考虑流固耦合效应的重力坝水力劈裂模拟

裂缝的高压水力劈裂是混凝土高坝安全评估的重要部分,研究其过程中的流固耦合作用是准确预测在各种情况下裂纹扩展路径和危险程度的关键.该文利用扩展有限元法在模拟裂纹扩展方面的优势,对大坝的裂纹进行水力劈裂模拟研究.裂纹中的水压分布模型采用Brühwiler和Saouma水力劈裂试验的成果,体现了水压和裂纹宽度的耦合关系,给出了扩展有限元在裂纹面上施加水压力荷载的实施方法,对一典型重力坝裂纹的水力劈裂进行了数值模拟分析.研究结果表明:采用扩展有限元法模拟水力劈裂,克服了常规有限元法存在的缺点,裂纹扩展时不用重新划分网格,裂纹的实时宽度可以由加强节点的附加自由度得到,裂纹面上水压的施加也变得简单易行.当考虑裂纹内的流固耦合效应时,裂纹的扩展路径相比不考虑耦合效应时的扩展路径(均布全水头水压),扩展角变大,扩展距离变短.     

应用模糊综合评判方法优选水力压裂井

考虑到水力压裂井压裂效果影响因素之间的关系复杂,且各影响因素本身具有模糊性,这些因素很难用常规方法量化研究,尝试应用模糊综合评判的方法进行水力压裂井优选.通过对影响压裂效果的各个因素进行分析,优选出生产压差、含水率、压前增油量、孔隙度、渗透率、小层有效厚度、加砂量等7个主要因素,并应用层次分析法得到各个影响因素的权重,最后采用模糊综合评判方法对水力压裂井进行评估,最终判定其是否适合压裂并对压裂井进行优选,现场实际应用表明,该方法可以提高现场的工作效率和选井的客观性、准确性.     

煤层压裂裂缝三维延伸模拟及产量预测研究

针对煤层气井的压裂特点和产出机理,综合应用流体力学、线弹性断裂力学、传热学、计算数学和软件工程等方面的知识,提出了煤层压裂裂缝三维延伸模型和产量动态预测模型,其中裂缝三维延伸模型考虑了煤层、上下遮挡层之间的地应力和岩石力学参数变化的影响,产量动态预测模型考虑了煤层气先解吸扩散后渗流入井的产出机理。在此基础上研制了煤层气井三维压裂优化设计软件,并通过实例计算验证了其实用性和可靠性。     

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.     

Saturated-unsaturated flow in a fractured unconfined aquifer

Saturated-unsaturated flow is investigated in an unconfined aquifer containing a distribution of fractures such that on some macroscopic scale there can be defined a smooth averaged hydraulic conductivity. After constructing the conditions which relate the hydraulic properties between the unsaturated and saturated zones, it is shown that the flow in the unsaturated zone is essentially vertical. Below the water table the macropores are conduits for groundwater and the flow has a large horizontal component. Some important implications on previous models is discussed.     

Maximum-likelihood adjoint-state finite-element estimation of groundwater parameters under steady- and nonsteady-state conditions

A method is presented for estimating the hydraulic parameters of groundwater flow models under steady- and nonsteady-state conditions. The estimation problem is posed in the framework of maximum-likelihood theory by means of a log-likelihood criterion that includes prior estimates of the parameters. To allow for an incomplete knowledge of the covariances of the prior head and parameter errors, these covariances are expressed in terms of a few unknown statistical parameters that may be estimated jointly with the hydraulic parameters. Computational efficiency is achieved by evaluating the gradient of the estimation criterion with an adjoint-state finite-element scheme and using a combination of conjugate-gradient algorithms, coupled with Newton's method for determining the step size to be taken at each iteration. Model structure identification criteria developed in the time-series literature (all of which utilize the maximum-likelihood concept) are shown to be useful for selecting the best way to parametrize a groundwater flow region when a number of alternative schemes of parametrization are given. The paper also demonstrates the potential utility of the proposed estimation method for the optimum design of space-time measurement networks. A case study dealing with three-dimensional flow in a multiaquifer system is briefly discussed.     

The pressure distribution around a growing crack

Exact solutions of the problem of the pressure distribution around an ideal hydraulic fracture are derived. The crack propagates in a permeable porous medium following a square-root growth law. The case of the penetration of the fracturing fluid into a reservoir is also considered.     

