Abstract
We investigate the coupled dynamics of fluid mixing and viscously unstable flow under both miscible (single‐phase) and partially miscible (two‐phase) conditions, and in both homogeneous and ...heterogeneous porous media. Higher‐order finite element methods and fine grids are used to resolve the small‐scale onset of fingering and tip splitting. An equation of state determines the thermodynamic phase behavior and Fickian diffusion. We compute global quantitative measures of the spreading and mixing of a diluting slug to elucidate key differences between miscible and partially miscible systems.
Hydrodynamic
instabilities are the main driver for mixing in miscible flow. In partially miscible flow, however, we find that relative permeabilities spread the two‐phase zone. Within this mixing zone dissolution and evaporation drive mixing
thermodynamically
while reducing mobility contrasts and thus fingering instabilities. The different mixing dynamics in systems involving multiple phases with mutual solubilities have important implications in hydrogeology and energy applications, such as geological carbon sequestration and gas transport in hydrocarbon reservoirs.
Plain Language Summary
When fluids propagate through subsurface porous media, flow instabilities can be either detrimental or advantageous depending on the application. The interplay between viscous instabilities and fluid mixing has been studied extensively for single‐phase two‐component mixtures, but not for applications that involve two phases (e.g., oil and gas) that exchange multiple species. In this first study of mixing in partially miscible two‐phase flow, we find that the dynamics are profoundly different. In single‐phase flow, viscous fingering increases the interface between two fluids (of the same phase) and diffusion across that interface drives the mixing. In two‐phase flow, mass exchange between the phases creates a two‐phase mixing zone. In this zone, two phases coexist that have different velocities, which lead to an expansion of the mixing zone. Diffusion occurs both within each phase and between the phases, and the interphase mass exchange significantly enhances mixing. Because this thermodynamic mixing is extremely efficient, viscosity contrasts are quickly homogenized, and hydrodynamic instabilities (fingering) are less pronounced. In fluid mechanical terms, dissipation drives mixing in single phase, while production may dominate in two‐phase flow. These findings have broad implications for the prediction of instabilities and mixing behavior in subsurface applications that involve multiple partially miscible fluid phases.
Key Points
The mixing dynamics of two partially miscible fluids are revealed for the first time
Mixing is governed by interphase multispecies exchange interacting with flow fingering and channeling
Expansion of a two‐phase mixing zone reduces global variance budget in an interplay with dissipation
•An upscaling framework is proposed to predict roof water inflow.•The framework includes multiscale analyses and derivation of upscaling formulas.•Statistical and inversion models of effective ...fracture aperture are established.
Underground coal mining suffers from groundwater intrusion from the aquifers overlying coal seams. Therefore, developing methods for the accurate prediction of roof water inflow is urgently needed to design a safe drainage system. In this study, we developed a novel upscaling framework to predict roof water inflow by integrating the multiscale hydrogeological properties of roof aquifers. In this framework, we imaged rock samples via scanning electron microscopy and performed pore-scale analysis based on fractal theory. A fractal model of permeability was introduced to calculate the seepage capacity of the pore structure in the samples. The effect of fractures was further evaluated via core-scale pneumatic experiments. Subsequently, we derived an upscaling formula of hydraulic conductivity used for predicting roof water inflow at the field scale. The proposed upscaling approach was demonstrated using data from a coal mine in Northern China. The results indicate that the actual water inflow (21 m3/h) is within the predicted range of our upscaling framework (9.32–92.78 m3/h), and the initial line fracture rate dx is distributed between 0.02 % and 0.03 %. Therefore, these findings can guide the development of methods for considering micropores and fractures simultaneously and scaling them up to the field scale for effective prediction of water inflow from roof aquifers.
Depleted gas reservoirs are appealing targets for carbon dioxide (CO 2 ) sequestration because of their storage capacity, proven seal, reservoir characterization knowledge, existing infrastructure, ...and potential for enhanced gas recovery. Low abandonment pressure in the reservoir provides additional voidage-replacement potential for CO 2 and allows for a low surface pump pressure during the early period of injection. However, the injection process poses several challenges. This work aims to raise awareness of key operational challenges related to CO 2 injection in low-pressure reservoirs and to provide a new approach to assessing the phase behavior of CO 2 within the wellbore. When the reservoir pressure is below the CO 2 bubble-point pressure, and CO 2 is injected in its liquid or supercritical state, CO 2 will vaporize and expand within the well-tubing or in the near-wellbore region of the reservoir. This phenomenon is associated with several flow assurance problems. For instance, when CO 2 transitions from the dense-state to the gas-state, CO 2 density drops sharply, affecting the wellhead pressure control and the pressure response at the well bottom-hole. As CO 2 expands with a lower phase viscosity, the flow velocity increases abruptly, possibly causing erosion and cavitation in the flowlines. Furthermore, CO 2 expansion is associated with the Joule–Thomson (IJ) effect, which may result in dry ice or hydrate formation and therefore may reduce CO 2 injectivity. Understanding the transient multiphase phase flow behavior of CO 2 within the wellbore is crucial for appropriate well design and operational risk assessment. The commonly used approach analyzes the flow in the wellbore without taking into consideration the transient pressure response of the reservoir, which predicts an unrealistic pressure gap at the wellhead. This pressure gap is related to the phase transition of CO 2 from its dense state to the gas state. In this work, a new coupled approach is introduced to address the phase behavior of CO 2 within the wellbore under different operational conditions. The proposed approach integrates the flow within both the wellbore and the reservoir at the transient state and therefore resolves the pressure gap issue. Finally, the energy costs associated with a mitigation process that involves CO 2 heating at the wellhead are assessed.
