低渗透多孔介质渗流动边界模型的解析与数值解

考虑启动压力梯度的低渗透多孔介质非达西渗流模型属于强非线性动边界问题, 分别利用相似变量变换方法和基于空间坐标变换的有限差分方法, 对内边界变压力情况下、考虑启动压力梯度的一维低渗透多孔介质非达西渗流动边界模型进行了精确解析与数值求解研究. 研究结果表明:该动边界模型存在唯一的精确解析解, 且所求得的精确解析解可严格验证数值解的正确性;且当启动压力梯度值趋于零时, 非达西渗流动边界模型的精确解析解将退化为达西渗流情况下的精确解析解. 由求解结果作出的非零无因次启动压力梯度下的地层压力分布曲线表现出紧支性特点, 其与达西渗流模型的有显著不同. 因此, 研究低渗透多孔介质中非稳态渗流问题时, 应该考虑动边界的影响. 研究内容完善了低渗透多孔介质的非达西渗流力学理论, 为低渗透油气藏开发的试井解释与油藏数值模拟技术提供了理论基础.      

变形三重介质低渗透油藏垂直裂缝井的非线性流动分析

不仅考虑低渗透油藏具有启动压力梯度的渗流特征,还考虑应力敏感地层中介质的变形;发展了Cinco-Ley H.提出的有限导流垂直裂缝井双线性流理论,将流体在垂直裂缝与地层中形成的流动划分为两个区域—垂直裂缝中的线性流区域和变形三重介质低渗透油藏中的非线性流区域;由此建立了变形三重介质低渗透油藏有限导流垂直裂缝井的非线性流...     

低渗透煤层气有限导流垂直裂缝井压力动态分析

作为典型的致密多孔介质,煤岩储层已被证实存在启动压力梯度.根据煤层气垂直裂缝井的双线性流动机制,综合考虑启动压力梯度和井筒储存效应的影响,建立了一个新的低渗透煤层气有限导流垂直裂缝井双线性流动数学模型,采用Laplace变换和Stehfest数值反演方法对数学模型进行了求解,并分析了无因次启动压力梯度等参数对无因次井底压力及其导数曲线的影响规律.分析结果表明:典型的低渗透煤层气垂直裂缝井双线性流动曲线可划分为早期续流段、双线性流段、煤层线性流段、过渡流段和煤层边界线性流段5个特征阶段,其中由于启动压力梯度存在的影响,无因次井底压力及其导数曲线自煤层线性流段开始出现明显上翘,且启动压力梯度值越大,曲线上翘趋势越明显;此外,煤层边界线性流段呈现为单位斜率的直线,而非1/2斜率的线性流段直线.这些结果表现出启动压力梯度对低渗透煤层气垂直裂缝井双线性流动的影响,可用于指导现场煤层气井试井分析.     

低速非达西渗流动边界问题的积的分解

研究了低渗透油藏低速非达西径向流的动边界问题,给出了高精度的积分解,分析了启动压力梯度对压力分布的影响,发现启动压力梯度越大,井底附近压力下降越快,外边界传播越慢．     

非达西渗流拟启动压力梯度推算

岩体启动压力梯度的大小是石油开采,工程防渗处理等方面需要考虑的影响因素。非线性渗流现象已被广泛所认同,低渗透性岩渗流存在启动压力梯度,它基本代表了流体产生渗流时的压力梯度大小。试验对试样进水端水压进行长期稳定控制,出水端采用精确测定流出水体积变化量的方法进行流量测定; 当渗出端水体积的变化量与时间呈直线关系时,即认为该时段渗透特征符合达西定律。通过对具有不同渗透性的软弱岩系统的试验测试,根据实测渗透系数与压力梯度的正相关关系,提出了拟启动压力梯度推算的"三次平均法",即:首先统一调整实测渗透系数值,然后确定绝对渗透系数值,再根据该值确定V0值, 3次取平均推算拟启动压力梯度的方法。分析表明:拟启动压力梯度随围压升高而增大,随岩石的绝对渗透系数降低而增大; 在渗透压差增大过程测得的拟启动压力梯度大于降低过程的拟启动压力梯度,这些都与理论分析结果相吻合。实例说明拟启动压力梯度推算"三次平均法"较为合理,易于推广使用。这为通过室内试验确定工程岩体启动渗流压力梯度的大小,提出了一种新的思路。     

低渗透油藏水平井分段采油优化模型

针对低渗透油藏水平井的分段采油,考虑变盲筛比的分段完井方法,引入启动压力梯度,基于势的叠加、镜像反映原理和微元线汇思想,分别建立了低渗透封闭油藏和低渗透底水油藏的分段采油耦合模型。以水平井的产量作为目标函数,以生产水平井段的长度和中心点位置作为优化变量,分别建立了两种边界条件的低渗透油藏水平井分段采油优化模型。利用遗传算法,编制数值模拟软件,对水平井分段采油时分段方案进行了优化设计,分别给出了不同分段模式下的最优分段方案。     

