Publications

Lefantzi, Sophia L.; Mckenna, Sean A.; Ray, Jaideep R.; van Bloemen Waanders, Bart G.

Abstract not provided.

Lefantzi, Sophia L.; Klise, Katherine A.; Salazar, Luke S.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.; Ray, Jaideep R.

We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loeve expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Lefantzi, Sophia L.

Abstract not provided.

Advances in Water Resources

Mckenna, Sean A.; van Bloemen Waanders, Bart G.; Ray, Jaideep R.

Abstract not provided.

Advances in Water Resources

Mckenna, Sean A.; Ray, Jaideep R.; Marzouk, Youssef; van Bloemen Waanders, Bart G.

Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distance-based upscaling algorithm and approximations of point process theory to develop an estimation approach for effective conductivity in two-dimensions. Estimation of effective conductivity is derived directly from knowledge of the kernel size used to create the multiGaussian field, defined as the full-width at half maximum (FWHM), the truncation threshold and conductance values of the two modes. Therefore, instantiation of the multiGaussian field is not necessary for estimation of the effective conductance. The critical component of the effective medium approximation developed here is the mean distance between high conductivity inclusions. This mean distance is characterized as a function of the FWHM, the truncation threshold and the ratio of the two modal conductivities. Sensitivity of the resulting effective conductivity to this mean distance is examined for two levels of contrast in the modal conductances and different FWHM sizes. Results demonstrate that the FWHM is a robust measure of mean travel distance in the background medium. The resulting effective conductivities are accurate when compared to numerical results and results obtained from effective media theory, distance-based upscaling and numerical simulation. © 2011 Elsevier Ltd.

Ober, Curtis C.; van Bloemen Waanders, Bart G.; Collis, Samuel S.

Abstract not provided.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

Abstract not provided.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

We present results from a recently developed multiscale inversion technique for binary media, with emphasis on the effect of subgrid model errors on the inversion. Binary media are a useful fine-scale representation of heterogeneous porous media. Averaged properties of the binary field representations can be used to characterize flow through the porous medium at the macroscale. Both direct measurements of the averaged properties and upscaling are complicated and may not provide accurate results. However, it may be possible to infer upscaled properties of the binary medium from indirect measurements at the coarse scale. Multiscale inversion, performed with a subgrid model to connect disparate scales together, can also yield information on the fine-scale properties. We model the binary medium using truncated Gaussian fields, and develop a subgrid model for the upscaled permeability based on excursion sets of those fields. The subgrid model requires an estimate of the proportion of inclusions at the block scale as well as some geometrical parameters of the inclusions as inputs, and predicts the effective permeability. The inclusion proportion is assumed to be spatially varying, modeled using Gaussian processes and represented using a truncated Karhunen-Louve (KL) expansion. This expansion is used, along with the subgrid model, to pose as a Bayesian inverse problem for the KL weights and the geometrical parameters of the inclusions. The model error is represented in two different ways: (1) as a homoscedastic error and (2) as a heteroscedastic error, dependent on inclusion proportionality and geometry. The error models impact the form of the likelihood function in the expression for the posterior density of the objects of inference. The problem is solved using an adaptive Markov Chain Monte Carlo method, and joint posterior distributions are developed for the KL weights and inclusion geometry. Effective permeabilities and tracer breakthrough times at a few 'sensor' locations (obtained by simulating a pump test) form the observables used in the inversion. The inferred quantities can be used to generate an ensemble of permeability fields, both upscaled and fine-scale, which are consistent with the observations. We compare the inferences developed using the two error models, in terms of the KL weights and fine-scale realizations that could be supported by the coarse-scale inferences. Permeability differences are observed mainly in regions where the inclusions proportion is near the percolation threshold, and the subgrid model incurs its largest approximation. These differences also reflected in the tracer breakthrough times and the geometry of flow streamlines, as obtained from a permeameter simulation. The uncertainty due to subgrid model error is also compared to the uncertainty in the inversion due to incomplete data.

Mckenna, Sean A.; Ray, Jaideep R.; van Bloemen Waanders, Bart G.

Multi-scale binary permeability field estimation from static and dynamic data is completed using Markov Chain Monte Carlo (MCMC) sampling. The binary permeability field is defined as high permeability inclusions within a lower permeability matrix. Static data are obtained as measurements of permeability with support consistent to the coarse scale discretization. Dynamic data are advective travel times along streamlines calculated through a fine-scale field and averaged for each observation point at the coarse scale. Parameters estimated at the coarse scale (30 x 20 grid) are the spatially varying proportion of the high permeability phase and the inclusion length and aspect ratio of the high permeability inclusions. From the non-parametric, posterior distributions estimated for these parameters, a recently developed sub-grid algorithm is employed to create an ensemble of realizations representing the fine-scale (3000 x 2000), binary permeability field. Each fine-scale ensemble member is instantiated by convolution of an uncorrelated multiGaussian random field with a Gaussian kernel defined by the estimated inclusion length and aspect ratio. Since the multiGaussian random field is itself a realization of a stochastic process, the procedure for generating fine-scale binary permeability field realizations is also stochastic. Two different methods are hypothesized to perform posterior predictive tests. Different mechanisms for combining multi Gaussian random fields with kernels defined from the MCMC sampling are examined. Posterior predictive accuracy of the estimated parameters is assessed against a simulated ground truth for predictions at both the coarse scale (effective permeabilities) and at the fine scale (advective travel time distributions). The two techniques for conducting posterior predictive tests are compared by their ability to recover the static and dynamic data. The skill of the inference and the method for generating fine-scale binary permeability fields are evaluated through flow calculations on the resulting fields using fine-scale realizations and comparing them against results obtained with the ground truth fine-scale and coarse-scale permeability fields.

