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Exact Averaging of Stochastic Equations for Flow in Porous Media

Description: It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods--for example, the convergence behavior and the accuracy of truncated perturbation series--are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for three-dimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem.
Date: March 15, 2008
Creator: Karasaki, Kenzi; Shvidler, Mark & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Averaging of Stochastic Equations for Flow and Transport in PorousMedia

Description: It is well known that at present exact averaging of theequations of flow and transport in random porous media have been realizedfor only a small number of special fields. Moreover, the approximateaveraging methods are not yet fully understood. For example, theconvergence behavior and the accuracy of truncated perturbation seriesare not well known; and in addition, the calculation of the high-orderperturbations is very complicated. These problems for a long time havestimulated attempts to find the answer for the question: Are there inexistence some exact general and sufficiently universal forms of averagedequations? If the answer is positive, there arises the problem of theconstruction of these equations and analyzing them. There are manypublications on different applications of this problem to various fields,including: Hydrodynamics, flow and transport in porous media, theory ofelasticity, acoustic and electromagnetic waves in random fields, etc.Here, we present a method of finding some general form of exactlyaveraged equations for flow and transport in random fields by using (1)some general properties of the Green s functions for appropriatestochastic problems, and (2) some basic information about the randomfields of the conductivity, porosity and flow velocity. We presentgeneral forms of exactly averaged non-local equations for the followingcases: (1) steady-state flow with sources in porous media with randomconductivity, (2) transient flow with sources in compressible media withrandom conductivity and porosity; and (3) Nonreactive solute transport inrandom porous media. We discuss the problem of uniqueness and theproperties of the non-local averaged equations for cases with some typeof symmetry (isotropic, transversal isotropic and orthotropic), and weanalyze the structure of the nonlocal equations in the general case ofstochastically homogeneous fields.
Date: January 7, 2005
Creator: Shvidler, Mark & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Development of Hydrologic Characterization Technology of Fault Zones -- Phase I, 2nd Report

Description: This is the year-end report of the 2nd year of the NUMO-LBNL collaborative project: Development of Hydrologic Characterization Technology of Fault Zones under NUMO-DOE/LBNL collaboration agreement, the task description of which can be found in the Appendix 3. Literature survey of published information on the relationship between geologic and hydrologic characteristics of faults was conducted. The survey concluded that it may be possible to classify faults by indicators based on various geometric and geologic attributes that may indirectly relate to the hydrologic property of faults. Analysis of existing information on the Wildcat Fault and its surrounding geology was performed. The Wildcat Fault is thought to be a strike-slip fault with a thrust component that runs along the eastern boundary of the Lawrence Berkeley National Laboratory. It is believed to be part of the Hayward Fault system but is considered inactive. Three trenches were excavated at carefully selected locations mainly based on the information from the past investigative work inside the LBNL property. At least one fault was encountered in all three trenches. Detailed trench mapping was conducted by CRIEPI (Central Research Institute for Electric Power Industries) and LBNL scientists. Some intriguing and puzzling discoveries were made that may contradict with the published work in the past. Predictions are made regarding the hydrologic property of the Wildcat Fault based on the analysis of fault structure. Preliminary conceptual models of the Wildcat Fault were proposed. The Wildcat Fault appears to have multiple splays and some low angled faults may be part of the flower structure. In parallel, surface geophysical investigations were conducted using electrical resistivity survey and seismic reflection profiling along three lines on the north and south of the LBNL site. Because of the steep terrain, it was difficult to find optimum locations for survey lines as it is desirable for ...
Date: March 31, 2009
Creator: Karasaki, Kenzi; Onishi, Tiemi; Black, Bill & Biraud, Sebastien
Partner: UNT Libraries Government Documents Department

Development of Hydrologic Characterization Technology of Fault Zones

Description: Through an extensive literature survey we find that there is very limited amount of work on fault zone hydrology, particularly in the field using borehole testing. The common elements of a fault include a core, and damage zones. The core usually acts as a barrier to the flow across it, whereas the damage zone controls the flow either parallel to the strike or dip of a fault. In most of cases the damage zone isthe one that is controlling the flow in the fault zone and the surroundings. The permeability of damage zone is in the range of two to three orders of magnitude higher than the protolith. The fault core can have permeability up to seven orders of magnitude lower than the damage zone. The fault types (normal, reverse, and strike-slip) by themselves do not appear to be a clear classifier of the hydrology of fault zones. However, there still remains a possibility that other additional geologic attributes and scaling relationships can be used to predict or bracket the range of hydrologic behavior of fault zones. AMT (Audio frequency Magneto Telluric) and seismic reflection techniques are often used to locate faults. Geochemical signatures and temperature distributions are often used to identify flow domains and/or directions. ALSM (Airborne Laser Swath Mapping) or LIDAR (Light Detection and Ranging) method may prove to be a powerful tool for identifying lineaments in place of the traditional photogrammetry. Nonetheless not much work has been done to characterize the hydrologic properties of faults by directly testing them using pump tests. There are some uncertainties involved in analyzing pressure transients of pump tests: both low permeability and high permeability faults exhibit similar pressure responses. A physically based conceptual and numerical model is presented for simulating fluid and heat flow and solute transport through fractured fault zones ...
Date: March 31, 2008
Creator: Karasaki, Kenzi; Onishi, Tiemi & Wu, Yu-Shu
Partner: UNT Libraries Government Documents Department

