The Measurement of Racial Discrimination in Pay between Job Categories: Theory and Test

The traditional model of taste discrimination in labor markets presumes perfect substitution, making it unsuitable for the measurement of discrimination across job assignments. We extend the model to explain cross-assignment discrimination and test it on data from Major League Baseball. A competitive firm with a Generalized Leontief production function fills each job assignment with whites and nonwhites in an environment of customer prejudice. According to the model, cross-assignment discrimination depends upon racial productivity differences, the productivity x prejudice interaction, technology, relative labor supply and racial integration. We find strong evidence of ceteris paribus racial salary differences between hitters and pitchers.wages, discrimination, imperfect substitutability, integration

Cross-Assignment Discrimination in Pay: A Test Case of Major League Baseball

The traditional Becker/Arrow style model of discrimination depicts majority and minority and workers as perfectly substitutable inputs, implying that all workers have the same job assignment. The model is only appropriate for determining whether pay differences between, for example, whites and non-whites doing job assignment A are attributable to prejudice ('within-assignment discrimination'); It is inappropriate, however, for determining whether pay differences between whites in job assignment A and non-whites in job assignment B reflect discriminatory behaviour ('cross-assignment discrimination'). We test the model of such cross assignment discrimination developed by Bodvarsson and Sessions (2011) using data on Major League Baseball hitters and pitchers for four different seasons during the 1990s, a decade during which monopsony power fell. We find strong evidence of ceteris paribus racial pay differences between hitters and pitchers, as well as evidence that cross-assignment discrimination varies with labour market structure.wage discrimination, complementarity, monopsony power

An Improvement to DCPT: The Particle Transfer Probability as a Function of Particle's Age

Multi-scale features of transport processes in fractured porous media make numerical modeling a difficult task of both conceptualization and computation. Dual-continuum particle tracker (DCPT) is an attractive method for modeling large-scale problems typically encountered in the field, such as those in unsaturated zone (UZ) of Yucca Mountain, Nevada. The major advantage is its capability to capture the major features of flow and transport in fractured porous rock (i-e., a fast fracture sub-system combined with a slow matrix sub-system) with reasonable computational resources. However, like other conventional dual-continuum approach-based numerical methods, DCPT (v1.0) is often criticized for failing to capture the transient features of the diffusion depth into the matrix. It may overestimate the transport of tracers through the fractures, especially for the cases with large fracture spacing, and predict artificial early breakthroughs. The objective of this study is to develop a new theory for calculating the particle transfer probability to captures the transient features of the diffusion depth into the matrix within the framework of the dual-continuum random walk particle method (RWPM)

CAPILLARY BARRIERS IN UNSATURATED FRACTURED ROCKS

This work presents modeling studies investigating the effects of capillary barriers on fluid-flow and tracer-transport processes in the unsaturated zone of Yucca Mountain, Nevada, a potential site for storing high-level radioactive waste. These studies are designed to identify factors controlling the formation of capillary barriers and to estimate their effects on the extent of possible large-scale lateral flow in unsaturated fracture rocks. The modeling approach is based on a continuum formulation of coupled multiphase fluid and tracer transport through fractured porous rock. Flow processes in fractured porous rock are described using a dual-continuum concept. In addition, approximate analytical solutions are developed and used for assessing capillary-barrier effects in fractured rocks. This study indicates that under the current hydrogeologic conceptualization of Yucca Mountain, strong capillary-barrier effects exist for significantly diverting moisture flow

Thermal Loading Studies Using the Unsaturated Zone Model

Several factors will affect Thermal-Hydrological (TH) response of the Unsaturated Zone (UZ) to thermal load at the potential repository. These factors include small and large-scale heterogeneity, the thermal load within the repository drifts and presence of lithophysal cavities. The objective of this study is to quantify these effects. Numerical modeling was used to investigate the effects of heat on UZ flow, temperature and liquid saturation on two spatial scales, for a range of potential repository operating modes. The TH simulations were conducted on two dual-permeability numerical grids. The first grid is a refined North-South Mountain-scale 2D model with layer-wise constant fracture permeability. The second grid is a refined half-drift (1-m grid near drift) 2D model with several realizations of spatially variable fracture permeability in the Topopah Spring welded unit (TSw). In the TSw lithophysal units, the thermal capacity and thermal conductivity of the lithophysal units were scaled using the lithophysal porosity. The second model includes both small-scale (less than 1-meter correlation length) heterogeneity in the fracture permeability and discrete high permeability fractures. Monte Carlo methods were used to generate several realizations of spatially variable fracture permeability (up to 4 orders of magnitude) in the TSw, based on the measured distribution of fracture permeability within the exploration drifts. Above boiling and below boiling repository operating modes are investigated by varying the initial thermal load and the amount of heat removed by ventilation. The simulations of coupled heat and mass flow were conducted using TOUGH2 (EOS3 module) over a simulated period of 100,000 years