垂直裂缝气井生产动态预测及参数识别

为了摆脱分析解释水力压裂裂缝参数时选择图版的繁复工作和克服人为的误差,在引入非达西因子的基础上,考虑裂缝导流能力在生产过程中的变化,提出了垂直裂缝气井中真实气体在地层-裂缝系统中非达西渗流的数学模型和生产动态预测模型,建立了识别垂直裂缝气井水力裂缝参数的生产历史自动拟合模型,并给出了数值解法,为认识和了解气层、分析和评估气井压裂施工质量,提供了准确可靠的方法。     

Hydraulic fracturing modeling using the enriched numerical manifold method

Recent attempts to solve rock mechanics problems using the numerical manifold method (NMM) have been regarded as fruitful. In this paper, a coupled hydro-mechanical (HM) model is incorporated into the enriched NMM to simulate fluid driven fracturing in rocks. In this HM model, a “cubic law” is employed to model fluid flow through fractures. Several benchmark problems are investigated to verify the coupled HM model. The simulation results agree well with the analytical and experimental results, indicating that the coupled HM model is able to simulate the hydraulic fracturing process reliably and correctly.     

垂直裂缝井试井分析模型和方法

根据压裂井的流动机制,综合考虑井筒储存、裂缝壁面污染和各种边界条件,通过组合线性流模型与有效井径模型,建立了垂直裂缝井试井分析的新模型,提出了确定垂直裂缝井有效井径的方法,给出了有效井径随裂缝长度、裂缝导流能力和裂缝表皮系数的变化关系．该模型形式简明,曲线完整,计算速度快,可满足实时计算和快速响应的试井解释要求．以实测的压力或产量为拟合目标函数,建立了识别地层和水力裂缝参数的最优化模型,提出了综合应用逐步线性最小二乘法和约束变尺度法的垂直裂缝井试井分析自动拟合方法,并通过算例说明了该方法的准确性和可靠性．应用情况表明,该技术可科学合理地分析评估压裂施工质量,指导并改进压裂设计,提高压裂设计水平和施工效果．     

Simple stochastic models of cracks

The stochastic Markov models describe various natural and technological processes. They are often used in rather diverse areas. The Markov models are distinguished with discrete time and relatively few states. In concrete cases, such models allow us to carry out effective calculations. In the article are considered some special models with two, four and eight states. The processes are simulated that are connected with hydraulic fracturing and wave front development.     

Coupled SPH and Phase Field method for hydraulic fracturing

Simulation of fracture initiation and propagation using classical mesh-based methods involves computationally expensive operations for pre-processing and (adaptive) remeshing of complex geometries. To overcome the difficulties we propose to use a Smoothed Particle Hydrodynamics (SPH) method to model hydraulic fracturing. SPH is a meshless Lagrangian method highly suitable for large deformations [1]. The present contribution discusses a numerical approach to model fractures initiation and propagation, by coupling SPH with the Phase Field method [2]. The proposed hybrid method overcomes the instability problems that can present SPH due to kernel incompleteness. We first validate the proposed model with a stationary elastic fracture and compare the results with the classical SPH to the SPH-Phase Field approach. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Recovery of an Anisotropic Conductivity in Groundwater Modelling

In order to model groundwater flow effectively, one is faced inevitably with the problem of suitably estimating the various subsurface parameters in the differential equations governing the flow from measurements, over time, of the piezometric head at various well sites, together with certain ancillary data. A new method is presented that allows for the estimation of an anisotropic hydraulic conductivity as the unique global minimum of a convex functional.     

Phase Field Approximation of Dynamic Brittle Fracture

The numerical assessment of fracture has gained importance in fields like the safety analysis of technical structures or the hydraulic fracturing process. The modelling technique discussed in this work is the phase field method which introduces an additional scalar field. The smooth phase field distinguishes broken from undamaged material and thus describes cracks in a continuum. The model consists of two coupled partial differential equations - the equation of motion including the constitutive behaviour of the material and a phase field evolution equation. The crack growth follows implicitly from the solution of this system of PDEs. The numerical solution with finite elements can be accelerated with an algorithm that performs computationally extensive tasks on a graphic processing unit (GPU). A numerical example illustrates the capability of the model to reproduce realistic features of dynamic brittle fracture. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dimension Estimates of Earthquake Epicentres and Hypocentres

