一类抛物型方程反问题的数值解法

讨论了一类二阶抛物型方程反问题的数值解法。应用拟解法的思想,把原问题分解为一系列适定的正问题和一个不适定的线性代数方程组。对于相应的正问题,证明了解连续依赖于初始分布,由此得到了在时刻的稳定性估计。使用古典欧拉差分格式求解正问题和用截断奇异值分解法求解病态方程组。数值结果显示数值解与理论解吻合很好。     

非线性抛物型方程反问题的一种新算法

利用反问题新算法—时间域正演反演法研究非线性抛物型方程的逆时反问题。该方法处理反问题的主要思路是先求解相对应的正问题,获得解在特定时间网格处的近似值;然后构造一个合适的全纯映射,在象空间中获得解在时间网格对应点处的近似值;最后利用解析函数的唯一延拓性质实现反问题的逆时间反演。数值模拟例子说明了方法的有效性。     

Effective Permeability Estimation for 2-D Fractal Permeability Fields

Hurst exponents (H) of the distribution of permeability at micro (pore) scale were measured as close to 0.1 for sandstone and limestone samples. Based on these observations and previously reported H values for field scale permeability distribution ranging between 0.6 and 0.9, square permeability fields at different scales varying between 1 and 100 ft were generated for the H values of 0.1, 0.5, and 0.9. The study also considered different permeability fields and number of grids ranging from 10 to 500 md and from 8 × 8 to 64 × 64, respectively. The effective permeability of fractally distributed 2-D fields was calculated using different averaging techniques and compared to the actual (equivalent) permeability obtained through numerical simulation. The geometric mean and power averaging techniques as well as the perturbation theory yielded the most reasonable agreement between the actual and calculated effective permeabilities. The accuracy of these techniques increases with increasing average model permeability. It was also observed that as the H decreases, the permeability values obtained were higher than the actual values. Two extreme values of the number of grids (8 × 8 and 64 × 64) yielded the highest error percentages. Thus, the optimum number of grids was found to be 16 × 16 and 32 × 32 depending on the average permeability of the model. The exponent of the power law model was correlated to the fractal dimension of the permeability field for 8 × 8 and 64 × 64 grids. While a good correlation exists for 8 × 8 number of grids, no correlation was obtained for 64 × 64. Hence, an alternate model was proposed for 8 × 8 grids but for grid numbers higher than 32 × 32, no technique was found suitable for averaging of the fractal permeability fields.     

一种基于Kozeny-Carmen方程改进的渗透率预测新方法

在计算复杂孔隙结构储层渗透率时,常规采用的孔渗指数方法或流动单元分类方法几乎很难准确评价渗透率。针对这一问题,本文提出一种引入修正迂曲度因子的改进的Kozeny-Carmen方程渗透率计算新方法。首先引入迂曲度因子修正Kozeny-Carmen方程,迂曲度因子可以表达为孔隙度与岩电参数的函数;然后对改进的Kozeny-Carmen方程进行推演变换,得到新的流动单元指数,能够更好地将储层进行分类;最后利用自适应神经模糊推理系统建立取心段岩心渗透率与测井曲线的模型,并将此模型应用到非取心段的渗透率评价中。岩心渗透率与预测渗透率的对比验证了该方法的正确性与有效性,且渗透率计算精度较常规孔渗指数方法和流动单元分类方法有较大提高。该方法在南海西部海域莺歌海盆地东方气田储层评价中应用效果良好。     

Error Estimates for a Time Discretization Method for the Richards' Equation

We present a numerical analysis of a time discretization method applied to Richards' equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is based on an implicit Euler time discretization scheme and includes a regularization step, combined with the Kirchhoff transform. Convergence is shown by obtaining error estimates in terms of the time step and of the regularization parameter.     

Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses simple examples to illustrate the clear differences between these two methods     

蛟路江河口海域污染非线性扩散数值解法

在分析蚊路江河口海域流态和污染规律的基础上,用有限元解法对盐淡水混合河口海域的污染非线性扩散,进行数值分析计算,并对数值解的稳定性进行了分析探讨,通过计算值与实测值的比较,验证了该解法具有较好的精度。     

一类非线性对流扩散问题的差分-流线扩散法

求解了一类非线性对流扩散问题，用差分—流线扩散法建立了差分格式，给出L^2模误差估计。讨论了其收敛性。     

基于GDS系统的非饱和土渗透试验方法研究

非饱和土渗透系数的测量,是研究非饱和土渗透特性的重要方法,但由于渗透系数测量困难,多数研究仍然以理论为主。为试验研究非饱和土渗透系数,利用GDS系统,研究非饱和土渗透系数测量的试验方法,研究结果表明：基于GDS系统的非饱和土渗透试验细化了试验阶段,简化了试验过程,得到有效的试验数据,为试验研究非饱和土渗透系数提供了研究思路。     

低渗透油藏压裂水平井产能计算方法

针对低渗透油藏存在启动压力梯度和压敏效应的问题,在前人研究的基础上,根据水电相似原理,应用等值渗流阻力法,建立了压裂水平井补孔和不补孔两种情况下的产能公式,并且与其他压裂水平井产能公式与数值模拟结果进行了对比。对比结果表明:如果水平井压裂后补孔,建议使用本研究建立的公式;如果压裂后不补孔,建议使用郎兆新的计算公式。建立的压裂水平井产能公式,对目前低渗透油藏利用水平井进行开发具有重要的理论和现实意义。     

确定渗透系数的地下水位计试验法

以摆纪磷石膏堆场为例,应用空压机对磷石膏含水层进行提水试验,采用地下水位计方法求解磷石膏渗透系数。实例研究表明,结果与室内试验一致,且该方法求解简单、速度快、精度高,既适用于潜水含水层渗透系数的求解,又可推广到承压含水层渗透系数的求解,有着较好的实际应用价值。     

Identification of the diffusion coefficient for a semi-linear hyperbolic-parabolic problem with discontinuous nonlinear terms

Numerical computations concerning geochemical processes in porous media require a knowledge of the values of the macroscopic parameters. In the context of the interpretation of leaching tests one such parameter is the apparent macroscopic diffusivity. In this paper, a mathematical model for dissolution in the presence of diffusion is considered. It is shown that the constant diffusion coefficient can be identifiable when the time integral of the flux is known. Moreover, a practical algorithm for computing the diffusion coefficient is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Anisotropic Variation Law of Rock Permeability with the Burial Depth of Limestone

Permeability tensors of both macrofracture and microfracture systems were measured progressively along the depth of limestone formations at severed sites. It was found that the principal permeability values KX, Ky and Kz in these permeability tensors all decrease simultaneously and logarithmically with depth. However, the limestone aquifers are composed of an upper region where the larger permeability ellipsoid is upright or prolate and characterized by Kz>Kx and Kz>Ky, a transitional zone, and a lower zone whose smaller permeability ellipsoid is horizontal or oblate and characterized by KZ相似文献   

利用斯通利波评价复杂岩性储层渗透性

针对海拉尔盆地贝尔凹陷区复杂岩性储层,进行了利用斯通利波估算储层渗透率的应用研究,并把斯通利波渗透率与岩心渗透率和核磁处理渗透率进行了对比。对比结果表明,可依据获得的斯通利波渗透率曲线进行储层的有效性划分。     

