Research advances in non-Darcy flow in low permeability media

More and more experimental results show that Darcy’s law is not fully applicable in low permeability media,and non-Darcy flow has been identified.In this paper we reviewed the research of non-Darcy flow experiments in low-permeability media in recent decades,discuss the existence of non-Darcy flow,and summarize its constitutive equations.The reasons for the threshold gradient were also discussed and summarized for the criterion of the critical point of non-Darcy flow.On this basis,the future development of non-Darcy flow experiments in the rock and clay media were discussed,in order to provide a certain reference for subsequent research on seepage laws in low permeability media.

Modeling of multiphase flow in low permeability porous media:Effect of wettability and pore structure properties

Multiphase flow in low permeability porous media is involved in numerous energy and environmental applications.However,a complete description of this process is challenging due to the limited modeling scale and the effects of complex pore structures and wettability.To address this issue,based on the digital rock of low permeability sandstone,a direct numerical simulation is performed considering the interphase drag and boundary slip to clarify the microscopic water-oil displacement process.In addition,a dual-porosity pore network model(PNM)is constructed to obtain the water-oil relative permeability of the sample.The displacement efficiency as a recovery process is assessed under different wetting and pore structure properties.Results show that microscopic displacement mechanisms explain the corresponding macroscopic relative permeability.The injected water breaks through the outlet earlier with a large mass flow,while thick oil films exist in rough hydrophobic surfaces and poorly connected pores.The variation of water-oil relative permeability is significant,and residual oil saturation is high in the oil-wet system.The flooding is extensive,and the residual oil is trapped in complex pore networks for hydrophilic pore surfaces;thus,water relative permeability is lower in the water-wet system.While the displacement efficiency is the worst in mixed-wetting systems for poor water connectivity.Microporosity negatively correlates with invading oil volume fraction due to strong capillary resistance,and a large microporosity corresponds to low residual oil saturation.This work provides insights into the water-oil flow from different modeling perspectives and helps to optimize the development plan for enhanced recovery.

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

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.

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy＇s linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir~ is established. This model can describe various patterns of porous flow, as Darcy＇s linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.

MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.

Research on Well Testing Interpretation of Low Permeability Deformed Dual Medium Reservoir

Considering the influence of quadratic gradient term and medium deformation on the seepage equation, a well testing interpretation model for low permeability and deformation dual medium reservoirs was derived and established. The difference method was used to solve the problem, and pressure and pressure derivative double logarithmic curves were drawn to analyze the seepage law. The research results indicate that the influence of starting pressure gradient and medium deformation on the pressure characteristic curve is mainly manifested in the middle and late stages. The larger the value, the more obvious the upward warping of the pressure and pressure derivative curve;the parameter characterizing the dual medium is the crossflow coefficient. The channeling coefficient determines the time and location of the appearance of the “concave”. The smaller the value, the later the appearance of the “concave”, and the more to the right of the “concave”.

SENSITIVITY COEFFICIENTS OF SINGLE-PHASE FLOW IN LOW-PERMEABILITY HETEROGENEOUS RESERVOIRS

Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained. It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridblocks away from the well. When an initial pressure gradient existent sensitivity coefficients in the region are closer to the active well than to the observation well. Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient.

Threshold pressure gradient of fluid flow through multi-porous media in low and extra-low permeability reservoirs

After analyzing many studies of fluid flow theory of multi-porous media in low and extra-low permeability reservoirs and the numerical simulation of non-Darcy flow, we found that a negative flow rate occurs in the existing non-Darcy flow equation, which is unreasonable. We believe that the existing equation can only be considered as a discriminant to judging Darcy flow or non-Darcy flow, and cannot be taken as a fluid flow governing equation of multi-porous media. Our analysis of the experimental results shows that the threshold pressure gradient(TPG) of low and extra-low permeability reservoirs is excessively high, and does not conform to fluid flow through multi-porous media in the actual reservoir situation. Therefore, we present a reasonable TPG ranging from 0.006 to 0.04 MPa/m at the well depth of 1500 m and oil drainage distance of 500 m. The results of our study also indicate that the non-Darcy flow phenomenon will disappear when the TPG reaches a certain value. In addition, the TPG or non-Darcy flow in low and extra-low permeability reservoirs does not need to be considered in the productivity prediction and reservoir numerical simulation. At present, the black oil model or dual-porous media is suitable for simulating low and extra-low permeability reservoirs.

