三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

高斯束射线追踪

Using the approximate high-frequency asymptotic methods to solve the scalar wave equation, we can get the eikonal equation and transport equation. Solving the eikonal equation by the method of characteristics provides a mathematical derivation of ray tracing equations. So, the ray tracing system is folly based on the approximate high-frequency asymptotic methods. If the eikonal is complex, more strictly, the eikonal is real value at the rays and complex outside rays, we can derive the Gaussian beam. This article mainly concentrates on the theory of Gaussian beam. To classical ray tracing theory, the Gaussina beam method (GBM) has many advantages. First, rays are no longer required to stop at the exact position of the receivers; thus time-consuming two-point ray tracing can be avoided. Second, the GBM yields stable results in regions of the wavefield where the standard ray theory fails (e.g., caustics, shadows zones and critical distance). Third, unlike seismograms computed by conventional ray tracing techniques, the GBM synthetic data are less influenced by minor details in the model representation. Here, I realize kinematical and dynamical system, and based on this, realize the GBM. Also, I give some mathematical examples. From these examples, we can find the importance and feasibility of the ray tracing system. Besides, I've studied about the reflection coefficient of inhomogeneous S-electromagnetic wave at the interface of conductive media. Basing on the difference of directions of phase shift constant and attenuation constant when the electromagnetic wave propagates in conductive medium, and using the boundary conditions of electromagnetic wave at the interface of conductive media, we derive the reflection coefficient of inhomogeneous S-electromagnetic wave, and draw the curves of it. The curves show that the quasi total reflection will occur when the electromagnetic wave incident from the medium with greater conductivity to the medium with smaller conductivity. There are two peak, values at the points of the critical angles of phase shift constant and attenuation constant, and the reflection coefficient is smaller than 1. This conclusion is different from that of total reflection light obviously.

井间地震技术研究和应用

Cross well seismic technique is a new type of geophysical method, which observes the seismic wave of the geologic body by placing both the source and receiver in the wells. By applying this method, it averted the absorption to high-frequency component of seismic signal caused by low weathering layers, thus, an extremely high-resolution seismic signal can be acquired. And extremely fine image of cross well formations, structure, and reservoir can be achieved as well. An integrated research is conducted to the high-frequency S-wave and P-wave data and some other data to determine the small faults, small structure and resolving the issues concerning the thin bed and reservoir's connectivity, fluid distribution, steam injection and fracture. This method connects the high-resolution surface seismic, logging and reservoir engineering. In this paper, based on the E & P situation in the oilfield and the theory of geophysical exploration, a research is conducted on cross well seismic technology in general and its important issues in cross well seismic technology in particular. A technological series of integrated field acquisition, data processing and interpretation and its integrated application research were developed and this new method can be applied to oilfield development and optimizing oilfield development scheme. The contents and results in this paper are as listed follows: An overview was given on the status quo and development of the cross well seismic method and problems concerning the cross well seismic technology and the difference in cross well seismic technology between China and international levels; And an analysis and comparison are given on foreign-made field data acquisition systems for cross-well seismic and pointed out the pros and cons of the field systems manufactured by these two foreign companies and this is highly valuable to import foreign-made cross well seismic field acquisition system for China. After analyses were conducted to the geometry design and field data for the cross well seismic method, a common wave field time-depth curve equation was derived and three types of pipe waves were discovered for the first time. Then, a research was conducted on the mechanism for its generation. Based on the wave field separation theory for cross well seismic method, we believe that different type of wave fields in different gather domain has different attributes characteristics, multiple methods (for instance, F-K filtering and median filtering) were applied in eliminating and suppressing the cross well disturbances and successfully separated the upgoing and downgoing waves and a satisfactory result has been achieved. In the area of wave field numerical simulation for cross well seismic method, a analysis was conducted on conventional ray tracing method and its shortcomings and proposed a minimum travel time ray tracing method based on Feraiat theory in this paper. This method is not only has high-speed calculation, but also with no rays enter into "dead end" or "blinded spot" after numerous iterations and it is become more adequate for complex velocity model. This is first time that the travel time interpolation has been brought into consideration, a dynamic ray tracing method with shortest possible path has been developed for the first arrivals of any complex mediums, such as transmission, diffraction and refraction, etc and eliminated the limitation for only traveling from one node to another node and increases the calculation accuracy for minimum travel time and ray tracing path and derives solution and corresponding edge conditions to the fourth-order differential sonic wave equation. The final step is to calculate cross well seismic synthetics for given source and receivers from multiple geological bodies. Thus, real cross-well seismic wave field can be recognized through scientific means and provides important foundation to guide the cross well seismic field geometry designing. A velocity tomographic inversion of the least square conjugated gradient method was developed for cross well seismic velocity tomopgraphic inversion and a modification has been made to object function of the old high frequency ray tracing method and put forward a thin bed oriented model for finite frequency velocity tomographic inversion method. As the theory model and results demonstrates that the method is simple and effective and is very important in seismic ray tomographic imaging for the complex geological body. Based on the characteristics of the cross well seismic algorithm, a processing flow for cross well seismic data processing has been built and optimized and applied to the production, a good section of velocity tomopgrphic inversion and cross well reflection imaging has been acquired. The cross well seismic data is acquired from the depth domain and how to interprets the depth domain data and retrieve the attributes is a brand new subject. After research was conducted on synthetics and trace integration from depth domain for the cross well seismic data interpretation, first of all, a research was conducted on logging constraint wave impedance of cross well seismic data and initially set up cross well seismic data interpretation flows. After it applied and interpreted to the cross well seismic data and a good geological results has been achieved in velocity tomographic inversion and reflection depth imaging and a lot of difficult problems for oilfield development has been resolved. This powerful, new method is good for oilfield development scheme optimization and increasing EOR. Based on conventional reservoir geological model building from logging data, a new method is also discussed on constraining the accuracy of reservoir geological model by applying the high resolution cross well seismic data and it has applied to Fan 124 project and a good results has been achieved which it presents a bight future for the cross well seismic technology.