The geologic architecture in sedimentary reservoirs affects the behavior of density-driven flow and the dispersion of CO2-rich brine. The spatial organization and connectivity of facies types play an ...important role. Low-permeability facies may suppress fingering and reduce vertical spreading, but may also increase transverse mixing. This is more pronounced when geologic structures create preferential flow pathways through connected facies types. We perform high-resolution simulations of three-dimensional (3D) heterogeneous formations whose connectivity cannot be represented in two-dimensional models consistent with percolation theory. This work focuses on the importance of 3D facies-based heterogeneity and connectivity on advection-diffusion transport of dissolved CO2. Because the dissolution of CO2 and the subsequent density increase of brine are the driving force for gravitational instabilities, we model the phase behavior with the accurate cubic-plus-association equation-of-state, which accounts for the self-association of polar water molecules and the cross-association between CO2 and water. Our results elucidate how the spatial organization of facies affects the dynamics of CO2 convective mixing. Scaling relations for the evolution of a global dispersion-width provide insights that can be universally applied. The results suggest that the long-term evolution and scaling of dispersion are surprisingly similar for homogeneous and (binary and multiscale) heterogeneous porous media.
Parameter estimation for reactive transport models (RTMs) is important in improving their predictive capacity for accurately simulating subsurface hydrogeochemical processes. This paper introduces a ...deep learning approach called the tandem neural network architecture (TNNA), which consists of a forward network and a reverse network to estimate input parameters for RTMs. The TNNA approach has a limitation in that the approximation error from the forward network often results in biased inversion results. To solve this problem, we proposed to enhance TNNA using an adaptive updating strategy (AUS), which locally reduces the approximation error of the forward network. The developed framework updates the forward network by iteratively using local sampling and transfer learning. The TNNA‐AUS was verified by a cation exchange example. The results show that TNNA‐AUS successfully reduces the inversion bias and improves the computational efficiency and inversion accuracy, compared with the global improvement strategy of adding training samples according to the prior distribution of model parameters. After verification, the TNNA‐AUS was applied to a real‐world and well‐documented RTM problem of the Aquia aquifer, Maryland, USA. The inversion results demonstrate that the developed TNNA‐AUS algorithm is an excellent tool for us to understand the complex subsurface hydrogeochemical processes and estimate the associated reaction parameters.
Key Points
Approximate errors from the forward network may cause biased results for tandem neural network architecture inverse modeling
Surrogate adaptive updating strategy is proposed for improving the tandem neural network architecture inversion
The TNNA‐AUS is developed for multicomponent reactive inverse modeling with excellent computational efficiency and accuracy comparing TNNA
•NS-ES-MDA accurately identifies model parameters with limited uncertainty.•Calibrating tracer parameters or conduit length elevates uncertainty of model parameters.•Identification performance is ...correlated with limit and error of observation.
Transient storage model (TSM) is widely used to describe solute transport processes in karst areas. Accurately identifying model parameters is essential for predicting and mitigating groundwater contamination. This paper employs the normal-score ensemble smoother with multiple data assimilation (NS-ES-MDA) algorithm to automatically identify model parameters (cross-sectional area of main channel A, dispersion coefficient D, cross-sectional area of storage zone As, and exchange coefficient α), while evaluating their uncertainty across four cases: identification of only model parameters (case 1), model parameters alongside tracer parameters (case 2), model parameters with conduit length (case 3), and all three –model parameters, tracer parameters, and conduit length (case 4). We examine the variations in uncertainty of model parameters when tracer parameters and/or conduit length are known or unknown. We further investigate the effects of concentration observation limits and observation error variance on the identification performance. The results demonstrate that the proposed method can successfully identify model parameters, even in cases where tracer parameters and/or conduit length are unknown, although with a certain level of uncertainty. However, the calibration of tracer parameters leads to an increase in uncertainty for A and D, and a slight rise in uncertainty for α. The calibration of conduit length significantly elevates the uncertainties of A and As and causes an increase in uncertainty for D. Compared with tracer parameters, conduit length causes larger uncertainty in A and As. The identification performance significantly deteriorates when the tail of observed breakthrough curve (BTC) is truncated, and reaches its peak at an observation error variance of 1 × 10-4. This implies that it is crucial to monitor the tail in BTC and to assign a reasonable observation error when using this method to identify model parameters. Although these findings are derived from a synthetic karst conduit, they offer valuable insights for identifying model parameters as tracer data and/or conduit length are uncertain in field conditions.
