Quantum algorithms for geologic fracture networks.

Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10-1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

Predictive scale-bridging simulations through active learning.

Throughout computational science, there is a growing need to utilize the continual improvements in raw computational horsepower to achieve greater physical fidelity through scale-bridging over brute-force increases in the number of mesh elements. For instance, quantitative predictions of transport in nanoporous media, critical to hydrocarbon extraction from tight shale formations, are impossible without accounting for molecular-level interactions. Similarly, inertial confinement fusion simulations rely on numerical diffusion to simulate molecular effects such as non-local transport and mixing without truly accounting for molecular interactions. With these two disparate applications in mind, we develop a novel capability which uses an active learning approach to optimize the use of local fine-scale simulations for informing coarse-scale hydrodynamics. Our approach addresses three challenges: forecasting continuum coarse-scale trajectory to speculatively execute new fine-scale molecular dynamics calculations, dynamically updating coarse-scale from fine-scale calculations, and quantifying uncertainty in neural network models.

Enhancing high-fidelity nonlinear solver with reduced order model.

We propose the use of reduced order modeling (ROM) to reduce the computational cost and improve the convergence rate of nonlinear solvers of full order models (FOM) for solving partial differential equations. In this study, a novel ROM-assisted approach is developed to improve the computational efficiency of FOM nonlinear solvers by using ROM's prediction as an initial guess. We hypothesize that the nonlinear solver will take fewer steps to the converged solutions with an initial guess that is closer to the real solutions. To evaluate our approach, four physical problems with varying degrees of nonlinearity in flow and mechanics have been tested: Richards' equation of water flow in heterogeneous porous media, a contact problem in a hyperelastic material, two-phase flow in layered porous media, and fracture propagation in a homogeneous material. Overall, our approach maintains the FOM's accuracy while speeding up nonlinear solver by 18-73% (through suitable ROM-assisted FOMs). More importantly, the proximity of ROM's prediction to the solution space leads to the improved convergence of FOMs that would have otherwise diverged with default initial guesses. We demonstrate that the ROM's accuracy can impact the computational efficiency with more accurate ROM solutions, resulting in a better cost reduction. We also illustrate that this approach could be used in many FOM discretizations (e.g., finite volume, finite element, or a combination of those). Since our ROMs are data-driven and non-intrusive, the proposed procedure can easily lend itself to any nonlinear physics-based problem.

Mesoscale carbon sequestration site screening and CCS infrastructure analysis.

We explore carbon capture and sequestration (CCS) at the meso-scale, a level of study between regional carbon accounting and highly detailed reservoir models for individual sites. We develop an approach to CO(2) sequestration site screening for industries or energy development policies that involves identification of appropriate sequestration basin, analysis of geologic formations, definition of surface sites, design of infrastructure, and analysis of CO(2) transport and storage costs. Our case study involves carbon management for potential oil shale development in the Piceance-Uinta Basin, CO and UT. This study uses new capabilities of the CO(2)-PENS model for site screening, including reservoir capacity, injectivity, and cost calculations for simple reservoirs at multiple sites. We couple this with a model of optimized source-sink-network infrastructure (SimCCS) to design pipeline networks and minimize CCS cost for a given industry or region. The CLEAR(uff) dynamical assessment model calculates the CO(2) source term for various oil production levels. Nine sites in a 13,300 km(2) area have the capacity to store 6.5 GtCO(2), corresponding to shale-oil production of 1.3 Mbbl/day for 50 years (about 1/4 of U.S. crude oil production). Our results highlight the complex, nonlinear relationship between the spatial deployment of CCS infrastructure and the oil-shale production rate.

Greening coal: breakthroughs and challenges in carbon capture and storage.

Like it or not, coal is here to stay, for the next few decades at least. Continued use of coal in this age of growing greenhouse gas controls will require removing carbon dioxide from the coal waste stream. We already remove toxicants such as sulfur dioxide and mercury, and the removal of CO2 is the next step in reducing the environmental impacts of using coal as an energy source (i.e., greening coal). This paper outlines some of the complexities encountered in capturing CO2 from coal, transporting it large distances through pipelines, and storing it safely underground.

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks.

Here we employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

A machine learning framework for rapid forecasting and history matching in unconventional reservoirs.

We present a novel workflow for forecasting production in unconventional reservoirs using reduced-order models and machine-learning. Our physics-informed machine-learning workflow addresses the challenges to real-time reservoir management in unconventionals, namely the lack of data (i.e., the time-frame for which the wells have been producing), and the significant computational expense of high-fidelity modeling. We do this by applying the machine-learning paradigm of transfer learning, where we combine fast, but less accurate reduced-order models with slow, but accurate high-fidelity models. We use the Patzek model (Proc Natl Acad Sci 11:19731-19736, https://doi.org/10.1073/pnas.1313380110 , 2013) as the reduced-order model to generate synthetic production data and supplement this data with synthetic production data obtained from high-fidelity discrete fracture network simulations of the site of interest. Our results demonstrate that training with low-fidelity models is not sufficient for accurate forecasting, but transfer learning is able to augment the knowledge and perform well once trained with the small set of results from the high-fidelity model. Such a physics-informed machine-learning (PIML) workflow, grounded in physics, is a viable candidate for real-time history matching and production forecasting in a fractured shale gas reservoir.

