ANALYSIS OF STRESS FIELD NEAR CRACK TIP BASED ON ELECTRIC SATURATION MODEL

Within the framework of nonlinear eleetroelasticity, the stress field near to the crack tip in an infinite piezoelectric media subject to a far field uniform loading is studied by using an electrical strip saturation model and the complex variable method. And the emphasis is placed on the stress field near to the crack tip. The obtained solutions show that the normalized stress components at an arbitrary point near to the crack tip are determined by the angle of the point. Moreover, the stress components are independent of the distance from the point to the ori- gin of the coordinate. The distributions of in-plane stress components near to the crack tip are analyzed based on numerical results for PZT-SH. Compared with some related solutions, results show that the solutions are valid.

Coupled thermo-hydro-mechanical-migratory model for dual-porosity medium and numerical analysis

A coupled thermo-hydro-mechanical-migratory model of dual-porosity medium for saturated-unsaturated ubiquitous-joint rockmass was established,in which the stress field and the temperature field were single,but the seepage field and the concentration field were double,and the influences of sets,spaces,angles,continuity ratios,stiffnesses of fractures on the constitutive relationship of the medium were considered.Also,the relative two-dimensional program of finite element method was developed.Taking a hypothetical nuclear waste repository as a calculation example,the case in which the rockmass was unsaturated dual-porosity medium and radioactive nuclide leak was simulated numerically,and the temperatures,negative pore pressures,saturations,flow velocities,nuclide concentrations and principal stresses in the rockmass were investigated.The results show that the negative pore pressures and nuclide concentrations in the porosity and fracture present different changes and distributions.Even though the saturation degree in porosity is only about 1/10 that in fracture,the flow velocity of underground water in fracture is about three times that in porosity because the permeability coefficient of fracture is almost four orders higher than that of porosity.The value of nuclide concentration in fracture is close to that in porosity.

Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed. Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model （DPM）. The comparisons results show that the DPM overestimates the inter-porosity coefficient ）, and the storage factor w. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density. The pressure propagation is slower in the direction of larger fracture density.

Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′ i at any time.

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker-Planck equation and analytic expressions of the steady-state probability distribution function （SPD） of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that （i） the correlation strength A of correlated noises always enhances the fluctuation of laser intensity; （ii） the correlation time v of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.

Theoretical characterization of the temperature-dependent saturation magnetization of magnetic metallic materials

Based on the force-heat equivalence energy density principle,a theoretical model for magnetic metallic materials is developed,which characterizes the temperature-dependent magnetic anisotropy energy by considering the equivalent relationship between magnetic anisotropy energy and heat energy;then the relationship between the magnetic anisotropy constant and saturation magnetization is considered.Finally,we formulate a temperature-dependent model for saturation magnetization,revealing the inherent relationship between temperature and saturation magnetization.Our model predicts the saturation magnetization for nine different magnetic metallic materials at different temperatures,exhibiting satisfactory agreement with experimental data.Additionally,the experimental data used as reference points are at or near room temperature.Compared to other phenomenological theoretical models,this model is considerably more accessible than the data required at 0 K.The index included in our model is set to a constant value,which is equal to 10/3 for materials other than Fe,Co,and Ni.For transition metals(Fe,Co,and Ni in this paper),the index is 6 in the range of 0 K to 0.65T_(cr)(T_(cr) is the critical temperature),and 3 in the range of 0.65T_(cr) to T_(cr),unlike other models where the adjustable parameters vary according to each material.In addition,our model provides a new way to design and evaluate magnetic metallic materials with superior magnetic properties over a wide range of temperatures.

Effect of gas saturation on P-wave velocity in tight sandstone

By measuring the variation of the P-and S-wave velocities of tight sandstone samples under water saturation,it was confirmed that with the decrease in water saturation,the P-wave velocity first decreased and then increased.The variation in velocity was influenced by the sandstone’s porosity.The commonly used Gassmann equation based on fluid substitution theory was studied.Comparing the calculated results with the measured data,it was found that the Gassmann equation agreed well with the measured data at high water saturation,but it could not explain the bending phenomenon of P-wave velocity at low saturation.This indicated that these equations could not accurately describe the relationship between fluid content and rock acoustic velocity.The reasons for this phenomenon were discussed through Taylor’s expansion.The coefficients of the fitting formula were calculated and verified by fitting the measured acoustic velocity changes of the cores.The relationship between P-wave velocity and saturation was discussed,which provides experimental support for calculating saturation using seismic and acoustic logging data.

