Stefan Finsterle

T2VOC user`s guide

T2VOC is a numerical simulator for three-phase, three-component, non-isothermal flow of water, air, and a volatile organic compound (VOC) in multidimensional heterogeneous porous media. Developed at the Lawrence Berkeley Laboratory, T2VOC is an extension of the TOUGH2 general-purpose simulation program. This report is a self-contained guide to application of T2VOC to subsurface contamination problems involving nonaqueous phase liquids (NAPLs). It gives a technical description of the T2VOC code, including a discussion of the physical processes modeled, and the mathematical and numerical methods used. Detailed instructions for preparing input data are presented along with several illustrative sample problems.

Using the continuum approach to model unsaturated flow in fractured rock

The appropriateness of using the continuum approach for simulations of unsaturated flow through fractured rock is examined in a numerical study of water seepage into an underground opening. A continuum model is calibrated against data generated with a high-resolution model that created discrete flow and seepage behavior. Probabilistic predictions of injection data and seepage rates are then compared to the values from the discrete model. The study shows that reasonable results can be obtained with a calibrated continuum model even for fractured systems in which the underlying flow processes are discrete. Calibration is a crucial step in this approach because it yields effective, model-related, and process-specific parameters. The impact of discretization on the estimated parameters is discussed. Prediction uncertainty is evaluated by means of Monte Carlo simulations, including both the impact of parameter uncertainties and the effect of local heterogeneity. In this paper, the advantages and limitations of the continuum approach are discussed from a practical perspective, which includes a critical examination of project objectives, data needs, robustness of assumptions, and prediction uncertainty.

Determining permeability of tight rock samples using inverse modeling

Data from gas-pressure-pulse-decay experiments have been analyzed by means of numerical simulation in combination with automatic model calibration techniques to determine hydrologic properties of low-permeability, low-porosity rock samples. Porosity, permeability, and Klinkenberg slip factor have been estimated for a core plug from The Geysers geothermal field, California. The experiments were conducted using a specially designed permeameter with small gas reservoirs. Pressure changes were measured as gas flowed from the pressurized upstream reservoir through the sample to the downstream reservoir. A simultaneous inversion of data from three experiments performed on different pressure levels allows for independent estimation of absolute permeability and gas permeability which is pressure-dependent due to enhanced slip flow. With this measurement and analysis technique we can determine matrix properties with permeabilities as low as 10 221 m 2 . In this paper we discuss the procedure of parameter estimation by inverse modeling. We will focus on the error analysis, which reveals estimation uncertainty and parameter correlations. This information can also be used to evaluate and optimize the design of an experiment. The impact of systematic errors due to potential leakage and uncertainty in the initial conditions will also be addressed. The case studies clearly illustrate the need for a thorough error analysis of inverse modeling results.

Field tests and model analyses of seepage into drift

Abstract This paper focuses on field test results and model analyses of the first set of five niche seepage tests conducted in the Exploratory Studies Facility at Yucca Mountain. The test results suggest that (1) a niche opening (short drift excavated for this study) acts as a capillary barrier; (2) a seepage threshold exists; and (3) the seepage is a fraction of the liquid released above the ceiling. Before seepage quantification, air injection and liquid release tests at two niche locations were conducted to characterize the fracture flow paths. Nearly two-order-of-magnitude changes in air permeability values were measured before and after niche excavation. The dyed liquid flow paths, together with a localized wet feature potentially associated with an ambient flow path, were mapped during dry excavation operations. After niche excavation, the seepage is quantified by the ratio of the water mass dripped into a niche to the mass released above the opening at selected borehole intervals. For the first set of five tests conducted at Niche 3650 site, the ratios range from 0% (no dripping for two tests) to 27.2%. Changes in flow path distributions and water accumulation near seepage threshold were observed on the niche ceiling. The seepage test results compare reasonably well with model results without parameter adjustments, using capillary barrier boundary condition in the niche and two-dimensional and three-dimensional conceptualizations to represent discrete fracture and fracture network for the flow paths. Model analyses of the niche tests indicate that the seepage is very sensitive to the niche boundary condition and is moderately sensitive to the heterogeneity of the fracture flow paths and to the strengths of matrix imbibition. Strong capillary strength and large storage capacity of the fracture flow paths limit the seepage. High permeability value also enhances diversion and reduces seepage for low liquid release rate.

Solving iTOUGH2 simulation and optimization problems using the PEST protocol

The PEST protocol has been implemented into the iTOUGH2 code, allowing the user to link any simulation program (with ASCII-based inputs and outputs) to iTOUGH2s sensitivity analysis, inverse modeling, and uncertainty quantification capabilities. These application models can be pre- or post-processors of the TOUGH2 non-isothermal multiphase flow and transport simulator, or programs that are unrelated to the TOUGH suite of codes. PEST-style template and instruction files are used, respectively, to pass input parameters updated by the iTOUGH2 optimization routines to the model, and to retrieve the model-calculated values that correspond to observable variables. We summarize the iTOUGH2 capabilities and demonstrate the flexibility added by the PEST protocol for the solution of a variety of simulation-optimization problems. In particular, the combination of loosely coupled and tightly integrated simulation and optimization routines provides both the flexibility and control needed to solve challenging inversion problems for the analysis of multiphase subsurface flow and transport systems.

