Coarsening of three-dimensional structured and unstructured grids for subsurface flow

We present a generic, semi-automated algorithm for generating non-uniform coarse grids for modeling subsurface flow. The method is applicable to arbitrary grids and does not impose smoothness constraints on the coarse grid. One therefore avoids conventional smoothing procedures that are commonly used to ensure that the grids obtained with standard coarsening procedures are not too rough. The coarsening algorithm is very simple and essentially involves only two parameters that specify the level of coarsening. Consequently the algorithm allows the user to specify the simulation grid dynamically to fit available computer resources, and, e.g., use the original geomodel as input for flow simulations. This is of great importance since coarse grid-generation is normally the most time-consuming part of an upscaling phase, and therefore the main obstacle that has prevented simulation workflows with user-defined resolution. We apply the coarsening algorithm to a series of two-phase flow problems on both structured (Cartesian) and unstructured grids. The numerical results demonstrate that one consistently obtains significantly more accurate results using the proposed non-uniform coarsening strategy than with corresponding uniform coarse grids with roughly the same number of cells.     

Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces

Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale.     

潜流湿地中微生物对三峡库区微污染水净化效果的影响

为了探讨潜流湿地对三峡库区微污染河水的净化效果,在野外构建芦竹、菖蒲、空心菜和无植物(空白)水平潜流人工湿地,研究人工湿地系统中微生物基本菌群和功能菌群数量分布,探讨污染物去除与微生物菌群种类和数量的相关性.结果表明:实验湿地系统运行情况良好,植物湿地系统对各污染物指标的去除效果优于空白湿地系统;芦竹、菖蒲、空心菜和空白湿地系统的微生物数量均随温度的降低而减少,其中,植物湿地系统的微生物数量高于空白系统;各湿地系统的微生物数量与水质指标去除率之间的相关性较强,在夏季,不同人工湿地系统的细菌总数与CODMn的去除率之间存在着显著的正相关,真菌、亚硝酸细菌总数与铵氮去除率之间均存在着显著的正相关,在冬季,不同人工湿地系统的反硝化细菌总数与总氮去除率之间存在着显著的正相关.     

A multiscale method for subsurface inverse modeling: Single-phase transient flow

High-resolution geologic models that incorporate observed state data are expected to effectively enhance the reliability of reservoir performance prediction. One of the major challenges faced is how to solve the large-scale inverse modeling problem, i.e., to infer high-resolution models from the given observations of state variables that are related to the model parameters according to some known physical rules, e.g., the flow and transport partial differential equations. There are typically two difficulties, one is the high-dimensional problem and the other is the inverse problem. A multiscale inverse method is presented in this work to attack these problems with the aid of a gradient-based optimization algorithm. In this method, the model responses (i.e., the simulated state data) can be efficiently computed from the high-resolution model using the multiscale finite-volume method. The mismatch between the observations and the multiscale solutions is then used to define a proper objective function, and the fine-scale sensitivity coefficients (i.e., the derivatives of the objective function with respect to each node’s attribute) are computed by a multiscale adjoint method for subsequent optimization. The difficult high-dimensional optimization problem is reduced to a one-dimensional one using the gradient-based gradual deformation method. A synthetic single-phase transient flow example problem is employed to illustrate the proposed method. Results demonstrate that the multiscale framework presented is not only computationally efficient but also can generate geologically consistent models. By preserving spatial structure for inverse modeling, the method presented overcomes the artifacts introduced by the multiscale simulation and may enhance the prediction ability of the inverse-conditional realizations generated.     

于桥水库风季流场的计算与分析

本文依据水流运动的基本理论,并考虑风对水体的剪切作用,应用改进的移步ADI法,建立了风作用下流场的数值模似系统,其结果与连续四年的实测资料验证相吻合。计算预报了于桥水库三个典型水文年定常风不同风速、风向的流场,并由计算机绘制出彩色流场图。文中还针对计算应用成果进行了分析。     

Towards identifying sources of subsurface flow: A comparison of components identified by a physically based runoff model and those determined by chemical mixing techniques

A physically-based semidistributed model, TOPMODEL, is applied to a 340 hectare spruce forested catchment in mid-Wales. the model is calibrated to runoff and the subsurface flow is divided into components of flow identified by depth of origin. in addition, chemical mixing techniques are used to provide a hydrograph separation between acidic soil waters and well buffered deep waters. the short-term variations in the components of flow identified by these two approaches compare well.     

