Calibration of discrete element modeling: Scaling laws and dimensionless analysis

In this paper,dynamic similarity conditions are derived for discrete element simulations by non-dimensionalising the governing equations.These conditions must be satisfied so that the numerical model is a good representation of the physical phenomenon.For a pure mechanical system,if three independent ratios of the corresponding quantities between the two models are set,then the ratios of other quantities must be chosen according to the similarity principles.The scalability of linear and non-linear contact laws is also investigated.Numerical tests of 3D uni-axial compression are carried out to verify the theoretical results.Another example is presented to show how to calibrate the model according to laboratory data and similarity conditions.However,it is impossible to reduce computer time by scaling up or down certain parameters and continue to uphold the similarity conditions.The results in this paper provide guidelines to assist discrete element modelers in setting up the model parameters in a physically meaningful way.

Characteristics of non-Darcy flow in low-permeability reservoirs

Well testing is recognized as an effective means of accurately obtaining the formation parameters of low-permeability reservoirs and effectively analyzing the deliverability.Well test models must comply with the particular characteristics of flow in low-permeability reservoirs in order to obtain reasonable well test interpretation.At present,non-Darcy flow in low-permeability reservoirs is attracting much attention.In this study,displacement tests were conducted on typical cores taken from low-permeability reservoirs.Two dimensionless variables were introduced to analyze the collected experimental data.The results of the dimensionless analysis show whether non-Darcy flow happens or not depends on the properties of fluid and porous media and the pressure differential.The combination of the above three parameters was named as dimensionless criteria coefficient（DCC）.When the value of the DCC was lower than a critical Reynolds number（CRN）,the flow could not be well described by Darcy＇s law（so-called non-Darcy flow）,when the DCC was higher than CRN,the flow obeyed Darcy＇s law.Finally,this paper establishes a transient mathematical model considering Darcy flow and non-Darcy flow in low-permeability reservoirs,and proposes a methodology to solve the model.The solution technique,which is based on the Boltzmann transformation,is well suited for solving the flow model of low-permeability reservoirs.Based on the typical curves analysis,it was found that the pressure and its derivative curves were determined by such parameters as non-Darcy flow index and the flow characteristics.The results can be used for well test analysis of low-permeability reservoirs.

Comprehensive evaluation of water-inrush risk from coal floors

Lower groups of coal seams are presently being mined from water-inrush from coal floors in order to have safe production in the Yanzhou coal mining area. We need to evaluate the risk in the lower groups of coal seams in mines. Based on a systematic collection of hydrogeological data and some data from mined working faces in these lower groups, we evaluated the factors affecting water-inrush from coal floors of the area by a method of dimensionless analysis. We obtained the order of the factors affecting water-inrush from coal floors and recalculated data on depths of destroyed floors by multiple linear regression analysis and obtained new empirical formulas. We also analyzed the water-inrush coefficient of mined working faces of the lower groups of coal seams and improved the evaluation standard of the water-inrush coefficient method. Finally, we made a comprehensive evaluation of water-inrush risks from coal floors by using the water-inrush coefficient method and a fuzzy clustering method. The evaluation results provide a solid foundation for preventing and controlling the damage caused by water of an Ordovician limestone aquifer in the lower group of coal seams in the mines of Yanzhou. It provides also important guidelines for lower groups of coal seams in other coal mines.

Elastic-plastic properties of thin film on elastic-plastic substrates characterized by nanoindentation test

To characterize the elastic-plastic properties of thin film materials on elastic-plastic substrates,a simple theory model was proposed,which included three steps:dimensionless analysis,finite element modeling and data fitting.The dimensionless analysis was applied to deriving two preliminary nondimensional relationships of the material properties,and finite element modeling and data fitting were carried out to establish their explicit forms.Numerical indentation tests were carried out to examine the effectiveness of the proposed model and the good agreement shows that the proposed theory model can be applied in practice.