Collis, Samuel S.; Ober, Curtis C.; van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.; Mckenna, Sean A.

Abstract not provided.

Collis, Samuel S.; Ober, Curtis C.; van Bloemen Waanders, Bart G.

This abstract explores the potential advantages of discontinuous Galerkin (DG) methods for the time-domain inversion of media parameters within the earth's interior. In particular, DG methods enable local polynomial refinement to better capture localized geological features within an area of interest while also allowing the use of unstructured meshes that can accurately capture discontinuous material interfaces. This abstract describes our initial findings when using DG methods combined with Runge-Kutta time integration and adjoint-based optimization algorithms for full-waveform inversion. Our initial results suggest that DG methods allow great flexibility in matching the media characteristics (faults, ocean bottom and salt structures) while also providing higher fidelity representations in target regions. Time-domain inversion using discontinuous Galerkin on unstructured meshes and with local polynomial refinement is shown to better capture localized geological features and accurately capture discontinuous-material interfaces. These approaches provide the ability to surgically refine representations in order to improve predicted models for specific geological features. Our future work will entail automated extensions to directly incorporate local refinement and adaptive unstructured meshes within the inversion process.

van Bloemen Waanders, Bart G.; Mckenna, Sean A.; Ray, Jaideep R.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

Barone, Matthew F.; van Bloemen Waanders, Bart G.

Abstract not provided.

Mckenna, Sean A.; Vugrin, Eric D.; Hart, William E.; van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

ASCE Journal of Water Resources Management and Planning

van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.; Long, Kevin R.; Hill, Judith C.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

Cooper, Scott P.; Elbring, Gregory J.; Jakaboski, Blake E.; Lorenz, John C.; Mani, Seethambal S.; Normann, Randy A.; Rightley, Michael J.; van Bloemen Waanders, Bart G.; Weiss, Chester J.

The project objective was to detail better ways to assess and exploit intelligent oil and gas field information through improved modeling, sensor technology, and process control to increase ultimate recovery of domestic hydrocarbons. To meet this objective we investigated the use of permanent downhole sensors systems (Smart Wells) whose data is fed real-time into computational reservoir models that are integrated with optimized production control systems. The project utilized a three-pronged approach (1) a value of information analysis to address the economic advantages, (2) reservoir simulation modeling and control optimization to prove the capability, and (3) evaluation of new generation sensor packaging to survive the borehole environment for long periods of time. The Value of Information (VOI) decision tree method was developed and used to assess the economic advantage of using the proposed technology; the VOI demonstrated the increased subsurface resolution through additional sensor data. Our findings show that the VOI studies are a practical means of ascertaining the value associated with a technology, in this case application of sensors to production. The procedure acknowledges the uncertainty in predictions but nevertheless assigns monetary value to the predictions. The best aspect of the procedure is that it builds consensus within interdisciplinary teams The reservoir simulation and modeling aspect of the project was developed to show the capability of exploiting sensor information both for reservoir characterization and to optimize control of the production system. Our findings indicate history matching is improved as more information is added to the objective function, clearly indicating that sensor information can help in reducing the uncertainty associated with reservoir characterization. Additional findings and approaches used are described in detail within the report. The next generation sensors aspect of the project evaluated sensors and packaging survivability issues. Our findings indicate that packaging represents the most significant technical challenge associated with application of sensors in the downhole environment for long periods (5+ years) of time. These issues are described in detail within the report. The impact of successful reservoir monitoring programs and coincident improved reservoir management is measured by the production of additional oil and gas volumes from existing reservoirs, revitalization of nearly depleted reservoirs, possible re-establishment of already abandoned reservoirs, and improved economics for all cases. Smart Well monitoring provides the means to understand how a reservoir process is developing and to provide active reservoir management. At the same time it also provides data for developing high-fidelity simulation models. This work has been a joint effort with Sandia National Laboratories and UT-Austin's Bureau of Economic Geology, Department of Petroleum and Geosystems Engineering, and the Institute of Computational and Engineering Mathematics.

Ho, Clifford K.; Mckenna, Sean A.; Wright, Jerome L.; van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.; Webb, Stephen W.

Abstract not provided.

van Bloemen Waanders, Bart G.

Chemical/Biological/Radiological (CBR) contamination events pose a considerable threat to our nation's infrastructure, especially in large internal facilities, external flows, and water distribution systems. Because physical security can only be enforced to a limited degree, deployment of early warning systems is being considered. However to achieve reliable and efficient functionality, several complex questions must be answered: (1) where should sensors be placed, (2) how can sparse sensor information be efficiently used to determine the location of the original intrusion, (3) what are the model and data uncertainties, (4) how should these uncertainties be handled, and (5) how can our algorithms and forward simulations be sufficiently improved to achieve real time performance? This report presents the results of a three year algorithmic and application development to support the identification, mitigation, and risk assessment of CBR contamination events. The main thrust of this investigation was to develop (1) computationally efficient algorithms for strategically placing sensors, (2) identification process of contamination events by using sparse observations, (3) characterization of uncertainty through developing accurate demands forecasts and through investigating uncertain simulation model parameters, (4) risk assessment capabilities, and (5) reduced order modeling methods. The development effort was focused on water distribution systems, large internal facilities, and outdoor areas.