Nonequilibrium Effects and Multiphase Flow in Porous Media

In this paper we develop a more general formulation for transient multiphase flow in porous media based on physics observed in core-scale and micromodel experiments. We account for non-equilibrium effects by considering redistribution time and treat saturation by evolving locally moving time-averages of the saturation. Several families of models arise from approximations to the general formulation with various degrees of accuracy. The classical Buckley-Leverett and Barenblatt expressions are special cases of these families. We explore the behaviors of a number of special cases arising from the proposed general formulation using established and novel numerical schemes that provide nonlinear physics-based preconditioning. The agreement observed between numerical and experimental results demonstrates the consistency of the proposed abstraction.     

Analysis of Multiphase Non-Darcy Flow in Porous Media

Recent laboratory studies and analyses (Lai et al. Presented at the 2009 Rocky Mountain Petroleum Technology Conference, 14–16 April, Denver, CO, 2009) have shown that the Barree and Conway model is able to describe the entire range of relationships between flow rate and potential gradient from low- to high-flow rates through porous media. A Buckley and Leverett type analytical solution is derived for non-Darcy displacement of immiscible fluids in porous media, in which non-Darcy flow is described using the Barree and Conway model. The comparison between Forchheimer and Barree and Conway non-Darcy models is discussed. We also present a general mathematical and numerical model for incorporating the Barree and Conway model in a general reservoir simulator to simulate multiphase non-Darcy flow in porous media. As an application example, we use the analytical solution to verify the numerical solution for and to obtain some insight into one-dimensional non-Darcy displacement of two immiscible fluids with the Barree and Conway model. The results show how non-Darcy displacement is controlled not only by relative permeability, but also by non-Darcy coefficients, characteristic length, and injection rates. Overall, this study provides an analysis approach for modeling multiphase non-Darcy flow in reservoirs according to the Barree and Conway model.     

Effects of Brownian Motion and Thermophoresis on the Mixed Convection of Nanofluid in a Porous Channel Including Flow Reversal

This article is devoted to combined convection heat transfer of nanofluids through a vertical channel filled with a homogeneous and isotropic porous medium. The flow is assumed to be fully developed and the “Brinkman extended Darcy” model is used for the flow in the porous media and “clear compatible” viscous dissipation model is considered. Also the model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing momentum, energy, and nanopartices volume fraction equations are solved both analytically and numerically. The effects of the influential dimensionless parameters such as Brownian and thermophoresis parameters, mixed convection parameter (Gr/Re), Brinkman, Darcy and Lewis numbers on dimensionless velocity and temperature distributions and pressure drop are studied. Also, the results of the Nusselt number for the both left and right walls are presented and discussed.     

Ergodicity of the Infinite Dimensional Fractional Brownian Motion

In this short note we prove that an infinite dimensional fractional Brownian motion B _H of any Hurst parameter ${H \in (0, 1)}In this short note we prove that an infinite dimensional fractional Brownian motion B _H of any Hurst parameter H ? (0, 1){H \in (0, 1)} forms an ergodic metric dynamical system. For the proof we mainly use the fundamental theorems of Kolmogorov.     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

Electrical Resistivity Index in Multiphase Flow through Porous Media

The simultaneous flow of two phases through a three-dimensional porous medium is calculated by means of a Lattice-Boltzmann algorithm. The time-dependent phase configurations can be derived and also macroscopic quantities such as the relative permeabilities. When one phase only is supposed to be conductive, the Laplace equation which governs electrical conduction can be solved in each phase configuration; an instantaneous value of the macroscopic conductivity is obtained and it is averaged over many configurations. The influence of saturation on the resistivity index is studied for six different samples and two viscosity ratios. The saturation exponent is systematically determined. The numerical results are also compared to other possible models and also to experimental results; finally, they are discussed and criticized.     

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。     

中国力学学会第五届全国多相流,非牛顿流,物理化学流学术会议简介

中国力学学会第五届全国多相流,非牛顿流,物理化学流学术会议于２０００年１０月３１日到１１月１日在武汉华中科技大学召开．本次会议是过去１９７９年在成都召开的第一届会议,１９８２年在北京召开的第二届会议,１９９０年在杭州召开的第三届会议,１９９３年召开的第四届会议,以及１９９７年在北京召开的第一届国际会议的继续．参加本届会议的代表来自国内力学,工程热物理和热能,化工,冶金,石油,水利等行业共４０人左右,发表论文３１篇,其中气固和液固流动８篇：气液和液液流动９篇,非牛顿流７篇,渗流７篇． 在气固和液固…     

Predictive Pore-Scale Modeling of Single and Multiphase Flow

We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. The pore space is represented by a topologically disordered lattice of pores connected by throats that have angular cross-sections. We successfully predict single-phase non-Newtonian rheology, and two and three-phase relative permeability for water-wet media. The pore size distribution of the network can be tuned to match capillary pressure data when a network representation of the system of interest is unavailable. The aim of this work is not simply to match experiments, but to use easily acquired data to estimate difficult to measure properties and to predict trends in data for different rock types or displacement sequences.     