基于粒度控制的复杂储层渗透性建模方法

岩石颗粒大小反映了沉积岩结构的主要特征,是岩石岩性的主要评价指标,同时也是影响沉积物渗透性的主要因素。沉积环境在纵向上表现出来的差异性,使得粒序控制下的地层渗透性在纵向上也表现出非均质性。为了精细地描述由于粒度大小造成的渗透率的非均质性,本文首先结合岩心粒度分析资料,分析了研究区粒度大小对物性影响的规律,利用自然伽马、中子、密度、声波曲线,通过测井地质分析提取敏感参数,建立了粒度计算模型;然后以粒度为指标,建立了不同粒度大小条件下的渗透率计算模型。通过现场资料的处理及其与岩心资料的对比,认为这种渗透率建模方法能够较好地反映沉积物粒度对岩石渗透性的控制作用,能够更加精确地描述复杂岩性地层渗透率的非均质性特征,从而可为地质开发研究提供更为准确的渗透率剖面。     

低渗透油藏菱形反九点井网不等缝长优化研究

在低渗透油藏开发中广泛使用菱形反九点井网,但针对不同位置生产井及注水井的裂缝缝长配比关系还缺少广泛深入的研究。基于长庆油田某低渗透油藏参数,建立了数值模拟模型,在菱形反九点井网中分别设置不同的边井、角井和注水井裂缝穿透比,研究不同裂缝配置模式对水驱开发效果的影响。流线模拟及数值模拟计算结果表明,在注水开发中,注水井缝长是影响油田产液量及水驱效果的关键因素;边井裂缝较角井裂缝更易见水,对油田综合含水影响较大,在菱形反九点井网中需要进行不等缝长优化设计;边井裂缝缝长对水驱效果的影响分为早、中、晚期(Ⅰ、Ⅱ、Ⅲ)曲线段,随着注水井裂缝穿透比增加,早期(Ⅰ)曲线段增长,中期(Ⅱ)曲线段缩短,而晚期(Ⅲ)曲线段变化较小;随着角井裂缝穿透比增加,采出程度逐渐增大,当角井裂缝穿透比较大时,存在“反转”现象;随着注水井裂缝穿透比增加,角井裂缝优化穿透比减小,而边井裂缝优化穿透比增加。该研究成果对于指导低渗透油藏菱形反九点井网裂缝优化设计,提高波及系数和开发效果具有重要的指导意义。     

拟合三参数对数正态分布时第三参数c的优选方法探讨

在地质数据中，许多数据常呈正偏或负偏分布，但并不服从对数或反对娄正态态分布。这时可考虑它们是否服从三参数对数或反对数正态分布。本给出一种估计第三参数ｃ的方法。它可快速、客观、较优地确定此参数，弥补以往凭经验多次选择、反复试算等缺陷，为检验地质数据的统计分布型式，掌握分布规律，从而用于统计预测等提供了方便。     

一类热传导方程多点源反演的唯一性和稳定性

在第一类Dirichlet边界条件下,研究了由表面热流密度来反演热传导方程多点源的唯一性和稳定性。即反演点源个数n、热源强度组合系数αi、点源位置si的唯一性和反演点源位置si的稳定性。利用热变换方法将热传导方程反问题转化为等价的双曲型方程反问题,然后通过分析等价的双曲型方程反问题得到原反问题的唯一性和条件稳定性结论。     

镇泾油田低渗透油藏岩石渗透率应力敏感性研究

对镇泾油田低渗透油藏岩石进行了渗透率应力敏感性实验研究,并对其进行了应力敏感性评价。实验是在一定围压下,通过降低和增加内压的方式完成的,共进行了2个围压下的变内压实验。实验结果和应力敏感性评价结果表明,镇泾油田低渗透油藏不存在渗透率强应力敏感性,在原始地层压力条件下,衰竭式开发对地层的渗透率几乎没有影响,注水开发对地层的渗透率会有一定程度的改善。同时,通过对有效应力定律方程的研究,得出渗透率有效应力系数为常数且值很小,这从机理上解释了镇泾油田低渗透油藏岩石的渗透率对应力不敏感的原因。     

Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling： Porosity-Permeability Relations Revisited

An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations (e.g., porosity-permeability transforms). The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equationswithin those transformations need corrections via residual cumulants. A generalization of this result isthat transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.