Application of infrared thermography for temperature distributions in fluid-saturated porous media

Infrared thermography has increasingly gained importance because of environmental and technological advancements of this method and is applied in a variety of disciplines related to non-isothermal flow. However, it has not been used so far for quantitative thermal analysis in saturated porous media. This article suggests infrared thermographic approach to obtain the entire surface temperature distribution(s) in water-saturated porous media. For this purpose, infrared thermal analysis is applied with in situ calibration for a better understanding of the heat transfer processes in porous media. Calibration is achieved with a combination of invasive sensors which are inserted into the medium and non-invasive thermal sensors in which sensors are not inserted to measure temperatures but it works through the detection of infrared radiation emitted from the surface. Thermocouples of relatively thin diameter are used to minimize the disturbance for flow. Thermocouples give the temperature values at specified positions inside the porous medium, and these values are compared with the values suggested by the infrared thermographic device at the same positions, in the calibration exercise. The calibration process was repeated for different temperatures and flow rates to get the temperature distributions of the whole material inside the system. This technique enables us to measure accurate two-dimensional temperature distributions, which is not possible by using thermocouples only. Continuous point heat sources at different flow rates and temperatures are studied experimentally. Additionally, it offers numerical simulations of the experiments utilizing a finite element-based model. A two-dimensional density and viscosity-dependent flow and transport model accounting for thermal dispersion is utilized to simulate the experimental results. Possible small heat losses from the surface are incorporated in the model according to the properties and thickness of the Plexiglass material used for the construction of the experiment tank. The numerical results agree well with the experimental observations.     

Computational simulation of seepage instability problems in fluid-saturated porous rocks: Potential dynamic mechanisms for controlling mineralisation patterns

Pore-fluid flow associated with seepage instabilities can play an important role in controlling large mineralisation patterns within the upper crust of the Earth. To demonstrate this process, two kinds of seepage instability problems in fluid-saturated porous rocks are considered in this paper. The first kind of seepage instability problem is caused by the temperature-induced buoyancy of pore fluid, so that it can be called the buoyancy-driven seepage instability problem, while the second kind of seepage instability problem is caused by chemical dissolution reactions that are commonly encountered in the upper crust of the Earth, so that it can be called the chemical-dissolution-driven seepage instability problem. After the mathematical governing equations of and computational methods for these two kinds of seepage instability problems are introduced, two numerical examples are used to elucidate how and why these two kinds of seepage instabilities can provide favorable places for the formation of large mineralisation patterns within the upper crust of the Earth. The related computational simulation results have demonstrated that: (1) the convective pore-fluid flow caused by the buoyancy-driven seepage instability not only can dissolve minerals at the lower part of the upper crust, but also can transport the dissolved minerals from the lower part to the upper part of the upper crust, resulting in large mineralisation patterns near the surface of the Earth's upper crust. (2) The chemical-dissolution-driven seepage instability in fluid-saturated porous rock can provide some favorable places, such as finger-like channels created by porosity enhancement in the porous rock, for the formation of large mineralisation patterns within the upper crust of the Earth.     

A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility

In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility.     

基于精细时程积分的饱和两相介质波动问题时域解法

针对u-p形式的饱和两相介质的波动方程,采用精细时程积分方法计算固相位移u,采用向后差分算法求解流体压力p,建立了基于精细时程积分技术的饱和两相介质波动问题的时域求解方法。针对标准算例,将该方法的计算结果与可视为标准结果的Zienkiewicz隐式算法的计算结果进行比较分析,二者符合较好,表明了该方法具有良好的计算精度。同时,该方法的计算过程为交替迭代求解,避免了在每个时间分析步上求解耦联方程组,因而具有较高的计算效率。该方法具有时域显式计算方法的基本特点,是进行饱和两相介质动力问题计算与分析的一种有效方法。     

多孔介质中非水相流体运移的数值模拟

针对多孔介质中水、气和非水相流体(NAPLs)的多相流动特点,建立了非水相流体(NAPLs)污染物迁移模型,分析了非水相流体在土壤非饱和区和地下水系统中的运移规律。通过有限元数值解对轻非水相流体和重非水相流体在土壤系统中的迁移过程进行模拟,得到了污染物的时空分布特征和污染范围。计算结果表明,数值模拟方法能够合理地描述非水相流体的运移过程和污染特征。土体渗透性和污染物残余饱和度是其重要影响因素。     

Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media

This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd.     

