H21K-01 INVITED
Efficient, Non-Intrusive Stochastic Approaches for Multiphase Flow in Porous Media
We present an accurate and efficient stochastic modeling approach for multiphase flow in porous media. In this approach, the random log transformed permeability (or porosity) field is represented by the Karhunen-Loeve expansion and the fluid saturations and pressures are expressed by the polynomial chaos expansions. Probabilistic collocation method (PCM) is used to determine the coefficients of the polynomial chaos expansions by solving for the fluid saturations (and pressures) at different collocation points via the original partial differential equations. This approach is non-intrusive because it results in independent deterministic differential equations, which similar to the Monte Carlo method, can be implemented with existing codes or simulators. The approach is demonstrated with multiphase flow problems in heterogeneous formations with an existing deterministic simulator. The accuracy, efficiency, and compatibility of this approach are compared against Monte Carlo simulations. This study reveals that while its computational efforts are greatly reduced compared to Monte Carlo method, PCM is able to accurately estimate the statistical moments and probability density functions of the fluid saturations and pressures. Comparisons with other non-intrusive stochastic approaches are also made.
H21K-02
Markov Models and the Ensemble Kalman Filter for Estimation of Sorption Rates
Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude. Sandia is a multi program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000. This work was supported under the Sandia Laboratory Directed Research and Development program.
H21K-03 INVITED
Application of Model Based Uncertainty Analysis to Hydrocarbon Reservoirs
Model-Based Uncertainty Analysis (MBUA) is a method to evaluate reservoir performance uncertainty using multiple 3D models. Experimental Design techniques are used to determine what 3D models are built (unique geologic models which are then simulated) based on the number of identified uncertain factors. This method captures main effects and factor interactions and results in a multivariable response surface for each desired outcome (e.g. expected ultimate recovery, original hydrocarbon in place) which can be used for Monte Carlo simulations. The entire MBUA process results in tornado plots, exceedence curves, and a method to build representative models. A key strength of the MBUA process is the ability to capture dynamic responses such as water rate, production at early times, and plateau length. These responses provide project teams a greater understanding of how their subsurface uncertainties impact field performance and can help guide additional technical work, development planning decisions and representative model building. We have applied either a full or partial MBUA process to several fields for the purposes of identifying key technical uncertainties and improving the development plan across likely outcomes. Once an initial base case model has been built, subsequent models (totaling 16-54 models) can be rapidly built and simulated using normal geologic and flow simulation model workflows. While the analysis is quick, all model results are required to complete the analysis, thus simulation time is the biggest bottleneck in the process. Production data have been incorporated through either history-matching the initial base case or examining Monte Carlo simulation results for potential trends. The uncertainty analysis provides a streamlined process to examine potential uncertainty factors and allows a project to make informed decisions regarding future technical work or potential mitigation plans. A process overview will be presented along with sample results and lessons from completing the full MBUA.
H21K-04
Effects of Heterogeneities, Sampling Frequencies, Tools and Methods on Uncertainties in Subsurface Contaminant Concentration Measurements
Long-term monitoring (LTM) is particularly important for contaminants which are mitigated by natural processes of dilution, dispersion, and degradation. At many sites, LTM can require decades of expensive sampling at tens or even hundreds of existing monitoring wells, resulting in hundreds of thousands, or millions of dollars per year for sampling and data management. Therefore, contaminant sampling tools, methods and frequencies are chosen to minimize waste and data management costs while ensuring a reliable and informative time-history of contaminant measurement for regulatory compliance. The interplay play between cause (i.e. subsurface heterogeneities, sampling techniques, measurement frequencies) and effect (unreliable data and measurements gap) has been overlooked in many field applications which can lead to inconsistencies in time- histories of contaminant samples. In this study we address the relationship between cause and effect for different hydrogeological sampling settings: porous and fractured media. A numerical model has been developed using AMR-FEM to solve the physicochemical processes that take place in the aquifer and the monitoring well. In the latter, the flow is governed by the Navier-Stokes equations while in the former the flow is governed by the diffusivity equation; both are fully coupled to mimic stressed conditions and to assess the effect of dynamic sampling tool on the formation surrounding the monitoring well. First of all, different sampling tools (i.e., Easy Pump, Snapper Grab Sampler) were simulated in a monitoring well screened in different homogeneous layered aquifers to assess their effect on the sampling measurements. Secondly, in order to make the computer runs more CPU efficient the flow in the monitoring well was replaced by its counterpart flow in porous media with infinite permeability and the new model was used to simulate the effect of heterogeneities, sampling depth, sampling tool and sampling frequencies on the uncertainties in the concentration measurements. Finally, the models and results were abstracted using a simple mixed-tank approach to further simplify the models and make them more accessible to field hydrogeologists. During the abstraction process a novel method was developed for mapping streamlines in the fractures as well within the monitoring well to illustrate mixing and mixing zones. Applications will be demonstrated for both sampling in porous and fractured media. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
H21K-05
Quantifying Groundwater Model Uncertainty
Groundwater models are characterized by the (a) processes simulated, (b) boundary conditions, (c) initial conditions, (d) method of solving the equation, (e) parameterization, and (f) parameter values. Models are related to the system of concern using data, some of which form the basis of observations used most directly, through objective functions, to estimate parameter values. Here we consider situations in which parameter values are determined by minimizing an objective function. Other methods of model development are not considered because their ad hoc nature generally prohibits clear quantification of uncertainty. Quantifying prediction uncertainty ideally includes contributions from (a) to (f). The parameter values of (f) tend to be continuous with respect to both the simulated equivalents of the observations and the predictions, while many aspects of (a) through (e) are discrete. This fundamental difference means that there are options for evaluating the uncertainty related to parameter values that generally do not exist for other aspects of a model. While the methods available for (a) to (e) can be used for the parameter values (f), the inferential methods uniquely available for (f) generally are less computationally intensive and often can be used to considerable advantage. However, inferential approaches require calculation of sensitivities. Whether the numerical accuracy and stability of the model solution required for accurate sensitivities is more broadly important to other model uses is an issue that needs to be addressed. Alternative global methods can require 100 or even 1,000 times the number of runs needed by inferential methods, though methods of reducing the number of needed runs are being developed and tested. Here we present three approaches for quantifying model uncertainty and investigate their strengths and weaknesses. (1) Represent more aspects as parameters so that the computationally efficient methods can be broadly applied. This approach is attainable through universal model analysis software such as UCODE-2005, PEST, and joint use of these programs, which allow many aspects of a model to be defined as parameters. (2) Use highly parameterized models to quantify aspects of (e). While promising, this approach implicitly includes parameterizations that may be considered unreasonable if investigated explicitly, so that resulting measures of uncertainty may be too large. (3) Use a combination of inferential and global methods that can be facilitated using the new software MMA (Multi-Model Analysis), which is constructed using the JUPITER API. Here we consider issues related to the model discrimination criteria calculated by MMA.
