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An accurate assessment of the physical states of the Earth system is an essential component of many scientific, societal and economical considerations. These assessments are becoming an increasingly challenging computational task since we aim to resolve models with high resolutions in space and time, to consider complex coupled partial differential equations, and to estimate uncertainties, which often requires many realizations. Machine learning methods are becoming a very popular method for the construction of surrogate 5 models to address these computational issues. However, they also face major challenges in producing explainable, scalable, interpretable and robust models. In this manuscript, we evaluate the perspectives of geoscience applications of physics-based machine learning, which combines physics-based and data-driven methods to overcome the limitations of each approach taken alone. Through three designated examples (from the fields of geothermal energy, geodynamics, and hydrology), we show that the non-intrusive reduced basis method as a physics-based machine learning approach is able to 10 produce highly precise surrogate models that are explainable, scalable, interpretable, and robust.

Mechanistic models facilitate understanding complex biogeochemical interactions and process chains in soil. However, biogeochemical soil models often have weakly constraint parameters and show sloppiness. That means the dimensionality of parameter spaces is overly large and parameters often cannot be inferred based on available experimental data. Thus, equifinality arises, i.e. many different parameter combinations lead to very similar or identical model predictions.Expert knowledge represents a synthesis of existing knowledge on processes in soil systems that can be used to find viable parameter regions such that models give plausible predictions in line with evidence-based expectations. Here, we present an approach to leverage expert knowledge. This is achieved by formulating expert knowledge in terms of parameter and process constraints that must be fulfilled. Viable parameter sets are then identified by model conditioning using a novel Bayesian constraint-based parameter search algorithm that extends a previously published iterative constraint-based parameter search method. The algorithm successively applies stricter conditions by increasing the minimum acceptable number of process constraints to be satisfied in each iteration. We present the concept of the algorithm and demonstrate a successful application to a complex model simulating biodegradation of the herbicide Atrazine that has a high-dimensional parameter space. The presented approach can be widely applied to other soil biogeochemical models and provides a powerful tool to leverage expert knowledge for constructing robust prior parameter distributions for model sensitivity analysis or calibration.

Industrial-scale injection of CO2 into the subsurface increases the fluid pressure in the reservoir, which if not properly controlled can potentially lead to geomechanical damage (i.e., fracturing of the caprock or reactivation of faults) and subsequent CO2 leakage. Brine extraction is one approach for managing formation pressure, effective stress, and plume movement in response to CO2 injection. The management of the extracted brine can be expensive (i.e., due to transportation, treatment, disposal, or re-injection), with added cost to the carbon capture and sequestration (CCS); thus, minimizing the volume of extraction brine is of great importance to ensure that the economics of CCS are favorable. The main objective of this study is to demonstrate the use of adaptive optimization methods in the planning of brine extraction and to investigate how the quality of initial site characterization data and the use of newly acquired monitoring data (e.g. pressure at observation wells) impact the optimization performance. We apply an adaptive management approach that integrates monitoring, calibration, and optimization of brine extraction rates to achieve pre-defined pressure constraints. Our results show that reservoir pressure management can be extremely benefited by early and high frequency pressure monitoring during early injection times, especially for poor initial reservoir characterization. Low frequencies of model calibration and optimization with monitoring data may lead to optimization problems because either pressure buildup constraints are violated or excessively high extraction rates are proposed. The adaptive pressure management approach may constitute an effective tool to manage pressure buildup under uncertain reservoir conditions by minimizing the volumes of extracted brine while controlling pressure buildup.