Streamline method for resolving sharp fronts for complex two-phase flow in porous media

In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully implicit finite-volume methods are provided.     

An approximate spring–dashpot artificial boundary for transient wave analysis of fluid-saturated porous media

Practical civil engineering problems are usually formulated in an infinite half-space domain, and a selected finite domain is required to analyze the dynamic responses of a fluid-saturated porous medium by the finite element method (FEM). Devising a method to deal with the boundaries of the finite domain is the key issue for this open system. In this paper, a two-dimensional spring–dashpot artificial boundary (SDAB) for transient analysis in a fluid-saturated porous media is developed. Based on Biot’s dynamic theory of fluid-saturated porous media, the normal and tangential boundary stress formulae are deduced for out-going cylindrical body waves. The boundary stress is proportional to displacement and velocity, thus continuously distributed dashpots and springs can be placed on the artificial boundaries in the normal and tangential directions to simulate the energy absorption of the infinite media outside of the finite domain for the interior distributed source problems. In this paper, the input seismic motion can be realized by applying an equivalent load on the SDAB for the seismic scattering problems of exterior distributed sources. Numerical examples are given and the analyzed results show that the SDAB and the method of wave motion input have good stability and acceptable accuracy.     

A mixed solution for two-dimensional unsteady flow in fractured porous media

A mixed finite element–boundary element solution for the analysis of two-dimensional flow in porous media composed of rock blocks and discrete fractures is described. The rock blocks are modelled implicitly by using boundary elements whereas finite elements are adopted to model the discrete fractures. The computational procedure has been implemented in a hybrid code which has been validated first by comparing the numerical results with the closed-form solution for flow in a porous aquifer intercepted by a vertical fracture only. Then, a more complex problem has been solved where a pervious, homogeneous and isotropic matrix containing a net of fractures is considered. The results obtained are shown to describe satisfactorily the main features of the flow problem under study. © 1997 by John Wiley & Sons, Ltd.     

饱和土半空间中圆柱形孔洞对平面P波的散射

在 Biot饱和多孔介质动力学理论的基础上,首次建立了求解饱和土半空间中圆柱形孔洞对平面 P 波散射问题的波函数展开法。首先。分析了具有圆柱形孔洞的饱和土半空间场地在平面 P 波入射下产生散射波系,并将入射波和散射波的波函数在圆柱坐标下展开。然后,引入边界条件,求出散射波函数的待定系数,从而,得到饱和土半空间中圆柱形孔洞对平面P波的散射问题的解析解。根据所得的波函数的解,可求解区域内的位移、应力的值,同时,分析了入射波频率、入射角对柱面上的应力集中因子的影响。     

单层不可压缩饱和多孔介质一维瞬态响应精确解

基于Biot理论,考虑惯性、黏滞和机械耦合作用,假定固体颗粒和流体均不可压缩,得到了表面任意竖向荷载作用下单层饱和多孔介质一维瞬态响应的精确解。导出了以固体骨架位移表示的无量纲控制方程,并将边界条件齐次化。求解对应无黏滞耦合作用的特征值问题,得到一组满足齐次边界条件、关于空间坐标的正交函数基。利用变异系数法和基函数的正交性,得到一系列相互解耦的、关于时间的二阶常微分方程及相应的初始条件,并采用状态空间法求解常微分方程,得到位移分量。对整体平衡方程关于空间坐标积分,根据边界条件可确定总应力,并进而求得孔隙压力。通过算例验证所得解法的正确性     

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton–Rogers–Lapwood problem in a fluid-saturated porous medium. The Horton–Rogers–Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton–Rogers–Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton–Rogers–Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton–Rogers–Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. © 1997 by John Wiley & Sons, Ltd.     

A front-tracking method for the simulation of three-phase flow in porous media

Under certain physically reasonable assumptions, three-phase flow of immiscible, incompressible fluids can be described by a 2×2 nongenuinely nonlinear, hyperbolic system. We combine analytical solutions to the corresponding Riemann problem with an efficient front-tracking method to study Cauchy and initial-boundary value problems. Unlike finite difference methods, the front-tracking method treats all waves as discontinuities by evolving shocks exactly and approximating rarefactions by small entropy-violating discontinuities. This way, the method can track individual waves and give very accurate (or even exact) resolution of discontinuities. We demonstrate the applicability of the method through several numerical examples, including a streamline simulation of a water-alternating-gas (WAG) injection process in a three-dimensional, heterogeneous, shallow-marine formation.     

