APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .3. THE CONDITION FOR QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS AT ULTRAMICRODISK ELECTRODES IN THE STEADY-STATE

The conditions for quasi-first and second order homogeneous catalytic reactions and their variation with each other at an ultramicrodisk electrode in the steady state are discussed in this paper. The order of reaction can be controlled by changing the dimension of the ultramicroelectrode: the second order reaction can be changed to quasi-first by decreasing the dimension of the ultramicroelectrode. An example of this is given. The main factor effect on the reaction order is the dimension of the ultramicroelectrode. The K4Fe(CN)6-aminopyrine system is selected to confirm the theory, the experiments showing that the system is a second order reaction at a 432 mum microelectrode, and a quasi-first order reaction at a 19 mum ultramicroelectrode. The kinetic constant of the system can be determined by applying the previous theory of homogeneous catalytic reaction.

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given. (C) 2003 Elsevier Science B.V. All rights reserved.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

地震波谱元法数值模拟和偏移研究

With the development of both seismic theory and computer technology, numerical modeling technology of seismic wave has achieved great advancement during the past half century. The current methods under development include finite differentiation method (FDM), finite element method (FEM), pseudospectral method (PSM), integral equation method (IEM) and spectral element method (SEM). They exert their very important roles in every corner of seismology and seismic prospecting. Large quantity of researches towards spectral element method in the end of last century bring this method to a new era, which results in perfect solution of many difficult problems. However, parts of posterior works such as seismic migration and inversion which base on spectral element method have never been studied widely at least up to the present whereas are of importance to seismic imaging and seismic wave propagation. Based on previous work, this paper uses spectral element method to investigate the characteristics and laws of the seismic wave propagation in isotropic and anisotropic media. By thoroughly studying this high-accuracy method, we implement a kind of reverse-time pre- and post-stack migration based on SEM. In order to verify the validity of the SEM method, we have simulated the propagation of seismic wave in several different models. The simulation results show that: (1) spectral element method can be used to model any complex models and the computational results are comparable with the expected results and the analytic results; (2) the optimum accuracy can be achieved when the rank is between 4 and 9. When it is below 4, the dispersion may occur; and when it is above 9, the time step-length will be changed accordingly with the reducing space step-length in order to keep the computation stability. This will exponentially increase the computation time and at the same time the memory even if simulating the same media. This paper also applies explosive reflection surface imaging technology, time constancy principle of wave-filed extrapolation and least travetime raytracing technology of surface source to SEM pre- and post-stack migration of isotropic and anisotropic media. All imaging results derived by the above methods agree well with the real geological models and the position of interface and inflexions can also return to their right location well. This indicates that the method proposed in this paper is a kind of technology with high accuracy and robust stability. It can serve as an alternative method in real seismic data processing. All these work can boost the development of high-accuracy seismic imaging, and therefore have significant inference value.

准噶尔盆地中拐东北斜坡油气成藏条件研究——西部压性盆地含油气系统理论的研究与实践

This paper builds the model of oil accumulation and achieves the prediction of exploration goal. It uses multiple subject means, the ways of synthetic research and the viewpoint of analyzing genesis, with the academic guidance of sedimentology, structural geology, petroleum geology and geochemistry, the basis of strata sequence frame and structural frame, the frame of "four history" - the burying history, the structural history, the filling history and the evolving history of oil, the masterstroke of hydrocarbon's generation, migration and accumulation, the aim of revealing the genetic relation between mature source rock and oil reservoir in space and time. Some achievements and viewpoints in this study are following. 1. It is proposed that the structural evolution in this area had many periods, and the structural movement of the Xiazijie group telophase formed the structural pattern for the first time. 2. The character of strata sequence in this area is divided by the character of episodic cycle firstly. The study of dividing the facies of single well and the facies of well tie is based on the data of single well. The character of sedimentary facies is con-structed initially. 3. It is believed that Jiamuhe group is the main source rock, which can supply considerable oil and gas resources for the first time. Some criterions of source rock such as the type ,the abundance in Jiamuhe group are analysed. Using the thermal history of source rock, we drawn a conclusion that the original type of source rock in Jiamuhe group is II_1-III, and the abundance achived the level of good source rock, and this set of source rock had contributed to this area. 4. The reservoir strata in this area are assessed and analysed with the reservoir evaluation. There are multi-type reservoirs, such as volcanic lava facies, sedimentary clast facies, continental belch facies. The physical property in reservoir strata is characterized by low porosity and low permeability. The study of diagenetic stage show that the diageneses in Jiamuhe group is A-Bsubage, and the reservoir room is mainly secondary corroded hollow and cleft. 5. The synthetic research on oil system in Jiamuhe group is made for the first time. The type of petroleum system is divided , and we consider that the petroleum system of Jiamuhe group is at the reliable rank. There are two critical time in oil accumulation through studying the critical time of oil accumulation : the early generation of hydrocarbon is oil, and the later is gas. 6. The mechanism of accumulation is analysed. We consider that the accu-mulation of oil in this area has many periods, and the early generated hydrocarbon is expeled by the later , and formed the character of zonal distribution in planar. 7. A bran-new model of oil and gas is proposed. Beneficial enrichment area of oil and gas is analyzed, which can be divided into three sections: Section I can be divided into two sections: I_1 and I_2. The lower subgroup of Jiamuhe is covered by the triassic layer of I_1 section. Fault zone and near the foot wall of fault are charactered with thick phase belt. Then the cover capability in this area is relatively poor, oil can migrate into triassic layer by vertical or lateral migration , and forms I_1 Kelamayi triassic oil pool consequently. The lower subgroup of Jiamuhe is covered by the triassic layer of I_2 section ,which is charactered with thin phase belt. Then the cover capability in this area is relatively good, and forms I_1 Kelamayi triassic oil pool consequently. Section II can be divided into two sections: II_1-I_(I~2). The cover of Jiamuhe group in section II_1 is the low resistivity segment in Wuerhe group, which has thin lithology and poor porosity and permeability. Oil and gas in Jiamuhe group can be covered to form beneficial accumulation area. There are some wells in this area, such as Ke 007 well, 561 well. The thick phase belt layer of Wuerhe high resistivity segment in section II_2 has unconformable relation with Jiamuhe group. The cover ability of the high resistivity segment is poor, petroleum in Jiamuhe can migrate into Wuerhe layer vertically. This area is the beneficial area for accumulating petroleum in Wuerhe layer. there are some wells in this area, such as Ke 75 well, Ke 76 well, Ke 77 well, Ke 78 well, Ke 79 well. Section III can also be divided into two sections: III_1 and III_2. Wuerhe group in section III_1 has unconformable relation with Jiamuhe group. There is thick lithology and poor cover in Wuerhe group, but the strata sequence evolution character of upper subgroup in Jiamuhe group has determined that it has lateral and vertical cover ability. thus, this area is petroleum abundant belt of jiamuhe group, which has the trap. Section III_2 is an area controled by wedgeout of Fengcheng group, Fengcheng group in this area has quite thick lithology so that It has beneficial resevoir phase belt. It can accumulate oil in itself or accept some oil in Jiamuhe group. Jiamuhe group has some oil accumulation condition in this area. Thus, section III_2 is jiamuhe-Fengcheng multiple petroleum accumulation belt, such as Ke 80 well. 8. The goal of exploration is suggested: Depositional trap or combination trap is the important aspect in later exploration. Both types of traps are the goal of the next drilling: Fault block trap in the east of 576 well and the NO. 2 fault block trap in the north of Ke 102 well It is suggested that we should study the law of oil and gas in Jiamuhe group and enhance the study of combination in forming reservoir and trap scale. We do some lithology forecast and reservoir diatropic forecast in order to know the area of oil and gas.

