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Images associated to paper of the same name by B. Vega, A.R. Kovscek This research was funded by the Center for Mechanistic Control of Unconventional Formations (CMC-UF), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science under DOE (BES) Award DE-SC0019165.
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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.
This paper provides a comprehensive review on the application of proppants to maintain fracture permeability over the lifetime of a well based on published observations from experiments and modeling. The review identifies and describes important processes occurring during proppant embedment, during hydraulic fracturing, laboratory testing of fracture conductivity, proppant embedment and modeling of proppant embedment. Lastly, this paper identifies the challenges and knowledge gaps that also provide future avenues of research and opportunities for collaborative technological development which requires an interdisciplinary approach of science, engineering in academia, government, and private sector.
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Models suggest that rock-derived nitrogen (N) inputs are of global importance to ecosystem N budgets; however, field studies demonstrating the significance of rock N inputs are rare. We examined rock-derived N fluxes in soils derived from sedimentary rocks along a catena formed under a semi-arid climate. Our measurements demonstrate that there are distinct and traceable pools of N in the soil and bedrock and that the fraction of rock-derived N declines downslope along the catena. We used geochemical mass balance weathering flux measurements to estimate a rock-derived N flux of 0.145 to 0.896 kg ha -1 yr -1 at the ridgecrest. We also developed independent N flux estimates using a 15 N-based isotope mixing model. While geochemical mass-balance-based estimates fell within the 95% confidence range derived from the isotope mixing model (-1.1 to 44.3 kg ha -1 yr -1 ), this range was large due to uncertainty in values for atmospheric 15 N deposition. Along the catena, N isotopes suggest a diminishing effect of rock-derived N downslope. Overall, we found that despite relatively large N pools within the saprolite and bedrock, slow chemical weathering and landscape denudation limit the influence of rock-derived N, letting atmospheric N deposition (7.1 kg ha -1 yr -1 ) and N fixation (0.9-3.1 kg ha -1 yr -1 ) dominate N inputs to this grassland ecosystem.
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