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.

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Two-phase flow in porous media is a very active field of research,due to its important applications in groundwater pollution,CO_(2)sequestration,or oil and gas production from petroleum reservoirs,just to name a few of them.Fractional flow equations,which make use of Darcy's law,for describing the movement of two immiscible fluids in a porous medium,are among the most relevant mathematical models in reservoir simulation.This work aims to solve a fractional flow model formed by an elliptic equation,representing the spatial distribution of the pressure,and a hyperbolic equation describing the space-time evolution of water saturation.The numerical solution of the elliptic part is obtained using a finite-element(FE)scheme,while the hyperbolic equation is solved by means of two dif-ferent numerical approaches,both in the finite-volume(FV)framework.One is based on a monotonic upstream-centered scheme for conservation laws(MUSCL)-Hancock scheme,whereas the other makes use of a weighted essentially non-oscillatory(ENO)reconstruc-tion.In both cases,a first-order centered(FORCE)-αnumerical scheme is applied for inter-cell flux reconstruction,which constitutes a new contribution in the field of fractional flow models describing oil-water movement.A relevant feature of this work is the study of the effect of the parameterαon the numerical solution of the models considered.We also show that,in the FORCE-αmethod,when the parameterαincreases,the errors diminish and the order of accuracy is more properly attained,as verified using a manufactured solution technique.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

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”.

The Construction Method for Solving Radial Flow Problem through the Homogeneous Reservoir

On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.

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.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

Experimental investigations on the fluid flow mechanism in porous media of enhanced oil recovery by alkli/surfactant/polymer flooding

The fluid flow mechanism in porous media of enhanced oil recovery by Alkli/ Surfactant/ Polymer (ASP) flooding is investigated by measuring production performance, pressure distribution and saturation distribution through installing differential pressure transducers and saturation measuring probes in a physical model of vertical heterogeneous reservoir. The fluid flow variation in porous media is the main reason of enhanced oil recovery of ASP flooding. The pressure field and saturation field are nonlinearly coupled together and the interaction between them results in the fluid flow variation in the reservoir. In a vertical heterogeneous reservoir, the ASP agents initially flow in the high permeability layer, and fluid changes the flow direction toward the low and the middle permeability layers because the resistance in the high permeability layer is increased under the physical and chemical action of adsorption, retention and emulsion. ASP flooding displaces out not only the residual oil in the high permeability layer, but also the remaining oil in the low and the middle permeability layers by increasing swept volume and displacing efficiency.

裂缝性油藏水驱过程中基质的动用程度及基质贡献率

裂缝性(双重介质)油藏渗流过程复杂、注水开发过程中含水上升快、开发难度大,针对注水能否有效采出基质中原油问题,研究基质动用机理、程度及规律。采用ECLIPSE油藏数模模拟软件,分析裂缝系统和基质系统的采出程度、基质产油量在总产油量中的比例,分析窜流系数、基质渗透率、裂缝渗透率、注水速度等因素对水驱基质贡献率的影响。研究表明:裂缝越发育,基质渗透率越高,基岩的渗吸排油作用越明显,越有利于提高水驱油效果;注水速度越低,越能发挥基质的渗吸排油作用,水驱效果越好。该研究获得了基质贡献率和动用程度的数值范围及变化规律,建议对裂缝性油藏采取低速注水开发策略。

新疆火山岩双重介质气藏供排气机理数值模拟研究

根据火山岩气藏特点建立了反映气藏渗流特征的双重介质数学模型,应用数值模拟的方法研究基质孔隙-裂缝-井筒之间的供排气机制,定量分析了不同产量的气井定产条件下,窜流系数λ对火山岩气藏稳产的影响程度。数值模拟结果表明,双重介质气藏气体窜流过程包括过渡段和稳定段,过渡段基质窜流量小于井底产出量,井底压降快,稳定段窜流量与井底产量相当,井底压降变缓,气体窜流进入稳定段所需时间决定于窜流系数。当窜流系数大于10-7时,窜流对气井生产影响较小;但当窜流系数小于10-8时,气井稳产受窜流影响严重,此时根据气井窜流系数的大小合理配产显得十分重要。结合新疆某口井的实例进行计算,验证了数值模拟结果的可靠性,证明供排气机理数值模拟对气藏高效稳产开采有一定的指导意义。

裂缝性油气藏渗流系统模型与应用研究综述

介绍了研究裂缝性油藏的渗流特征的意义。针对裂缝油气藏中的渗流问题，总结和评价以往研究者提出的不同裂缝渗流模型和数值求解方法。着重介绍了裂缝性油气藏多重介质物理模型，包括等效孔隙介质、离散裂缝网络、双重介质、双重裂缝、三重介质和分形模型的特点、数学描述方法及应用，比较了各种模型的优劣及局限性。分析了裂缝性油气藏渗流力学存在的复杂性和面临的挑战，指出今后研究趋势，对裂缝性油气田开发过程中的渗流工作提供一定参考。

