Upscaling Microscale Flow Effects in Fractures using Differentiable Programming
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Engineering topics
Publications and source records attributed to O'Malley, Daniel.
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On Thursday, September 12 OpenAI released “a new series of models designed to spend more time thinking… they can reason through complex tasks and solve harder problems than previous models in science, coding, and math.” These models are referred to as o1-preview and o1-mini and appear to be first results of what had been a closely held project called Strawberry within OpenAI. The models are not described as successors in the earlier GPT series because they provide a qualitatively different type of capability, especially step-by-step reasoning.
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Orphaned wells are wells for which the operator is unknown or insolvent. The location of hundreds of thousands of these wells remain unknown in the United States alone. Cost-effective techniques are essential to locate orphaned wells to address environmental problems. In this paper, we present a dataset consisting of 120,948 aerial images of recently documented orphan wells. Each of these 512 × 512 images is paired with segmentation masks that indicate the presence or absence of such well. These images, sourced from the National Agriculture Imagery Program, cover the continental United States with spatial resolutions ranging from 30 centimeters to 1 meter. Additionally, we included negative examples by selecting locations uniformly across the United States. Accompanying metadata includes the IDs and spatial resolution of the original images, which are available for free through the United States Geological Survey, and the pixel coordinates of documented orphaned wells identified in these images. This dataset is intended to support the development of deep-learning models that can help locating undocumented orphan wells from such imagery, thereby blunting the environmental damage they do.
Reconstructing complex, high-dimensional global fields from limited data points is a challenge across various scientific and industrial domains. This is particularly important for recovering spatio-temporal fields using sensor data from, for example, laboratory-based scientific experiments, weather forecasting, or drone surveys. Given the prohibitive costs of specialized sensors and the inaccessibility of
certain regions of the domain, achieving full field coverage is typically not feasible. Therefore, the development of machine learning algorithms trained to reconstruct fields given a limited dataset is of critical importance. In this study, we introduce a general
approach that employs moving sensors to enhance data exploitation during the training of an attention based neural network, thereby improving field reconstruction. The training of sensor locations is accomplished using an end-to-end workflow, ensuring
differentiability in the interpolation of field values associated to the sensors, and is simple to implement using differentiable programming. Additionally, we have incorporated a correction mechanism to prevent sensors from entering invalid regions within the domain. We evaluated our method using two distinct datasets; the results show that our approach enhances learning, as evidenced by improved test scores.
Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics—in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning (ML) models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our ML model exhibits strong performance (R 2 = 0.9) when tested on extremely diverse real domains at multiple scales.
Here, we comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.
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Experience has suggested that pressure maintenance in hydraulically fractured reservoirs via lower, more sustained production drawdowns may offer improved cumulative recovery and overall resource extraction efficiency compared to more rapid drawdown approaches aimed at generating high initial production. However, given the inherent variability of oil and natural gas markets, operators pursue production strategies that maximize profitability over resource extraction efficiency. This study focuses on evaluating the implications of contrasting pressure drawdown strategies on the long-term production and resulting economics for a real, producing unconventional gas well in the Marcellus Shale of the Appalachian Basin using a techno-economic analysis approach. Our research combines elements of well-specific horizontal well design, production forecasting, equipment sizing and capital cost estimation, operating cost estimation, and revenue and tax calculations. Gas production forecast outlook scenarios were generated under varying pressure drawdowns using two approaches: 1) a novel physics-informed machine learning workflow and 2) traditional reservoir simulation. A discounted cash flow model was used to evaluate the resulting economic implications for each drawdown scenario—generating output for exploring the coupled effect of factors like the timing and volume of gas production, prevailing economic and market conditions for natural gas, and overall estimated ultimate recovery on profitability metrics such as internal rate of return and net present value. Results show that there is potential to maximize the cumulative gas produced in the specific case study well by employing a lower pressure drawdown. Conversely, the greatest profitability is achieved using rapid drawdown as signified by a small, specific subset of our outlook scenarios. On an averaging basis, we find that the combinations of highest cumulative producing and most profitable scenarios occur under lower drawdowns with long (>40 years) producing timeframes, but require higher relative gas price and lower discounting considerations. Further, the machine learning predictive outlooking capability proved effective for enabling rapid generation of a multitude of scenario forecasts. As a result, a variety of prominent example cases could be generated to strike the balance of greater productivity and economic return given their associated producing features and economic conditions when compared to similar producing scenarios—critical insight that offers improved decision support for unconventional oil and gas operations.
About 2.3 million orphan oil and gas (O&G) wells exist and are estimated to emit 200G g CH 4 y -1 by EPA/Enverus that implies an average CH 4 leak rate of 10 g CH 4 hr -1 per well. US government has an aggressive plan to plug orphan wells at costs of around $100K/well. In order to manage the costs of plugging millions of wells, quantifying leaks from individual wells is essential for prioritization. Current methods to quantify leaks require costly hardware, labor-intensive protocols and expensive analysis.
