致密油藏体积压裂水平井不稳定压力分析

水平井结合体积压裂改造成为目前开发致密油藏的关键技术。考虑到致密油藏多尺度渗流(基质、天然裂缝和水力裂缝)及多种流动机理(启动压力梯度和应力敏感)相互耦合的复杂渗流过程,该文建立了综合考虑致密油藏启动压力梯度和应力敏感的体积压裂水平井不稳定压力分析模型。通过Laplace变换和摄动变换等求解得到了拉氏空间中的井底压力,应用Stehfest数值反演绘制了相应的压力动态响应曲线。研究结果表明:压力响应曲线可以划分为6个流动阶段,模型的退化结果与Ozkan模型一致,验证了该文模型的正确性,并在此基础上进行了影响因素分析。该文研究结果可为致密油藏体积压裂水平井的不稳定压力分析提供一定的理论依据。     

EFFECT OF A MOVING BOUNDARY ON THE FLUID TRANSIENT FLOW IN LOW PERMEABILITY RESERVOIRS

In a low permeability reservoir, the existence of a moving boundary is considered in the study of the transient porous flow with threshold pressure gradient. The transmission of the moving boundary directly indicates the size of the drainage area as well as the apparent influences on the pressure behavior. The nonlinear transient flow mathematical model in which the threshold pressure gradient and the moving boundary are incorporated is solved by advanced mathematical methods. This paper presents some new analytical solutions describing the pressure distribution at a constant rate and the production decline in a constant pressure production with the boundary propagation. It is shown that the greater the threshold pressure gradient, the slower the transmission of the moving boundary, the larger the pressure loss will be, and there is no radial flow in the middle and later phases of the wellface pressure for a well at a constant rate. We have the the maximum moving boundary at a specific drawdown pressure for a low permeability reservoir. The greater the threshold pressure gradient, the smaller the maximum moving boundary distance, the quicker the production decline for a well in a constant pressure production will be. The type curve charts for the modern well test analysis and the rate transient analysis with a moving boundary are obtained and the field test and the production data are interpreted as examples to illustrate how to use our new results.     

低渗透油藏中水平井两相渗流分析

大量实验表明，在低渗透多孔介质中，渗流不再符合线性达西定律，而具有启动压力梯度，本文从Buckley-Leverret不混溶两相渗流驱替理论出发，考虑启动压力梯度的影响，对水平井两相渗流进行分析，得到了椭球形边水油藏中水平井定产时的压力分布公式和定压生产时的产量公式，以及饱和度分布公式。经图示分析得出结论：启动压力梯度不仅增大油藏的生产压差，而且使油藏的无水采收率和水驱采收率减少；增大注入量可以降低启动压力梯度对两相渗流的不利影响，从而提高水驱采收率，因此开发含启动压力梯度油藏，应小井距，大流量，大压差进行注水开发；水平井的两相渗流解析解为数值模拟中水平井的处理提供很好的方法。     

WELL TESTING ANALYSIS FOR HORIZONTAL WELL WITH CONSIDERATION OF THRESHOLD PRESSURE GRADIENT IN TIGHT GAS RESERVOIRS

A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed. The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.     

致密油藏体积压裂水平井变窜流系数模型研究

水平井结合水力压裂技术已经成为高效开发致密油藏的有效手段。该文针对水平井经过压裂后在主裂缝周围形成的微裂缝密度随着到主裂缝的距离递减变化的特点,基于双重介质模型建立了窜流系数随着到主裂缝距离变化的体积压裂水平井线性流动模型,通过引入Airy函数及Laplace变换求得了模型的解析解,运用Stehfest数值反演技术得到了在实空间中的解,最后对定产量生产时的井底压力动态及定井底流压生产时的产能动态进行了分析。研究结果表明:井底压力及产能动态曲线可分为4个流动阶段,基质形状假设为球形及柱状对结果影响不大;窜流系数最大值越大,总系统线性流就发生得越早,双线性流阶段无因次产能就越大;窜流系数最小值越大,双线性流发生的时间越早,而且持续的时间越长,总系统线性流阶段无因次产能越大。研究结果可为致密油藏压力及产能动态的合理分析提供科学依据。     

THE SIMILAR STRUCTURE OF SOLUTIONS IN FRACTAL MUITILAYER RESERVOIR INCLUDING A QUADRATIC GRADIENT TERM

When the classical nonlinear partial differential equations are used to model the fractal reservoir, based on the assumption of low compressibility fluids, the effects of the quadratic gradient term are ignored, which would be questionable for mixed gas reservoirs and low permeability reservoirs. To consider the influence of the wellbore storage, the nonlinear mathematical flow model of the fractal multilayer reservoir is built in this paper, with three kinds of outer boundaries (infinite boundaries, constant pressure boundaries and closed boundaries). Using the Laplace transform method, the solutions for the dimensionless reservoir pressure and the bottom hole pressure in the Laplace space are obtained. An analysis shows that the solutions involve similar structures even for three different kinds of outer boundaries, and can be unified as a continuous fraction. The unified expression would make it more convenient to analyze the formation parameters, which greatly facilitates the development of the well test analysis software.     

