Simulation of Three-Phase Displacement Mechanisms Using a 2D Lattice-Boltzmann Model

Using a numerical technique, known as the lattice-Boltzmann method, we study immiscible three-phase flow at the pore scale. An important phenomenon at this scale is the spreading of oil onto the gas–water interface. In this paper, we recognize from first principles how injected gas remobilizes initially trapped oil blobs. The two main flow mechanisms which account for this type of remobilization are simulated. These are the double-drainage mechanism and (countercurrent) film flow of oil. The simulations agree qualitatively with experimental findings in the literature. We also simulate steady-state three-phase flow (fixed and equal saturations) in a small segment of a waterwet porous medium under both spreading and nonspreading conditions. The difference between the two conditions with respect to the coefficients in the generalized law of Darcy (which also includes viscous coupling) is investigated.     

粘塑性损伤模型模拟准超塑性单轴拉伸行为

发展了Chaboche粘塑性本构模型的大变形隐式算法，用损伤(DM)和无损伤(NDM)模型模拟准超塑性单轴拉伸。发现变形过程可分为三个阶段：均匀变形、颈缩发展、断裂破坏阶段。DM可准确模拟前两个阶段变形，NDM只能较好地模拟均匀变形阶段，表明DM可以较精确地描述稳定发展的动态过程。由于有限元方法只能描述连续介质，因此对于断裂破坏阶段，NDM模拟载荷大于试验结果，DM的载荷小于试验结果，这是由高应变速率敏感性造成。DM能够描述试验中出现地多处颈缩现象，局部应变速率分布随时间演化反映了颈缩发展程度。严重颈缩部位的距离代表着超塑性变形能力，距离越大，抗颈缩能力越好。     

含污染物的弱弯曲明渠弯道湍流数值模拟

建立了可模拟弯道中含污染物湍流的三维部分抛物型代数应力模型。针对左右两岸分别泄放污染物的环流非充分发展弯道流进行了计算。分析了水流结构及污染物浓度分布的特点。     

有杆抽油泵井下抽油示功图计算机诊断系统

本文研制了有杆抽油泵井下示功图计算机诊断系统。能直接根据所测地面光杆的载荷和位移信号,计算及绘制井下示功图,并据此诊断整个抽油系统的工作状况。     

Upscaling in Subsurface Transport Using Cluster Statistics of Percolation

Transport/flow problems in soils have been treated in random resistor network representations (RRNs). Two lines of argument can be used to justify such a representation. Solute transport at the pore-space level may probably be treated using a system of linear, first-order differential equations describing inter-pore probability fluxes. This equation is equivalent to a random impedance network representation. Alternatively, Darcys law with spatially variable hydraulic conductivity is equivalent to an RRN. Darcys law for the hydraulic conductivity is applicable at sufficiently low pressure head in saturated soils, but only for steady-state flow in unsaturated soils. The result given here will have two contributions, one of which is universal to any linear conductance problem, i.e., requires only the applicability of Darcys (or Ohms) law. The second contribution depends on the actual distribution of linear conductances appropriate. Although nonlinear effects in RRNs (including changes in resistance values resulting from current, analogous to changes in matric potential resulting from flow) have been treated within the framework of percolation theory, the theoretical development lags the corresponding development of the linear theory, which is, in principle, on a solid foundation. In practice, calculations of the nonlinear conductivity in relatively (compared with soils) well characterized solid-state systems such as amorphous or impure semiconductors, do not agree with each other or with experiment. In semiconductors, however, experiments do at least appear consistent with each other.In the limit of infinite system size the transport properties of a sufficiently inhomogeneous medium are best calculated through application of critical rate analysis with the system resistivity related to the critical (percolating) resistance value, R_c. Here well-known cluster statistics of percolation theory are used to derive the variability, W (R,x) in the smallest maximal resistance, R of a path spanning a volume x³ as well as to find the dependence of the mean value of the conductivity, (x). The functional form of the cluster statistics is a product of a power of cluster size, and a scaling function, either exponential or Gaussian, but which, in either case, cuts off cluster sizes at a finite value for any maximal resistance other than R_c. Either form leads to a maximum in W (R,x) at R=R_c. When the exponential form of the cluster statistics is used, and when individual resistors are exponential functions of random variables (as in stochastic treatments of the unsaturated zone by the McLaughlin group [see Graham and MacLaughlin (1991), or the series of papers by Yeh et al. (1985, 1995), etc.], or as is known for hopping conduction in condensed matter physics), then W (R,x) has a power law decay in R/R_c (or R_c/R, the power being an increasing function of x. If the statistics of the individual resistors are given by power law functions of random variables (as in Poiseiulles Law), then an exponential decay in R for W (R,x) is obtained with decay constant an increasing function of x. Use, instead, of the Gaussian cluster statistics alters the case of power law decay in R to an approximate power, with the value of the power a function of both R and x.     

