Research on the nonlinear spherical percolation model with quadratic pressure gradient and its percolation characteristics

For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spheri-cal flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the ef-fect of wellbore storage. By variable substitu-tion, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the nu-merical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear per-colation type curves in shape and characteris-tics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical off-set of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the in-fluence of the quadratic pressure gradient is very distinct, especially for the low permeabil-ity and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in res-ervoir, therefore the research on nonlinear per-colation theory should be strengthened and reinforced.

Percolation Model of Graphite-modified Asphalt Concrete

The addition of graphite powder in conventional asphalt mixture can produced asp halt concrete with excellent electrical performance. Percolation theor y was employed to discuss the relation between the conductivity and graphite con tent of graphite-modified asphalt concrete. It was found that the results of pe rcolation model are consistent with experimental values. The percolation thresho ld of graphite-modified asphalt concrete is 10.94% graphite content account for the total volume of the binder phase consisting of asphalt and graphite. The cr itical exponent is 3.16, beyond the range of 1.6-2.1 for the standard lattice c ontinuous percolation problem. Its reason is that the tunnel conduction mec hanism originates near the critical percent content, which causes this system to be not universal. Tunnel mechanism is demonstrated by the nonlinear voltage-cu rrent characteristic near percolation threshold.The percolation model is able to well predict the formation and development of conductive network in graphite- modified asphalt concrete.

Research on percolation model and criticality of seismicity

Making use of modern nonlinear physics theory and earthquake focus theory, combined with seismicity characteristics, the percolation model of earthquake activity is given in this paper. We take the seismogenic process of alarge earthquake as a phase transition process of percolation and apply the renormalization method to phase transition of percolation. The critical property of the system, which is like percolation probability exponential andcorrelative length exponential, etc, can be calculated under the fixed point as which in the renormalization transformation infinite correlative length in percolation phase transition is taken. The percolation phase transition process of two large earthquakes, which are Haicheng and Tangshan event occurred in 1975 and 1976 respectively, hasbeen discussed by means of seismicity data before and after two shocks.

Determination of a Pore Structure Parameter of Porous Media by Analysis of Percolation Network Model

According to the simulation of nitrogen sorption process in porous media with three-dimensional network model, and the analysis for such a process with percolation theory, a new method is proposed to determine a pore structure parameter--mean coordination number of pore network, which represents the connectivity among a great number of pores. Here the 'chamber-throat' model and the Weibull distribution are used to describe the pore geometry and the pore size distribution respectively. This method is based on the scaling law of percolation theory after both effects of sorption thermodynamics and pore size on the sorption hysteresis loops are considered. The results show that it is an effective procedure to calculate the mean coordination number for micro- and meso-porous media.

Temperature- and voltage-dependent trap generation model in high-k metal gate MOS device with percolation simulation

High-k metal gate stacks are being used to suppress the gate leakage due to tunneling for sub-45 nm technology nodes.The reliability of thin dielectric films becomes a limitation to device manufacturing,especially to the breakdown characteristic.In this work,a breakdown simulator based on a percolation model and the kinetic Monte Carlo method is set up,and the intrinsic relation between time to breakdown and trap generation rate R is studied by TDDB simulation.It is found that all degradation factors,such as trap generation rate time exponent m,Weibull slope β and percolation factor s,each could be expressed as a function of trap density time exponent α.Based on the percolation relation and power law lifetime projection,a temperature related trap generation model is proposed.The validity of this model is confirmed by comparing with experiment results.For other device and material conditions,the percolation relation provides a new way to study the relationship between trap generation and lifetime projection.

Four Types of Percolation Transitions in the Cluster Aggregation Network Model

We study the percolation transition in a one-species cluster aggregation network model, in which the parameter α describes the suppression on the cluster sizes. It is found that the model can exhibit four types of percolation transitions, two continuous percolation transitions and two discontinuous ones. Continuous and discontinuous percolation transitions can be distinguished from each other by the largest single jump. Two types of continuous percolation transitions show different behaviors in the time gap. Two types of discontinuous percolation transitions are different in the time evolution of the cluster size distribution. Moreover, we also find that the time gap may also be a measure to distinguish different discontinuous percolations in this model.