双重介质油藏低速非达西渗流封闭外边界试井模型

已有的研究表明低渗透油藏存在低速非达西渗流机理。针对低渗透双重介质油藏，在低速非达西渗流条件下建立了考虑启动压力梯度、表皮效应、井筒存储效应和封闭外边界的试井理论模型，应用Laplace变换方法求解得到了该模型在Laplace空间的解，采用Stehfest方法对该解进行了数值反演，绘制了封闭外边界条件下的井底压力理论图版，讨论了启动压力梯度、边界距离等参数对理论图版的影响规律。研究表明：由于启动压力梯度的存在，使得理论图版中的导数曲线在后期出现上翘现象，其上翘幅度随启动压力梯度的增大而增大。理论图版可用于低渗透双重介质油藏试井资料的分析和解释。

基于相似结构的双孔复合油藏的渗流模型研究

针对双孔复合油藏,建立了引入有效井筒半径在三种外边界条件下的试井分析模型;利用Laplace变换,在Laplace空间中得到了变流率生产情形下的储层压力和井壁压力的精确解;根据相似结构理论,发现了三种外边界条件下的解式具有相似结构,此项研究给编制试井分析软件带来了极大的便利,对油气藏渗流规律的理论研究也具有深远的意义。

基于解的相似结构的双渗油藏渗流问题

针对双渗介质油藏,建立了考虑有效井筒半径和井筒储集效应的试井分析模型。利用拉普拉斯变换,在拉普拉斯空间中得到了储层压力和井底压力的无因次表达式;又根据相似结构理论,发现在不同外边界条件下的解式具有统一的结构。

双渗渗流数学模型的精确解

针对双渗油藏的渗流特征 ,在两渗流层之间存在流体的交换 ;以往的双渗油藏并没有考虑流体之间的渗流 ,仅仅将两层之间的流体交换作为源和汇 ;在此考虑了两层之间渗流耦合的微分方程及压差对两层的影响 ,对方程采用无因次化 ,而将方程简化。通过正交变换获得该模型的精确解 ,该解对理解双渗油藏的渗流规律和试井分析都具有重要的指导意义。

双孔介质有界地层低速非达西渗流模型新解

运用一种新的数学解法,研究双重介质有界地层低速非达西渗流问题。基于低渗透渗流理论,建立起双孔介质有界地层低速非达西渗流模型并予以求解,编程绘制出井底压力动态样版曲线,获得低速非达西流三段拟合实用复合图版。

双重介质气藏不稳态产能变化特征研究

稳定试井是对气井进行产能分析的重要手段,通常采用回压试井和等时或修正等时试井,这两种试井方法都需要较长的时间,而实际的气体渗流都是不稳定的,流量和压力也会随时间发生变化,因此研究不稳态的产能变化特征更为合理。首先针对双重介质气藏渗透率具有方向性的特点,考虑在椭圆坐标系中建立气体渗流微分方程,进而对求解该渗流微分方程所要用到的马丢函数进行数值计算,从而可以求出双重介质气藏的不稳态产能表达式,最后绘制不稳态产能曲线,并讨论双重介质气藏的不稳态产能,表皮系数、各向异性、弹性储容比等参数的变化对不稳态产能曲线的影响。

变形双重介质分形油藏压力动态分析

研究了变形双重介质分形油藏渗流问题的压力不稳定响应,考虑了储层的双重介质特征和分形特征以及应力敏感地层中裂缝发生形变的问题,建立了应力敏感地层双重分形介质数学模型,采用数值方法以求解数学模型;此外,还给出了典型的压力曲线图板,并利用这些图版对模型中的有关参数进行了敏感性分析,探讨了分形参数、变形参数、双重介质参数以及井筒储集系数变化时压力的变化规律。

裂缝-孔隙型双重介质气藏开发影响分析

为了研究裂缝-孔隙型双重介质气藏开发特征,建立了考虑应力敏感、气体滑脱效应和高速非达西流的裂缝-孔隙型双重介质气藏渗流模型,通过数值模拟分析了不同渗流效应对气井生产的影响。结果表明,当窜流系数大于等于10^(-6)时,双重介质气藏与等效均质气藏的生产特征基本一致,此时可以运用分析均质气藏的方法和理论来研究双重介质气藏。气井生产早期,应力敏感对井底压降和稳产期的变化规律影响不大;气井生产中后期,应力敏感作用增强;窜流系数越小,应力敏感对井底压降的影响越早表现出来,对稳产期的影响也就越大。气井生产初期,高速非达西渗流对井底压降影响很小,气井生产中后期,高速非达西渗流对井底压降的影响增大;窜流系数越小,高速非达西渗流效应影响越早显现出来,对井底压降和稳产期的影响也就越大。裂缝-孔隙型双重介质气藏虽然存在气体滑脱效应,但由于储层及井底,压力相对较高,气体滑脱效应对裂缝-孔隙型双重介质气藏气井生产的影响很小。

Transient pressure analysis in porous and fractured fractal reservoirs

Fluid flow in porous and fractured fractal reservoirs is studied in the paper. The basic formulae of seepage velocity,permeability and porosity in both porous and fractured fractal media are developed. The pressure diffusion equation of slightly compressible fluid in fractal reservoirs is derived. The analytical solutions of the transient pressure are given for the line-source well and the well with well-bore storage and skin factor. The typical curves of pressure and the derivative of pressure are established,along with the interpretation of the well-testing method via type-curve matching. In addition,3-D pressure diffusion equations for anisotropic fractal media are given in both Cartesian coordinates and Cy-lindrical coordinates.