The natural degradation pathways of the herbicide atrazine (AT) are highly complex. These pathways involve the metabolic activity of several bacterial guilds (that use AT as a source of carbon, nitrogen or both) and abiotic degradation mechanisms. The co-occurrence of multiple degradation pathways, combined with challenges in quantifying bacterial guilds and relevant intermediate metabolites, has led to the development of competing model formulations, which all represent valid descriptions of the fate of AT. A proper understanding of the fate of this complex compound is needed to develop effective management and mitigation strategies.Here, we propose a model discrimination process in combination with prospective optimal design of experiments. We performed Monte-Carlo simulations using a first-order model that reflects a simple reaction chain of complete AT degradation and a set of Monod-based model variants that consider different bacterial consortia and degradation pathways. We used a Bayesian statistical analysis of these simulation ensembles to simulate virtual degradation experiments and chemical analysis strategies, thus obtaining predictions on the utility of experiments to deliver conclusive data for model discrimination. To do so, we defined different experimental protocols including a combination of: i) the metabolites to measure (AT, metabolites and CO2), ii) sampling frequency (sampling every day, every two days and every four days), iii) features difficult to quantify (specific bacterial guilds). As a statistical metric to measure the conclusiveness of these virtual experiments, we used the so-called energy distance.Our results show that simulated AT degradation pathways following first-order reaction chains can be clearly distinguished from simulations using Monod-based models. Within the Monod-based models, we detected three clusters of models that differ in the number of bacterial guilds involved in AT degradation. Experimental designs considering main AT metabolites and sampling frequencies of once every two or four days at durations of 50 or 100 days provided the most informative data to discriminate models. Including measurements of bacterial guilds only slightly improved model discrimination. Our study highlights that environmental fate studies should prioritize measuring metabolites to elucidate active AT degradation pathways in soil and identify robust model formulations supporting risk assessment and mitigation strategies.

The feasibility of geological carbon storage (GCS) sites depends on their capacity to retain safely $${\hbox {CO}_{2}}$$ . While deep saline formations and depleted gas/oil reservoirs are good candidates to sequester $${\hbox {CO}_{2}}$$ , gas/oil reservoirs typically have a limited storage capacity compared to ideal targets ( $$\sim $$ 1 Mt/year) considered for $${\hbox {CO}_{2}}$$ disposal (Celia et al. in Water Resour Res 51(9):6846–6892, 2015. doi: 10.1002/2015WR017609 ). In this respect, deep saline aquifers are considered more appropriate formations for GCS, but present the disadvantage of having limited characterization data. In particular, information about the continuity of the overlying sealing formations (caprock) is often sparse if it exists at all. In this work, a study of $${\hbox {CO}_{2}}$$ leakage is conducted for a candidate GCS site located in the Michigan Basin, whose sealing properties of the caprock are practically unknown. Quantification of uncertainty on $${\hbox {CO}_{2}}$$ leakage from the storage formation is achieved through a Monte Carlo simulation approach, relying on the use of a computationally efficient semi-analytical leakage model based upon the solution derived by Nordbotten et al. (Environ Sci Technol 43(3):743–749, 2009), which assumes leakage occurs across “passive” wells intersecting caprock layers. A categorical indicator Kriging simulator is developed and implemented to represent the caprock sealing properties and model the permeability uncertainty. Binary fields of caprock permeability are generated and exhibit mostly low permeability, with sparsely-occurring local high permeability areas where brine and $${\hbox {CO}_{2}}$$ may leak out of the storage formation. In addition, the feasibility of extending the use of the semi-analytical model to large-area leakage pathways is studied. This work advances a methodology for preliminary uncertainty quantification of $${\hbox {CO}_{2}}$$ leakage at sites of GCS with little or no information on the sealing properties of the caprock. The implemented analysis shows that, for the considered site, $${\hbox {CO}_{2}}$$ leakage may not be negligible even for relatively low ( $$\sim $$ 1%) probabilities of finding permeable inclusions in the caprock and highlights the importance of being able to characterize caprock sealing properties over large areas.

The role of capillary forces during buoyant migration of CO2 is critical towards plume immobilization during post-injection of geological carbon sequestration. However, the inherent heterogeneity of most candidate reservoirs makes it very challenging to evaluate the effects of capillary forces on the storage capacity of these formations and to assess in-situ plume evolution. Given the technical challenges in characterizing deep reservoir's migration and trapping phenomena, the development of carefully controlled laboratory experiments allows recreating the interplay of governing forces that are expected in-situ. Visual observations, complemented by saturation measurements across homogeneous and heterogeneous sand packs, provide direct insight into capillary/buoyancy-dominated flow processes, allowing assessment of predictive ability of existing and new two-phase flow simulators.