Evaluation of uncertainties due to hydrogeological modeling and groundwater flow analysis: Effective continuum model using TOUGH2

Description: Starting with regional geographic, geologic, hydrologic, geophysical, and meteorological data, we develop an effective continuum model to simulate subsurface flow and transport in a 4 km by 6 km by 3 km thick fractured granite rock mass overlain sedimentary layers. Individual fractures are not modeled explicitly. Rather, continuum permeability and porosity distributions are assigned stochastically, based on well-test data and fracture density measurements. Large-scale features such as lithologic layering and major fault zones are assigned deterministically. We employ the TOUGH2 simulator for the flow calculation. The model simulates the steady-state groundwater flow through the site, then streamline analysis is used to calculate travel times for particles leaving specified monitoring points to reach the boundary of the model. Model results for the head distribution compare favorably with head profiles measured in several deep boreholes and the overall groundwater flow is consistent with regional water balance data. Predicted travel times range from 1 to 25 years.
Date: July 13, 2001
Creator: Doughty, Christine & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Evaluation of uncertainties due to hydrogeological modeling and groundwater flow analysis: Steady flow, transient flow, and thermal studies

Description: Starting with regional geographic, geologic, surface and subsurface hydrologic, and geophysical data for the Tono area in Gifu, Japan, we develop an effective continuum model to simulate subsurface flow and transport in a 4 km by 6 km by 3 km thick fractured granite rock mass overlain by sedimentary layers. Individual fractures are not modeled explicitly. Rather, continuum permeability and porosity distributions are assigned stochastically, based on well-test data and fracture density measurements. Lithologic layering and one major fault, the Tsukiyoshi Fault, are assigned deterministically. We conduct three different studies: (1) the so-called base case, in which the model simulates the steady-state groundwater flow through the site, and then stream trace analysis is used to calculate travel times to the model boundary from specified release points; (2) simulations of transient flow during long term pump tests (LTPT) using the base-case model; and (3) thermal studies in which coupled heat flow and fluid flow are modeled, to examine the effects of the geothermal gradient on groundwater flow. The base-case study indicates that the choice of open or closed lateral boundaries has a strong influence on the regional groundwater flow patterns produced by the models, but no field data exist that can be used to determine which boundary conditions are more realistic. The LTPT study cannot be used to distinguish between the alternative boundary conditions, because the pumping rate is too small to produce an analyzable pressure response at the model boundaries. In contrast, the thermal study shows that the temperature distributions produced by the open and closed models differ greatly. Comparison with borehole temperature data may be used to eliminate the closed model from further consideration.
Date: December 11, 2002
Creator: Doughty, Christine & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Constraining hydrologic models using thermal analysis

Description: Starting with regional geographic, geologic, hydrologic, geophysical, and meteorological data for the Tono area in Gifu, Japan, we develop a numerical model to simulate subsurface flow and transport in a 4 km by 6 km by 3 km thick fractured granite rock mass overlain by sedimentary layers. Individual fractures are not modeled explicitly. Rather, continuum permeability and porosity distributions are assigned stochastically, based on well-test data and fracture density measurements. The primary goal of the study is to simulate steady-state groundwater flow through the site, then calculate travel times to the model boundaries from specified monitoring points. The lateral boundaries of the model follow topographic features such as ridgelines and rivers. Assigning lateral boundary conditions is a major point of uncertainty in model construction. We evaluate two models with opposing boundary conditions: mostly closed and mostly open boundaries. The two models show vastly different spatial distributions of groundwater flow, so we would like to find a means of choosing the more realistic model. Surface recharge is much larger for the closed model, but field recharge data are of too limited spatial extent to provide a definitive model constraint. Temperature profiles in 16 boreholes show consistent trends with conduction-dominated (linear) temperature profiles below depths of about 300 m. The open and closed models predict strongly different temperature versus depth profiles; with the closed model showing a strong convective signature produced by widespread surface recharge effects to the depth. The open model shows more linear temperature profiles, better agreeing with measurements from the field. Based on this data we can eliminate from consideration the closed model, at least in its present form in which surface recharge penetrates deep into the model.
Date: December 12, 2002
Creator: Doughty, Christine & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Exactly averaged stochastic equations for flow and transport in random media

