Non-Newtonian flow in porous media

In this article we present a review of the single-phase flow of non-Newtonian fluids in porous media. The four main approaches for describing the flow through porous media in general are examined and assessed in this context. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.     

Slow immiscible displacement flow in disordered porous media

The immiscible displacement of a wetting fluid by a non-wetting fluid in a disordered porous medium is studied in the capillary region, i.e. when capillary forces are dominant, by using the invasion percolation model to describe the displacement mechanism. The porous medium is represented by a two-dimensional network of interconnected capillaries whose radii follow a uniform size distribution. Disorder is assigned to the medium by considering the probabilities of occurrence of inaccessible pores, p_s, and non-conductive capillaries, p_b. It is found that the dynamic behaviour of the displacing fluid and the fraction of invaded pores depend on the degree of disorder of the medium. The results can provide an interpretation of the effects of the dead-end pore volume on the oil recovery and the displacement behaviour.     

Modelling the flow of power-law fluids through anisotropic porous media at low-pore Reynolds number

The flow of power-law fluids through fibrous media at low-pore Reynolds number is investigated using the homogenization method for periodic structures with multiple scale expansions. This upscaling process shows that the macroscopic pressure gradient is also a power-law of the volume averaged velocity field. To determine the complete structure of the macroscopic flow law, numerical simulations have to be performed on representative elementary volume of porous media. In this paper, this has been achieved on 2D periodic arrays of parallel fibers with elliptical cross section of different aspect ratios. It is found that macroscopic flow models already proposed in the literature fail in reproducing numerical data within the whole volume fractions of fibers and aspect ratios ranges. Consequently, a novel methodology is proposed to establish the macroscopic tensorial seepage law within the framework of the theory of anisotropic tensor functions and using mechanical iso-dissipation curves. This methodology is illustrated through our numerical results.     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

Viscoelastic flow in packed beds or porous media

An analysis of viscoelastic flow in packed beds or porous media is presented based on a capillary hybrid model of the flow which incorporates a viscous mode and an elongational mode. The development includes modelling of the elongational mode of the flow to obtain the elongational flow contribution to the potential drop for a viscoelastic fluid. A general expression describing viscoelastic flow in porous media is developed which utilizes the viscous response determined by the fluid model equation and an elongational flow response characterized by an elongational viscosity difference for the fluid. The expression applies to all three traditional bed models employing the tortuosity and Kozeny constant. The relationship yielded extensions of Darcy's law applicable to viscoelastic flow in porous media and an expression representing the flow of a viscoelastic fluid in a packed bed or porous core of length L. The relationship of the friction factors and respective Reynolds numbers is also presented.     

泡沫液在均质多孔介质内动态驱替过程的二维数值模拟研究

利用随机泡沫数目守恒模型,针对具有收缩进口及收缩出口的均质多孔介质二维模型,对泡沫流体驱替突破前的动态过程开展了数值模拟研究。采用IMPES方法对二维两相泡沫动态驱替过程的控制方程组进行求解,通过液相压力、液相饱和度、气泡数目等参数在多孔介质内的分布结果对泡沫动态驱替特性进行了分析研究。数值模拟结果表明,泡沫驱替过程显示出明显的入口效应,其压力分布、液相饱和度及泡沫数目分布随气体与活化剂溶液在缩小入口的注入呈现明显的发展过程。在泡沫液未完成驱替突破的情况下,缩小出口未显示出对泡沫液驱替特性的影响。数值计算结果与相应实验结果趋势一致,表明所采用的随机泡沫数目守恒模型能够正确表征多孔介质中泡沫的生成及湮灭机理,进而对泡沫液在均质多孔介质内的动态驱替特性进行准确模拟和预测。     

多孔介质内颗粒流动特性的格子Boltzmann模拟

地下岩石孔隙中小颗粒的运移和沉积会使得储层渗透性能降低,影响石油开发。为了探究悬浮颗粒在多孔介质中的流动过程,采用格子Boltzmann方法对三维多孔介质内流体和颗粒的运动过程进行了数值模拟,采用有限体积颗粒法构建多孔介质中骨架颗粒和悬浮颗粒。通过Half-Way反弹格式实现流体与颗粒间的相互作用,考虑孔隙结构、入口流速、孔隙率和颗粒直径对颗粒流动特性的影响,探究颗粒的运移和沉积规律。结果表明,入口速度对不同孔隙结构下颗粒的运动作用显著。随着入口速度增大,颗粒与颗粒、孔隙壁面以及流体之间的动量和能量交换作用增强,缩短了颗粒的运移路径,颗粒沉积率逐渐变小,颗粒拟温度增大。孔隙率的下降强化了颗粒间的碰撞,孔隙率由0.581降低至0.400,使得颗粒拟温度提升至9倍。颗粒拟温度随颗粒直径的增加而增加。但随着孔隙率增加,颗粒轴向速度增加,颗粒最高轴向速度可达入口流速的11倍,而颗粒接触力降低。     