Analyzing Flow Patterns in Unsaturated Fractured Rock of Yucca Mountain Using an Integrated Modeling Approach

Abstract This paper presents a series of modeling investigations to characterize percolation patterns in the unsaturated zone of Yucca Mountain, Nevada, a proposed underground repository site for storing high-level radioactive waste. The investigations are conducted using a modeling approach that integrates a wide variety of moisture, pneumatic, thermal, and isotopic geochemical field data into a comprehensive three-dimensional numerical model through model calibration. This integrated modeling approach, based on a dualcontinuum formulation, takes into account the coupled processes of fluid and heat flow and chemical isotopic transport in Yucca Mountain's highly heterogeneous, unsaturated fractured tuffs. In particular, the model results are examined against different types of field-measured data and used to evaluate different hydrogeological conceptual models and their effects on flow patterns in the unsaturated zone. The objective of this work to provide understanding of percolation patterns and flow behavior through the unsaturated zone, which is a crucial issue in assessing repository performance. Introduction Since the 1980s, the unsaturated zone (UZ) of the highly heterogeneous, fractured tuff at Yucca Mountain, Nevada, has been investigated by the U.S. Department of Energy as a possible repository site for storing high-level radioactive waste. Characterization of flow and transport processes in fractured rock of the Yucca Mountain UZ has received significant attention and generated tremendous interest in scientific communities over the last two decades. During this long and extensive study, many types of data have been collected from the Yucca Mountain UZ, and these data have helped to develop a conceptual understanding of various physical processes within the UZ system. The complexity of geological conditions and physical processes within the Yucca Mountain has posed a tremendous challenge for site-characterization effort, while quantitative evaluation of fluid flow, chemical transport, and heat transfer has proven to be essential. The need for quantitative investigations of flow and transport at the Yucca Mountain site has motivated a continual effort in developing and applying large, mountain-scale flow and transport models [e.g., Wu et al., 1999a and The site characterization studies of the unsaturated tuff at the Nevada Test Site and at Yucca Mountain began in the late 1970s and early 1980s. Those early hydrological, geological, and geophysical investigations of Yucca Mountain and the surrounding region were conducted to assess the feasibility of the site as a geological repository for storing high-level radioactive waste and to provide conceptual understanding of UZ flow processes In the early 1990s, more progress was made in UZ model development. Wittwer et al. [1992, 1995] developed a three-dimensional (3-D) site-scale model that incorporated several geological and hydrological complexities, such as geological layering, degree of welding, fault offsets, and different matrix and fracture properties. The 3-D model handled fracture-matrix flow using an effective continuum method (ECM) and was applied to evaluate various assumptions concerning faults and infiltration patterns. Using the ECM concept, Ahlers et al. [1995a, 1995b] continued development of the UZ site-scale model with increased numerical and spatial resolution. Their studies considered more processes, such as gas and heat flow analyses, and introduced an inverse modeling approach for estimating model-input properties. However, more comprehensive UZ models were not developed until a couple of years later, when the UZ models were developed for total system performance assessment-viability assessment (TSPA-VA) [e.g., Wu et al., 1999a and The next generation of UZ models included those primarily developed for the TSPA-site recommendation (SR) calculations [e.g., Wu et al., 2002a; Moridis et al., 2003; Robinson et al., 2003]. These TSPA-SR models were enhanced from the TSPA-VA model. More 4 importantly, the newer models took into account the coupled processes of flow and transport in highly heterogeneous, unsaturated fractured porous rock, and were applied to analyzing the effect of current and future climates on radionuclide transport through the UZ system. The site-scale UZ flow and transport models developed during the site characterization of Yucca Mountain have built upon the past research as well as the above-referenced work and many other studies [e.g., McLaren et al., 2000; Robinson et al., 1996 and 1997; This paper presents the results of our continuing effort to develop a realistic and representative UZ flow model to characterize the Yucca Mountain UZ system. More specifically, we focus on analyzing unsaturated flow patterns in the Yucca Mountain UZ under various climates and different hydrogeological conceptual models using an integrated modeling approach. This effort integrates different field-observed data, such as water potential, liquid saturation, perched water, gas pressure, chloride, and temperature logs into one single 3-D UZ flow and transport model. Using the dual-permeability modeling approach, the integrated modeling effort provides consistent model predictions for different, but inter-related hydrological, pneumatical, geochemical, and geothermal processes in the