Joint conditional simulations and the spectral approach for flow modeling

The use of data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the true conditional distribution at several locations is compared with the iterative solution.The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible.     

Joint conditional simulations and the spectral approach for flow modeling

The use of data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the true conditional distribution at several locations is compared with the iterative solution.The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible.     

Improved numerical solvers for implicit coupling of subsurface and overland flow

Due to complex dynamics inherent in the physical models, numerical formulation of subsurface and overland flow coupling can be challenging to solve. ParFlow is a subsurface flow code that utilizes a structured grid discretization in order to benefit from fast and efficient structured solvers. Implicit coupling between subsurface and overland flow modes in ParFlow is obtained by prescribing an overland boundary condition at the top surface of the computational domain. This form of implicit coupling leads to the activation and deactivation of the overland boundary condition during simulations where ponding or drying events occur. This results in a discontinuity in the discrete system that can be challenging to resolve. Furthermore, the coupling relies on unstructured connectivities between the subsurface and surface components of the discrete system, which makes it challenging to use structured solvers to effectively capture the dynamics of the coupled flow. We present a formulation of the discretized algebraic system that enables the use of an analytic form of the Jacobian for the Newton–Krylov solver, while preserving the structured properties of the discretization. An effective multigrid preconditioner is extracted from the analytic Jacobian and used to precondition the Jacobian linear system solver. We compare the performance of the new solver against one that uses a finite difference approximation to the Jacobian within the Newton–Krylov approach, previously used in the literature. Numerical results explores the effectiveness of using the analytic Jacobian for the Newton–Krylov solver, and highlights the performance of the new preconditioner and its cost. The results indicate that the new solver is robust and generally outperforms the solver that is based on the finite difference approximation to the Jacobian, for problems where the overland boundary condition is activated and deactivated during the simulation. A parallel weak scaling study highlights the efficiency of the new solver.     

数值模拟方法驱动的数据流过套管电阻率测井技术

过套管电阻率测井在寻找剩余油、油藏动态监测方面是一种重要的测井技术.文中依据大数据流技术原理,建立以Hadoop架构为核心、集成仪器响应模拟、仪器关键参数设计、影响因素分析校正、岩石物理参数获取与测井评价为一体的过套管电阻率测井系统.这将打破了测井方法、仪器制造、测井采集、岩石物理与测井解释之间的部门界限,实现了不同用户实时访问统一的数据库,实时解决仪器刻度、数据采集与校正,以及综合解释中的岩石物理参数的选择等问题.基于"众包算法"实现测井解释专家的知识共享.根据过套管电阻率测井各种模拟方法特点,建立对应全空间、半空间、三层模型、径向分层纵向分层所对应不同地层模型所对应的解析法、传输线方程法、边界元、模式匹配法、有限元法所的优化高效模块,在系统中快速实现仪器响应分析、影响因素校正及仪器刻度等功能.实例表明,基于这种模拟方法驱动的大数据流过套管电阻率测井技术,能从过套管电测井数据源头上保证数据质量,从而准确求取剩余油饱和度,实现过套管测井地层评价,进而为油藏监测提供可靠的保证,最终为油藏开发方案的决策提供可靠依据.     

A new solution and data analysis for gas flow to a barometric pumping well

When an open well is installed in an unsaturated zone, gas will flow to/from the well depending on the pressure difference between the well and the surrounding media. This process is called barometric pumping and the well is called a barometric pumping well (BPW). Understanding subsurface gas pressure distribution and gas flow rate to/from a BPW is indispensable to optimize passive soil vapor extraction. This study presents a 2-D semi-analytical solution to calculate the subsurface gas pressure and gas flow rate to/from a BPW with and without a check valve. The problem is conceptualized as a mixed-type boundary value problem. The solution for pumping without a check valve is used to analyze the behavior of the radius of influence (ROI). Results show that ROI is time-dependent. It increases with radial gas permeability and decreases with vertical gas permeability. Field application of the solution without a check valve demonstrates the high accuracy of the developed solution.     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Evaluations of subsurface flow for reconstructions of climate change using borehole temperature and isotope data in Kamchatka