Reverse Monte Carlo Modeling of the Rigidity Percolation Threshold in Ge<SUB>x</SUB>Se<SUB>1-x</SUB>Glassy Networks

Based on Maxwell’s constraint counting theory, rigidity percolation in GexSe1-x glasses occurs when the mean coordination number reaches the value of 2.4. This corresponds to Ge0.20Se0.80 glass. At this composition, the number of constraints experienced by an atom equals the number of degrees of freedom in three dimensions. Hence, at this composition, the network changes from a floppy phase to a rigid phase, and rigidity starts to percolate. In this work, we use reverse Monte Carlo (RMC) modeling to model the structure of Ge0.20Se0.80 glass by simulating its experimental total atomic pair distribution function (PDF) obtained via high energy synchrotron radiation. A three-dimensional configuration of 2836 atoms was obtained, from which we extracted the partial atomic pair distribution functions associated with Ge-Ge, Ge-Se and Se-Se real space correlations that are hard to extract experimentally from total scattering methods. Bond angle distributions, coordination numbers, mean coordination numbers and the number of floppy modes were also extracted and discussed. More structural insights about network topology at this composition were illustrated. The results indicate that in Ge0.20Se0.80 glass, Ge atoms break up and cross-link the Se chain structure, and form structural units that are four-fold coordinated (the GeSe4 tetrahedra). These tetrahedra form the basic building block and are connected via shared Se atoms or short Se chains. The extent of the intermediate ranged oscillations in real space (as extracted from the width of the first sharp diffraction peak) was found to be around 19.6 ?. The bonding schemes in this glass are consistent with the so-called “8-N” rule and can be interpreted in terms of a chemically ordered network model.

A Study on Numerical Calculation Method of Small Cluster Density in Percolation Model

Percolation theory deals with the numbers and properties of the clusters formed in the different occupation probability. In this Paper, we study the calculation method of small clusters. We calcu-lated the small cluster density of 1, 2 and 3 in the percolation model with the exact method and the numerical method. The results of the two methods are very close, which can be verified by each other. We find that the cluster density of all three kinds of small clusters reaches the highest value when the occupation probability is between 0.1 and 0.2. It is very difficult to get the analytical formula for the exact method when the cluster area is relatively large (such as the area is more than 50), so we can get the density value of the cluster by numerical method. We find that the time required calculating the cluster density is proportional to the percolation area, which is indepen-dent of the cluster size and the occupation probability.

段家河流域泥石流发育的渗流(Percolation)模型

在观察资料的基础上,提出了泥石流发育的渗流(Percolation)模型。由类比得到泥石流爆发的临界值P_c=d/(Z(d-1)),其中d是欧氏空间维数,z是配位数。根据广义Fibonacci数列,得到临界状态时的分形维数D_t(p,q)=In N/2ln,其中p、q是与人类活动、环境因素有关的参数.用以上结果对段家河流域的泥石流的发生作了理论分析。

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.

Continuum percolation of porous media via random packing of overlapping cube-like particles

The pore configuration in porous medium is assumed to be the randomly distributed cube-like particles which can overlap each other in the periodic cubic domain, and the impact of particle characteristics on the percolation property of these cube-like particle packing systems is analyzed.Firstly, by combining the percolation models and finite-size scaling analysis, three numerical parameters(i.e., percolation transition width △L, local percolation threshold ψ_c(L), and correlation length exponent v) for the cube-like particle systems with shape parameter s in[1.0, +∞] are derived successively. Then, based on the relation between the percolation thresholdψ_c in infinite space and the local percolation threshold ψ_c(L), the corresponding ψ_c with s in[1.0, +∞] are further determined. It is shown from the study that the characteristics of cube-like particles have significant influence on the global percolation threshold ψ_c of the particle packing systems. As the parameter s increases from 1.0 to +∞, the percolation threshold ψ_c will go down persistently. When the surface of cube-like particles is cubical and spherical, respectively, the minimum and maximum thresholds ψ_c,min and ψ_c,max are obtained.