明渠效应在多相计量中的应用研究

在多相流体力学和多相流测量方面大量的基础理论研究和实验研究的基础上,提出了全新的明渠流模型等多个流量计测模型用于多相流量计量。通过自主开发的智能型多相流量计测系统在室内多相流测试环道上,对模型的运用效果做了大量的实验研究。并且利用基于神经网络技术和模糊模式识别技术开发的计测软件对实验数据进行处理,结果表明:液相计测数据中 80%以上误差位于±5%的范围以内,除个别小流量外,所有误差位于±10%的范围以内;气相计测结果中 90%以上误差位于±10%的范围以内, 97%的误差位于±15%的范围以内。实验数据表明:该计测模型可以适用于多相流中不同粘度的液相流量计量;可适用于较宽的气、液相流量变化范围,模型计测误差稳定在可接受的水平。     

Pore-Scale Simulation of Interphase Multicomponent Mass Transfer for Subsurface Flow

A simulation framework is proposed to simulate multicomponent multiphase flow in porous media at the pore scale. It solves equations for the species concentrations in the framework of the volume-of-fluid approach including thermodynamics equilibrium at the fluid/fluid interface. Particular attention is paid to the derivation of the boundary condition for the concentration at the solid walls. The method is validated by comparison with analytical solutions of simple setups. Then, the approach is used to investigate and upscale mass transfer across interfaces in different configurations, including the drainage of water in a tube by a gas carrying a contaminant, mass transfer in thin films, and mass transfer in complex porous structures under various flow conditions.     

Numerical Simulation of Ferrofluid Flow for Subsurface Environmental Engineering Applications

Ferrofluids are suspensions of magnetic particles of diameter approximately 10nm stabilized by surfactants in carrier liquids. The large magnetic susceptibility of ferrofluids allows the mobilization of ferrofluid through permeable rock and soil by the application of strong external magnetic fields. We have developed simulation capabilities for both miscible and immiscible conceptualizations of ferrofluid flow through porous media in response to magnetic forces arising from the magnetic field of a rectangular permanent magnet. The flow of ferrofluid is caused by the magnetization of the particles and their attraction toward a magnet, regardless of the orientation of the magnet. The steps involved in calculating the flow of ferrofluid are (1) calculation of the external magnetic field, (2) calculation of the gradient of the external magnetic field, (3) calculation of the magnetization of the ferrofluid, and (4) assembly of the magnetic body force term and addition of this term to the standard pressure gradient and gravity force terms. We compare numerical simulations to laboratory measurements of the magnetic field, fluid pressures, and the twodimensional flow of ferrofluid to demonstrate the applicability of the methods coded in the numerical simulators. We present an example of the use of the simulator for a fieldscale application of ferrofluids for barrier verification.     