Subsurface temperature is affected by heat advection due to groundwater flow and surface temperature changes. To evaluate their effects, it was implemented the measurements of temperature-depth profile (T-D profile) and the continuous monitoring of soil temperature in the southern part of Kamchatka which has not affected by human activity. Additionally, stable isotopic compositions of surface water and groundwater were analyzed. T-D profile and stable isotopic compositions show groundwater flow system is differ from the shallow aquifer to the deep aquifer. In the shallow aquifer, T-D profile suggests the existence of upward groundwater flux. On the other hand, the annual variation of soil temperature is divided into the large variation period (VP) and the stable period (SP) by the magnitude of daily and seasonal variation. VP and SP correspond to the summer and the winter season, respectively, and it considers that the difference between VP and SP is caused by the effect of snow cover. Therefore, the T-D profile is affected by not only upward groundwater flux but also the surface warming particularly in the summer season (VP).     

3-D spherical shell modeling of mantle flow and its implication for global tectogenesis

In order to study the relationship between mantle flow and global tectogenesis, we present a 3-D spherical shell model with incompressible Newtonian fluid medium to simulate mantle flow which fits the global tectogenesis quite well. The governing equations are derived in spherical coordinates. Both the thermal buoyancy force and the self-gravitation are taken into account. The velocity and pressure coupled with temperature are computed, using the finite-element method with a punitive factor. The results show that the lithosphere, as the boundary layer of the earth's thermodynamic system, moves with the entire mantle. Both its horizontal and vertical movements are the results of the earth's thermal motion. The orogenesis occurs not only in the collision zones at the plates' boundaries, but also occurs within the plates. If the core-mantle boundary is impermeable and the viscosity of the lower mantle is considerable, the vertical movement is mostly confined to the upper mantle. The directions of the asthenospheric movements are not fully consistent with those of the lithospheric movements. The depths of spreading movements beneath all ridges are less than 220 km. In some regions, the shear stresses, acting on the base of the lithosphere by the asthenosphere, are the main driving force; but in other regions, the shear stresses are the resisting force.     

A finite element model for simulating surface run‐off and unsaturated seepage flow in the shallow subsurface

This work introduces water–air two‐phase flow into integrated surface–subsurface flow by simulating rainfall infiltration and run‐off production on a soil slope with the finite element method. The numerical model is formulated by partial differential equations for hydrostatic shallow flow and water–air two‐phase flow in the shallow subsurface. Finite element computing formats and solution strategies are presented to obtain a numerical solution for the coupled model. An unsaturated seepage flow process is first simulated by water–air two‐phase flow under the atmospheric pressure boundary condition to obtain the rainfall infiltration rate. Then, the rainfall infiltration rate is used as an input parameter to solve the surface run‐off equations and determine the value of the surface run‐off depth. In the next iteration, the pressure boundary condition of unsaturated seepage flow is adjusted by the surface run‐off depth. The coupling process is achieved by updating the rainfall infiltration rate and surface run‐off depth sequentially until the convergence criteria are reached in a time step. A well‐conducted surface run‐off experiment and traditional surface–subsurface model are used to validate the new model. Comparisons with the traditional surface–subsurface model show that the initiation time of surface run‐off calculated by the proposed model is earlier and that the water depth is larger, thus providing values that are closer to the experimental results.     

Differences in preferential flow with antecedent moisture conditions and soil texture: Implications for subsurface P transport