H21K-06
Parameter Estimation and Parameterization Uncertainty Using Bayesian Model Averaging
This study proposes Bayesian model averaging (BMA) to address parameter estimation uncertainty arisen from non-uniqueness in parameterization methods. BMA provides a means of incorporating multiple parameterization methods for prediction through the law of total probability, with which an ensemble average of hydraulic conductivity distribution is obtained. Estimation uncertainty is described by the BMA variances, which contain variances within and between parameterization methods. BMA shows the facts that considering more parameterization methods tends to increase estimation uncertainty and estimation uncertainty is always underestimated using a single parameterization method. Two major problems in applying BMA to hydraulic conductivity estimation using a groundwater inverse method will be discussed in the study. The first problem is the use of posterior probabilities in BMA, which tends to single out one best method and discard other good methods. This problem arises from Occam's window that only accepts models in a very narrow range. We propose a variance window to replace Occam's window to cope with this problem. The second problem is the use of Kashyap information criterion (KIC), which makes BMA tend to prefer high uncertain parameterization methods due to considering the Fisher information matrix. We found that Bayesian information criterion (BIC) is a good approximation to KIC and is able to avoid controversial results. We applied BMA to hydraulic conductivity estimation in the 1,500-foot sand aquifer in East Baton Rouge Parish, Louisiana.
H21K-07
Large-Scale Transport Model Uncertainty and Sensitivity Analysis: Distributed Sources in Complex, Hydrogeologic Systems
The Underground Test Area (UGTA) Project of the U.S. Department of Energy, National Nuclear Security Administration Nevada Site Office is in the process of assessing and developing regulatory decision options based on modeling predictions of contaminant transport from underground testing of nuclear weapons at the Nevada Test Site (NTS). The UGTA Project is attempting to develop an effective modeling strategy that addresses and quantifies multiple components of uncertainty including natural variability, parameter uncertainty, conceptual/model uncertainty, and decision uncertainty in translating model results into regulatory requirements. The modeling task presents multiple unique challenges to the hydrological sciences as a result of the complex fractured and faulted hydrostratigraphy, the distributed locations of sources, the suite of reactive and non-reactive radionuclides, and uncertainty in conceptual models. Characterization of the hydrogeologic system is difficult and expensive because of deep groundwater in the arid desert setting and the large spatial setting of the NTS. Therefore, conceptual model uncertainty is partially addressed through the development of multiple alternative conceptual models of the hydrostratigraphic framework and multiple alternative models of recharge and discharge. Uncertainty in boundary conditions is assessed through development of alternative groundwater fluxes through multiple simulations using the regional groundwater flow model. Calibration of alternative models to heads and measured or inferred fluxes has not proven to provide clear measures of model quality. Therefore, model screening by comparison to independently-derived natural geochemical mixing targets through cluster analysis has also been invoked to evaluate differences between alternative conceptual models. Advancing multiple alternative flow models, sensitivity of transport predictions to parameter uncertainty is assessed through Monte Carlo simulations. The simulations are challenged by the distributed sources in each of the Corrective Action Units, by complex mass transfer processes, and by the size and complexity of the field- scale flow models. An efficient methodology utilizing particle tracking results and convolution integrals provides insitu concentrations appropriate for Monte Carlo analysis. Uncertainty in source releases and transport parameters including effective porosity, fracture apertures and spacing, matrix diffusion coefficients, sorption coefficients, and colloid load and mobility are considered. With the distributions of input uncertainties and output plume volumes, global analysis methods including stepwise regression, contingency table analysis, and classification tree analysis are used to develop sensitivity rankings of parameter uncertainties for each model considered, thus assisting a variety of decisions. The National Security Technologies, LLC component of this work is DOE/NV/25946—xxx and was done under contract number DE-AC52-O6NA25946 with the U.S. Department of Energy