The question of whether carbon dioxide enhanced oil recovery (CO 2 -EOR) constitutes a valid alternative for greenhouse gas emission reduction has been frequently asked by the general public and environmental sectors. Through this technology, operational since 1972, oil production is enhanced by injecting CO 2 into depleted oil reservoirs in order displace the residual oil toward production wells in a solvent/miscible process. For decades, the CO 2 utilized for EOR has been most commonly sourced from natural CO 2 accumulations. More recently, a few projects have emerged where anthropogenic CO 2 (A-CO 2 ) is captured at an industrial facility, transported to a depleted oil field, and utilized for EOR. If carbon geologic storage is one of the project objectives, all the CO 2 injected into the oil field for EOR could technically be stored in the formation. Even though the CO 2 is being prevented from entering the atmosphere, and permanently stored away in a secured geologic formation, a question arises as to whether the total CO 2 volumes stored in order to produce the incremental oil through EOR are larger than the CO 2 emitted throughout the entire CO 2 -EOR process, including the capture facility, the EOR site, and the refining and burning of the end product. We intend to answer some of these questions through a DOE-NETL funded study titled “Carbon Life Cycle Analysis of CO 2 -EOR for Net Carbon Negative Oil (NCNO) Classification”. NCNO is defined as oil whose carbon emissions to the atmosphere, when burned or otherwise used, are less than the amount of carbon permanently stored in the reservoir in order to produce the oil. In this paper, we focus on the EOR site in what is referred to as a gate-to-gate system, but are inclusive of the burning of the refined product, as this end member is explicitly stated in the definition of NCNO. Finally, we use Cranfield, Mississippi, as a case study and come to the conclusion that the incremental oil produced is net carbon negative.

The role of capillary forces during buoyant migration of CO2 is critical toward plume immobilization within the postinjection phase of a geological carbon sequestration operation. However, the inherent heterogeneity of the subsurface makes it very challenging to evaluate the effects of capillary forces on the storage capacity of these formations and to assess in situ plume evolution. To overcome the lack of accurate and continuous observations at the field scale and to mimic vertical migration and entrapment of realistic CO2 plumes in the presence of a background hydraulic gradient, we conducted two unique long-term experiments in a 2.44 m × 0.5 m tank. X-ray attenuation allowed measuring the evolution of a CO2-surrogate fluid saturation, thus providing direct insight into capillarity-dominated and buoyancy-dominated flow processes occurring under successive drainage and imbibition conditions. The comparison of saturation distributions between two experimental campaigns suggests that layered-type heterogeneity plays an important role on nonwetting phase (NWP) migration and trapping, because it leads to (i) longer displacement times (3.6 months versus 24 days) to reach stable trapping conditions, (ii) limited vertical migration of the plume (with center of mass at 39% versus 55% of aquifer thickness), and (iii) immobilization of a larger fraction of injected NWP mass (67.2% versus 51.5% of injected volume) as compared to the homogenous scenario. While these observations confirm once more the role of geological heterogeneity in controlling buoyant flows in the subsurface, they also highlight the importance of characterizing it at scales that are below seismic resolution (1–10 m).

Incorporating hysteresis into models is important to accurately capture the two phase flow behavior when porous media systems undergo cycles of drainage and imbibition such as in the cases of injection and post-injection redistribution of CO2 during geological CO2 storage (GCS). In the traditional model of two-phase flow, existing constitutive models that parameterize the hysteresis associated with these processes are generally based on the empirical relationships. This manuscript presents development and testing of mathematical hysteretic capillary pressure—saturation—relative permeability models with the objective of more accurately representing the redistribution of the fluids after injection. The constitutive models are developed by relating macroscopic variables to basic physics of two-phase capillary displacements at pore-scale and void space distribution properties. The modeling approach with the developed constitutive models with and without hysteresis as input is tested against some intermediate-scale flow cell experiments to test the ability of the models to represent movement and capillary trapping of immiscible fluids under macroscopically homogeneous and heterogeneous conditions. The hysteretic two-phase flow model predicted the overall plume migration and distribution during and post injection reasonably well and represented the postinjection behavior of the plume more accurately than the nonhysteretic models. Based on the results in this study, neglecting hysteresis in the constitutive models of the traditional two-phase flow theory can seriously overpredict or underpredict the injected fluid distribution during post-injection under both homogeneous and heterogeneous conditions, depending on the selected value of the residual saturation in the nonhysteretic models.