A stochastic analysis of the flow of two immiscible fluids in porous media: The case when the viscosities of the fluids are equal

A new stochastic theory is developed to explain the flow of two immiscible fluids in porous medium when the viscosity difference between two fluids is zero. In an individual micropore the radius of curvature of the interface separating the fluids is assumed constant and flow is modeled by the random jumping of microscopic interfaces. A one dimensional model composed of an array of parallel capillary tubes of constant radius is analyzed in detail. For the case in which two fluids have equal viscosity an analytical solution is obtained. The fluid displacement process is Fickian and dispersion is described in terms of a diffusion or spreading constant.     

流体绝热流动过程的损失

本文运用热力学和传递过程的理论,对流体流动过程进行了(火用)分析。结果表明,对于不同工况,(火用)损失的大小及其影响因素是不同的。     

地下水人工补给过程中流速对多孔介质胶体堵塞的影响机理

通过一系列室内砂柱模拟实验,研究了流速对胶体在饱和多孔介质中滞留-迁移行为的影响;运用COMSOL软件模拟,拟合实验数据后得到表征胶体沉积的关键参数。结果表明：流速增大缩短了胶体在多孔介质中的滞留时间,并增强水动力拖拽力,导致介质对胶体的吸附量减少,有利于胶体的迁移;回灌时间的延续造成的多孔介质渗透系数降低,可通过瞬间增大流速使渗透系数在较短时间内恢复,然而随后形成新的吸附渗透性仍会降低。水源离子强度、介质粗糙度等因素会影响胶体迁移的流速效应。在相同条件下,吸附系数随着离子强度的增大而增加,随着流速的增大而增加。综合来看,离子强度的增加可抵消一部分水动力拖拽力的影响,提高胶体在多孔介质中滞留的概率;介质表面粗糙度的增加,可削弱水动力拖拽力作用,同时增加胶体与介质的吸附、沉积点位和接触面积,导致胶体易于在多孔介质中发生滞留并可能进一步导致介质堵塞。     

Experimental study of diffusivity of hexane in bitumen-saturated porous media under high temperature/pressure conditions

Solvent mass transfer plays a key role in a thermal gravity drainage process involving solvent. The diffusion coefficients of solvent in such a process are not well studied. This article presents the effective diffusion coefficients of solvent in bitumen-saturated sands under high temperature/pressure conditions measured using a CT scanning technique. Experimental results show that the effective diffusion coefficient of n-hexane in bitumen-saturated sands varied with the solvent concentration or with the viscosity of solvent–bitumen mixture (i.e., D_e ∝ c^0.4 or D_e ∝ μ_m^−0.46). The solvent concentration weighted diffusion coefficient of n-hexane in the bitumen under the condition 160–170°C/1,900 kPa had an order of magnitude of about 10⁻⁵ cm²/s for solvent volume concentration less than 0.2. The penetration distance of n-hexane in bitumen-saturated sands depended on the nonlinearity of diffusion and had a value of −2 cm after 1-day diffusion. The stronger the nonlinearity of diffusion, the shorter the penetration distance.     

Motion of viscous drops in tubes filled with yield stress fluid

The dynamics of deformable viscous drops in yield stress medium is investigated experimentally. Tetrachloroethylene drops settle in a cylindrical tube filled with neutralized Carbopol solution under the action of gravity. For a single fluid particle, stopping conditions, established velocities and deformation patterns are examined for a variety of the physical parameters of the continuous medium determined by Carbopol concentration and the geometry of the system. For a pair of drops, we present time evolution of separation distance and of the shapes of the drops. It was found that if the initial separation between equal size drops does not exceed some critical value, the trailing particle moves with a considerably higher velocity than that of the leading one and eventually the two drops coalesce. Afterwards, a single large fluid particle is formed and it sometimes breaks up forming one large leading drop and one or several small trailing satellites. This behavior is qualitatively similar to that obtained previously in numerical simulations.     

