Identifying the heterogeneous conductivity field and reconstructing the contaminant release history are key aspects of subsurface remediation. Achieving these two goals with limited and noisy hydraulic head and concentration measurements is challenging. The obstacles include solving an inverse problem for high-dimensional parameters, and the high-computational cost needed for the repeated forward modeling. We use a convolutional adversarial autoencoder (CAAE) for the parameterization of the heterogeneous non-Gaussian conductivity field with a low-dimensional latent representation. Additionally, we trained a three-dimensional dense convolutional encoder-decoder (DenseED) network to serve as the forward surrogate for the flow and transport processes. Combining the CAAE and DenseED forward surrogate models, the ensemble smoother with multiple data assimilation (ESMDA) algorithm is used to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE-DenseED-ESMDA inversion framework. We applied this CAAE-DenseED-ESMDA inversion framework in a three-dimensional contaminant source and conductivity field identification problem. A comparison of the inversion results from CAAE-ESMDA with physical flow and transport simulator and CAAE-DenseED-ESMDA is provided, showing that accurate reconstruction results were achieved with a much higher computational efficiency.

Field-scale properties of fractured rocks play crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross-borehole thermal experiments data. It is based on a particle-based heat-transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of heat-transfer model runs, and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to-be-estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding non-uniform prior information related to the DFN connectivity improves the inference of this parameter.

Multiscale heterogeneity and insufficient characterization data for the specific subsurface formation of interest render predictions of multi-phase fluid flow in geologic formations highly uncertain. Quantification of the propagation uncertainty from the geomodel to the fluid-flow response is typically done within a probabilistic framework. This task is computationally demanding due to, e.g., the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that will be used for risk assessment and decision-making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two-phase fluid flow problems; however, FROST still relies on MCS to compute the travel-time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of the travel time. The resulting CDF-FROST approach yields the CDF of the saturation field without resorting to sampling-based strategies. Our numerical experiments demonstrate the high accuracy of CDF-FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in practice because of its high computational cost associated with multiple solves of contaminant transport equations. We propose an adaptive MCMC method, in which a transport model is replaced with a fast and accurate surrogate model in the form of a deep convolutional neural network (CNN). The CNN-based surrogate is trained on a small number of the transport model runs based on the prior knowledge of the unknown release history. Thus reduced computational cost allows one to reduce the sampling error associated with construction of the approximate likelihood function. As all MCMC strategies for source identification, our method has an added advantage of quantifying predictive uncertainty and accounting for measurement errors. Our numerical experiments demonstrate the accuracy comparable to that of MCMC with the forward transport model, which is obtained at a fraction of the computational cost of the latter.

A document by Abdulrahman A Alawadhi. Click on the document to view its contents.

Probabilistic models of subsurface flow and transport are required for risk assessment and reliable decision making under uncertainty. These applications require accurate estimates of confidence intervals, which generally cannot be ascertained with such statistical moments as mean (unbiased estimate) and variance (a measure of uncertainty) of a quantity of interest (QoI). The method of distributions provides this information by computing either the probability density function or the cumulative distribution functions (CDF) of the QoI. The method can be orders of magnitude faster than Monte Carlo simulations (MCS), but is applicable to stationary, mildly-to-moderately heterogeneous porous media in which the coefficient of variation of input parameters (e.g., log-conductivity) is below three. Our CDF-RDD framework alleviates these limitations by combining the method of distributions and the random domain decomposition (RDD); it also accounts for uncertainty in the geologic makeup of a subsurface environment. For a given realization of the geological map, we derive a deterministic equation for the conditional CDF of hydraulic head of steady single-phase flow. The solutions of this equation are then averaged over realizations of the geological maps to compute the hydraulic head CDF. Our numerical experiments reveal that the CDF-RDD remains accurate for two-dimensional flow in a porous material composed of two heterogeneous hydrofacies, a setting in which the original CDF method fails. For the same accuracy, the CDF-RDD is an order of magnitude faster than MCS.

Quantitative prediction of natural and induced phenomena in fractured rock is one of the great challenges in the Earth and Energy Sciences with far-reaching economic and environmental impacts. Fractures occupy a very small volume of a subsurface formation but often dominate flow, transport and mechanical deformation behavior. They play a central role in CO2 sequestration, nuclear waste disposal, hydrogen storage, geothermal energy production, nuclear nonproliferation, and hydrocarbon extraction. These applications require prediction of fracture-dependent quantities of interest such as CO2 leakage rate, hydrocarbon production, radionuclide plume migration, and seismicity; to be useful, these predictions must account for uncertainty inherent in subsurface systems. Here, we review recent advances in fractured rock research that cover field- and laboratory-scale experimentation, numerical simulations, and uncertainty quantification. We discuss how these have greatly improved the fundamental understanding of fractures and one’s ability to predict flow and transport in fractured systems. Dedicated field sites provide quantitative measures of fracture flow that can be used to identify dominant coupled processes and to validate models. Laboratory-scale experiments fill critical knowledge gaps by providing direct observations and measurements of fracture geometry and flow under controlled conditions that cannot be obtained in the field. Physics-based simulation of flow and transport provide a bridge in understanding between controlled simple laboratory experiments and the massively complex field-scale fracture systems. Finally, we review the use of machine learning-based emulators to rapidly investigate different fracture property scenarios and to accelerate physics-based models by orders of magnitude to enable uncertainty quantification and near real-time analysis.