Yu-Shu Wu

A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock

Abstract This paper presents the methodology in which two computer codes—TOUGH2 and FLAC3D—are linked and jointly executed for coupled thermal–hydrologic–mechanical (THM) analysis of multiphase fluid flow, heat transfer, and deformation in fractured and porous rock. TOUGH2 is a well-established code for geohydrological analysis with multiphase, multicomponent fluid flow and heat transport, while FLAC3D is a widely used commercial code that is designed for rock and soil mechanics with thermomechanical and hydromechanical interactions. In this study, the codes are sequentially executed and linked through external coupling modules: one that dictates changes in effective stress as a function of multi-phase pore pressure and thermal expansion, and one that corrects porosity, permeability, and capillary pressure for changes in stress. The capability of a linked TOUGH-FLAC simulator is demonstrated on two complex coupled problems related to injection and storage of carbon dioxide in aquifers and to disposal of nuclear waste in unsaturated fractured porous media.

Gas flow in porous media with Klinkenberg effects

Gas flow in porous media differs from liquid flow because of the large gas compressibility and pressure-dependent effective permeability. The latter effect, named after Klinkenberg, may have significant impact on gas flow behavior, especially in low permeability media, but it has been ignored in most of the previous studies because of the mathematical difficulty in handling the additional nonlinear term in the gas flow governing equation. This paper presents a set of new analytical solutions developed for analyzing steady-state and transient gas flow through porous media including Klinkenberg effects. The analytical solutions are obtained using a new form of gas flow governing equation that incorporates the Klinkenberg effect. Additional analytical solutions for one-, two- and three-dimensional gas flow in porous media could be readily derived by the following solution procedures in this paper. Furthermore, the validity of the conventional assumption used for linearizing the gas flow equation has been examined. A generally applicable procedure has been developed for accurate evaluation of the analytical solutions which use a linearized diffusivity for transient gas flow. As application examples, the new analytical solutions have been used to verify numerical solutions, and to design new laboratory and field testing techniques to determine the Klinkenberg parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs from The Geysers geothermal field. We show that this new approach and the traditional method of Klinkenberg yield similar results of Klinkenberg constants for the laboratory tests; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.

Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media

Abstract A robust numerical method for saturated-unsaturated flow is developed which uses a monotone discretization and variable substitution. This method is compared to a conventional formulation and to a two phase (active air phase) model. On some published test examples of infiltration into dry media, the variable substitution method shows an order of magnitude improvement (in terms of nonlinear iterations) compared to the conventional pressure based method. One, two and three dimensional computations using both finite element and finite volume discretizations are presented.

User's Guide for TOUGH2-MP - A Massively Parallel Version of the TOUGH2 Code

TOUGH2-MP is a massively parallel (MP) version of the TOUGH2 code, designed for computationally efficient parallel simulation of isothermal and nonisothermal flows of multicomponent, multiphase fluids in one, two, and three-dimensional porous and fractured media. In recent years, computational requirements have become increasingly intensive in large or highly nonlinear problems for applications in areas such as radioactive waste disposal, CO2 geological sequestration, environmental assessment and remediation, reservoir engineering, and groundwater hydrology. The primary objective of developing the parallel-simulation capability is to significantly improve the computational performance of the TOUGH2 family of codes. The particular goal for the parallel simulator is to achieve orders-of-magnitude improvement in computational time for models with ever-increasing complexity. TOUGH2-MP is designed to perform parallel simulation on multi-CPU computational platforms. An earlier version of TOUGH2-MP (V1.0) was based on the TOUGH2 Version 1.4 with EOS3, EOS9, and T2R3D modules, a software previously qualified for applications in the Yucca Mountain project, and was designed for execution on CRAY T3E and IBM SP supercomputers. The current version of TOUGH2-MP (V2.0) includes all fluid property modules of the standard version TOUGH2 V2.0. It provides computationally efficient capabilities using supercomputers, Linux clusters, or multi-core PCs, and also offers many user-friendly features. The parallel simulator inherits all process capabilities from V2.0 together with additional capabilities for handling fractured media from V1.4. This report provides a quick starting guide on how to set up and run the TOUGH2-MP program for users with a basic knowledge of running the (standard) version TOUGH2 code, The report also gives a brief technical description of the code, including a discussion of parallel methodology, code structure, as well as mathematical and numerical methods used. To familiarize users with the parallel code, illustrative sample problems are presented.