A method to calculate the multiphase flow properties of heterogeneous porous media by using network simulations

A method is suggested to compute the capillary pressure and relative permeability curves of heterogeneous porous media. The broad pore radius distribution (PRD) and throat radius distribution (TRD) are decomposed into relatively narrow component distribution functions which are used for the computer‐aided construction of pore‐and‐throat networks. The quasi‐static motion of menisci in pores and throats is tracked by accounting for capillary forces. The presence of fractal roughness along pore walls ensures the coexistence of both phases in pores. The calculation of the hydraulic conductance of each phase is based on the concept of constricted unit cell. Simulations in component pore networks constructed from narrow PRD and TRD produce a set of capillary pressure and relative permeability functions, the arithmetic averaging of which yields the corresponding functions for a heterogeneous synthetic pore network. This information is used by a dynamic simulator of drainage in permeability networks to predict experimental results of soil columns. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Using electrical resistance tomography and computational fluid dynamics modeling to study the formation of cavern in the mixing of pseudoplastic fluids possessing yield stress

Electrical resistance tomography (ERT) provides a non-intrusive technique to examine, in three dimensions, the homogeneity and flow pattern inside the mixing tank. In this study, a 4-plane 16-sensor ring ERT system was employed to study the shape and the size of cavern generated around a radial-flow Scaba 6SRGT impeller in the mixing of xanthan gum solution, which is a pseudoplastic fluid possessing yield stress. The size of cavern measured using ERT was in good agreement with that calculated using Elson's model (cylindrical model). The 3D flow field generated by the impeller in the agitation of xanthan gum was also simulated using the commercial computational fluid dynamics (CFD) package (Fluent). The CFD model provided useful information regarding the impeller pumping capacity, flow pattern, and the formation of cavern around the impeller. CFD results showed good agreement with the experimental data and theory.     

多孔介质中CO2-CH4水合物置换过程的强化方法研究进展

CO2置换天然气水合物中的CH4是一种非常有前途的天然气水合物开采方法,该法兼具能源安全开采和温室气体地层封存的双重优势。首先综述了多孔介质中CO2-CH4水合物置换的研究进展,分析了制约CO2置换法开采天然气水合物商业应用的关键瓶颈问题,即置换过程存在的反应周期长、速率慢和效率低等问题。针对此问题,主要详述了强化CO2-CH4水合物置换的强化方法研究进展,包括注入不同的CO2相态、小分子及混合气体的强化、结合传统开采法的联合强化以及其他强化方法的作用机理,讨论了各种强化方法尚待完善和改进的地方。最后提出了多孔介质中CO2-CH4水合物置换强化方法目前研究的不足和未来的研究方向。     

Modeling drying in thin porous media after coupling pore-level drying dynamics with external flow field

This article uses a novel, fully coupled method to solve the isothermal slow drying of porous media in laminar flow. The film effect is included and a novel logistic equation is used to relate the pore network variables with the external field variables. The model is used to simulate the drying of several thin porous media with different aspect ratios in a flow. One, two, or all sides of the pore network are opened to the flow. The studies show that the higher exposed area vs. total volume ratio leads to faster drying while the orientation of the porous media is immaterial.     

Permeability analysis and seepage process study on crystal layer in melt crystallization with fractal and porous media theory

In this paper a porous media seepage model was applied to analyze the permeability and study the seepage process of crystal pillar formed in the preparation of electronic grade phosphoric acid (EGPA). By inspecting the seeping process, the structure parameter of crystal pillar could be obtained. Two basic ideal models (perfectly separated model and perfectly connected model) were presented and a characterized factor φ was introduced to modify the model. A good simulation result was obtained which met the experiment result well. The relationship between φ and permeability were also discussed. The characterized factor φ showed potential application on optimizing process.     

Simulation of deformable preformed particle gel propagation in porous media

Preformed particle gel (PPG) treatment is a proven cost‐effective method for improving oil recovery. Although PPG system has a suspension‐like property, it has different propagation rules from the rigid particle suspension in porous media because of its good deformation property. In this study, an advanced phenomenological model of PPG propagation in porous media is presented. The model includes both PPG plugging and restarting behaviors. Log‐normal and normal distribution functions have been introduced in this model to calculate the PPG plugging probability. Power‐law equation is used to calculate the PPG restarting rate. This method can represent the commensurate relation between PPG and throat size. Then, the equations are solved numerically, using an explicit finite‐difference formulation in conjunction with a fourth‐order Runge‐Kutta method. The results match favorably with several laboratory experiments. Finally, the propagation rules and sensitivity analysis of PPG size, permeability and injection rate to propagation rules, and permeability reduction are performed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4628–4641, 2017