低渗砂岩油藏多孔介质特性

以中国石化中原油田W区块低渗砂岩油藏为例,针对目前该区块开发效果逐渐变差,气驱开采发生气窜等问题,以室内实验为基础,结合油层物理、分形理论、渗流机理,利用计算机分形分析软件Frac Lab和Frac Lac分析该区块多孔介质的岩石表面粗糙度、孔隙分布均匀程度和均质性,基于Gaussian分布、Fourier分析工具、幂律定律和最小二乘回归分析等数学基础理论计算出该区块多孔介质的分维数。结果表明:W区块低渗砂岩油藏多孔介质具有分形特征,分维数约为2.58,壁面较粗糙,孔隙内结构复杂,微小孔隙较多,不规则非均质性严重,流动阻力大,且Frac Lab和Frac Lac软件得到的分维数具有较好的一致性。研究结果为低渗砂岩油藏提高采收率、油气渗流规律和多孔介质输运性质的研究提供基础研究支撑,具有重要的现实意义。

低渗透储层特征研究

不同低渗透储层特征差异大,储层特征对渗流能力和开发效果有重要影响。通过对大庆和长庆低渗透储层岩芯恒速压汞、核磁共振、启动压力梯度、粘土类型与含量分析测试,对比研究了低渗透储层特征。研究结果表明主流喉道半径是渗流能力的主控因素,粘土类型及含量和可动流体饱和度进一步减小了储层的有效渗流空间,特别是大庆低渗透储层粘土含量高,以伊利石和蒙脱石为主,对渗流空间影响很大。气测渗透率相近的储层,长庆低渗透储层与大庆低渗透储层相比,主流喉道半径大、可动流体饱和度高以及启动压力梯度小。这些特征参数揭示了大庆和长庆低渗透油藏开发难度差异的原因。

低渗透孔隙-裂隙介质气体非线性渗流运动方程

已有的煤层气渗流研究基于达西定律,而实验表明低渗透介质气体渗流为非线性流。采用实验、理论与计算相结合的方法建立低渗透孔隙-裂隙介质气体非线性渗流运动方程。实验结果表明,低渗透孔隙-裂隙介质气体渗流曲线是从较低压力梯度下的凹形曲线至较高压力梯度下的直线,是连续变化的曲线,直线延长线不通过坐标原点,存在拟启动压力梯度。根据该普遍特征,建立了非线性渗流运动方程。其参数量纲与物理意义清楚,运动方程计算的理论曲线与实验结果吻合很好,达西定律是运动方程的特例,运动方程可运用于低渗透孔隙-裂隙介质气体渗流理论及开发计算研究。

低速非达西渗流的全隐式模拟模型

许多研究表明,低渗透介质中的流体渗流需要启动压力梯度,并不遵循达西定律;而传统的油藏数值模拟理论都是建立在达西定律之上的,因而它很难反映低渗介质中的流体渗流特征。为了让油藏模拟模型能正确描述低渗介质中这种特殊的渗流现象,基于前人的研究成果,建立了一种非达西渗流的全隐式数值模拟模型,并给出了该数学模型的有限差分形式和相应的全隐式处理方法,完成了已有模拟器的功能改造。最后给出了计算实例,结果表明,在其它条件相同的情况下,启动压力梯度越大,则在相同时间内的采出程度越低,累计注水量越少;相反,启动压力梯度越小,则在相同时间内的采出程度越高,累计注水量越多。分析表明,算例的模拟结果是合理的,此模型能够反映低渗介质中流体的低速非达西渗流特征。图3参5（周涌沂摘）

低渗透气藏气体渗流速度修正式

渗流的基本规律达西定律 ,是 10 0多年前法国水利工程师达西提出的 ,他是通过液体实验得到的。对于气体渗流来讲 ,存在着滑脱效应 ,特别是在低渗、低速和低压时 ,滑脱效应更为显著。在考虑了气体渗流的特点后 ,结合分子扩散理论得到了考虑滑脱效应的气体渗流速度方程 ,为进一步开展低渗透气藏渗流理论研究 ,油藏工程研究和动态分析建立了基础。

低渗透多孔介质中的非线性渗流理论

文中论述了低渗透性多孔介质中非线性渗流理论的几个问题,阐明了渗流流体的性质,指出了多孔介质对流体通过的选择性,提出了新的非线性渗流方程,用实验资料对其进行了验证,分析了该方程演变功能,表明它可以描述各种渗流规律.该方程的各项参数都可从实验中直接得到,应用方便,并且参数的物理意义明确.