基于滑移速度壁模型的复杂边界湍流大涡模拟

采用滑移速度壁模型实现了浸入边界方法与壁模型相结合的大涡模拟.本文首先分别采用平衡层模型和非平衡壁模型对周期山状流进行数值模拟,以考查在壁模型中考虑切向压力梯度的作用.数值结果表明,流场的压力对本文所采用的壁模型形式并不敏感,但是考虑切向压力梯度可以显著改进壁面摩擦力的计算结果,并且能够准确的预测强压力梯度区以及分离区内的流动平均统计特性.不考虑压力梯度效应的平衡层模型显著低估了壁面摩擦力的分布,同时无法准确预测分离区内的平均速度剖面.非平衡模型的修正项正比于切向压力梯度和壁面法向距离,因此在强压力梯度区或者网格较粗时,计算得到的平均压力和摩擦力分布以及流动的低阶统计量均与参考的实验和计算结果吻合.在此基础上,通过回转体绕流的大涡模拟考查了该方法用于模拟高雷诺数壁湍流的适用性,非平衡壁模型可以准确地捕捉流动的物理结构并较准确地预测其水动力学特性.结果表明,将浸入边界方法与非平衡滑移速度壁模型相结合的大涡模拟,有望成为数值模拟复杂边界高雷诺数壁湍流的工具.      

基于滑移速度壁模型的复杂边界湍流大涡模拟

采用滑移速度壁模型实现了浸入边界方法与壁模型相结合的大涡模拟.本文首先分别采用平衡层模型和非平衡壁模型对周期山状流进行数值模拟,以考查在壁模型中考虑切向压力梯度的作用.数值结果表明,流场的压力对本文所采用的壁模型形式并不敏感,但是考虑切向压力梯度可以显著改进壁面摩擦力的计算结果,并且能够准确的预测强压力梯度区以及分离区内的流动平均统计特性.不考虑压力梯度效应的平衡层模型显著低估了壁面摩擦力的分布,同时无法准确预测分离区内的平均速度剖面.非平衡模型的修正项正比于切向压力梯度和壁面法向距离,因此在强压力梯度区或者网格较粗时,计算得到的平均压力和摩擦力分布以及流动的低阶统计量均与参考的实验和计算结果吻合.在此基础上,通过回转体绕流的大涡模拟考查了该方法用于模拟高雷诺数壁湍流的适用性,非平衡壁模型可以准确地捕捉流动的物理结构并较准确地预测其水动力学特性.结果表明,将浸入边界方法与非平衡滑移速度壁模型相结合的大涡模拟,有望成为数值模拟复杂边界高雷诺数壁湍流的工具.     

动边界双重介质油藏低速非达西渗流试井模型

裂缝性油藏中基质岩块的渗透率一般很低,大量岩心测试实验证实在基质岩块内的液体渗流和在一定含水饱和度下的气体渗流将偏离达西渗流,往往出现低速非达西渗流,表现出启动压力梯度以及流体流动边界不断向外扩展等特殊现象。本文充分考虑启动压力梯度与动边界的影响,建立了微可压缩双重介质油藏低速非达西渗流的试井数学模型,对时间和空间变量...     

低渗透煤层气藏中气-水两相不稳定渗流动态分析

针对低渗透煤层渗流问题,考虑启动压力梯度及其引起的动边界和动边界内吸附气解吸作用的渗流模型研究目前仅限于单相流,而更符合实际的气-水两相渗流动边界模型未见报道.本文综合考虑了煤层吸附气的解吸作用、气-水两相渗流、非达西渗流、地层应力敏感等影响因素,进行了低渗透煤层的气-水两相渗流模型研究.采用了试井技术中的"分相处理"方法,修正了两相渗流的综合压缩系数和流度,并基于含气饱和度呈线性递减分布的假设,建立了煤层气藏的气-水两相渗流耦合模型.该数学模型不仅可以描述由于低渗透煤层中渗流存在启动压力梯度而产生的可表征煤层有效动用范围随时间变化的移动边界,还可以描述煤层有效动用范围内吸附气的解吸现象以及吸附气解吸作用所引起的煤层含气饱和度的上升;为了提高模型精度,控制方程还保留了二次压力梯度项.采用了稳定的全隐式有限差分方法进行了模型的数值求解,并验证了数值计算方法的正确性,获得了模型关于瞬时井底压力与压力导数响应的双对数特征曲线,由此分析了各渗流参数的敏感性影响.本文研究结果可为低渗透煤层气藏开发的气-水两相流试井技术提供渗流力学的理论基础.     