Description: It is well known that exact averaging of the equations of flow and transport in random porous media are at present realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series are not well known. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding some general forms of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2 ) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present some general forms of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure of non-local equations in a general ...
Date: November 30, 2001
Creator: Shvidler, Mark & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Sensitivity study on hydraulic well testing inversion using simulated annealing

Description: For environmental remediation, management of nuclear waste disposal, or geothermal reservoir engineering, it is very important to evaluate the permeabilities, spacing, and sizes of the subsurface fractures which control ground water flow. Cluster variable aperture (CVA) simulated annealing has been used as an inversion technique to construct fluid flow models of fractured formations based on transient pressure data from hydraulic tests. A two-dimensional fracture network system is represented as a filled regular lattice of fracture elements. The algorithm iteratively changes an aperture of cluster of fracture elements, which are chosen randomly from a list of discrete apertures, to improve the match to observed pressure transients. The size of the clusters is held constant throughout the iterations. Sensitivity studies using simple fracture models with eight wells show that, in general, it is necessary to conduct interference tests using at least three different wells as pumping well in order to reconstruct the fracture network with a transmissivity contrast of one order of magnitude, particularly when the cluster size is not known a priori. Because hydraulic inversion is inherently non-unique, it is important to utilize additional information. The authors investigated the relationship between the scale of heterogeneity and the optimum cluster size (and its shape) to enhance the reliability and convergence of the inversion. It appears that the cluster size corresponding to about 20--40 % of the practical range of the spatial correlation is optimal. Inversion results of the Raymond test site data are also presented and the practical range of spatial correlation is evaluated to be about 5--10 m from the optimal cluster size in the inversion.
Date: November 1, 1997
Creator: Nakao, Shinsuke; Najita, J. & Karasaki, Kenzi
Partner: UNT Libraries Government Documents Department

Development of Characterization Technology for Fault Zone Hydrology

Description: Several deep trenches were cut, and a number of geophysical surveys were conducted across the Wildcat Fault in the hills east of Berkeley, California. The Wildcat Fault is believed to be a strike-slip fault and a member of the Hayward Fault System, with over 10 km of displacement. So far, three boreholes of ~;; 150m deep have been core-drilled and borehole geophysical logs were conducted. The rocks are extensively sheared and fractured; gouges were observed at several depths and a thick cataclasitic zone was also observed. While confirming some earlier, published conclusions from shallow observations about Wildcat, some unexpected findings were encountered. Preliminary analysis indicates that Wildcat near the field site consists of multiple faults. The hydraulic test data suggest the dual properties of the hydrologic structure of the fault zone. A fourth borehole is planned to penetrate the main fault believed to lie in-between the holes. The main philosophy behind our approach for the hydrologic characterization of such a complex fractured system is to let the system take its own average and monitor a long term behavior instead of collecting a multitude of data at small length and time scales, or at a discrete fracture scale and to ?up-scale,? which is extremely tenuous.
Date: August 6, 2010
Creator: Karasaki, Kenzi; Onishi, Tiemi; Gasperikova, Erika; Goto, Junichi; Tsuchi, Hiroyuki; Miwa, Tadashi et al.
Partner: UNT Libraries Government Documents Department

Feature Detection, Characterization and Confirmation Methodology: Final Report

Description: This is the final report of the NUMO-LBNL collaborative project: Feature Detection, Characterization and Confirmation Methodology under NUMO-DOE/LBNL collaboration agreement, the task description of which can be found in the Appendix. We examine site characterization projects from several sites in the world. The list includes Yucca Mountain in the USA, Tono and Horonobe in Japan, AECL in Canada, sites in Sweden, and Olkiluoto in Finland. We identify important geologic features and parameters common to most (or all) sites to provide useful information for future repository siting activity. At first glance, one could question whether there was any commonality among the sites, which are in different rock types at different locations. For example, the planned Yucca Mountain site is a dry repository in unsaturated tuff, whereas the Swedish sites are situated in saturated granite. However, the study concludes that indeed there are a number of important common features and parameters among all the sites--namely, (1) fault properties, (2) fracture-matrix interaction (3) groundwater flux, (4) boundary conditions, and (5) the permeability and porosity of the materials. We list the lessons learned from the Yucca Mountain Project and other site characterization programs. Most programs have by and large been quite successful. Nonetheless, there are definitely 'should-haves' and 'could-haves', or lessons to be learned, in all these programs. Although each site characterization program has some unique aspects, we believe that these crosscutting lessons can be very useful for future site investigations to be conducted in Japan. One of the most common lessons learned is that a repository program should allow for flexibility, in both schedule and approach. We examine field investigation technologies used to collect site characterization data in the field. An extensive list of existing field technologies is presented, with some discussion on usage and limitations. Many of the technologies on the list ...
Date: March 1, 2007
Creator: Karasaki, Kenzi; Apps, John; Doughty, Christine; Gwatney, Hope; Onishi, Celia Tiemi; Trautz, Robert et al.
Partner: UNT Libraries Government Documents Department