非均质介质中重非水相污染物运移受泄漏速率影响数值分析

重非水相污染物(DNAPL)在地下介质中运移和分布受多种因素控制,包括DNAPL本身的物理化学性质,土的性质,泄漏条件等等。由于介质的非均质性,使得多相流运移行为更为复杂。基于地下水随机理论构建渗透率随机场,采用蒙特卡罗方法探讨泄漏速率对非均质饱和介质中DNAPL运移的影响。数值结果表明,在泄漏总量一定的情况下,泄漏速率越低,介质非均质性对DNAPL运移的影响程度越高。反之,DNAPL的渗漏速率越高,小尺度地层的非均质性影响越低。由于DNAPL运移过程中在垂直方向受重力的影响,污染羽在空间上的质心位置(一阶矩)以及展布范围(二阶矩)在垂直方向上的变异程度要高于水平方向。     

轻非水相液体在地下环境中的运移特征与模拟预测研究

通过自行设计制备的二维砂箱模拟轻非水相液体(LNAPL)在湿润多孔介质中的渗漏,得出LNAPL在地下环境中的入渗、迁移及分布规律,并利用多相流体理论对其污染机理进行分析.在实验基础上建立模型来预测渗漏的基本特征,即渗流带中污染锋面扩展速度和透镜体的最终形状,预测结果与实测结果较为接近.这种预测模型对控制和治理地下水中LNAPL污染是至关重要的.     

Analysis of the solid phase stress tensor in multiphase porous media

Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Computational homogenization of uncoupled consolidation in micro‐heterogeneous porous media

Variationally consistent homogenization is exploited for the analysis of transient uncoupled consolidation in micro‐heterogeneous porous solids, whereby the classical approach of first‐order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are introduced in quadrature points in standard fashion. Along with the classical averages, a higher‐order conservation quantity is obtained. An iterative FE²‐algorithm is devised for the case of nonlinear permeability and storage coefficients, and it is applied to pore pressure changes in asphalt‐concrete (particle composite). Various parametric studies are carried out, in particular, with respect to the influence of the ‘substructure length scale’ that is represented by the size of the RVE's. Copyright © 2009 John Wiley & Sons, Ltd.     

Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media

Three node-centered finite volume discretizations for multiphase porous media flow are presented and compared. By combination of these methods two additional discretization methods are generated. The ability of these schemes to describe flows at textural interfaces of different geologic formations is investigated. It was found that models with nonzero-entry pressures for the capillary pressure-saturation relationship in conjunction with the Box discretization may give rise to spurious oscillations for flows around low permeable lenses. Furthermore, the applicability and sensitivity of the discretization methods with regard to the used computational grids is discussed. The schemes are used for the numerical study of two-phase flow in porous media with zones of different material properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantification of the saturation degree of nonaqueous phase liquid in the vadose zone using hydrocarbon partitioning tracers

Partitioning tracer tests, as an alternative to the core sampling method, were conducted to quantify the degree of saturation of water and nonaqueous phase liquids (NAPL) in the vadose zone. Hydrocarbon gases, which have less effect on global warming than conventional tracers, were used as partitioning tracers. Column tests using CH₄, C₃H₅, and C₄H₁₀ as non-partitioning and partitioning tracers were performed to determine the retardation factor and partition coefficient of the tracer into water and NAPL. The retardation factors of these tracers were estimated to be in the range of 1.0–7.0 based on breakthrough curves of the tracers. The partition coefficient of C₃H₅ to water and diesel phase was calculated to be 0.57 and 8.45, respectively. For a heavier tracer, C₄H₁₀, the partition coefficient to the water and diesel phases was 1.2 and 40.5, respectively. The average value of water and diesel saturation estimated from column tests agreed well with known values in unsaturated soil. A residence time longer than 7.5 h within soil pores was found to provide local equilibrium partitioning of the tracer to the diesel phase. The concentration of tracer had no effect on the partitioning process.