Study on Anti-ship Missile Saturation Attack Model

Based on the analysis for the interception process of ship-to-air missile system to the anti-ship missile stream, the antagonism of ship-to-air missile and anti-ship missile stream was modeled by Monte Carlo method. This model containing the probability of acquiring anti-ship missile, threat estimation, firepower distribution, interception, effectiveness evaluation and firepower turning, can dynamically simulate the antagonism process of anti-ship missile attack stream and anti-air missile weapon system. The anti-ship missile's saturation attack stream for different ship-to-air missile systems can be calculated quantitatively. The simulated results reveal the relations among the anti-ship missile saturation attack and the attack intensity of anti-ship missile, interception mode and the main parameters of anti-air missile weapon system. It provides a theoretical basis for the effective operation of anti-ship missile.

A new model for predicting irreducible water saturation in tight gas reservoirs

The irreducible water saturation(Swir) is a significant parameter for relative permeability prediction and initial hydrocarbon reserves estimation.However,the complex pore structures of the tight rocks and multiple factors of the formation conditions make the parameter difficult to be accurately predicted by the conventional methods in tight gas reservoirs.In this study,a new model was derived to calculate Swir based on the capillary model and the fractal theory.The model incorporated different types of immobile water and considered the stress effect.The dead or stationary water(DSW) was considered in this model,which described the phenomena of water trapped in the dead-end pores due to detour flow and complex pore structures.The water film,stress effect and formation temperature were also considered in the proposed model.The results calculated by the proposed model are in a good agreement with the experimental data.This proves that for tight sandstone gas reservoirs the Swir calculated from the new model is more accurate.The irreducible water saturation calculated from the new model reveals that Swir is controlled by the critical capillary radius,DSW coefficient,effective stress and formation temperature.

Zircon saturation model in silicate melts:a review and update

Zircon stability in silicate melts-which can be quantitatively constrained by laboratory measurements of zircon saturation-is important for understanding the evolution of magma.Although the original zircon saturation model proposed by Watson and Harrison(Earth Planet Sci Lett 64(2):295-304,1983) is widely cited and has been updated recently,the three main models currently in use may generate large uncertainties due to extrapolation beyond their respective calibrated ranges.This paper reviews and updates zircon saturation models developed with temperature and compositional parameters.All available data on zircon saturation ranging in composition from mafic to silicic(and/or peralkaline to peraluminous)at temperatures from 750 to 1400℃ were collected to develop two refined models(1 and 2) that may be applied to the wider range of compositions.Model 1 is given by lnCZr(melt)=(14.297±0.308)+(0.964 ± 0.066).M-(11113±374)/r,and model 2 given by lnCZr(melt)=(18.99±0.423)-(1.069±0.102)·lnG-(12288±593)/T,where CZr(melt) is the Zr concentration of the melt in ppm and parameters M [=(Na+K+2 Ca)/(Al·Si)](cation ratios) and G [=(3·Al2 O3+SiO2)/(Na2-O+K2 O+CaO+MgO+FeO)](molar proportions)represent the melt composition.The errors are at one sigma,and T is the temperature in Kelvin.Before applying these models to natural rocks,it is necessary to ensure that the zircon used to date is crystallized from the host magmatic rock.Assessment of the application of both new and old models to natural rocks suggests that model 1 may be the best for magmatic temperature estimates of metaluminous to peraluminous rocks and that model 2 may be the best for estimating magmatic temperatures of alkaline to peralkaline rocks.

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed math- ematically using a complex variable approach in two-dimensional （2D） semipermeable piezoelectric media. In this model, an existing polarization saturation （PS） model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displace- ment （COD）, the crack opening potential （COP）, and the local stress intensity factors （SIFs） are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.

Gas hydrate saturation from NGHP 02 LWD data in the Mahanadi Basin

During the Indian National Gas Hydrate Program(NGHP)Expedition 02,Logging-while-drilling(LWD)logs were acquired at three sites(NGHP-02-11,NGHP-02-12,and NGHP-02-13)across the Mahanadi Basin in area A.We applied rock physics theory to available sonic velocity logs to know the distribution of gas hydrate at site NGHP-02-11 and NGHP-02-13.Rock physics modeling using sonic velocity at well location shows that gas hydrate is distributed mainly within the depth intervals of 150-265 m and 100 -215 mbsf at site NGHP-02-11 and NGHP-02-13,respectively,with an average saturation of about 4%of the pore space and the maximum concentration of about 40%of the pore space at 250 m depth at site NGHP-02-11,and at site NGHP-02-13 an average saturation of about 2%of the pore space and the maximum concentration of about 20%of the pore space at 246 m depth,as gas hydrate is distributed mainly within 100-246 mbsf at this site.Saturation of gas hydrate estimated from the electrical resistivity method using density derived porosity and electrical resistivity logs from Archie's empirical formula shows high saturation compared to that from the sonic log.However,estimates of hydrate saturation based on sonic P-wave velocity may differ significantly from that based on resistivity,because gas and hydrate have higher resistivity than conductive pore fluid and sonic P-wave velocity shows strong effect on gas hydrate as a small amount of gas reduces the velocity significantly while increasing velocity due to the presence of hydrate.At site NGHP-02-11,gas hydrate saturation is in the range of 15%e30%,in two zones between 150-180 and 245-265 mbsf.Site NGHP-02-012 shows a gas hydrate saturation of 20%e30%in the zone between 100 and 207 mbsf.Site NGHP-02-13 shows a gas hydrate saturation up to 30%in the zone between 215 and 246 mbsf.Combined observations from rock physics modeling and Archie’s approximation show the gas hydrate concentrations are relatively low(<4%of the pore space)at the sites of the Mahanadi Basin in the turbidite channel system.