准噶尔盆地吉木萨尔凹陷含油气系统形成与分布研究

On the basis of the theory and method of petroleum system, by using formation analysis and multi-discipline ways, we study the formation and .distribution of petroleum system of the Jimusaer sag in the Zhungaer Basin. Through analysis and description of main formation factors, petroleum system is classified and subdivided into several ranks. At the same time, we describe the main elements of reservoir formation and the contribution to the petroleum system. By analyzing the process of reservoir formation, we define the quantitative relationship of petroleum sources, migration and oil accumulation. Through a comprehensive studying method, the next step is to build the reservoir formation model of petroleum system and confirm the exploration target. Finally, a method which fits to study the petroleum system formation and distribution in this type of basin is created. It broadens the quantitative theory of petroleum system. The following are the main conclusions. 1. The division of rank concept of petroleum system and the classification of multi-ranks combination are put forwarded for the first time. The petroleum system is classified into 5 ranks. These ranks, in an ascending order, are compounded petroleum system, independent petroleum system, sub-petroleum system, reservoir formation structure and the main factors of reservoir formation respectively. Therefore the Jimusaer sag is divided into 1 first ranked compounded petroleum system, 2 independent petroleum systems (The first is Jiang first member ~ Jiang second member+Pingdiquan member+ Wutonggou member petroleum system and the second Pingdiquan member - Wutonggou member+Triassic + Jurassic petroleum system) and 22 sub- petroleum systems. 2. The existence of the Jiangjunmiao member petroleum system in P_1 is put forwarded for the first time in the target zone except for Pingdiquan member hydro-source rock in P2 Both two hydro-source rock experience two evolvement movements, sub-mature and mature. It is estimated that there is the matured oil&gas in the sag. 3. By introduction of the basin simulation method, regaining and formation process of the different independent petroleum system are achieved. The sources, migration, accumulation and evolution rule are all indicated. It proposed that Jiang first member ~ Jiang second member+Pingdiquan member + Wutonggou member petroleum system formed primarily in Triassic and Jurassic. The oil&gas predominantly accumulated in layers of Jiang second member and Wutonggou member. Pingdiquan member ~ Wutonggou member+Triassic + Jurassic petroleum system formed in middle of Jurassic, and middle and late of the Kreaceous. In addition the oil&gas mostly accumulated in layers of Pingdiquan member and Wutonggou member. 4. By comprehensively analyzing the reservoir formation mechanism, it is proposed that oil&gas reservoir in this zone is formed in multiple periods. Major migration and accumulation power of oil&gas can be explained by an abnormal stratum pressure. There are six channels for the migration and accumulation -of oil&gas and therefore, can be considered as multi-circular distribution. 5. Combining the rank theory of petroleum system with mode identification method, we developed a quantitative evaluation method and judgment system for the exploration target. Using this technique, we confirmed three exploration target zones, four favorable oil&gas reservoir combinations, three exploration wells. Ji -15 well has been drilled and has provided a breakthrough on the oil&gas exploration.