UZ. More importantly, such an integrated modeling exercise will improve the model's capability and credibility in describing and predicting current and future conditions and processes of the UZ system. At the same time, the combined model calibration will present a consistent check on modeled percolation fluxes and reveal better insight into the UZ flow patterns. The modeling study of this work consists of (1) UZ model description; (2) model development and calibration using liquid saturation, water potential, perched water, and pneumatic data; (3) assessing percolation patterns and flow behavior using thermal and geochemical data; and (4) simulated percolation pattern analysis. Conceptual Model of UZ Flow Over the past two decades, extensive scientific investigations have been conducted for the site characterization of Yucca Mountain, including data collection from surface mapping, sampling from many deep and shallow boreholes, constructing underground tunnels, and field testing [e.g., Rousseau, 1998]. of faults and perched water on the UZ system. As illustrated in In fact, the PTn's capability of attenuating episodic percolation fluxes has been observed in field tests of water release into the PTn matrix In addition, the possibility for capillary barriers exists at both upper and lower PTn contacts, as well as within the PTn layers PTn layers. However, the extent of lateral flow diversion within the PTn remains a topic of debate. For example, a recent study using a conceptual model with transitional changes in rock properties argues that lateral diversion may be small Perched Water Perched water has been encountered in a number of boreholes at Yucca Mountain, including UZ-14, SD-7, SD-9, SD-12, NRG-7a, G-2, and WT-24 ( Perched water may occur where percolation flux exceeds the capacity of the geological media to transmit vertical flux in the UZ [Rousseau et al., 1998]. Several conceptual models have been investigated for explaining the genesis of perched water at Yucca Mountain [e.g., Wu et al., 1999b and Faults In addition to possible capillary and permeability barriers, major faults in the UZ are also expected to play an important role in controlling percolation flux. Permeability within faults is much higher than that in the surrounding tuff Pneumatic permeability measurements taken along portions of faults revealed low airentry pressures, indicating that large fracture apertures are present in the fault zones. Highly brecciated fault zones may act as vertical capillary barriers to lateral flow. Once water is diverted into a fault zone, however, its high permeability could facilitate rapid vertical flow through the unsaturated system Heterogeneity A considerable amount of field data, obtained from tens of boreholes, two underground tunnels, and hundreds of outcrop samples at the site, constrains the distribution of rock properties within different units. In general, field data indicate that the Yucca Mountain formation is more heterogeneous vertically than horizontally, such that layer-wise representations are found to provide reasonable approximations of the complex geological system. This is because many model calibration results using this approximation are able to match different types of observation data obtained from different locations and depths [e.g., Bandurraga and Bodvarsson, 1999; 8 In summary, as shown in Ambient water flow in the UZ system is at a quasi-steady state condition, subject to spatially varying net infiltration on the ground surface. Hydrogeological units/layers are internally homogeneous, unless interrupted by faults or altered. There may exist capillary barriers in the PTn unit, causing lateral flow. Perched water results from permeability barrier effects. Major faults serve as fast vertical flow pathways for laterally diverted flow. Numerical Modeling Approach and Model Description Because of the complexity of the UZ geological system and the highly nonlinear nature of governing equations for UZ flow and transport, numerical modeling approaches were used in this study. Numerical simulations were carried out using the TOUGH2 and T2R3D codes [Pruess, 1991; Wu et al., 1996]. Most UZ flow simulations in this study were performed using an unsaturated flow module of the TOUGH2 code, which solves Richards' equation. Two active phases (liquid and gas) and heat flow was simulated using a two-phase fluid and heat flow module. Tracer and geochemical transport runs were carried out with the T2R3D code. Numerical Model Grids There are two 3-D numerical model grids used in this study, as shown in plan view in consists of 980 mesh columns of fracture and matrix continua, 86,440 gridblocks, and 350,000 connections in a dual-permeability grid. Vertically, the thermal grid has an average of 45 computational grid layers. Modeling Fracture-Matrix Interaction Modeling fracture and matrix flow and interaction under multiphase, multicomponent, isothermal or nonisothermal conditions has been a key issue for simulating fluid and heat flow in the Yucca Mountain UZ. Different modeling approaches have been tested for handling fracture-matrix interaction at Yucca Mountain The dual-permeability methodology considers global flow and transport occurring not only between fractures but also between matrix gridblocks. In this approach, the rockvolume domain is represented by two overlapping (yet interacting) fracture and matrix 10 continua, and local fracture-matrix