NCMAS系统熔体结构和动力学性质压力效应的分子动力学研究

Molecular dynamics simulations were used to study the pressure dependence of the structure and the dynamic properties of forsterite melt (Mg_2SiO_4), diopside melt (CaMgSi_2O_6), anorthite melt (CaAl_2Si_2O_8), jadite melt (NaAlSi_2O_6) and albite melt (NaAlSi3O8) from 0 GPa to 25 GPa at about 2000 K and the following conclusions have been reached. Firstly, the ratio of NBO to T (NBO and T denote the content of non-bridging oxygen and the total content of Si~(4+) and Al~(3+) respectively) is closely related to the pressure and the composition of the melts. It decreases monotonously in forsterite, diopside and anorthite melts while increases at the initial stage and then decreases in jadite and albite melts with increasing pressure. At a fixed pressure, the shear viscosity of the melts decreases with increasing NBO/T and the variation rate is almost 150 times higher in fully polymerized melts than that in de-polymerized melts in comparison with anorthite melts. Secondly, it is generally accepted that the formation of the Si and A1 will promote the diffusion of the network-forming ions. The hypothesis is frequently employed to explain the emergence of the maximum self-diffusion coefficient of the network-forming ions in fully polymerized melts. However, I detected that the pressure corresponding to the peak of the self-diffusion coefficient of the network-forming ions is lower than that corresponding to the maximum content of Si and A1, and that there exists an approximately linear relationship between the self-diffusion coefficient of the ions and the breaking frequency of the bonds under a given pressure, which is different from the present understanding about the mechanism of self-diffusion. Thirdly, the relationship between the self-diffusion coefficient of Si~(4+), Al~(3+) and O~(2-) and the shear viscosity of the melts evolves from the Stokes-Einstein equation and Sutherland-Einstein equation to the Eyring equation with increasing pressure. And the key to obtain self-diffusion coefficient from shear viscosity under difference pressures is to determine A. in the Eyring equation. For Si~(4+) and O~(2-), this could be done using the linear relationship between A, and NBO% in anorthite melts. However, this method is inapplicable in other kinds of melts.