A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain, Nevada

Abstract A three-dimensional unsaturated-zone numerical model has been developed to simulate flow and distribution of moisture, gas and heat at Yucca Mountain, Nevada, a potential repository site for high-level radioactive waste. The model takes into account the simultaneous flow dynamics of liquid water, vapor, air and heat in the highly heterogeneous, fractured porous rock in the unsaturated zone (UZ). This model is intended for use in the prediction of the current and future conditions in the UZ so as to aid in the assessment of the system performance of the proposed repository. The modeling approach is based on a mathematical formulation of coupled multiphase, multicomponent fluid and heat flow through porous and fractured rock. Fracture and matrix flow is treated using both dual-permeability and effective-continuum modeling approaches. The model domain covers a total area of approximately 43 km 2 , and uses the land surface and the water table as its top and bottom boundaries. In addition, site-specific data, representative surface infiltration, and geothermal conditions are incorporated into the model. The reliability and accuracy of the model have been the subject of a comprehensive model calibration study, in which the model was calibrated against measured data, including liquid saturation, water potential and temperature. It has been found that the model is generally able to reproduce the overall system behavior at Yucca Mountain with respect to moisture profiles, pneumatic pressure variations in different geological units, and ambient geothermal conditions.

Quantifying and relating land-surface and subsurface variability in permafrost environments using LiDAR and surface geophysical datasets