THE FLOW ANALYSIS OF FLUIDS IN FRACTAL RESERVOIR WITH THE FRACTIONAL DERIVATIVE

1. INTRODUCTION Chang and Yortsos [1 ]presented the theoretical model for infinite fractal reservoir. Acuna et al. [ 2]explained the fractal characteristic of a naturally fractured geothermal field. Acuna [ 3] reviewed the theoretical background of fractal analysis. They alsodemonstrated the application of various diagnostic techniques for fractal pressure transient analysis as developed by Chang and Yortsos [1 ].Tong[4 ? 7]give the analytical solution of various cases for transient flow…     

THE PRESSURE TRANSIENT ANALYSIS OF DEFORMATION OF FRACTAL MEDIUM

The assumption of constant rock properties in pressure-transient analysis of stress-sensitive reservoirs can cause significant errors in the estimation of temporal and spatial variation of pressure. In this article, the pressure transient response of the fractal medium in stress-sensitive reservoirs was studied by using the self-similarity solution method and the regular perturbation method. The dependence of permeability on pore pressure makes the flow equation strongly nonlinear. The nonlinearities associated with the governing equation become weaker by using the logarithm transformation. The perturbation solutions for a constant pressure production and a constant rate production of a linear-source well were obtained by using the self-similarity solution method and the regular perturbation method in an infinitely large system, and inquire into the changing rule of pressure when the fractal and deformation parameters change. The plots of typical pressure curves were given in a few cases, and the results can be applied to well test analysis.     

Transient flow model and pressure dynamic features of tree-shaped fractal reservoirs

A transient flow model of tree-shaped fractal reservoirs is built by embedding a fracture network simulated by a tree-shaped fractal network into a matrix system. The model can be solved using the Laplace conversion method. The dimensionless bottom hole pressure can be obtained using the Stehfest numerical inversion method. The bi-logarithmic type curves for the trce-shaped fractal reservoirs are thus obtained. The pressure transient responses under different fractal factors are discussed. The factors with a primary effect on the inter-porosity flow regime include the initial branch number N, the length ratio α, and the branch angle θ. The diameter ratio β has a significant effect on the fracture radial flow, the inter-porosity and the total system radial flow regimes. The total branch level M of the network mainly influences the total system radial flow regime. The model presented in this paper provides a new methodology for analyzing and predicting the pressure dynamic characteristics of naturally fractured reservoirs.     

INVESTIGATION OF THE FLOW IN FRACTAL RESERVOIR INCLUDING THE EFFECTS OF QUADRATIC GRADIENT TERM

According to the assumption of slightly compressible fluid, the quadratic gradient term in the nonlinear partial differential equations for the traditional well-test model is usually neglected. The linear partial differential equation is thus established. It is known that neglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flow model for fractal medium is constructed and the quadratic gradient term is considered. The exact solutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in a constant-rate and constant-pressure production for an infinitely large system. This paper addresses the variation of pressure with fluid compressibility coefficient and fractal reservoir parameters. The plots of the typical pressure curves are constructed, and the results can be applied to well-test analysis.     

不同库水消落方式下动水压力型滑坡变形与稳定性响应研究

水库滑坡灾害是大型水库运行调度工作中备受关注的问题.为了科学指导汛期水库运行调度中的滑坡灾害风险防控,基于库水动力作用效应及类型分析,通过大型离心模型试验和数值模拟研究了库水下降诱发滑坡变形破坏机理,重点分析了库水持续性下降、不同间歇期下降、相同间歇期多阶段下降三种消落方式下的滑坡稳定性响应规律.研究表明:在库水下降末...     

压力管道中有压气囊运动的试验研究

为探讨压力管道中滞留气囊运动引起压力振荡的影响因素，更全面地表征气囊运动的瞬态效应，区别于以往简单管道系统末端的无压气囊运动试验，以较为复杂的试验管道系统的有压气囊为研究对象，探讨了不同流量和不同气囊体积条件下气囊运动引起的升压规律。试验结果表明：管道系统流量及气囊体积这两个单因素与气囊通过末端阀门产生的最大升压均不成线性关系，而是成上凸形抛物线关系；末端阀门的开度、气体排出引起的水体流速梯度变化、剩余气囊的缓冲作用三者共同决定最大升压值。     

PRESSURE TRANSIENT ANALYSIS OF HETEROGENOUS RESERVOIRS WITH IMPERMEABILITY BARRIER USING PERTURBATION BOUNDARY ELEMENT METHOD

The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the solution of model is expanded into a series in powers of perturbation parameter. By using the Boundary Element Method (BEM) and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barriers. Finally, the results obtained by perturbation boundary element method is compared with the analytical solution and is available for the transient pressure analysis of arbitrary shaped reservoirs.     