flow and transport is approximated as a quasi-steady state. When applied in this work, however, the traditional dual-permeability concept is first modified by using an active fracture model Model Input Parameters Since the Richards' and two-active-phases flow equations are used in modeling unsaturated flow of water and air through fracture and matrix, relative permeability and capillary pressure curves are needed for the two media. In addition, other intrinsic fracture and matrix properties are also needed, such as porosity, permeability, density, and fracture geometric parameters, as well as rock thermal properties. In our modeling study, the van Genuchten models of relative permeability and capillary pressure functions The model input parameters of fractured and matrix rock were determined by two steps: (1) using field and laboratory measurements Model Boundary Conditions The ground surface of the mountain (or the tuff-alluvium contact in the area of significant alluvial cover) is taken as the top model boundary, while the water table is treated as the bottom model boundary. For flow simulations, net infiltration is applied to fractures along the top boundary using a source term. The bottom boundary at the water table is treated as a Dirichlet-type boundary. All the lateral boundaries, as shown in Net infiltration of water, resulting from precipitation that penetrates the top-soil layer of the mountain, is the most important factor affecting the overall hydrological, geochemical and thermal-hydrological behavior of the UZ. Net infiltration is the ultimate source of groundwater recharge and deep-zone percolation through the UZ, and provides a vehicle for transporting radionuclides from the repository to the water table. To cover the various possible scenarios and uncertainties of current and future climates at Yucca Mountain, we have incorporated a total of nine net infiltration maps, provided by US Geological Survey (USGS) scientists [Hevesi and Flint, 2000; As shown in Model Calibration The complexities of the heterogeneous geological formation at the Yucca Mountain UZ, A total of 18 flow simulation scenarios are studied in this work, as listed in In these calibrations, the gas flow model uses the UZ thermal model grid Comparison of model simulation results and field-measured pneumatic data for boreholes UZ-7a is shown in Flow Patterns and Analyses The primary objective of modeling UZ flow at Yucca Mountain is to estimate percolation flux through the UZ system. This is because percolation is the most critical factor that affects overall repository performance under current and future climates. However, in situ Past studies [e.g., Wu et al., 2002a] have shown that it is very difficult even to quantify the range of percolation fluxed by using hydrological data alone. Percolation patterns inside the UZ strongly depend on infiltration rates and their spatial distribution, among other factors. Therefore, over the past two decades, significant research effort has been devoted to estimating the infiltration rates [e.g., Flint et al., 1996; Hevesi and Flint, 2000; 17 Simulated Percolation Fluxes Percolation Patterns at Repository: Percolation fluxes at the repository horizon, as predicted using 18 3-D UZ flow simulation results of Flow Pattern Analyses Simulated In this study, heat flow simulations use the 3-D thermal model grid Temperature distributions at the bottom boundary of the thermal model are taken from deep-borehole-measured temperature profiles All Cl transport simulations were run using the T2R3D code for 100,000 years to approximate the current, steady-state condition under the infiltration scenarios considered. Chloride is treated as a conservative component transported through the UZ, subject to advection, diffusion, and first-order delay. The mechanical dispersion effect through the fracture-matrix system was ignored. A constant molecular diffusion coefficient of 2.032 × 10 -9 m 2 /s is used for matrix diffusion for Cl and the half-life for radioactive decay is 301,000 years. Concluding Remarks This paper presents a large-scale modeling study to characterize percolation patterns in the unsaturated zone of Yucca Mountain, Nevada, a proposed underground repository site for storing high-level radioactive waste. The modeling studies are conducted using an integrated modeling approach, which incorporates a wide variety of field data into a This study summarizes our current research effort to characterize UZ flow patterns at Yucca Mountain. Even with the significant progress made in quantitative evaluation of UZ flow and transport processes at the site using numerical models over the last two decades, there still exist a number of limitations and shortcomings with these models and their results. In general, accuracy and reliability of UZ site-scale models and simulation results are critically dependent on the accuracy of estimated model-related properties and other types of input parameters as well as hydrogeological conceptual models. The main limitations and uncertainties with the current UZ site-scale models are (1) the lack of indepth knowledge of the mountain system (including the geological and conceptual models and the availability of field and laboratory data), and (2) the approximations of a large volume-averaged modeling approach. As a result, continual research effort is still 26 needed toward a better understanding of the Yucca Mountain UZ system