The value of remote sensing and surface geophysical data for characterizing the spatial variability and relationships between land-surface and subsurface properties was explored in an Alaska (USA) coastal plain ecosystem. At this site, a nested suite of measurements was collected within a region where the land surface was dominated by polygons, including: LiDAR data; ground-penetrating radar, electromagnetic, and electrical-resistance tomography data; active-layer depth, soil temperature, soil-moisture content, soil texture, soil carbon and nitrogen content; and pore-fluid cations. LiDAR data were used to extract geomorphic metrics, which potentially indicate drainage potential. Geophysical data were used to characterize active-layer depth, soil-moisture content, and permafrost variability. Cluster analysis of the LiDAR and geophysical attributes revealed the presence of three spatial zones, which had unique distributions of geomorphic, hydrological, thermal, and geochemical properties. The correspondence between the LiDAR-based geomorphic zonation and the geophysics-based active-layer and permafrost zonation highlights the significant linkage between these ecosystem compartments. This study suggests the potential of combining LiDAR and surface geophysical measurements for providing high-resolution information about land-surface and subsurface properties as well as their spatial variations and linkages, all of which are important for quantifying terrestrial-ecosystem evolution and feedbacks to climate.ResuméLa portée de la télédétection et des données géophysique de surface pour caractériser la variabilité spatiale et les relations entre la surface du terrain et les propriétés de la subsurface a été étudiée sous tous ses aspects dans l’écosystème de la plaine côtière d’Alaska (USA). Dans cette région, sur un site où la surface du sol est dominée par des polygones, une série de données se recoupant a été collectée, incluant : données LiDAR; géoradar, tomographie électromagnétique et résistivité; profondeur de la couche aquifère, température, teneur en humidité, texture, teneur en carbone et en azote du sol; et cations du fluide des pores. Les données Lidar ont été utilisées pour établir les cotes géomorphiques, qui peuvent indiquer un drainage potentiel. Des données géophysiques ont été utilisées pour déterminer la profondeur de la couche aquifère, la teneur en humidité du sol, et la variabilité du pergélisol. L’analyse par agglomérat des données LiDAR et des attributs géophysiques ont révélé la présence de trois zones spatiales ayant une distribution similaire des propriétés géomorphiques, hydrogéologiques, thermales et géochimiques. La correspondance entre la zonation géomorphique basée sur LiDAR, la couche aquifère selon la géophysique et la zonation permafrost, met en lumière la relation significative entre ces compartiments de l’écosystème. Cette étude montre le potentiel d’une combinaison des mesures LiDAR et des mesures géophysiques de surface pour fournir une information haute résolution sur les propriétés de surface et de subsurface du sol aussi bien que sur leur variations spatiales et liens, toutes étant importantes pour quantifier l’évolution de l’écosystème terrestre et les réponses au climat.ResumenSe exploró el valor de los sensores remotos y de los datos geofísicos de superficie para caracterizar la variabilidad espacial y las relaciones entre la superficie y las propiedades subsuperficiales en un ecosistema de planicie costera en Alaska (EEUU). En este sitio, un conjunto anidado de medidas fue colectado dentro de una región donde la superficie estaba dominada por polígonos, incluyendo: datos LiDAR; datos de radar, electromagnéticos, y tomografías de resistividad eléctrica; profundidad de la capa activa, temperatura del suelo, contenido de humedad del suelo, textura del suelo, contenido de carbono y nitrógeno en suelo; y cationes del fluido de poros. Los datos LiDAR fueron usados para extraer los indicadores geomórficos, que posiblemente indican un drenaje potencial. Los datos geofísicos fueron para caracterizar la profundidad de la capa activa, el contenido de humedad del suelo y la variabilidad del permafrost. En análisis de cluster de los LiDAR y los atributos geofísicos revelaron la presencia espacial de tres zonas, que tenían una única distribución de propiedades geomórficas, hidrológicas, térmicas y geoquímicas. La correspondencia entre la zonación geomórfica basada en LiDAR y la capa activa basada en geofísica y la zonación del permafrost destaca la vinculación significativa entre estos compartimentos del ecosistema. Este estudio sugiere el potencial de la combinación LiDAR y las mediciones geofísicas de superficie para proveer información de alta resolución acerca de las propiedades de la superficie y de la subsuperficie así como su variación espacial y su articulación, todos los cuales son importantes para cuantificar la evolución del ecosistema terrestre y las reacciones con el clima.摘要用来描述地表和地下性质的空间变异性和两者之间的关系的遥感和地面地球物理数据已在阿拉斯加(美国)的一个沿海平原生态系统进行了探讨。在本次研究场地的一个表面呈多边形的区域收集到了一套测量数据,包括激光雷达数据;探地雷达数据,电磁和电阻断层扫描数据;活性层深度,土壤温度,土壤水气含量,土壤质地,土壤碳和氮的含量;以及孔隙流体阳离子数据。激光雷达数据用来提取地貌指标,这可能指示出潜在的排泄。地球物理数据用来刻画活性层的深度,土壤水气含量和永久冻土的变化特征。通过对激光雷达和地球物理数据属性的聚类分析发现了三个在地形,水文,热和地球化学性质分布上存在异常的空间区域。基于激光雷达测量的地貌分区与基于地球物理数据的活性层和永久冻土分区之间的对应关系突出了这些生态系统分区间的紧密联系。本次研究表明可以通过结合激光雷达和地表地球物理测量来为地表和地下的性质以及它们在空间上的变化和关系提供高分辨率的信息,所有这些对于量化陆地生态系统的演化和对气候变化的反应都是非常重要的。ResumoNum ecossistema da planície costeira do Alaska (EUA) foi explorado o valor da deteção remota e de dados de geofísica de superfície para caracterizar a variabilidade espacial e as relações entre propriedades da superfície do terreno e da subsuperfície. Neste local, inserido numa região onde o terreno superficial é dominado por polígonos, foi recolhido um conjunto agregado de medições, incluindo: dados de LiDAR; dados de geoadar, eletromagnéticos e de tomografia de resistência elétrica; profundidade da camada ativa, temperatura do solo, teor de água no solo, textura do solo, teor de carbono e azoto no solo; e catiões no fluido poroso. Os dados LiDAR foram usados para extrair dimensões geomórficas que potencialmente indicam o potencial de drenagem. Os dados geofísicos foram usados para caracterizar a profundidade da camada ativa, o teor de humidade no solo e a variabilidade no permafrost. A análise grupal de atributos LiDAR e geofísicos revelou a presença de três zonas espaciais que tinham distribuições únicas de propriedades geomórficas, hidrológicas, térmicas e geoquímicas. A correspondência entre o zonamento geomórfico baseado no LiDAR e a zonação da camada activa baseada na geofísica e do permafrost, demonstra a significativa conexão entre estes compartimentos do ecossistema. Este estudo sugere o potencial da combinação de medições de LiDAR e de geofísica de superfície para fornecer informação de alta resolução acerca das propriedades da superfície do terreno e da subsuperfície, assim como sobre as variações espaciais e conexões, sendo todas elas importantes para a quantificação da evolução do ecossistema terrestre e as retroações com o clima.