水电站长输水道管流气泡动力特性研究

本文以水电站瞬变过程中调压室漏空压力钢管中的气液两相流作为研究对象，在模型实验的基础上，探讨了气泡对管道水压变化的影响及其数学描述.由流动的连续性，导出了瞬变过程中计算调压室进气流量的公式；引入了气团质点的新概念，将每一时间步长内进入压力管道的空气视为一个质点；发展了用拉格朗日研究固体质点运动的方法研究气团质点在管道中运动的原理和方法；研究了采用Wylie的自由气体——离散模型计算瞬变压力变化过程.数值计算和模型实验数据的对比表明，本文所发展的数学模型能够较好地描述调压室漏空压力钢管中气液两相流的压力变化过程.     

脉动压力及压力梯度对不平整突体空化初生的影响

本文对六种不平整突体在正负压力梯度状况下的初生空化数进行了试验研究和理论分析，并根据气泡动力学方程建立了脉动压力与气泡振荡半径之间的关系，讨论了脉动压力及压力梯度对不平整突体空化初生的影响，试验结果表明，同一突体在负压力梯度状况下的初生空化数高于正压力梯度状况下的初生空化数；对于非流线型突体，在负压力梯度状况下空化初生时的壁面脉动压力强度低于正压力梯度状况下的脉动压力强度，脉动压力峰值约为七至十二倍的脉动压力均方根值。     

贯流式水轮机内部压强变化对鱼体损伤分析研究

鱼类在通过贯流式水轮机流道时会遭遇撞击、压强变化等引发的损伤.本文基于试验和CFD分析方法探究了不同工况下贯流式水轮机全流道压强变化对鱼的损伤机理及阈值.通过试验实现鱼经过水轮机过程中压强变化情况的高精度仿真,研究鱼类在贯流式水轮机内部受压强及压强梯度的影响.试验结果表明:正压状态下加压至最大压强0.68MPa时,对鱼...     

A NUMERICAL PRESSURE TRANSIENT MODEL FOR MULTILAYERED GAS RESERVOIRS WITH PSEUDOSTEADY STATE FORMATION CROSSFLOW

ＮＯＭＥＮＣＬＡＴＵＲＥＡＤｊ=Ａｊ·ｒ2 ｗ(ｋｈ) ｔＣＤｅ =ＴＶｗ2πＴｗｒｗ2 (ｈ) ｔｒＤ =ｒｒｗｐＤｊ=2π(ｋｈ) ｔＴｓｃｐｓｃｑｓｃＴ (Ｐμｚ) ｊ(φ0 - φｊ)ＴａＤ =(ｋｈ) ｔｔａ(ｈ) ｔ(μＣｇ) 0 ｒｗ2ｑＤｊ=ｑｊｑＷＤｊ=(ｋｈ) ｊ(ｋｈ) ｔωｊ=(     

UNSTEADY FLOW OF NON-NEWTONIAN VISCO-ELASTIC FLUID IN DUAL-POROSITY MEDIA WITH THE FRACTIONAL DERIVATIVE

The fractional order derivative was introduced to the seepage flow research to establish the relaxation models of non-Newtonian viscoelastic fluids in dual porous media. The flow characteristics of non-Newtonian viscoelastic fluids through a dual porous medium were studied by using the Hankel transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions were obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation were also resulted. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite dual porous media was studied by using Stehfest's inversion method of the numerical Laplace transform. It shows that the characteristics of the fluid flow are appreciably affected by the order of the fractional derivative.     

水平井分段注采产能模型研究

该文针对面积较小或井场开采条件受限的油气藏提出了采用水平井的分段注采的开发方式,它利用水平井的长井段优势,在一定注采管柱条件下实现水平井分段注采,以达到维持地层能量的目的.利用势能叠加原理推导出了定压边界时不同水平井的井段长度、注采封隔间距下的产能模型,并给出了定注入段的注入压力与生产段的生产流压下的产能关系及沿程流量分布,若要保持注采平衡,只需要给定注入压力和生产井流压中的一个即可由注采平衡为约束条件通过迭代进行求解另外一个压力;研究结果表明,注水井对生产井的跟端和趾端干扰不同,生产井流量分布不对称,且井段越长干扰程度越大;注采井段封隔间距对流量分布具有一定影响,封隔间距越大注入段对生产段的干扰越小;当总井长度一定时,产量与注采压差呈正比关系,且随着生产井段长度增加产量逐渐增加,因此对大位水平井进行配产配注时,需要充分考虑注采压差的限制.     

液流通过节流孔的惯性长的数值研究

该文对初始稳定流开始的液流通过节流孔的过渡过程进行了数值解析计算。压力差为阶跃变化的情况下数值计算结果说明了收缩部的断面积的时间变化减少了收缩部的惯性效果。流量变化时收缩部的断面积也变化，而收缩部的平均流速保持一定，所以收缩部的惯性对系统的动特性没有什么影响，为了迅速地对流量的动特性进行仿真，本文提出了简单易算的等效惯性长公式。理论模型和数值计算结果一致。