja ◽  
C. Puente ◽  
A. Medina

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Yang Yi ◽  
Juhua Li ◽  
Lei Ji

Critical condensate saturation, Scc, is a key parameter for the evaluation of well deliverability in gas condensate reservoirs. We propose a new method to determine Scc by performing three-phase flow simulations with three-dimensional (3D) pore network model. First, we establish a network model with random fractal methodology. Second, based on the condensation model in the literature of Li and Firoozabadi, we develop a modified condensation model to describe the condensation phenomenon of gas with connate water in the porous medium. The numerical model is verified by experimental measurements in the literature. Then, we investigate the influence of different factors on the critical condensate saturation, including micro pore structure (pore radius and fractal dimension), condensate gas/oil interfacial tension (IFT), and flow rate at different irreducible water saturation, Swi. The simulation results show that Scc decreases with increasing of average pore radius, but increases with increasing of fractal dimension. In the case of the same gas/oil interfacial tension, the higher the connate water saturation, the higher the critical condensate saturation. There is a critical gas/oil interfacial tension, below the critical value, the critical condensate saturation increases drastically with increasing of interfacial tension while it keeps almost unchanged when the interfacial tension is above the critical value. The critical condensate saturation decreases with increasing in the gas flow rate. High capillary number results in low critical condensate saturation. Reasonable increase in producing pressure drop can effectively improve the flow capacity of condensate oil.


Author(s):  
Е.В. ТОНКИХ ◽  
А.И. ПАРАМОНОВ ◽  
А.Е. КУЧЕРЯВЫЙ

В работе представлен метод планирования структуры сети интернета вещей на основе использования фракталов. Предлагается применять фрактальные фигуры для описания структуры целевого окружения, которое определяет размещение сетевых устройств. Для планирования используются значения оценки фрактальной размерности и доли площади, занимаемой целевым окружением и моделью сети. Полученные результаты могут быть использованы при планировании структуры сети интернета вещей в городской или иной среде на основе данных, полученных о целевом окружении в виде планов, карт или фотоснимков. The paper proposes a method for planning the structure of the I nternet of Things network based on the use of fractals. It is proposed to use fractal figures to describe the target environment, which determines the placement of network devices. The values of the estimate of the fractal dimension and the fraction of the area occupied by the target environment and the network model are used for planning. The results obtained can be used to describe the structure of the IoT network in an urban or other environment based on data obtained about the target environment in the form of plans, maps, or photographs.


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