第四届国际多相流会议简介

１会议概况第四届国际多相流会议于２００１年５月２７日到６月１日在美国Ｎｅｗ　Ｏｒｌｅａｎｓ召开．本次会议约有８００多名来自美国,加拿大,欧洲,亚洲（包括中,日,韩,　印等国）的代表参加,宣读论文共５６５篇,其中邀请报告２０篇,分组口头报告和张贴论文５４５篇．中国有清华大学周力行,杨瑞昌,西安交大陈学俊,林宗虎,陈听宽等,中科院工程热物理所蔡瑞贤,浙江大学林建忠,华中科技大学柳朝晖和大庆石油学院的２位代表共１１人参加,宣读论文１０余篇,其中周力行应邀做邀请报告１篇,宣读分组口头报告２篇,张贴论文１…     

Microvisual Study of Multiphase Gas Condensate Flow in Porous Media

Gas condensate reservoirs constitute a significant portion of hydrocarbon reserves worldwide. The liquid drop-out in these reservoirs may lead to recovery problems such as near wellbore permeability impairment and uncertainty in the actual location of the target condensate. Such technical issues can be addressed through improved understanding of the formation of condensate and the multiphase flow of gas/condensate/water in the reservoir as characterized by relative permeability curves. The appropriate relative permeability curves in turn can be used in reservoir simulators to assist in optimization of field development. This paper reports results of experiments conducted in micromodels, in support of possible core flow tests, using reservoir fluids under reservoir conditions. In particular, visualizations of condensate formation with and without connate water are presented and the differences between the two cases as well as the possible implications for the relative permeability measurements are discussed. Furthermore, the flow of gas and condensate at different force ratios (capillary and Bond numbers) are presented. It is postulated that a single dimensionless number may not be sufficient to characterize the multiphase flow in gas condensate reservoirs. The physical mechanisms occurring under various field conditions are examined in the light of these observations.     

A Fractional Linear System View of the Fractional Brownian Motion

A definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.     

A Fractional Linear System View of the Fractional Brownian Motion

A definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.     

关于二相流、多相流、多流体模型和非牛顿流等概念的探讨

本文分析了单相流、二相流和多相流等概念上的差异,也分析了单流体模型、双流体模型和多流体模型等概念上的差异,指出前面三种概念是按流动介质的客观物理构成划分的,而后者是按主观采用的研究方法划分的．目前这些概念在使用中存在一些混乱,如二相流与多相流,多相流与多流体模型等．本文还研究了扩散模型、非牛顿流模型和颗粒流模型等,指出前两种模型在分类上属于单流体模型,分析了非牛顿流模型、扩散模型和双（多）流体模型的特点和应用范围,最后,以泥石流为例讨论了以上概念的应用．      

Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media

This study is concerned with developing a two-dimensional multiphase model that simulates the movement of NAPL in heterogeneous aquifers. Heterogeneity is dealt with in a probabilistic sense by modeling the intrinsic permeability of the porous medium as a stochastic process. The deterministic finite element method is used to spatially discretize the multiphase flow equations. The intrinsic permeability is represented in the model via its Karhunen–Loeve expansion. This is a computationally expedient representation of stochastic processes by means of a discrete set of random variables. Further, the nodal unknowns, water phase saturations and water phase pressures, are represented by their stochastic spectral expansions. This representation involves an orthogonal basis in the space of random variables. The basis consists of orthogonal polynomial chaoses of consecutive orders. The relative permeabilities of water and oil phases, and the capillary pressure are expanded in the same manner, as well. For these variables, the set of deterministic coefficients multiplying the basis in their expansions is evaluated based on constitutive relationships expressing the relative permeabilities and the capillary pressure as functions of the water phase saturations. The implementation of the various expansions into the multiphase flow equations results in the formulation of discretized stochastic differential equations that can be solved for the deterministic coefficients appearing in the expansions representing the unknowns. This method allows the computation of the probability distribution functions of the unknowns for any point in the spatial domain of the problem at any instant in time. The spectral formulation of the stochastic finite element method used herein has received wide acceptance as a comprehensive framework for problems involving random media. This paper provides the application of this formalism to the problem of two-phase flow in a random porous medium.     

Multiphase Flow Fields in In-situ Air Sparging and its Effect on Remediation

In-situ air sparging (IAS) is used for the clean-up of soil and groundwater that are contaminated with volatile organic compounds in relatively permeable subsurface environments. In this study, we investigated the secondary groundwater and gas flow fields that develop in the vicinity of single and multiple air sparging wells. The purpose is to evaluate their effects on contaminant plume migration and thus, remediation. Governing equations describing multiphase flow and contaminant transport in a three-dimensional domain were formulated and solved using the Galerkin finite element technique. Trichloroethylene was selected as a target contaminant. The increase in air injection contributed to an increase in the size of the IAS cone of influence and the gas saturation levels within the cone. This reduced the groundwater velocity within the cone and increased the zone of detour of groundwater around the air sparging wells. This outcome was quantified and compared under several IAS operations. Different soil permeability characteristics also affected the groundwater and gas flow patterns, and this impacted the remedial performance of the IAS system. Under high ambient groundwater velocity, an air sparging system that uses a single injection well caused the detour of contaminant plumes around injection wells, regardless of air injection rates, and failed to meet the remedial goal specified here. This system was successful for relatively low ambient groundwater velocity environments used here. An IAS system with multiple injection wells was effective in capturing and remediating the detoured contaminant plume, and showed superior performance when compared to a single injection well IAS system. Using IAS simulation, we also analyzed the impact of injection rates on site remediation using single or multiple wells. Design criteria that are based on the results of this study would be useful in enhancing the performance of the IAS systems.