The impact of geologic heterogeneity on capillary trapping of supercritical CO2 (scCO2) has been recognized and appraised through laboratory experimentation and modeling. However, how different injection strategies can be optimized to improve capillary trapping has not received adequate attention. We present a study based on stochastic analysis to show the impact of injection scheduling on capillary trapping of scCO2 in heterogeneous geological formations. Improvement of trapping efficiency consists of maximizing the trapped volume within a predefined secure zone of the storage formation with the goal of avoiding plume intersection with potential leakage pathways. Using knowledge acquired from physical experiments in intermediate-scale tanks with controlled heterogeneity, we conduct numerical simulations following a stochastic approach to extend the observed outcomes to a series of equally probable permeability scenarios. Our simulations involve the same combination of surrogate fluids that are used in the experiments to mimic viscosity and density contrasts between scCO2 and brine. To account for uncertainty of formation heterogeneity, several permeability fields with three different variances and two horizontal correlation lengths are generated. The same volume of scCO2 is emplaced using four different modes of injection scheduling. Results suggest that injection strategies aimed at enhancing capillary trapping of scCO2 and increasing the probability of constraining the plume within a secure zone are strictly related to the specific heterogeneity of the reservoir. This preliminary theoretical finding suggests the potential for maximizing secure capillary trapping through the proper selection of injection schedule to fit the formation heterogeneity. © 2016 Society of Chemical Industry and John Wiley & Sons, Ltd.

One of the main concerns of geological carbon storage (GCS) systems is the risk of leakage through “weak” permeable areas of the sealing formation or caprock. Since the fluid pressure pulse travels faster than the carbon dioxide (CO2) plume across the storage reservoir, the fluid overpressure transmitted into overlying permeable formations through caprock discontinuities is potentially detectable sooner than actual CO2 leakage occurs. In this work, an inverse modeling method based on fluid pressure measurements collected in strata above the target CO2 storage formation is proposed, which aims at identifying the presence, the location, and the extent of possible leakage pathways through the caprock. We combine a three-dimensional subsurface multiphase flow model with ensemble-based data assimilation algorithms to recognize potential caprock discontinuities that could undermine the long-term safety of GCS. The goal of this work is to examine and compare the capabilities of data assimilation algorithms such as the ensemble smoother (ES) and the restart ensemble Kalman filter (REnKF) to detect the presence of brine and/or CO2 leakage pathways, potentially in real-time during GCS operations. For the purpose of this study, changes in fluid pressure in the brine aquifer overlying to CO2 storage formation aquifer are hypothetically observed in monitoring boreholes, or provided by time-lapse seismic surveys. Caprock discontinuities are typically characterized locally by higher values of permeability, so that the permeability distribution tends to fit to a non-Gaussian bimodal process, which hardly complies with the requirements of the ES and REnKF algorithms. Here, issues related to the non-Gaussianity of the caprock permeability field are investigated by developing and applying a normal score transform procedure. Results suggest that the REnKF is more effective than the ES in characterizing caprock discontinuities.

Geological carbon storage (GCS) has been proposed as a favorable technology to reduce carbon dioxide (CO2) emissions to the atmosphere. One of the main concerns about GCS is the risk of CO2 escape from the storage formation through leakage pathways in the sealing layer. This study aims at understanding the main sources of uncertainty affecting the upward migration of CO2 through pre-existing “passive” wells and the risk of fissuring of target formation during GCS operations, which may create pathways for CO2 escape. The analysis focuses on a potential GCS site located within the Michigan Basin, a geologic basin situated on the lower Peninsula of the state of Michigan. For this purpose, we perform a stochastic analysis (SA) and a global sensitivity analysis (GSA) to investigate the influence of uncertain parameters, such as: permeability and porosity of the injection formation, passive well permeability, system compressibility, brine residual saturation, and CO2 end-point relative permeability. For the GSA, we apply the extended Fourier amplitude sensitivity test (FAST), which can rank parameters based on their direct impact on the output, or first-order effect, and capture the interaction effect of one parameter with the others, or higher-order effect. To simulate GCS, we use an efficient semi-analytical multiphase flow model, which makes the application of the SA and the GSA computationally affordable. Results show that, among model parameters, the most influential on both fluid overpressure and CO2 mass leakage is the injection formation permeability. Brine residual saturation also has a significant impact on fluid overpressure. While influence of permeability on fluid overpressure is mostly first-order, brine residual saturation’s influence is mostly higher-order. CO2 mass leakage is also affected by passive well permeability, followed by porosity and system compressibility through higher-order effects.

