Non-Darcian flow to a well in an aquifer–aquitard system

In this study, we use a linearization procedure and a finite difference method to solve non-Darcian flow to a well in an aquifer–aquitard system. The leakage effect is considered. Flow in the aquifer is assumed to be non-Darcian and horizontal, whereas flow in the aquitard is assumed to be Darcian and vertical. The Izbash equation [Izbash SV. O filtracii V Kropnozernstom Materiale. USSR: Leningrad; 1931 [in Russian]] is employed to describe the non-Darcian flow. The wellbore storage is also considered in this study. An approximate semi-analytical solution has been obtained by the linearization procedure, and a numerical solution has been obtained by using a finite difference method. The previous solutions for Darcian flow case and non-Darcian flow case without leakage can be described as special cases of the new solutions. The error caused by the linearization procedure has also been analyzed. The relative error caused by the linearization procedure is nearly 100% at early times, and decreases to zero at late times. We have also compared the results in this study with Wen et al. [Wen Z, Huang G, Zhan H. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. J Hydrol, 2008d [in revision]] in which the leakage effect is not considered, and Hantush and Jacob [Hantush MS, Jacob CE. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union 1955;36(1):95–100] who investigated a similar problem in Darcian flow case. The comparison of this study and Wen et al. (2008d) indicates the dimensionless drawdown in the aquifer with leakage is less than that without leakage, and the leakage has little effect at early times. The comparison between the results of this study and that of Hantush and Jacob (1955) indicates that the dimensionless drawdown in the aquifer for non-Darcian flow is larger at early times and smaller at late times, than their counterparts for Darcian flow. A larger dimensionless non-Darcian conductivity k_D results in a smaller dimensionless drawdown in the aquifer at late times, and leads to a larger dimensionless drawdown in the aquifer at early times. A smaller dimensionless leakage parameter B_D results in a smaller drawdown at late times, and the leakage does not affect the early-time drawdown. The analysis of the dimensionless drawdown inside the well has also been included in this study when the wellbore storage is considered.     

Plain strain problem of poroelasticity using eigenvalue approach

A plain strain problem of an isotropic elastic liquid-saturated porous medium in poroelasticity has been studied. The eigenvalue approach using the Laplace and Fourier transforms has been employed and these transforms have been inverted by using a numerical technique. An application of infinite space with concentrated force at the origin has been presented to illustrate the utility of the approach. The displacement and stress components in the physical domain are obtained numerically. The results are shown graphically and can be used for a broad class of problems related to liquid-saturated porous media.     

饱和土中圆柱形衬砌对瞬态弹性波的散射

基于Biot波动理论,运用Laplace变换和波函数展开法,得到瞬态弹性波入射条件下饱和土体及圆柱形衬砌的位移应力表达式.利用饱和土体与衬砌结构的连续条件和衬砌结构内边界上的应力自由条件确定表达式中的未知系数.利用Laplace逆变换的数值方法给出了问题的数值解.研究了衬砌结构的动应力集中系数的波型特性及材料剪切模量和衬砌厚度对动应力集中系数的影响.结论表明随着阶数n的增大波型明显衰减;土体较衬砌结构软时动应力集中系数越大;衬砌结构厚度越大动应力系数越小.     

裂缝性致密油藏直井体积改造产能评价模型

针对裂缝性致密油藏,基于拉普拉斯变换及Stehfest数值反演, 建立了一种可用于直井体积改造产能评价的半解析两区复合模型,模型内区包含有限条无限导流水力裂缝,外区是经典的Warren-Root双重介质系统. 并分析了导压系数比α、裂缝传导率比β、储容比ω、窜流系数λ以及改造半径r_eD等参数敏感性,绘制了产量递减图版。结果表明：从产量递减曲线,可以看出体积改造直井产能遵循“L”形递减规律;导压系数比越大,初期产量越高;裂缝传导率比对整个生产周期的产能都有影响,裂缝传导率比越大,单井产量越高,同时还会伴有明显的复合边界流特征;储容比和窜流系数分别影响双重介质基质-裂缝系统窜流发生的程度和时间;内区人工主裂缝条数越多或改造渗透率越大,复合边界流越明显,产能也越高,这说明改造程度与改造体积对产能的增加都很重要,应注意两者的合理优化。矿场实例验证了该模型在裂缝性封闭边界油藏直井多次压裂改造以及裂缝性致密油藏直井体积改造方面的适用性和实用性。     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.     