Effects of Organic Base Chemistry on Interfacial Tension,Wettability, and Capillary Pressure in Multiphase Subsurface Waste Systems

The presence of surfactants may have profound effects on the transport of organic contaminants in multiphase systems. It is a common practice, however, to model the subsurface migration of liquids independently of the aqueous phase composition. As such, transport in these systems may not be adequately characterized. This study investigates the impact of pH on interfacial tension, wettability, and the drainage capillary pressure–saturation relationship in air–water–quartz and oxylene–water–quartz systems containing dodecylamine, an organic base. In these systems, three mechanisms, speciation, partitioning, and sorption, are important in determining the interfacial tension and contact angle, and consequently, important in determining the capillary pressure. By adjusting the pH above and below, the pK_a of the base, the relative importance of these mechanisms was altered. Below dodecylamine's pK_a of 10.6, the base was primarily in a cationic form resulting in minimal partitioning into the nonaqueous liquid and greater sorption at the quartz surface. Above the pK_a, the base was primarily in a neutral form which did not sorb to the quartz, and, furthermore, partitioned into the organic liquid phase where its surface activity was minimized. The combination of these processes caused the capillary pressure to change in a manner consistent with porescale theory of capillarity. The utility in this approach lies in the possibility of predicting transport properties in multiphase systems while incorporating the direct effects of solution chemistry.     

Quasi-Hydrodynamic Model of Multiphase Fluid Flows Taking into Account Phase Interaction

A quasi-hydrodynamic system of equations describing flows of a heat-conducting viscous compressible multiphase multicomponent fluid is constructed taking into account surface effects. The system was obtained by generalizing the methods of obtaining a single-phase quasi-hydrodynamic system and a multicomponent flow model with surface effects based on the concept of microforces and microstresses. The equations are derived using the Coleman–Noll procedure. The results of the simulations show that the constructed model is applicable for modeling multiphase multicomponent flows with allowance for surface effects on the interfaces.     

Monte Carlo Simulation of Contaminant Transport: I. Long-range Correlations in Fracture Conductivity

We develop a network model of fractures, and use the model to study transport of contaminants by groundwater through natural geological media. The fractures are narrow rectangular channels between large flat parallel plates, which are embedded in the surrounding rock matrix. The fracture-permeabilities and the fracture-widths are obtained from both uniform and fBm distributions. The pressure distribution in the network, and subsequently the velocity of groundwater in each channel, is obtained. The transport problem in an individual fracture is solved in Laplace space using the realized groundwater velocities and network mass conservation. The transform space solutions are then inverted to real time using a fast and efficient inversion algorithm. Monte Carlo simulations are then carried out by repeating the above procedure for a large number of realizations. The main focus of this study is to explore the effects correlated fracture-permeabilities and fracture-widths have on the transport of contaminants. While the primary transport mechanism is convection, we also study such processes as adsorption onto the fracture surface, and radioactive decay. We show how these phenomena, individually and in combination with one another, affect the overall transport process. In addition, we investigate the nature of the mixing zone, and discuss how these results can be helpful in developing remediation techniques for a contaminated site.     

Monte Carlo Simulation of Contaminant Transport: II. Morphological Disorder in Fracture Connectivity

Simulating contaminant transport in fractured geologic media is challenging. Aside from the difficulties encountered in properly modeling the heterogeneities in the hydraulic properties of the fractures and the matrix, it is difficult to quantify and model the disorder in the fracture connectivity. Correct prediction of the spread of contaminants in fractured geologic media is not possible without considering this inherent morphological disorder. Here, we develop a network model of fractures, and use the model to study transport of contaminants. We investigate the influence of morphology on the transport process by introducing disorder in the fracture connectivity through a novel percolation scheme. The network close to the percolation threshold is very complex and allows the contaminant particles to follow many slow paths. This closely captures the physical situation. We show, how the disorder in the network changes the residence time distributions and its various temporal moments. We also show how the residence time distribution and the temporal moments are influenced by the interaction of the disorder with the various transport mechanisms, such as convection, dispersion, adsorption, and first-order decay.     

Effective Radius and Underpressure of an Air Extraction Well in a Heterogeneous Porous Medium

We consider the compressible steady state air flow in a porous medium caused by an extraction well and governed by Darcy's law. For a homogeneous soil matrix we have derived formulas (in 2-D and 3-D) to determine the effective radius of a single well depending on the well position and the depth of the domain. For inhomogeneous case (in 2-D) the influence of the heterogeneity, well position and the depth of the water table on the effective radius and on the pressure at the well is studied.     