VSP克希霍夫法多波联合成像

Geophones being inside the well, VSP can record upgoing and downgoing P waves, upgoing and downgoing S waves simultaneously.Aiming at overcoming the shortages of the known VSP velocity tomography , attenuation tomography , inverse Q filtering and VSP image method , this article mainly do the following jobs:CD; I do the common-source-point raytracing by soving the raytracing equations with Runge-Kutta method, which can provide traveltime , raypath and amplitude for VSP velocity tomography , attenuation tomography and VSP multiwave migration.(D. The velocity distribution can be inversed from the difference between the computed traveltime and the observed traveltime of the VSP downgoing waves. I put forward two methods: A. VSP building-velocity tomography method that doesn't lie on the layered model from which we can derive the slowness of the grids' crunodes . B. deformable layer tomography method from which we can get the location of the interface if the layer's velocity is known..(3). On the basis of the velocity tomography , using the attenuation information shown by the VSP seismic wave , we can derive the attenuation distribution of the subsurface. I also present an algorithm to solve the inverse Q filtering problem directly and accurately from the Q modeling equation . Numerical results presented have shown that our algorithm gives reliable results . ?. According to the theory that the transformed point is the point where the four kinds of wave come into being , and where the stacked energy will be the largest than at other points . This article presents a VSP multiwave Kirchhoff migration method . Application on synthetic examples and field seismic records have shown that the algorithm gives reliable results . (5). When the location of the interface is determined and the velocity of the P wave and S wave is known , we can obtain the transmittivity and reflection coefficient 5 thereby we can gain the elastic parameters . This method is also put into use derive good result.Above all, application on models and field seismic records show that the method mentioned above is efficient and accurate .

双聚焦偏移速度估计与可分表示叠前弹性反演

In exploration seismology, the geologic target of oil and gas reservoir in complex medium request the high accuracy image of the structure and lithology of the medium. So the study of the prestack image and the elastic inversion of seismic wave in the complex medium come to the leading edge. The seismic response measured at the surface carries two fundamental pieces of information: the propagation effects of the medium and the reflections from the different layer boundaries in the medium. The propagation represent the low-wavenumber component of the medium, it is so-called the trend or macro layering, whereas the reflections represent the high-wavenumber component of the medium, it is called the detailed or fine layering. The result of migration velocity analysis is the resolution of the low-wavenumber component of the medium, but the prestack elastic inversion provided the resolution of the high-wavvenumber component the medium. In the dissertation, the two aspects about the migration velocity estimation and the elastic inversion have been studied.Firstly, any migration velocity analysis methods must include two basic elements: the criterion that tell us how to know whether the model parameters are correct and the updating that tell us how to update the model parameters when they are incorrect, which are effected on the properties and efficiency of the velocity estimation method. In the dissertation, a migration velocity analysis method based on the CFP technology has been presented in which the strategy of the top-down layer stripping approach are adapted to avoid the difficult of the selecting reduce .The proposed method has a advantage that the travel time errors obtained from the DTS panel are defined directly in time which is the difference with the method based on common image gather in which the residual curvature measured in depth should be converted to travel time errors.In the proposed migration velocity analysis method, the four aspects have been improved as follow:? The new parameterization of velocity model is provided in which the boundaries of layers are interpolated with the cubic spline of the control location and the velocity with a layer may change along with lateral position but the value is calculated as a segmented linear function of the velocity of the lateral control points. The proposed parameterization is suitable to updating procedure.? The analytical formulas to represent the travel time errors and the model parameters updates in the t-p domain are derived under local lateral homogeneous. The velocity estimations are iteratively computed as parametric inversion. The zero differential time shift in the DTS panel for each layer show the convergence of the velocity estimation.? The method of building initial model using the priori information is provided to improve the efficiency of velocity analysis. In the proposed method, Picking interesting events in the stacked section to define the boundaries of the layers and the results of conventional velocity analysis are used to define the velocity value of the layers? An interactive integrate software environment with the migration velocity analysis and prestack migration is built.The proposed method is firstly used to the synthetic data. The results of velocity estimation show both properties and efficiency of the velocity estimation are very good.The proposed method is also used to the field data which is the marine data set. In this example, the prestack and poststack depth migration of the data are completed using the different velocity models built with different method. The comparison between them shows that the model from the proposed method is better and improves obviously the quality of migration.In terms of the theoretical method of expressing a multi-variable function by products of single-variable functions which is suggested by Song Jian (2001), the separable expression of one-way wave operator has been studied. A optimization approximation with separable expression of the one-way wave operator is presented which easily deal with the lateral change of velocity in space and wave number domain respectively and has good approach accuracy. A new prestack depth migration algorithm based on the optimization approximation separable expression is developed and used to testing the results of velocity estimation.Secondly, according to the theory of the seismic wave reflection and transmission, the change of the amplitude via the incident angle is related to the elasticity of medium in the subsurface two-side. In the conventional inversion with poststack datum, only the information of the reflection operator at the zero incident angles can be used. If the more robust resolutions are requested, the amplitudes of all incident angles should be used.A natural separable expression of the reflection/transmission operator is represented, which is the sum of the products of two group functions. One group function vary with phase space whereas other group function is related to elastic parameters of the medium and geological structure.By employing the natural separable expression of the reflection/transmission operator, the method of seismic wave modeling with the one-way wave equation is developed to model the primary reflected waves, it is adapt to a certain extent heterogeneous media and confirms the accuracy of AVA of the reflections when the incident angle is less than 45'. The computational efficiency of the scheme is greatly high.The natural separable expression of the reflection/transmission operator is also used to construct prestack elastic inversion algorithm. Being different from the AVO analysis and inversion in which the angle gathers formed during the prstack migration are used, the proposed algorithm construct a linear equations during the prestack migration by the separable expression of the reflection/transmission operator. The unknowns of the linear equations are related to the elasticity of the medium, so the resolutions of them provided the elastic information of the medium.The proposed method of inversion is the same as AVO inversion in , the difference between them is only the method processing the amplitude via the incident angle and computational domain.