Two Probability Plots of the Three-Parameter Lognormal Distribution

The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.

页岩油微观渗流机理研究进展

页岩油已成为全球非常规油气资源勘探开发的重点,但其开发面临诸多挑战。针对页岩油赋存孔隙空间复杂、渗流机理尚不明确和研究方法亟需探索的关键问题,从孔隙尺度和岩心尺度,系统阐述了页岩油微观渗流机理在实验方法和计算模拟方面的研究现状,探讨了目前存在的问题和未来研究的发展趋势。结果显示,目前多种实验方法结合能较好表征页岩孔隙结构,但对微尺度与岩心尺度流动的表征尚存在不足;孔隙尺度流动机理研究以格子玻尔兹曼方法为代表的直接法和以孔隙网络模拟为代表的间接法为主,但对微尺度效应的考虑有待完善;岩心尺度流动机理研究主要为基于毛管束模型和分形理论,建立考虑边界层效应的渗流模型。指出充分考虑页岩油微纳米孔隙中流动边界吸附/滑移、密度/黏度非均质性、应力敏感、启动压力梯度等因素,耦合不同尺度渗流机理,构建能够准确表征页岩油多相多尺度流动特征的数学模型是未来的主要研究方向。

电力社会耦合网络面对虚假信息传播的鲁棒性研究

为研究在电力社会耦合网络中电力社交用户受到虚假信息影响的后耦合网络的鲁棒性变化,基于用户自身的影响力以及虚假信息影响力,考虑虚假信息免疫节点,改进了信息传播的独立级联传播模型,将网络中受影响节点与耦合网络鲁棒性计算的渗流模型相结合,并在此基础上拓展了1种电力社会耦合网络鲁棒性评估指标.通过仿真实验模拟发现改进的独立级联模型传播模型避免了影响的随机性,影响结果合理,耦合网络鲁棒性计算的理论值与实际验证值相符,电力社会耦合网络鲁棒性评估指标结论与耦合网络鲁棒性变化情况符合,结果表明,社交网络中初始影响节点比例对耦合网络的鲁棒性具有一定影响,且电力-Facebook耦合网络的鲁棒性优于电力-Last FM耦合网络.

Extracting energetic disorder in organic solar cells using percolation models

The energetic disorder𝜎describes the energy state distribution in organic semiconducting materials.In organic solar cells(OSCs),energetic disorder is an important parameter for evaluating the charge transport behavior,and it is strongly correlated with the device performance.Thus far,a widely used approach for extracting energetic disorder values in OSCs is the Gaussian disorder model(GDM),in which the disorder values can be extracted by fitting the slope of lnμ∼1-T2,where𝜇is the charge mobility and𝑇is the temperature.Herein,we demonstrate the potential of the percolation approach to evaluate the energetic disorder values in OSCs and compare them with the data obtained using the GDM approach.Two typical non-fullerene acceptor(NFA)-based bulk heterojunction(BHJ)films,with PTB7-Th:ITIC and PM6:Y6,were selected as the model systems.When the percolation models were adopted in the two BHJ films,the energetic disorder values extracted from the Grünewald/Thomas and Nenashev percolation models gave similar results for electron transport in the PTB7-Th:ITIC and PM6:Y6 BHJ films.This work successfully demonstrates the feasibility of microresistance analysis in BHJ systems and the application potential of the percolation model for extracting energetic disorders in OSCs.