Study on water saturation computation models in complex pore volcanic reservoir

Determination of water saturation is important for reservoir evaluation. When complex pore structures such as fracture and cavity are present in reservoir, Archie equation is no longer suitable. According to different models of pore structure division, the authors studied water saturation conlputation models. The results show that dual porosity system is divided into four models. The first model is based on dual laterolog, the second is Dual Porosity I , the third is Dual Porosity Ⅱ , and the last one is based on the conductive pore. Besides, the triple porosity system is triple porosity model. Compute water saturation was using all the above five models in volcanic reservoir in Songnan gas field. The triple porosity system is the most suitable model for water saturation computation in complex pore structure volcanic reservoir.

Experimental Examination of Velocity-Models in Estimating Gas Hydrate Saturation in Sediments

Elastic velocities(v_p and v_s)have been widely used in estimating gas hydrate saturation in void spaces of sediments.The commonly used models are empirical equations or some physically based models,such as Wyllie’s time average,Effective Medium Theory (EMT),Modified Biot-Gassmann Theory by Lee (BGTL),etc.These equations or models are selective to distinct conditions.In order to evaluate the app-

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)- THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance

Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C（τ） and the associated relaxation time T（C） in the case of a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.

Improved Model of Radial Vibration in Switched Reluctance Motor Including Magnetic Saturation

This paper proposes an improved method for the prediction of radial vibration in switched reluctance motor(SRM)considering magnetic saturation.In this paper,the basic modeling principle is briefly introduced,it is based on the derivation that the peak acceleration is dependent on the product of phase current and current gradient idi/dt.However,the derivation may cause errors due to saturation effect.Thus in this paper,the discrete sample data are firstly acquired based on DC pulse measurement method,by which electromagnetic,torque and peak acceleration characteristics can all be acquired.Then the entire peak acceleration characteristics are obtained by improved Least Square Support Vector Machine(LSSVM).Based on the obtained static peak acceleration characteristics,the time-varied radial vibration model is established based on superposition of natural oscillations of dominant vibration modes.Finally,a simulation model is built up using MATLAB/Simulink.The good agreement between simulation and experiment shows that the proposed method for modeling is feasible and accurate,even under saturation.In addition,since LSSVM does not need any prior knowledge,it is much easier for modeling compared with other existing literatures.

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.

Digital image processing of saturation for two-phase flow in planar porous media model

In this paper, the accuracy of estimating stained non-wetting phase saturation using digital image processing is examined, and a novel post-processing approach for calculating threshold is presented. In order to remove the effect of the background noise of images and to enhance the high-frequency component of the original image, image smoothing and image sharpening methods are introduced. Depending on the correct threshold, the image binarization processing is particularly useful for estimating stained non-wetting phase saturation. Calculated saturation data are compared with the measured saturation data during the two-phase flow experiment in an artificial steel planar porous media model. The results show that the calculated saturation data agree with the measured ones. With the help of an artificial steel planar porous media model, digital image processing is an accurate and simple method for obtaining the stained non-wetting phase saturation.

Enhanced history matching process by incorporation of saturation logs as model selection criteria

This paper proposes a methodology for an alternative history matching process enhanced by the incorporation of a simplified binary interpretation of reservoir saturation logs(RST) as objective function. Incorporating fluids saturation logs during the history matching phase unlocks the possibility to adjust or select models that better represent the near wellbore waterfront movement, which is particularly important for uncertainty mitigation during future well interference assessments in water driven reservoirs. For the purposes of this study, a semi-synthetic open-source reservoir model was used as base case to evaluate the proposed methodology. The reservoir model represents a water driven, highly heterogenous sandstone reservoir from Namorado field in Brazil. To effectively compare the proposed methodology against the conventional methods, a commercial reservoir simulator was used in combination with a state-of-the-art benchmarking workflow based on the Big LoopTMapproach. A well-known group of binary metrics were evaluated to be used as the objective function, and the Matthew correlation coefficient(MCC) has been proved to offer the best results when using binary data from water saturation logs. History matching results obtained with the proposed methodology allowed the selection of a more reliable group of reservoir models,especially for cases with high heterogeneity. The methodology also offers additional information and understanding of sweep behaviour behind the well casing at specific production zones, thus revealing full model potential to define new wells and reservoir development opportunities.