Fluid Flow Across Capillary Heterogeneities,Experiments and Simulations

A comparative study of numerical modelling and laboratory experiments of two-phase immiscible displacements in a 33 cm × 10 × 3 cm thick cross-bedded reservoir model is reported. Dynamic two-dimensional fluid saturation development was obtained from experiments by use of a nuclear tracer imaging technique and compared to numerical predictions using a full-field black oil simulator.The laboratory cross-bedded reservoir model was a sandpack consisting of two strongly waterwet sands of different grain sizes, packed in sequential layers. The inlet and outlet sand consisted of low permeable, high capillary, sand while the central crosslayer with a dip angle of 30° was a high permeable, low capillary, sand. Results on moderate contrasts in permeability and capillary heterogeneities in the cross-bedded reservoir model at different mobility ratios and capillary number floods temporarily showed a bypass of oil, resulting in a prolonged two-phase production. The final remaining oil saturations, however, were as for isolated samples. Hence, permanently trapped oil was not observed.Simulations of waterfloods, using a commercial software package, displayed correct water breakthrough at low flow rate and unity viscosity ratio, but failed in predicting local saturation development in detail, probably due to numerical diffusion.The simulator was used to test several cases of heterogeneity contrasts, and influence from different relative permeability curves. Further, by altering the capillary pressure at the outlet, the end effects were proven important.     

Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

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Dual Porosity and Dual Permeability Modeling of Horizontal Well in Naturally Fractured Reservoir

This article is the first investigation on the dual permeability flow issue for horizontal well-production in a naturally fractured dual-porosity reservoir. Based on the inter-porosity flow from matrix system to fracture system and treating the media directly connected with horizontal wellbore as matrix and fracture systems, we established a model of horizontal well-production and then solved the model using some modern mathematical methods, such as Laplace integral transformation, separation of variables, eigenvalue, and eigenfunction. Later in the article, we obtained the standard log–log type curves using numerical simulation and analyzed the transient flow behavior thoroughly, which showed it is dual porosity and dual permeability flow behavior. The numerical simulation results showed that there are obvious differences between dual permeability and single permeability models. The dual permeability flow behavior accelerates energy supplement during production and reduces the classical matrix-fracture (V-shaped) response. We also showed that type curves characteristics are affected by external boundary conditions, the parameter κ, ω _f and λ _mf, etc. The research results show that our model would be a good semi-analytical model supplied to users. Because the single permeability modeling ignores the direct fluid supply from matrix to wellbore, we recommend using the dual permeability modeling to make well testing and rate decline interpretation in real case studies.     

Sensitivity coefficients of single-phase flow in low-permeability heterogeneous reservoirs

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Modelling fluid flow in cross-bedded sections

Beadpack experiments and numerical simulations have been carried out to study flow displacements, effluent profiles and streamline patterns for layered systems with flow not parallel to the layers. The effects of layer thickness, permeability contrast, angle of layer to flow direction, mobility ratio and flood rate have been examined. Each of these parameters influence the displacement profiles, and disperse the flood front. Such real effects must be considered when subsuming reservoir heterogeneities in average reservoir parameters in simulation studies, or interpreting core tests.     

页岩气藏压裂水平井试井分析

页岩气藏资源丰富,开发潜力巨大,已成为目前研究的热点.与常规气藏相比,页岩气藏运移机制复杂,流动模式呈非线性,有必要考虑页岩气的吸附解吸,天然微裂缝的应力敏感性,人工裂缝内的非达西流等非线性因素对压裂水平井压力响应的影响. 基于双重介质和离散裂缝混合模型,分别采用Langmuir等温吸附方程描述吸附解吸,渗透率指数模型描述应力敏感,Forchheimer方程描述非达西效应,建立页岩气藏压裂水平井数值试井模型. 运用伽辽金有限元法对模型进行求解.根据试井特征曲线,划分流动阶段,着重分析非线性因素对压力响应的影响.结果表明:页岩气藏压裂水平井存在压裂裂缝线性流、压裂裂缝径向流、地层线性流、系统径向流及封闭边界影响5 种流动阶段.吸附解吸的影响发生窜流之后,Langmuir吸附体积增大,拟压力导数曲线凹槽更加明显,系统径向流出现时间与压力波传播到边界时间均延迟;天然裂缝系统的应力敏感性主要影响试井曲线的晚期段,拟压力和拟压力导数曲线均表现为上翘,应力敏感效应越强,上翘幅度越大;高速非达西效应对早期段影响较大,非达西效应越强,拟压力降幅度越大,试井曲线上翘.与解析解的对比以及矿场实例验证了模型的正确性与适用性.      

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.     