Theory of Volumetric Moving Dislocation in Poroelastic Halfspace and Characterization of Magma Intrusion Events

The undrained change in pore fluid pressure that accompanies dike intrusion may be conveniently represented as a moving volumetric dislocation. The concept of a dilation center was developed to represent the field of undrained pressure change in a saturated linear elastic medium. Since instantaneous pore fluid pressures can be developed to a considerable distance from the dislocation, monitoring the rate of pressure generation and subsequent pressure dissipation in a fully coupled manner enables certain characteristics of the resulting dislocation to be defined. The principal focus of this study is the application of dislocation based methods to analyze the behavior of the fluid pressure response induced by intrusive dislocations in a semi infinite space, such as dike intrusion, hydraulic fracturing and piezometer insertion. Partially drained pore pressures result from the isothermal introduction of volumetric moving pencil like dislocations described as analogs to moving point dislocation within a semi infinite saturated elastic medium. To represent behavior within the halfspace, an image dislocation is positioned under the moving coordinate frame fixed to the front of the primary moving dislocation, to yield an approximate solution for pore pressure for constant fluid pressure conditions. Induced pore pressures are concisely described under a minimum set of dimensionless parameter groupings representing propagation velocity, and relative geometry. Charts defining induced pore fluid pressure at a static measuring point provide a meaningful tool for determining unknown parameters in data reduction. Two intrusive events at Krafla, Iceland are examined using the type curve matching techniques. Predicted parameters agree favorably with field data.

Characterization of Hydraulic Fracture with Inflated Dislocation Moving Within a Semi-infinite Medium

Hydraulic fracturing is accompanied by a change in pore fluid pressure. As a result,this may be conveniently represented as inflated dislocation moving within a semi-infinite medium. Theory is developed to describe the pore pressures that build up around an inflated volumetric dislocation migrating within a saturated porous-elastic semi-infinite medium as analog to hydraulic fracturing emplacement. The solution is capable of evaluating the system behavior of both constant fluid pressure and zero flux surface conditions through application of a superposition. Characterization of horizontal moving dislocation processes is conducted as an application of these techniques. Where the mechanical and hydraulic parameters are defined,a priori,type curve matching of responses may be used to evaluate emplacement location uniquely. Pore pressure response elicited at a dilation,subject to pressure control is of interest in representing hydraulic fracturing where leak-off is an important component. The effect of hydraulic fracturing on fracture fluid pressure is evaluated in a poroelastic hydraulic fracture model utilizing dislocation theory. A minimum set of dimensionless parameters are defined that describe the system. Pore fluid pressures recorded during hydraulic fracturing of a well in the San Joaquin Valley of Central California is examined using the proposed model. The estimated geometry of the hydraulic fracture is matched with reasonable fidelity with the measured data.

Dual-wavelength flash Raman mapping method for measuring thermal diffusivity of the suspended nanowire

In this paper,we present a dual-wavelength flash Raman(DFR)mapping method for measuring the thermal diffusivity of a suspended nanowire.A heating pulse is used to heat the nanowire sample,and a probing pulse of different wavelength is used to measure the increase in temperature.The laser absorption coefficient can be eliminated by normalization,and the thermal diffusivity of the sample can be extracted from the normalized temperature increase.An infinite heat conduction model is used in this method to avoid the influence of boundary thermal resistance.By changing the position of the probing laser center,the measurement sensitivity of thermal diffusivity can be further improved.The position of maximum sensitivity is influenced by the thermal diffusivity of the nanowire,width of the heating pulse,radius of the heating laser spot,and characteristic length of the sample.To comprehensively analyze the influences of the various parameters,obtain the best measurement conditions,and attain maximum sensitivity,we propose a dimensionless physical model to analyze the heat conduction of the suspended nanowire.Based on the analysis of the best dimensionless parameters,the corresponding appropriate measurement conditions can be determined.Sensitivity analysis shows that when the radius of the heating laser spot is 1%of the length of the nanowire,the sensitivity of the DFR mapping method can be more than four times that of the concentric DFR method for measuring the thermal diffusivity of the nanowire.