© 2015, Springer International Publishing Switzerland. Successful large-scale implementation of geological CO2 sequestration (GCS) will require the preliminary assessment of multiple potential injection sites. Risk assessment and optimization tools used in this effort typically require large numbers of simulations. This makes it important to choose the appropriate level of complexity when selecting the type of simulation model. A promising multi-phase semi-analytical method proposed by Nordbotten et al. (Environ. Sci. Technol. 43, 743–749 2009) to estimate key system attributes (i.e., pressure distribution, CO2 plume extent, and fluid migration) has been found to reduce computational run times by three orders of magnitude when compared to other standard numerical techniques. The premise of the work presented herein is that the existing semi-analytical leakage algorithm proposed by Nordbotten et al. (Environ. Sci. Technol. 43, 743–749 2009) may be further improved in computational efficiency by applying a fixed-point-type iterative global pressure solution to eliminate the need to solve large sets of linear equations at each time step. Results show that significant gains in computational efficiency are obtained with this new methodology. In addition, this modification provides the same enhancement to similar semi-analytical algorithms that simulate single-phase injection into multi-layer domains.

Geological carbon sequestration (GCS) has been identified as having the potential to reduce increasing atmospheric concentrations of carbon dioxide (CO2). However, a global impact will only be achieved if GCS is cost-effectively and safely implemented on a massive scale. This work presents a computationally efficient methodology for identifying optimal injection strategies at candidate GCS sites having uncertainty associated with caprock permeability, effective compressibility, and aquifer permeability. A multi-objective evolutionary optimization algorithm is used to heuristically determine non-dominated solutions between the following two competing objectives: (1) maximize mass of CO2 sequestered and (2) minimize project cost. A semi-analytical algorithm is used to estimate CO2 leakage mass rather than a numerical model, enabling the study of GCS sites having vastly different domain characteristics. The stochastic optimization framework presented herein is applied to a feasibility study of GCS in a brine aquifer in the Michigan Basin (MB), USA. Eight optimization test cases are performed to investigate the impact of decision-maker (DM) preferences on Pareto-optimal objective-function values and carbon-injection strategies. This analysis shows that the feasibility of GCS at the MB test site is highly dependent upon the DM’s risk-adversity preference and degree of uncertainty associated with caprock integrity. Finally, large gains in computational efficiency achieved using parallel processing and archiving are discussed.

Carbon Capture and Storage (CCS) represents a technology aimed to reduce atmospheric loading of CO2 from power plants and heavy industries by injecting it into deep geological formations, such as saline aquifers. A number of trapping mechanisms contribute to effective and secure storage of the injected CO2 in supercritical fluid phase (scCO2) in the formation over the long term. The primary trapping mechanisms are structural, residual, dissolution and mineralization. Knowledge gaps exist on how the heterogeneity of the formation manifested at all scales from the pore to the site scales affects trapping and parameterization of contributing mechanisms in models. An experimental and modeling study was conducted to fill these knowledge gaps. Experimental investigation of fundamental processes and mechanisms in field settings is not possible as it is not feasible to fully characterize the geologic heterogeneity at all relevant scales and gathering data on migration, trapping and dissolution of scCO2. Laboratory experiments using scCO2 under ambient conditions are also not feasible as it is technically challenging and cost prohibitive to develop large, two- or three-dimensional test systems with controlled high pressures to keep the scCO2 as a liquid. Hence, an innovative approach that used surrogate fluids in place of scCO2 andmore » formation brine in multi-scale, synthetic aquifers test systems ranging in scales from centimeter to meter scale developed used. New modeling algorithms were developed to capture the processes controlled by the formation heterogeneity, and they were tested using the data from the laboratory test systems. The results and findings are expected to contribute toward better conceptual models, future improvements to DOE numerical codes, more accurate assessment of storage capacities, and optimized placement strategies. This report presents the experimental and modeling methods and research results.« less