3-D consistency dynamic constitutive model of concrete

Based on the consistency-viscoplastic constitutive model,the static William-Warnke model with three-parameters is modified and a consistency-viscoplastic William-Warnke model with three-parameters is developed that considers the effect of strain rates. Then,the tangent modulus of the consistency viscoplastic model is introduced and an implicit backward Elure iterative algorithm is developed. Comparisons between the numerical simulations and experimental data show that the consistency model properly provides the uniaxial and biaxial dynamic behaviors of concrete. To study the effect of strain rates on the dynamic response of concrete structures,the proposed model is used in the analysis of the dynamic response of a simply-supported beam and the results show that the strain rate has a significant effect on the displacement and stress magnitudes and distributions. Finally,the seismic responses of a 278 m high arch dam are obtained and compared by using the linear elastic model,as well as rate-independent and rate-dependent William-Warnke three-parameter models. The results indicate that the strain rate affects the first principal stresses,and the maximal equivalent viscoplastic strain rate of the arch dam. Numerical calculations and analyses reveal that considering the strain rate is important in the safety assessments of arch dams located in seismically active areas.

Numerical Modeling of Elastic Modulus for Cement Paste Using Homogenization Method

This paper focused on the evolution over time of elasticity of the cement paste during the hydration, e g, Young＇s modulus and Poisson＇s ration, by the proposed homogenization method combined the percolation algorithm with individual phase intrinsic elasticity. A cement paste development model, named CEMHYD3D, was used to establish an accurate microstructure. The modelling results are in good agreement with the experimental data and other numerical results available in the open literatm＇e. The suitable homogeneous scheme, applied to each level, should be carefully chosen to result in a realistic prediction. The percolation concept should aims to correctly predict the elasticity for cement paste at very early age, especially under low w/c ratios.

SWAT Model Prediction of Phosphorus Loading in a South Carolina Karst Watershed with a Downstream Embayment

The SWAT model was used to predict total phosphorus (TP) loadings for a 1555-ha karst watershed—Chapel Branch Creek (CBC)—which drains to a lake via a reservoir-like embayment (R-E). The model was first tested for monthly streamflow predictions from tributaries draining three potential source areas as well as the downstream R-E, followed by TP loadings using data collected March 2007-October 2009. Source areas included 1) a golf course that received applied wastewater, 2) urban areas, highway, and some agricultural lands, and 3) a cave spring draining a second golf course along with agricultural and forested areas, including a substantial contribution of subsurface water via karst connectivity. SWAT predictions of mean monthly TP loadings at the first two source outlets were deemed reasonable. However, the predictions at the cave spring outlet were somewhat poorer, likely due to diffuse variable groundwater flow from an unknown drainage area larger than the actual surface watershed, for which monthly subsurface flow was represented as a point source during simulations. Further testing of the SWAT model to predict monthly TP loadings at the R-E, modeled as a completely mixed system, resulted in their over-predictions most of the months, except when high lake water levels occurred. The mean monthly and annual flows were calibrated to acceptable limits with the exception of flow over-prediction when lake levels were low and surface water from tributaries disappeared into karst connections. The discrepancy in TP load predictions was attributed primarily to the use of limited monthly TP data collected during baseflow in the embayment. However, for the 22-month period, over-prediction of mean monthly TP load (34.6 kg/mo) by 13% compared to measured load (30.6 kg/mo) in the embayment was deemed acceptable. Simulated results showed a 42% reduction in TP load due to settling in the embayment.

页岩油水平井体积压裂缝网波及体积评价新方法及应用

针对鄂尔多斯盆地庆城油田夹层型页岩油体积压裂缝网波及体积定量表征难度大的问题,应用物理模拟实验与矿场数据,耦合关键地质工程参数,建立缝网改造体积预测模型,基于岩石微观结构与润湿性,建立了考虑流体压力下的多尺度孔隙渗吸模型,对缝网渗吸体积进行定量表征,并提出新的缝网波及系数概念,定量评价缝网波及体积。研究表明:页岩油体积压裂裂缝总体呈现条带状缝网形态,形似“仙人掌”;影响缝网波及体积的主控因素依次为压裂液量、裂缝密度、脆性指数、施工排量、水平应力差、油层厚度、加砂量;缝网改造体积是水平井体积压裂缝网波及体积的主要贡献者,压裂液在缝网中的渗吸主要用于补充地层能量,典型平台缝网波及系数为33.2%~63.6%,需进一步提高缝网波及体积。研究成果可为页岩油水平井体积压裂效果评价提供参考。