土壤中溶质运移的数学模型及其解析解

首先给出了非均匀土壤中考虑水动力弥散尺度效应的一维溶质运移两区模型.然后在初始浓度为零,半无限一维空间内第一类边界条件下,推导出了可动区和不动区溶质浓度分布Cm(x,t),Cim(x,t)的解析表达式.     

Solution of the unsaturated soil moisture equation using repeated transforms

An alternative method of solution for the linearized ‘theta‐based’ form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ξ. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis‐equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi‐analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd.     

Modeling nitrogen–carbon cycling and oxygen consumption in bottom sediments

A model framework is presented for simulating nitrogen and carbon cycling at the sediment–water interface, and predicting oxygen consumption by oxidation reactions inside the sediments. Based on conservation of mass and invoking simplifying assumptions, a coupled system of diffusive–reactive partial differential equations is formulated for two-layer conceptual model of aerobic–anaerobic sediments. Oxidation reactions are modeled as first-order rate processes and nitrate is assumed to be consumed entirely in the anoxic portion of the sediments. The sediments are delineated into a thin oxygenated surface layer whose thickness is equal to the oxygen penetration depth, and a lower, but much thicker anoxic layer. The sediments are separated from the overlying water column by a relatively thin boundary layer through which mass transfer is diffusion controlled. Transient solutions are derived using the method of Laplace transform and Green’s function, which relate pore-water concentrations of the constituents to their concentrations in the bulk water and to the flux of decomposable settling organic matter. Steady-state pore-water concentrations are also obtained including expressions for the extent of methane saturation zone and methane gas flux. A relationship relating the sediment oxygen demand (SOD) to bulk water oxygen is derived using the two-film concept, which in combination with the depth-integrated solutions forms the basis for predicting the extent of oxygen penetration in the sediment. Iterative procedure and simplification thereof are proposed to estimate the extent of methane saturation zone and thickness of the aerobic layer as functions of time. Sensitivity of steady-state solutions to key parameters illustrates sediment processes interactions and synergistic effects. Simulations indicate that for a relatively thin diffusive boundary layer, d, oxygen uptake is limited by biochemical processes inside the sediments, whereas for a thick boundary layer oxygen transfer through the diffusive boundary layer is limiting. The results show an almost linear relationship between steady-state sediment oxygen demand and bulk water oxygen. For small d methane and nitrogen fluxes are sediment controlled, whereas for large d they are controlled by diffusional transfer through the boundary layer. It is shown that the two-layer model solution converges to the one-layer model (anaerobic layer) solution as the thickness of the oxygenated layer approaches zero, and that the transient solutions approach asymptotically their corresponding steady-state solutions.     

基于光流校正的复杂地形区多时相遥感影像配准

几何配准是影像后续处理的重要前提,是遥感信息处理领域研究的热点之一.复杂地形区多时相遥感影像的高精度配准一直是难以突破的难题,光流估计法通过逐像素位移增量解算为此提供了可行的解决思路,但光流法对地物变化异常敏感,经常导致计算的光流场及配准影像存在异常.为此,本文提出一种基于光流校正的复杂地形区多时相遥感影像配准方法,采...     

基于Laplace法的磁性球体参数确定

解析信号法被广泛应用于磁性目标平面位置确定中,然而,数值计算表明:斜磁化情况下,解析信号模极大值与磁性目标中心平面位置之间存在较大的偏差,最大可达探测深度的30%,从而制约了该方法在航空磁测或水深较深区域的应用.从理论上推导了磁性球体磁异常经拉普拉斯算子运算后信号(简称"拉普拉斯信号")表达式,分析了其具有的物理性质,在此基础上,提出采用Laplace法确定磁性目标中心平面位置,当地磁场与磁化强度倾角相同且大于30°时,仿真计算的磁性球体平面位置误差小于深度的4.3%,大大提高了平面位置的计算精度.此外,还给出了磁性目标的深度和磁性参数的计算方法.仿真结果表明,当磁性球体空间位置确定较为准确时,计算出的磁性球体空间位置与磁性参数和实际值较为相符.