低渗透气藏特殊渗流机理的产能评价分析

低渗透储层具有应力敏感性、启动压力等极其复杂的渗流特征,西南石油大学"油气藏地质及开发工程国家重点实验室"利用长岩心实验验证了低渗透气藏中反渗吸水锁启动压力这一新的特殊渗流机理的存在。在此基础上,通过分析推导了考虑启动压力(反渗吸启动压力和常规启动压力)的低渗透气井产能公式;同时由于低渗透储层普遍具有强或极强的应力敏感性,故而进一步推导了考虑启动压力和渗透率应力敏感性同时存在的低渗透气藏产能公式。在公式推导的基础上对其进行了实例计算分析,以此评价了低渗透气井考虑特殊渗流机理的产能特征。由分析结果可发现:①随着反渗吸水锁程度的加大,气井无阻流量逐渐减小,且在形成了反渗吸水锁后,气井开井不再是一有压差就有产量,而是表现出一定的启动压力现象;②随着应力敏感性指数的增加,气井无阻流量逐渐减小;③同时考虑应力敏感和启动压力后的气井无阻流量较单纯只考虑一个因素的无阻流量要低。

低渗透微尺度孔隙气体渗流规律

微尺度条件下气体流动特性的研究是现代渗流力学前沿领域之一.分析了低渗透岩石饱和气体渗 流实验结果,探索了微尺度孔隙气体渗流规律,探讨了气体非线性渗流力学机理,发现了低渗透岩石微尺度孔 隙气体与液体渗流遵循同一形式的运动定律,建立了气体与液体非线性运动定律统一模型.结果表明:新模型 与实验结果吻合很好,为微尺度孔隙气体微流动特性研究提供了新的理论依据,对工程地质环境保护及地下流 体资源开发有重要指导意义.

气体滑脱现象的综合特征参数研究

当气体在致密孔隙介质中低速渗流时 ,表现出有别于油、水等液体渗流的重要物理现象—滑脱现象 ,文章认为气体分子与孔隙壁的碰撞作用是滑脱现象发生的物理机理 ,它由孔隙介质的结构和气体分子随自由程的分布共同决定。滑脱现象将在低压力段引起气体渗流规律对达西线性关系的偏离 ,孔隙愈致密 ,气体压力愈低 ,该现象引起的偏离愈明显。通过对气体在孔隙介质中低速渗流时发生的基本作用分析和应用量纲理论 ,确定描述滑脱现象的综合特征参数是d/λ。实验测得当d/λ≤ 4 .5时 ,对于低速渗流的气体 ,这是既存在粘滞流动 ,同时滑脱流动又不可忽略的情况 ,在其渗流规律中应考虑由于滑脱现象的存在所带来的影响。文章分别由理论计算和对实验结果的分析拟合得到了关于d/λ的函数 ,二者基本吻合。该函数能正确描述这种情况下气体的渗流规律。

低渗透复杂介质中的渗流描述方法研究

杂乱的天然裂缝和因增产措施而诱发的人工压裂缝加剧了低渗透储层介质的复杂性。实验研究和现场实践表明 ,渗流的非线性和流态的多变性是低渗透复杂介质中的主要渗流特征 ,也是当今渗流力学界普遍关注的难题。本文根据实验并结合微分原理 ,提出了低渗透复杂介质系统内非线性渗流的微分线性描述方法 ,比较详细地介绍了该方法的原理、步骤和使用过程中应当注意的问题。该方法不但可以描述流体渗流的非线性 ,而且还能描述流体流态的多变性。

界面分子力作用与渗透率的关系及其对渗流的影响

将界面化学理论和渗流物理理论相结合，在毛细管模型与单分子层作用模型的基础上，推导出了固液界面分子力作用与多孔介质的渗透率或孔隙半径的近似关系式，并设计和进行了岩心流动对比实验。结果表明：在低渗透多孔介质中，液体渗流为非达西类型，渗流曲线特征为凹形曲线至直线，存在（拟）启动压力梯度；非达西特征取决于多孔介质的渗透率和流体性质；固液界面分子力作用随多孔介质的渗透率或孔隙半径增大而单调递减。在低渗透多孔介质中，固液界面分子力对液体渗流的影响较大，且为渗流具有非达西特征的主要原因；而在较高渗透率多孔介质中，它对渗流的影响可以忽略，液体渗流为达西类型。综述了非达西渗流应用研究现状。图２表１参１１（陈志宏摘）

低渗透变形介质气藏压裂井产能分析

低渗透变形介质气藏压裂井生产过程中,气体渗流一般不遵循达西定律,而是存在启动压力梯度和介质变形影响的低速非达西渗流。变形介质的渗透率随有效应力的增大而降低,一般与压力变化呈指数关系。为此,基于压裂井三线性渗流模型,建立并求解了低渗透变形介质气藏考虑启动压力梯度和介质变形影响的有限导流垂直裂缝井不稳定渗流的数学模型,来研究低渗透气藏压裂井定产量生产时井底压力的变化规律。计算结果表明,井底压力随启动压力梯度的变化很小,随介质变形系数的增大而减小,随裂缝导流能力的减小而增大。