A Simple Model of a Two-Layered High-Temperature Liquid-Dominated Geothermal Reservoir as a Part of a Large-Scale Hydrothermal Convection System

The Kakkonda geothermal reservoir, Japan, is a typical high-temperature liquid-dominated geothermal reservoir, except for its distinctive two-layered temperature structure. It has a shallow permeable reservoir of 230–260°, and a deep less permeable reservoir of 350–360°. Geology and hydrology indicate that the shallow reservoir is one to two orders of magnitude more permeable than the deep reservoir, but that the two reservoirs communicate. It has been widely assumed in engineering and scientific circles that the connection between the two reservoirs is a zero or low permeability barrier to fluid flow. We show that this hypothesis is untenable, based on both physical evidence and numerical simulation. We numerically model the evolution of the geothermal system as it heats after emplacement of an intrusion. The two-layered temperature structure is found to be a consequence of the permeability difference, i.e. the two-layered permeability structure.     

Lattice Boltzmann Simulation of Fluid Flow in Synthetic Fractures

Fractures play an important role in reservoir engineering as they dominate the fluid flow in the reservoir. All evidence suggests that rarely can one model flow and transport in a fractured rock consistently by treating it as a uniform or mildly nonuniform isotropic continuum. Instead, one must generally account for the highly erratic heterogeneity, directional dependence, dual or multicomponent nature and multiscale behavior of fractured rocks. As experimental methods are expensive and time consuming most of the time numerical methods are used to study flow and transport in a fractured rock. In this work, we present results of the numerical computations for single phase flow simulations through two-dimensional synthetically created fracture apertures. These synthetic rock fractures are created using different fractal dimensions, anisotropy factors, and mismatch lengths. Lattice Boltzmann method (LBM), which is a new computational approach suitable to simulate fluid flow especially in complex geometries, was then used to determine the permeability for different fractures. Regions of high velocity and low velocity flow were identified. The resulting permeability values were less than the ones obtained with the cubic law estimates. It has been found that as the mean aperture–fractal dimension ratio increased permeability increased. Moreover as the anisotropy factor increased permeability decreased. Neural network simulations were used to generalize the results.     

Numerical solutions for the transient flow in the homogenous closed circle reservoirs

There are many fault block fields in China. A fault block field consists of fault pools. The small fault pools can be viewed as the closed circle reservoirs in some case. In order to know the pressure change of the developed formation and provide the formation data for developing the fault block fields reasonably, the transient flow should be researched. In this paper, we use the automatic mesh generation technology and the finite element method to solve the transient flow problem for the well located in the closed circle reservoir, especially for the well located in an arbitrary position in the closed circle reservoir. The pressure diffusion process is visualized and the well-location factor concept is first proposed in this paper. The typical curves of pressure vs time for the well with different well-location factors are presented. By comparing numerical results with the analytical solutions of the well located in the center of the closed circle reservoir, the numerical method is verified.     

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.     

油田注水开发中水嘴节流与地层渗流耦合研究

配水器的选取会对油田注水效果产生明显影响。为精确地描述注水井注入过程中井底压力和流量的动态响应,本文在传统的内边界井处理模型的基础上建立了考虑水嘴压力损失影响的井处理模型。耦合求解井底压力、流量及地层流动,得到了注入过程中考虑水嘴压力损失影响的井底压力和流量响应情况。以此来分析不同水嘴、渗透率对井底压力、注入量随时间变...     

Numerical solution of the turbulent flow of an incompressible fluid in curved planar and axially symmetrical channels

The governing equations for axially symmetric flow, where the Reynolds stresses are expressed by scalar turbulent viscosity, are the Reynolds equations. The turbulence model k, ? is used in the well-known form for fully developed turbulent flow.The numerical method, a continuation of the MAC system¹, is adapted so that even for high Reynolds cell numbers precision (δx²) can be achieved for the steady flow. Irregular cells join the rectangular network on the curved surface. Von Neumann's stability condition of the linearised numerical system is investigated. Special problems concerning the numerical solution of the turbulence model equations are stated and a special procedure is worked out to ensure that the fields k, ? do not converge to physically meaningless values. The program for the computer is universal in that the boundary problems can be assigned by input data.As an example, an axially symmetrical diffuser with an area ratio of widening 1.40 is computed. Fields of velocity and pressure at the wall as well as fields v_T and k are assessed. The results are compared with an experiment. The conclusion is that this method is suitable for the problems mentioned in this study as well as for unsteady flow.     

Numerical Simulation of Single-Phase and Multiphase Non-Darcy Flow in Porous and Fractured Reservoirs

A numerical method as well as a theoretical study of non-Darcy fluid flow through porous and fractured reservoirs is described. The non-Darcy behavior is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The non-Darcy flow through a fractured reservoir is handled using a general dual-continuum approach. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in petroleum and geothermal reservoirs.     

Comparison of fast algorithms for estimating large-scale permeabilities of heterogeneous media

The problem of upscaling permeability data from the core to the reservoir grid block scale for input into flow simulators is addressed. Two fast, approximate algorithms which have been suggested for this purpose—one based on random walks and the other on real-space renormalisation group methods—are compared using the results of numerical tests performed on 30 different heterogeneous permeability realisations in 3-D. The results show that random walks outperform renormalisation for this problem, being computationally more efficient and demonstrating significantly better accuracy for particular cases.     