A Generalized Framework Model for Simulation of Gas Production in Unconventional Gas Reservoirs

Unconventional gas resources from tight-sand and shale gas reservoirs have received great attention in the past decade around the world because of their large reserves and technical advances in developing these resources. As a result of improved horizontaldrilling and hydraulic-fracturing technologies, progress is being made toward commercial gas production from such reservoirs, as demonstrated in the US. However, understandings and technologies needed for the effective development of unconventional reservoirs are far behind the industry needs (e.g., gas-recovery rates from those unconventional resources remain very low). There are some efforts in the literature on how to model gas flow in shale gas reservoirs by use of various approaches—from modified commercial simulators to simplified analytical solutions—leading to limited success. Compared with conventional reservoirs, gas flow in ultralow-permeability unconventional reservoirs is subject to more nonlinear, coupled processes, including nonlinear adsorption/ desorption, non-Darcy flow (at both high flow rate and low flow rate), strong rock/fluid interaction, and rock deformation within nanopores or microfractures, coexisting with complex flow geometry and multiscaled heterogeneity. Therefore, quantifying flow in unconventional gas reservoirs has been a significant challenge, and the traditional representative-elementary-volume(REV) based Darcy’s law, for example, may not be generally applicable. In this paper, we discuss a generalized mathematical framework model and numerical approach for unconventional-gas-reservoir simulation. We present a unified framework model able to incorporate known mechanisms and processes for two-phase gas flow and transport in shale gas or tight gas formations. The model and numerical scheme are based on generalized flow models with unstructured grids. We discuss the numerical implementation of the mathematical model and show results of our model-verification effort. Specifically, we discuss a multidomain, multicontinuum concept for handling multiscaled heterogeneity and fractures [i.e., the use of hybrid modeling approaches to describe different types and scales of fractures or heterogeneous pores—from the explicit modeling of hydraulic fractures and the fracture network in stimulated reservoir volume (SRV) to distributed natural fractures, microfractures, and tight matrix]. We demonstrate model application to quantify hydraulic fractures and transient flow behavior in shale gas reservoirs.

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.

Numerical simulation of non-isothermal multiphase tracer transport in heterogeneous fractured porous media

Abstract We have developed a new numerical method for modeling tracer and radionuclide transport through heterogeneous fractured rocks in a non-isothermal multiphase system. The model formulation incorporates a full hydrodynamic dispersion tensor, based on three-dimensional velocity fields with a regular or irregular grid in a heterogeneous geological medium. Two different weighting schemes are proposed for spatial interpolation of three-dimensional velocity fields and concentration gradients to evaluate the mass flux by dispersion and diffusion of a tracer or radionuclide. The fracture–matrix interactions are handled using a dual-continua approach, such as the double- or multiple-porosity, or dual-permeability. This new method has been implemented into a multidimensional numerical code to simulate processes of tracer or radionuclide transport in non-isothermal, three-dimensional, multiphase, porous/fractured subsurface systems. We have verified this new transport-modeling approach by comparing its results to the analytical solution of a parallel-fracture transport problem. In addition, we use published laboratory results and the particle-tracking scheme to further validate the model. Finally, we present two examples of field applications to demonstrate the use of the proposed methodology for modeling tracer and radionuclide transport in unsaturated fractured rocks.

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

Abstract A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPLs) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPLs in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.