Uncertainty quantification is an integral component of reservoir management, especially considering the inherent uncertainty in subsurface systems. While a standard practice to estimate the uncertainty, Monte Carlo (MC) simulation is computationally intense when the sampling population comprises high-fidelity simulations. Alternatively, the Multi-fidelity Monte Carlo (MFMC) simulation overcomes this computational intensity by integrating low- and high-fidelity simulations. Our goal is to minimize the number of expensive high-fidelity simulations while maintaining accuracy and using numerous fast and cheap low-fidelity simulations to efficiently sample to input parameter space of interest. We selected gas production from unconventional wells to demonstrate the potential speedups and accuracy of the MFMC approach. The model fidelity usually determines the trade-off between accuracy and efficiency. While the high-fidelity model is more accurate, the low-fidelity model is more efficient. Our high-fidelity simulation includes reservoir simulations of a hydraulically fractured well. On the other hand, our low-fidelity model comprises the parallel-plate flow model. We used differential programming to efficiently solve the 1D flow model, where automatic differentiation is used to efficiently compute the gradients. We matched the production profile of high-fidelity simulations with our low-fidelity simulations. Then, we used a support vector regression to map the high- and low-fidelity input parameters. The mapping function is essential to tune the low-dimensional parameter space of the low-fidelity model to the high-dimensional parameter space of the high-fidelity model. We found that we can use a combination of 9 high fidelity and 10,000 low fidelity simulations to efficiently and accurately simulate pressure management. This method is at least two orders of magnitude faster than only using high-fidelity simulations. Finally, from a broader perspective, MFMC could efficiently estimate the uncertainty of various systems and models, integrating low- and high-fidelity models.
The Bello et al. study evaluates the impact of contrasting pressure drawdown on gas productivity and the resulting economics of a well in the Marcellus Shale of the Appalachian Basin. This research applies a techno-economic analysis approach to help identify potential ways pressure management strategies can be used to improve cumulative recovery of hydraulically fractured horizontal wells while maintaining project profitability. Gas production forecast outlook scenarios of the Marcellus Shale Energy and Environment Laboratory Laboratory's MIP-3H well were generated under varying pressure drawdowns using two approaches: 1) a novel physics-informed machine learning (PIML) workflow and 2) via traditional reservoir simulation in Computer Modeling Group’s (CMG) GEM Compositional & Unconventional Simulator. Cash flow and other economic metrics of interest were compiled on the production outlook using the U.S. Department of Energy's (DOE) National Energy Technology Laboratory (NETL) Unconventional Shale Well Economic Model (UShWEM).The sheets within this Microsoft ExcelTM workbook provide the economic metric outputs for the baseline condition and the one-at-a-time (OAT) sensitivity analysis of UShWEM's input parameters for each of the production scenarios evaluated.
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We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.
Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO 2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10 6 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.
Inverse problems are applied to determine unknown properties by matching observational data with a physical model that often takes many parameters as input. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented involving regularization with a technique known as a variational autoencoder (VAE), which is trained to map a high-dimensional parameter space with a complex structure to a low-dimensional latent space with a simple structure. We apply this approach to unconditioned realizations of the parameters (heterogeneous hydraulic fields) for a hydrogeological inverse problem. Two types of hydraulic conductivity fields are used to evaluate the characterization for the different levels of heterogeneity complexity of the physical inputs. This approach keeps the computational cost of generating the training data low. The reason is unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any groundwater flow model forward runs. In addition, this approach applies regularization on a low-dimensional latent space from the VAE and increases optimization efficiency through automatic differentiation. Furthermore, two different neural network (NN) structures are tested for their utility in using the VAE for inverse analysis. The performance of a deep, convolutional neural network strongly depends on the dimensionality of the latent space, which requires tuning. In contrast, a shallow, dense neural network provides consistently accurate characterization without tuning. Furthermore, our approach evaluates the advantages of the shallow, dense neural network over the deep, convolutional one and enables future application to a wide range of inverse problems.
Modern NISQ devices are subject to a variety of biases and sources of noise that degrade the solution quality of computations carried out on these devices. A natural question that arises in the NISQ era, is how fairly do these devices sample ground state solutions. To this end, we run five fair sampling problems (each with at least three ground state solutions) that are based both on quantum annealing and, on the Grover Mixer, -QAOA algorithm for gate-based NISQ hardware. In particular, we use seven IBM Q devices, the Aspen-9 Rigetti device, the IonQ device, and three D-Wave quantum annealers. For each of the fair sampling problems, we measure the ground state probability, the relative fairness of the frequency of each ground state solution with respect to the other ground state solutions, and the aggregate error as given by each hardware provider. Overall, our results show that NISQ devices do not achieve fair sampling yet. Furthermore, we also observe differences in the software stack with a particular focus on compilation techniques that illustrate what work will still need to be done to achieve a seamless integration of frontend (i.e., quantum circuit description) and backend compilation.