Homogenization of Wall-Slip Gas Flow Through Porous Media

The permeability of reservoir rocks is most commonly measured with an atmospheric gas. Permeability is greater for a gas than for a liquid. The Klinkenberg equation gives a semi-empirical relation between the liquid and gas permeabilities. In this paper, the wall-slip gas flow problem is homogenized. This problem is described by the steady state, low velocity Navier–Stokes equations for a compressible gas with a small Knudsen number. Darcy's law with a permeability tensor equal to that of liquid flow is shown to be valid to the lowest order. The lowest order wall-slip correction is a local tensorial form of the Klinkenberg equation. The Klinkenberg permeability is a positive tensor. It is in general not symmetric, but may under some conditions, which we specify, be symmetric. Our result reduces to the Klinkenberg equation for constant viscosity gas flow in isotropic media.     

Numerical study of free-piston shock tunnel performance

A free-piston shock tunnel (FPST) is one of the most useful ground testing facilities for hypervelocity flow research of re-entry vehicles and scramjet engines. For an efficient operation with tuned piston motion, the design of facility and the comprehension of the physical phenomena in a FPST, a numerical simulation which can properly predicts the flow with actual losses is required. But there are few successful numerical methods which can simulate its overall performance. In the present study, numerical method was developed by using the KRC shock capturing scheme and by modeling the flow losses in suitable forms for a quasi-1D numerical computation. The present numerical results were compared with the data obtained in two different facilities, T4 and T5. The applicability of the present numerical method as a design tool is discussed briefly.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Numerical investigation of the decomposition of gas hydrates coexisting with gas in natural reservoirs

The problem of methane hydrate decomposition in a reservoir saturated with a gas and hydrate mixture is investigated numerically. The results of the numerical simulation and an analytic solution obtained in the linear approximation are compared. It is shown that for high-permeability rocks the convective heat transfer in the near-well space of the reservoir predominates over the conductive transfer. This makes the use of intra-well heaters ineffective. It is found that an increase in the reservoir and well pressures and a decrease in the permeability suppress the formation of an extended hydrate dissociation region. Critical diagrams of existence of the frontal decomposition regime are constructed.     

Permeability mapping in porous media by magnetization prepared centric-scan SPRITE

The ability of porous media to transmit fluids is commonly referred to as permeability. The concept of permeability is central for hydrocarbon recovery from petroleum reservoirs and for studies of groundwater flow in aquifers. Spatially resolved measurements of permeability are of great significance for fluid dynamics studies. A convenient concept of local Darcy’s law is suggested for parallel flow systems. The product of porosity and mean velocity images in the plane across the average flow direction is directly proportional to permeability. Single Point Ramped Imaging with T ₁ Enhancement (SPRITE) permits reliable quantification of local fluid content and flow in porous media. It is particularly advantageous for reservoir rocks characterized by fast magnetic relaxation of a saturating fluid. Velocity encoding using the Cotts pulsed field gradient scheme improves the accuracy of measured flow parameters. The method is illustrated through measurements of 2D permeability maps in a capillary bundle, glass bead packs and composite sandstone samples.     

考虑诱导缝多段压裂水平井非均质改造压力动态模型研究

为了准确模拟致密油藏水平井大规模压裂形成复杂裂缝网络系统和非均质储层井底压力变化,建立考虑诱导缝矩形非均质储层多段压裂水平井不稳定渗流数学模型,耦合裂缝模型与储层模型得到有限导流裂缝拉普拉斯空间井底压力解,对两种非均质储层模型分别利用数值解、边界元和已有模型验证其准确性.基于压力导数曲线特征进行流动阶段划分和参数敏感性分析,得到以下结果:和常规压裂水平井井底压力导数曲线相比较,理想模式下,考虑诱导缝影响时特有的流动阶段是综合线性流阶段、诱导缝向压裂裂缝“补充”阶段、储层线性流动阶段和拟边界控制流阶段.诱导缝条数的增加加剧了综合线性流阶段的持续时间,降低了流体渗流阻力,早期阶段压力曲线越低;当诱导缝与压裂裂缝导流能力一定时,裂缝导流能力越大,线性流持续时间越长;当所有压裂裂缝不在一个区域时,沿井筒方向两端区域低渗透率弱化了低渗区域诱导缝流体向压裂裂缝“补充”阶段,因此,沿井筒方向两端区域渗透率越低,早期阶段压力曲线越高;当所有压裂裂缝在一个区域时,渗透率变化只影响径向流阶段之后压力曲线形态,外区渗透率越低,早期径向流阶段之后压力曲线越高.通过实例验证,表明该模型和方法的实用性和准确性.