Preferential flowpaths transport phosphorus (P) to agricultural tile drains. However, if and to what extent this may vary with soil texture, moisture conditions, and P placement is poorly understood. This study investigated (a) interactions between soil texture, antecedent moisture conditions, and the relative contributions of matrix and preferential flow and (b) associated P distributions through the soil profile when fertilizers were applied to the surface or subsurface. Brilliant blue dye was used to stain subsurface flowpaths in clay and silt loam plots during simulated rainfall events under wet and dry conditions. Fertilizer P was applied to the surface or via subsurface placement to plots of different soil texture and moisture condition. Photographs of dye stains were analysed to classify the flow patterns as matrix dominated or macropore dominated, and soils within plots were analysed for their water‐extractable P (WEP) content. Preferential flow occurred under all soil texture and moisture conditions. Dye penetrated deeper into clay soils via macropores and had lower interaction with the soil matrix, compared with silt loam soil. Moisture conditions influenced preferential flowpaths in clay, with dry clay having deeper infiltration (92 ± 7.6 cm) and less dye–matrix interaction than wet clay (77 ± 4.7 cm). Depth of staining did not differ between wet (56 ± 7.2 cm) and dry (50 ± 6.6 cm) silt loam, nor did dominant flowpaths. WEP distribution in the top 10 cm of the soil profile differed with fertilizer placement, but no differences in soil WEP were observed at depth. These results demonstrate that large rainfall events following drought conditions in clay soil may be prone to rapid P transport to tile drains due to increased preferential flow, whereas flow in silt loams is less affected by antecedent moisture. Subsurface placement of fertilizer may minimize the risk of subsurface P transport, particularily in clay.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow

This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in this series, we demonstrate the TCAT approach for the case of single-fluid-phase flow. The formulated model is based upon conservation equations for mass, momentum, and energy and a general entropy inequality constraint, which is developed to guide model closure. A specific example of a closed model is derived under limiting assumptions using a linearization approach and these results are compared and contrasted with the traditional single-phase-flow model. Potential extensions to this work are discussed. Specific advancements in this work beyond previous averaging theory approaches to single-phase flow include use of macroscale thermodynamics that is averaged from the microscale, the use of derived equilibrium conditions to guide a flux–force pair approach to simplification, use of a general Lagrange multiplier approach to connect conservation equation constraints to the entropy inequality, and a focus on producing complete, closed models that are solvable.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow

This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models.     

Subsurface storm flow formation at different hillslopes and implications for the ‘old water paradox’

Although many studies over the past several decades have documented the importance of subsurface stormflow (SSF) in hillslopes, its formation is still not well understood. Therefore, we studied SSF formation in the vadose soil zone at four different hillslopes during controlled sprinkling experiments and natural rainfall events. Event and pre‐event water fractions were determined using artificially traced sprinkling water and ²²²Rn as natural tracer. SSF formation and the fraction of pre‐event water varied substantially at different hillslopes. Both intensity of SSF and fraction of pre‐event water depended on whether SSF in preferential flow paths was fed directly from precipitation or was fed indirectly from saturated parts of the soil. Soil water was rapidly mobilized from saturated patches in the soil matrix and was subsequently released into larger pores, where it mixed with event water. Substantial amounts of pre‐event water, therefore, were contained in fast flow components like subsurface storm flow and also in overland flow. This finding has consequences for commonly used hydrograph separation methods and might explain part of the ‘old water paradox’. Copyright © 2007 John Wiley & Sons, Ltd.     

A simulation of large‐scale groundwater flow and travel time in a fractured rock environment for waste disposal purposes

Two‐dimensional regional groundwater flow was simulated based on a conceptual model of low‐permeability crystalline rocks of the Whiteshell Research Area (WRA) in south‐eastern Manitoba. The conceptual model consists of fracture zones that strike in different directions and dip at various angles in the background rock mass. The thickness and hydraulic properties of the fracture zones in the conceptual model were varied as were the fluid properties and the boundary conditions of the groundwater flow system. The effects of these variations on the groundwater flow pattern and on the convective travel time along pathways from a hypothetical disposal vault at 500 m depth to discharge locations at the ground surface were evaluated. The vault was located in the regional discharge area of the groundwater system. A homogeneous conceptual model of the WRA, having only freshwater flow, formed a groundwater flow pattern with a regional flow system. Local flow systems developed increasingly with the introduction of fracture zones 20 m and 3 m thick, and depth‐dependent fluid density. This indicates a reduction in groundwater residence time by fracture zones and fluid density. Flow pathways were analysed using both a stream‐function and a particle‐tracking technique. The pathways and their lengths from the location of the vault to the surface varied spatially according to the flow patterns. The minimum travel time along these pathways was less than 150 000 and greater than 4 000 000 years in models with and without fracture zones, respectively, indicating that the presence of fracture zones was the major controlling factor. A precise knowledge and refinement of conceptual model parameters is necessary during site selection for waste disposal purposes. Copyright © 2004 John Wiley & Sons, Ltd.