3D particle transport in multichannel microfluidic networks with rough surfaces.

The transport of particles and fluids through multichannel microfluidic networks is influenced by details of the channels. Because channels have micro-scale textures and macro-scale geometries, this transport can differ from the case of ideally smooth channels. Surfaces of real channels have irregular boundary conditions to which streamlines adapt and with which particle interact. In low-Reynolds number flows, particles may experience inertial forces that result in trans-streamline movement and the reorganization of particle distributions. Such transport is intrinsically 3D and an accurate measurement must capture movement in all directions. To measure the effects of non-ideal surface textures on particle transport through complex networks, we developed an extended field-of-view 3D macroscope for high-resolution tracking across large volumes ([Formula: see text]) and investigated a model multichannel microfluidic network. A topographical profile of the microfluidic surfaces provided lattice Boltzmann simulations with a detailed feature map to precisely reconstruct the experimental environment. Particle distributions from simulations closely reproduced those observed experimentally and both measurements were sensitive to the effects of surface roughness. Under the conditions studied, inertial focusing organized large particles into an annular distribution that limited their transport throughout the network while small particles were transported uniformly to all regions.

Transient flow modeling in fractured media using graphs.

We describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the O(10^{4}) speedup that was obtained for steady-state flows earlier. However, the transient flows considered here involve an additional degree of complexity that was not present in the steady-state flows considered previously with a graph-based approach, that of time marching and solution of the flow equations within a time-stepping scheme. We verify our method with an analytical test case and demonstrate its use on a practical problem related to fluid flows in hydraulically fractured reservoirs. By enabling the study of transient flows, we create an opportunity for a wide set of possibilities where a steady-state approximation is not sufficient, such as the example motivated by hydraulic fracturing that we present here. This work validates the concept that graphs are able to reliably capture the topological properties of the fracture network and serve as effective surrogates in an uncertainty-quantification framework.

Modeling and scale-bridging using machine learning: nanoconfinement effects in porous media.

Fine-scale models that represent first-principles physics are challenging to represent at larger scales of interest in many application areas. In nanoporous media such as tight-shale formations, where the typical pore size is less than 50 nm, confinement effects play a significant role in how fluids behave. At these scales, fluids are under confinement, affecting key properties such as density, viscosity, adsorption, etc. Pore-scale Lattice Boltzmann Methods (LBM) can simulate flow in complex pore structures relevant to predicting hydrocarbon production, but must be corrected to account for confinement effects. Molecular dynamics (MD) can model confinement effects but is computationally expensive in comparison. The hurdle to bridging MD with LBM is the computational expense of MD simulations needed to perform this correction. Here, we build a Machine Learning (ML) surrogate model that captures adsorption effects across a wide range of parameter space and bridges the MD and LBM scales using a relatively small number of MD calculations. The model computes upscaled adsorption parameters across varying density, temperature, and pore width. The ML model is 7 orders of magnitude faster than brute force MD. This workflow is agnostic to the physical system and could be generalized to further scale-bridging applications.

Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning.

Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Current models either ignore or idealize microscale information at these larger scales because we lack a framework that efficiently utilizes it in its entirety to predict macroscale behavior in brittle materials. We propose a method that integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning. Our method has been shown to improve accuracy of predictions with up to four orders of magnitude speedup.

Introduction: energy and the subsurface.

This theme issue covers topics at the forefront of scientific research on energy and the subsurface, ranging from carbon dioxide (CO2) sequestration to the recovery of unconventional shale oil and gas resources through hydraulic fracturing. As such, the goal of this theme issue is to have an impact on the scientific community, broadly, by providing a self-contained collection of articles contributing to and reviewing the state-of-the-art of the field. This collection of articles could be used, for example, to set the next generation of research directions, while also being useful as a self-study guide for those interested in entering the field. Review articles are included on the topics of hydraulic fracturing as a multiscale problem, numerical modelling of hydraulic fracture propagation, the role of computational sciences in the upstream oil and gas industry and chemohydrodynamic patterns in porous media. Complementing the reviews is a set of original research papers covering growth models for branched hydraulic crack systems, fluid-driven crack propagation in elastic matrices, elastic and inelastic deformation of fluid-saturated rock, reaction front propagation in fracture matrices, the effects of rock mineralogy and pore structure on stress-dependent permeability of shales, topographic viscous fingering and plume dynamics in porous media convection.This article is part of the themed issue 'Energy and the subsurface'.

Geo-material microfluidics at reservoir conditions for subsurface energy resource applications.