Transient pressure of percolation through one dimension porous media with threshold pressure gradient

IntroductionManyexperimentsshow[1,2,3]thatthepercolationinlowPermeabilityisnotfittoDarcy'sLaw.Theparticularcharacteristheexistenceofthresholdpressuregradient[1],inotherwords:thefluidcanflow,onlywhentherealpressuregradientislargerthanthresholdpressuregradient.Thedevelopmentinthisresearchingfieldhasn'tmuchprogressbecauseofquestionsineconomicsandteelmologysincethisconceptwasformedin1951.ThisfieldisbecominganewwarmresearchingPOintasChinadevelopedthelowPermeabilityreservoirsinlastfewyears.Thego…     

七孔探针可压缩流场测量研究

介绍了七孔探针用于亚音速可压缩流的标定方法。作为一种可以同时获得流动速度大小、流动偏角、总压和静压的气动测量装置,七孔探针被广泛应用于各种流动测量,包括可压缩流动。但是它的校准过程周期很长,代价昂贵,影响了探针的推广。本文以数值计算为手段,对七孔探针进行亚音速可压缩流校准与测量的研究。结果表明,其校准拟合精度流动角为2%,内外区的总静压相对标准偏差都没有超过3%,高于相同状态下的实验校准精度。在实际应用中,本方法用于指导传统实验标定方法,可以节约大量的标定时间和成本,使七孔探针在亚音速可压缩流的测量变得简单可行。     

考虑二次梯度项及动边界的双重介质低渗透油藏流动分析

在传统试井模型的非线性偏微分方程中根据弱可压缩流体的假设,忽略了二次梯度项,对于低渗透油藏这种方法是有疑问的.低渗透问题一个显著的特点就是流体的流动边界随着时间不断向外扩展.为了更好地研究双重介质低渗透油藏中流体的流动问题,考虑了二次梯度项及活动边界的影响,同时考虑了低渗透油藏的非达西渗流特征,建立了双重介质低渗透油藏流动模型.采用Douglas-Jones预估-校正差分方法获得了无限大地层定产量生产时模型的数值解,分别讨论了不同参数变化时压力的变化规律及活动边界随时间的传播规律,还分析了考虑和忽略二次梯度项影响时模型数值解之间的差异随时间的变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析.     

Static pressure measurement along the centerline of an induced flow ejector

Conclusion The static pressure measuring system described in this paper is simple and does not disturb the flow perceptibly. Compared to wall pressure taps, the present measuring system has the advantage of being able to measure the static pressure at any section of the nozzle and to provide a continuous distribution, if necessary. An arrangement using a large number of wall pressure taps can be avoided.In addition, this system allows the internal static pressure of the flow to be measured, which is particularly interesting in the case of two coflowing streams inside an induced flow ejector. The primary jet can be investigated downstream of the primary nozzle exit plane. The static pressure at this exit plane, which is of great importance in numerical simulation of flows in ejectors, can be directly measured by means of this pressure probe (Lu 1986). This system also permits the detection of shock waves in the supersonic stream and gives accurate information about their location, their strength and the lengths of the disturbed areas. Hence, this system is useful for shock structure investigation, especially when flow visualization techniques are impossible to apply (non-transparent walls).However, the use of this measuring system is restricted to relatively short ejectors in order to limit the length of the capillary tube (less than 1.50 m in these experiments) and to minimize its oscillations in the flow.     

Analytical solution of a double moving boundary problem for nonlinear flows in one-dimensional semi-infinite long porous media with low permeability简

Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.     

超临界CO2在低渗透煤层中渗流规律的实验研究

利用自主研发的THM三场耦合渗流实验系统,进行不同孔隙压力和温度条件下的超临界CO2在低渗透煤层中的渗流实验,得出不同温度下流速和压力梯度之间的关系,从而得到了低渗透煤层注入超临界CO2的非达西渗流规律,即流速与压力梯度变化规律呈现正指数关系.随着压力梯度的增大,渗透系数也不断的增大,且呈现正指数关系;在同一体积应力和压力梯度的条件下,温度越高,流速越快;温度在临界点附近,流速和渗透系数增加很快.     

Measurement of the Permeability Tensor of Compressed Fibre Beds

A new method to measure the permeability tensor of highly compressed fibre beds is developed. The method is based on saturated parallel flow and is evaluated through experiments with various textile materials: press fabrics used in papermaking and fibre reinforcements designed for composites. Since the materials are in the form of sheets, two measuring cells are used, one for the principal in-plane permeabilities and the other for the out-of-plane permeability. A unique feature is that the edge and the bulk flow are measured separately, so that any influence from enhanced or suppressed edge flow may be eliminated. The technique is evaluated with good results in terms of scatter in the measured permeability and the influence of test geometry, pressure, and liquid properties.     

Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media.There is good agreement between the derived results and test ones.Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow.Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius.The interaction is an important reason why nonlinear flow in saturated clays occurs.An exact mathematical model was presented for nonlinear flow in micro-scaie pore of saturated clays.Dimension and physical meanings of parameters of it are definite.A new law of nonlinear flow in saturated clays was established.It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one.Darcy law is a special case of the new law.A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow.Equations of average mass conservation and moving boundary,and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer,a method of steady state in stead of transient state and a method of integral of an equation.Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained.Re- suits show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay.The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases.Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.