Coherent Vortex Simulation (CVS), A Semi-Deterministic Turbulence Model Using Wavelets

In the spirit of Ha Minh's semi-deterministic model, we propose a new method for computing fully-developed turbulent flows, called Coherent Vortex Simulation (CVS). It is based on the observation that turbulent flows contain both an organized part, the coherent vortices, and a random part, the incoherent background flow. The separation into coherent and incoherent contributions is done using the wavelet coefficients of the vorticity field and the Biot–Savart kernel to reconstruct the coherent and incoherent velocity fields. The evolution of the coherent part is computed using a wavelet basis, adapted at each time step to resolve the regions of strong gradients, while the incoherent part is discarded during the flow evolution, which models turbulent dissipation. The CVS method is similar to LES, but it uses nonlinear multiscale band-pass filters, which depend on the instantaneous flow realization, while LES uses linear low-pass filters, which do not adapt to the flow evolution. As example, we apply the CVS method to compute a time developing two-dimensional mixing layer and a wavelet forced two-dimensional homogeneous isotropic flow. We also demonstrate how walls or obstacles can be taken into account using penalization and compute a two-dimensional flow past an array of cylinders. Finally, we perform the same segmentation into coherent and incoherent components in a three-dimensional homogeneous isotropic turbulent flow. We show that the coherent components correspond to vortex tubes, which exhibit non-Gaussian statistics and long-range correlation, with the same k ^−5/3power-law energy spectrum as the total flow. In contrast, the incoherent components correspond to an homogeneous random background flow which does not contain organized structures and presents an energy equipartition together with a Gaussian PDF of velocity. This justifies their elimination during the CVS computation to model turbulent dissipation. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Application of the Density-Functional Method for Numerical Simulation of Flows of Multispecies Multiphase Mixtures

Numerical examples of application of the density functional used to describe isothermal flows of two-phase two-species mixtures are given. The following flows are calculated in a two-dimensional formulation: impact of a drop on a liquid layer, breakdown of a drop in the velocity field of the Couette flow, formation of the wetting angle of a drop on a solid surface, and development of the Rayleigh–Taylor and Kelvin–Helmholtz instabilities at the gas–liquid interface.     

In Situ Chemically-Selective Monitoring of Multiphase Displacement Processes in a Carbonate Rock Using 3D Magnetic Resonance Imaging

Accurate monitoring of multiphase displacement processes is essential for the development, validation and benchmarking of numerical models used for reservoir simulation and for asset characterization. Here we demonstrate the first application of a chemically-selective 3D magnetic resonance imaging (MRI) technique which provides high-temporal resolution, quantitative, spatially resolved information of oil and water saturations during a dynamic imbibition core flood experiment in an Estaillades carbonate rock. Firstly, the relative saturations of dodecane (\(S_{\mathrm{o}})\) and water (\(S_{\mathrm{w}})\), as determined from the MRI measurements, have been benchmarked against those obtained from nuclear magnetic resonance (NMR) spectroscopy and volumetric analysis of the core flood effluent. Excellent agreement between both the NMR and MRI determinations of \(S_{\mathrm{o}}\) and \(S_{\mathrm{w}}\) was obtained. These values were in agreement to 4 and 9% of the values determined by volumetric analysis, with absolute errors in the measurement of saturation determined by NMR and MRI being 0.04 or less over the range of relative saturations investigated. The chemically-selective 3D MRI method was subsequently applied to monitor the displacement of dodecane in the core plug sample by water under continuous flow conditions at an interstitial velocity of \(1.27\times 10^{-6}\,\hbox {m}\,\hbox {s}^{-1}\) (\(0.4\,\hbox {ft}\,\hbox {day}^{-1})\). During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of \(0.31\,\hbox {mm}\times 0.39\,\hbox {mm} \times 0.39\,\hbox {mm}\) were acquired on a timescale of 16 min per image. Using this technique the spatial and temporal dynamics of the displacement process have been monitored. This MRI technique will provide insights to structure–transport relationships associated with multiphase displacement processes in complex porous materials, such as those encountered in petrophysics research.