Summary. We use the Hill estimator to estimate the correlation dimension of epicentres and hypocentres from four earthquake catalogues: Wellington micro earthquakes, New Zealand catalogue, Kanto micro earthquakes, and the Japanese (JMA) catalogue. We wanted to determine if the fracturing process is fractal, and whether it is different in the four selected regions. We found that the spatial pattern of tabulated shallow events in Japan is more tightly clustered than in New Zealand, while for deeper events the spatial pattern is similar. In both regions, tabulated shallow events are more clustered than tabulated deeper events. It may appear that if one had a sufficiently large amount of data (enabling one to look at sufficiently small interpoint distances), the dimension of the epicentres and hypocentres would appear to be two or three, respectively; however, this may not be a true reflection of the fracturing process. Estimates that indicate that the fracturing tends ultimately to fill the entire space are probably caused by measurement errors in hypocentre locations. Similarly, for large values of interpoint distances, the power law exponent tends to be underestimated because of the boundary effect. When these two effects are sufficiently severe, they tend to merge, and it is difficult to determine power law exponents. These biases are not peculiar to the estimation procedure we have used. Received June 29, 1995; second revision received March 24, 1997; third revision received November 24, 1997     

Hydraulic fracturing with a simplified fluid model and XFEM

In hydraulic fracturing, the pressure exerted by the fracking fluid onto the surrounding solid, is typically obtained from solving the Reynolds equation. This is not always robust and leads to a complex behaviour at the crack front (toughness or viscous regimes). In the presented work, the Reynolds equation is replaced by a simplified fluid model, where pre-defined pressure distributions are assumed which lead to a simpler and robust coupled problem. The surface integration of the fluid pressure onto the surrounding solid is outlined without any limitations on the distributions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

压裂效果预测方法研究

预测油井压裂效果对实施增产措施决策意义重大.应用科学的数学统计方法建立了大庆油田采油二厂某区块压裂措施库,采用灰色关联方法分析影响压裂效果的主要因素,应用多元回归方法、逐步回归方法、人工组合回归方法分别建立预测模型,进而建立起适用于不同压前含水和液量级别的预测图版,增油量绝对误差在1.5t以内的井的符合率达到77.4%.方法可操作性强,预测符合率较高,可用于指导优化压裂工艺,提高剩余储量动用程度.     

Groundwater management: Waiting for a drought*

In this article we present a stylized model for optimal management of an unconfined groundwater resource when the threat of drought exists. The drought is modeled as a stochastic event that hits at an uncertain date and two benchmark management policies are investigated: (a) A policy of optimal dynamic management ignoring the threat of drought; and (b) an economically optimal policy that accounts for the threat of a drought. We show that the optimal predrought steady‐state equilibrium stock size of groundwater under policy b is larger than that under policy (a) Furthermore, we show that an increase in the probability of a drought gives rise to two counteracting effects: One in the direction of a larger predrought steady‐state equilibrium stock size (a recovery effect) and one in the direction of a lower predrought steady‐state equilibrium stock (an extinction effect). We find that the recovery effect dominates the extinction effect. Recommendations for Resource Managers: We analyze two groundwater extraction policies that can be used when a threat of drought exists: (a) Dynamic optimal management ignoring the threat of drought; and (b) dynamic optimal management taking the threat of drought into account. We show that the predrought steady‐state equilibrium stock size of water should be larger under the policy (b) than under policy (a). This conclusion has three implications for resource managers:

• Current groundwater management should take future extraction possibilities into account.

• A resource manager ought to take the threat of drought into account in groundwater management.

• A buffer stock of water should be built‐up before the drought to be drawn upon during the event.

     

关于Boussinesq方程Barenblatt幂级数解的注记

通过幂级数展开的方法推求得出了Barenblatt幂级数解的各项系数之间的递推公式(对半无限长多孔介质中地下水流动的Boussinesq方程的自相似解,在边界水头随时间幂函数变化的条件下,Barenblatt（1952）得到了一个幂级数解,但他仅仅列出了其前3项的系数,既没有给出整个幂级数解所有系数的递推关系式,也没有证明该幂级数解的收敛性．),并对该级数的收敛性进行了证明,同时对解的实际应用作了讨论．这些研究结论易于理解,方便工程技术人员应用于流域水文学和基流研究及解决农业排水等实际问题．