Microfluidic investigations of flow and transport in porous and fractured media have the potential to play a significant role in the development of future subsurface energy resource technologies. However, the majority of experimental systems to date are limited in applicability due to operating conditions and/or the use of engineered material micromodels. We have developed a high pressure and temperature microfluidic experimental system that allows for direct observations of flow and transport within geo-material micromodels (e.g. rock, cement) at reservoir conditions. In this manuscript, we describe the experimental system, including our novel micromodel fabrication method that works in both geo- and engineered materials and utilizes 3-D tomography images of real fractures as micromodel templates to better represent the pore space and fracture geometries expected in subsurface formations. We present experimental results that highlight the advantages of using real-rock micromodels and discuss potential areas of research that could benefit from geo-material microfluidic investigations. The experiments include fracture-matrix interaction in which water imbibes into the shale rock matrix from etched fractures, supercritical CO2 (scCO2) displacing brine in idealized and realistic fracture patterns, and three-phase flow involving scCO2-brine-oil.

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity.

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect.

Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999) and F. Civan, Transp. Porous Med. 82, 375 (2010)] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.

A geostatistical modeling study of the effect of heterogeneity on radionuclide transport in the unsaturated zone, Yucca Mountain.

Retardation of certain radionuclides due to sorption to zeolitic minerals is considered one of the major barriers to contaminant transport in the unsaturated zone of Yucca Mountain. However, zeolitically altered areas are lower in permeability than unaltered regions, which raises the possibility that contaminants might bypass the sorptive zeolites. The relationship between hydrologic and chemical properties must be understood to predict the transport of radionuclides through zeolitically altered areas. In this study, we incorporate mineralogical information into an unsaturated zone transport model using geostatistical techniques to correlate zeolitic abundance to hydrologic and chemical properties. Geostatistical methods are used to develop variograms, kriging maps, and conditional simulations of zeolitic abundance. We then investigate, using flow and transport modeling on a heterogeneous field, the relationship between percent zeolitic alteration, permeability changes due to alteration, sorption due to alteration, and their overall effect on radionuclide transport. We compare these geostatistical simulations to a simplified threshold method in which each spatial location in the model is assigned either zeolitic or vitric properties based on the zeolitic abundance at that location. A key conclusion is that retardation due to sorption predicted by using the continuous distribution is larger than the retardation predicted by the threshold method. The reason for larger retardation when using the continuous distribution is a small but significant sorption at locations with low zeolitic abundance. If, for practical reasons, models with homogeneous properties within each layer are used, we recommend setting nonzero K(d)s in the vitric tuffs to mimic the more rigorous continuous distribution simulations. Regions with high zeolitic abundance may not be as effective in retarding radionuclides such as Neptunium since these rocks are lower in permeability and contaminants can only enter these regions through molecular diffusion.

A system model for geologic sequestration of carbon dioxide.

In this paperwe describe CO2-PENS, a comprehensive system-level computational model for performance assessment of geologic sequestration of CO2. CO2-PENS is designed to perform probabilistic simulations of CO2 capture, transport, and injection in different geologic reservoirs. Additionally, the long-term fate of CO2 injected in geologic formations, including possible migration out of the target reservoir, is simulated. The simulations sample from probability distributions for each uncertain parameter, leading to estimates of global uncertainty that accumulate through coupling of processes as the simulation time advances. Each underlying process in the system-level model is built as a module that can be modified as the simulation tool evolves toward more complex problems. This approach is essential in coupling processes that are governed by different sets of equations operating at different time-scales. We first explain the basic formulation of the system level model, briefly discuss the suite of process-level modules that are linked to the system level, and finally give an in-depth example that describes the system level coupling between an injection module and an economic module. The example shows how physics-based calculations of the number of wells required to inject a given amount of CO2 and estimates of plume size can impact long-term sequestration costs.

Development of a hybrid process and system model for the assessment of wellbore leakage at a geologic CO2 sequestration site.

Sequestration of CO2 in geologic reservoirs is one of the promising technologies currently being explored to mitigate anthropogenic CO2 emissions. Large-scale deployment of geologic sequestration will require seals with a cumulative area amounting to hundreds of square kilometers per year and will require a large number of sequestration sites. We are developing a system-level model, CO2-PENS, that will predict the overall performance of sequestration systems while taking into account various processes associated with different parts of a sequestration operation, from the power plant to sequestration reservoirs to the accessible environment. The adaptability of CO2-PENS promotes application to a wide variety of sites, and its level of complexity can be increased as detailed site information becomes available. The model CO2-PENS utilizes a science-based-prediction approach by integrating information from process-level laboratory experiments, field experiments/observations, and process-level numerical modeling. The use of coupled process models in the system model of CO2-PENS provides insights into the emergent behavior of aggregate processes that could not be obtained by using individual process models. We illustrate the utility of the concept by incorporating geologic and wellbore data into a synthetic, depleted oil reservoir. In this sequestration scenario, we assess the fate of CO2 via wellbore release and resulting impacts of CO2 to a shallow aquifer and release to the atmosphere.