民众社会风险认知的影响因素及作用机制

Risk perception is one of important subjects in management psychology and cognitive psychology. It is of great value in the theory and practice to investigate the social risk events that the public cares a lot especially in this social transition period. Furthermore, this study explored the factors that influence the risk perception and the results caused by risk perception. A survey including 30 hazards and 8 risk attributes was designed and distributed to about 3, 200 residents of 8 districts, Beijing. The major findings are listed as following： Firstly, combining the methods of system science and psychology, GAE program was used to indentify 7 groups of social risk events, such as national safe, government management, social stability, general mood of society, economic and finance, resources and environment & daily life problems. This study provided substance for the following studies and it was also a new attempt in research method which is of certain reference value for the related researches. Secondly, a scale of societal risk perception was designed and 2 factors were identified (Dread Risk & Unknown Risk). Reliability analysis, EFA and CFA show the reliability and validity of the societal risk questionnaire is good enough. The investigation using this scale showed that older participants and higher socioeconomic status perceived the societal hazards to be more threatening than did younger participants and lower socioeconomic status. However, there is no gender difference. Thirdly, structural equation model was used to analyze the influence factors and mechanism of societal risk perception. Risk taking, government support and social justice could influence societal risk perception directly. Government support moderated the relationship between government trust and societal risk perception. Societal risk perception influenced life satisfaction, public policy preferences and social development belief. Multi-group analysis was used to find out that the participants who have different socioeconomic status express different mechanism. Fourthly, the result of the research was used to explore the risk event of 2008 Olympic game. The results showed that government support and preparation of Olympic game influenced societal risk perception directly. Preparation moderated the relationship between government trust and risk perception. Risk perception influenced worry, effect of Olympic game and belief of successl. This result proved that risk perception could be used as an indicator. The indictor of risk perception was used to identify the characteristics of higher risk perception group. Finally, suggestions to the related decision were provide to the government.