Inverse and predictive modeling of seepage into underground openings

We discuss the development and calibration of a model for predicting seepage into underground openings. Seepage is a key factor affecting the performance of the potential nuclear-waste repository at Yucca Mountain, Nevada. Three-dimensional numerical models were developed to simulate field tests in which water was released from boreholes above excavated niches. Data from air-injection tests were geostatistically analyzed to infer the heterogeneous structure of the fracture permeability field. The heterogeneous continuum model was then calibrated against the measured amount of water that seeped into the opening. This approach resulted in the estimation of model-related, seepage-specific parameters on the scale of interest. The ability of the calibrated model to predict seepage was examined by comparing calculated with measured seepage rates from additional experiments conducted in different portions of the fracture network. We conclude that an effective capillary strength parameter is suitable to characterize seepage-related features and processes for use in a prediction model of average seepage into potential waste-emplacement drifts.

Modeling Coupled Evaporation and Seepage in Ventilated Cavities

Cavities excavated in unsaturated geological formations are important to activities such as nuclear waste disposal and mining. Such cavities provide a unique setting for simultaneous occurrence of seepage and evaporation. Previously, inverse numerical modeling of field liquid-release tests and associated seepage into cavities were used to provide seepage-related large-scale formation properties, ignoring the impact of evaporation. The applicability of such models was limited to the narrow range of ventilation conditions under which the models were calibrated. The objective of this study was to alleviate this limitation by incorporating evaporation into the seepage models. We modeled evaporation as an isothermal vapor diffusion process. The semiphysical model accounts for the relative humidity (RH), temperature, and ventilation conditions of the cavities. The evaporation boundary layer thickness (BLT) over which diffusion occurs was estimated by calibration against free-water evaporation data collected inside the experimental cavities. The estimated values of BLT were 5 to 7 mm for the open underground drifts and 20 mm for niches closed off by bulkheads. Compared with previous models that neglected the effect of evaporation, this new approach showed significant improvement in capturing seepage fluctuations into open cavities of low RH. At high relative-humidity values (>85%), the effect of evaporation on seepage was very small.

Robust estimation of hydrogeologic model parameters

Inverse modeling has become a standard technique for estimating hydrogeologic parameters. These parameters are usually inferred by minimizing the sum of the squared differences between the observed system state and the one calculated by a mathematical model. The robustness of the least squares criterion, however, has to be questioned because of the tendency of outliers in the measurements to strongly influence the outcome of the inversion. We have examined alternative approaches to the standard least squares formulation. The robustness of these estimators has been tested by means of Monte Carlo simulations of a synthetic experiment, in which both non-Gaussian random errors and systematic modeling errors have been introduced. The approach was then applied to data from an actual gas-pressure-pulse-decay experiment. The study demonstrates that robust estimators have the potential to reduce estimation bias in the presence of noisy data and minor systematic errors, which may be a significant advantage over the standard least squares method.

Inverse modeling of a radial multistep outflow experiment for determining unsaturated hydraulic properties

Modeling flow and solute transport in the unsaturated zone on the basis of the Richards equation requires specifying values for unsaturated hydraulic conductivity and water potential as a function of saturation. The objectives of the paper are to evaluate the design of a transient, radial, multi-step outflow experiment, and to determine unsaturated hydraulic parameters using inverse modeling. We conducted numerical simulations, sensitivity analyses, and synthetic data inversions to assess the suitability of the proposed experiment for concurrently estimating the parameters of interest. We calibrated different conceptual models against transient flow and pressure data from a multi-step, radial desaturation experiment to obtain estimates of absolute permeability, as well as the parameters of the relative permeability and capillary pressure functions. We discuss the differences in the estimated parameter values and illustrate the impact of the underlying model on the estimates. We demonstrate that a small error in absolute permeability, if determined in an independent experiment, leads to biased estimates of unsaturated hydraulic properties. Therefore, we perform a joint inversion of pressure and flow rate data for the simultaneous determination of permeability and retention parameters, and analyze the correlations between these parameters. We conclude that the proposed combination of a radial desaturation experiment and inverse modeling is suitable for simultaneously determining the unsaturated hydraulic properties of a single soil sample, and that the inverse modeling technique provides the opportunity to analyze data from nonstandard experimental designs.

Dynamical inversion of geophysical ERT data: state estimation in the vadose zone

The imaging of the evolution of conductive fluids in porous media with electrical resistance tomography (ERT) can be considered as a dynamic inverse problem, in which the time-dependent electrical conductivity distribution in the target region is inferred from voltage measurements at electrodes placed in boreholes or on the ground surface. A petrophysical relationship is then used to relate the electrical conductivity to water saturation. We consider a state estimation approach that combines the complete electrode model for simulating ERT measurements and a hydrological evolution model for unsaturated flow. To demonstrate the approach, we consider synthetic measurements from a simulated experiment in which water is injected from a point source into an initially dry soil. The purpose is to carry out a feasible study. In the studied simple cases, the proposed method provides improved estimates of the water saturation distribution compared to the traditional reconstruction approach, which does not employ an evolution model.