组织中的规则行为：合法性、个体差异的认同-内化作用

This study employed the compliance, identification, and internalization model of attitude change to explore the mechanism of rule-following behaviors in organizations. The objectives of this study were to examine the effects of individual utilitarianism and formalism on rule compliance, deference and rule-breaking behaviors, and the relationships between legitimacy, organizational identification, and value internalization. I surveyed 262 employees from a high-tech corporation in Beijing. After Confirmative Factor Analysis, Regression Analysis, and Structural Equation Modeling, I summarized main conclusions as follow. First, rule legitimacy and organizational identification have different effects on different rule behaviors. Perceived rule legitimacy and organizational identification have direct positive effect on rule deference. But the effects of legitimacy on rule-compliance and rule-breaking are moderated by organizational identification and value internalization. Only under high identification or value congruence with organization, could legitimacy perception predict rule compliance and breaking. Second, individual formalism (IF) has positive effect on rule compliance. IF’s positive effect on rule deference only appear under high value congruence between individuals and organization. Third, organizational identification works as a “valve” in the relationship between individual viewpoints and rule-breaking. Organizational identification turns off the tendency of utilitarianism to break rules, and turns on the tendency of formalism to inhibit rule-breaking. Forth, attitudinal and behavioral facets of utilitarianism and formalism have different influences on rule-following behaviors. Only individuals who are both attitudinal and behavioral formalists show deference to rules, while formalism as behavioral tendency predicts less rule-breaking. Fifth, innovation behaviors coexist independently with compliance and deference to rules. But the division between innovation and rule-breaking is obscure. Organizational identification facilitate both rule following and innovation. Sixth, women comply with rules more than men do, while men break more rules than women do. More aged people develop deeper identification with their organizations, and higher deference to rules. Individuals with higher education are fewer formalists, and accordingly defer to rules less and break more.

7-12岁儿童执行功能与智力的关系

The nature of individual differences among children is an important issue in the study of human intelligence. There are close relation between intelligence and executive functions. Traditional theories, which are based mainly on the factor analysis, approach the problem only from the perspective of psychometrics. However, they do not study the relation of cognition and neurobiology. Some researchers try to explore the essential differences in intelligence from the basic cognitive level, by studying the relationship between executive function and intelligence. The aim of this study was to do the followings 1) to delineate and separate the executive function in children into measurable constructs; 2) to establish the relationship between executive function and intelligence in children; 3) to find out the difference and its neural mechanism between intellectually-gifted and normal children’s executive function. The participants were 188 children aged 7-12 year old. There were 6 executive function tasks. The results were follows: 1) The latent variables analyses showed that there was no stable construct of executive function in 7-10 year old children. The executive function construct of 11-12 year old children could be separated into updating, inhibition and shifting. And they had grown to be more or less the same as adults in the executive function. There were only moderate correlations between the three types of executive function, but they were largely independent of each other. 2) The correlations between the indices of updating, inhibition, shifting and intelligence were different in 7-12 year old children. The older the age, the more the indices were related to intelligence. The updating and shifting were related to intelligence in 7-10 year old children. There were significant correlations between the updating, inhibition, shifting and intelligence in 11-12 year old children. The correlation between updating and intelligence was higher than the correlation between shifting and intelligence. Furthermore, in structural equation models controlling for the three executive functions correlations, updating was highly related to intelligence, but the relations of inhibition and shifting to intelligence were not significant. 3) Intellectually-gifted children performed better than normal children in executive function tasks. The neural mechanism differences between intellectually gifted and average children were indicated by ERP component P3. The present study helps us to understand the relationship between intelligence and executive function; and throws light on the issue of individual differences in intelligence. The present results can provide theoretical support for the development a culture-free intelligence test and a method to promote the development of intelligence. Our present study lends support to the neural efficient hypothesis.

An empirical equation for the calculation of retention time with extrapolation of temperature in gas chromatography

An empirical equation is proposed to accurately correlate isothermal data over a wide range of temperature With the equation ln k = A* + B*/T-lambda the retention times of different solutes tested on OV-101, SE-54 and PEG 20M capillary columns have been achieved even when lambda is assigned a constant value of 1.7 Comparison with ln k = A + B/T and in k = c + d/T+ h/T-2, shows that the proposed equation is of higher accuracy and is applicable to extrapolation calculation, especially from data at high temperature to those at low temperature. Parameters A* and B* as well as A and B are also discussed. The linear correlation of A* and B* is weaker than that of A and B.