Permeability is one of the key parameters for quantitatively evaluating groundwater resources and accurately predicting the rates of water inflows into coal mines. This paper presents an efficient ...method to estimate the macroscopic permeability by using the scanning electron microscopy (SEM) images. A correlation between the microscopic features of sandstone porosity and the macropermeability is approached by an image identification technique. Firstly, the gray images were transformed into the binary images by using the histogram of the entropy method. Then, the Green and Euler distance methods were applied to calculate the length and area of the pores, and the fractal parameters were estimated according to the slit island method. Based on the theory of microscopic seepage flow, the seepage coefficient and permeability were calculated by fractal parameters. Typical water-bearing sandstone samples in the Kailuan coal field area in North China were selected to demonstrate the methodology. SEM microscopic images of nine groups of sandstone samples collected at different depths (from the outcrop to the deep mines) were analyzed. Based on the theoretical model of micropore structures and the fractal theory, the permeabilities were estimated. The results provide insights for understanding the hydraulic properties of the sandstone.
•Thermal-hydrological-mechanical-chemical processes are modeled for a GCS project.•Effect of facies-dependent features on CO2 migration is studied.•The efficacy of different trapping mechanisms ...during a GCS project is investigated.•Hot spots for CO2 fate and transport in fluvial-type aquifers are found.•Excellent agreement is found between numerical simulations and field observations.
Understanding geological sequestration of carbon dioxide (CO2) requires fully-coupled simulation of thermal-hydrological-mechanical-chemical (THMC) processes within well-characterized subsurface heterogeneity. A CO2 injection pilot project was performed in the Cranfield site, Mississippi, USA, where subsurface heterogeneity reflects fluvial deposition. During the project, CO2 was injected through an injection well and was monitored using two observation wells. We incorporate high-resolution three-dimensional heterogeneity model of the site into multiphase and multi-component flow and transport models. We validate our models and evaluate how bottom-hole pressure (BHP) in injection well, CO2 breakthrough times at observation wells, and efficiency of trapping mechanisms (i.e., dissolution, snap-off trapping, mobile CO2) are controlled by (1) non-isothermal CO2 injection, (2) geochemical reactions, (3) capillary pressure heterogeneity, (4) geomechanical effects, and (5) permeability enhancement close to the injection well. Results suggest that neglecting thermal effects lowers BHP, shortens breakthrough times, overestimates dissolution, and underestimates snap-off trapping. The BHP remains unchanged, breakthrough times are overestimated, and solubility and snap-off trapping are underestimated when geochemical reactions are ignored. Ignoring capillary pressure heterogeneity results in underestimation of BHP and dissolution and overestimation of breakthrough times. Ignoring geomechanical process results in lower BHP, shorter breakthrough times, increased dissolution, and decreased snap-off trapping. Ignoring permeability enhancement results in underestimation of breakthrough times and solubility trapping, and overestimation of snap-off trapping. Our results have important practical implication for designing effective field scale experiments and numerical simulations of geological carbon sequestration. Other multiphase flow problems in which subsurface heterogeneities are the main controlling factor (e.g., hydrogen storage) may benefit from this work.
The relationship between the scale-dependent dispersivity and heterogeneous sedimentary structures is investigated through conducting non-reactive tracer experiments in a three-dimensional ...heterogeneous sand tank. The heterogeneous porous media consists of three sedimentary facies of silty, fine, and medium sands collected from the west of the Songnen Plain, China. Moreover, several corresponding individual facies soil columns were constructed for comparison. A conservative tracer was continuously injected from an upstream source. The effective parameters were estimated by inverse modeling of a one-dimensional transport model. The results show that the scale dependence of the estimated dispersivities was discovered in the individual facies column (with relatively weaker effect) and the heterogeneous porous media (with more significant effect). With increasing transport distances, the dispersivities of the individual facies tend to reach an asymptotic value, while those of the heterogeneous media increase continuously. Furthermore, the results show that a power function can describe the relationship between effective dispersivities and transport distances. The exponent of the function is greater than one for the heterogeneous media, but less than one for the individual facies. The results also indicate that the dispersion plume is macroscopically dominated by the distribution of facies. The heterogeneity of hydraulic conductivity causes the variations of flow velocity, which further enhances the scale dependence of dispersivities. The tracer experiment in heterogeneous media provides the fundamental insight into the understanding of contaminant transport processes.
The subsurface region where river water and groundwater actively mix (the hyporheic zone) plays an important role in conservative and reactive solute transport along rivers. Deposits of ...high-conductivity (K) sediments along rivers can strongly control hyporheic processes by channeling flow along preferential flow paths wherever they intersect the channel boundary. Our goal is to understand how sediment heterogeneity influences conservative and sorptive solute transport within hyporheic zones containing high- and low-K sediment facies types. The sedimentary architecture of high-K facies is modeled using commonly observed characteristics (e.g., volume proportion and mean length), and their spatial connectivity is quantified to evaluate its effect on hyporheic mixing dynamics. Numerical simulations incorporate physical and chemical heterogeneity by representing spatial variability in both K and in the sediment sorption distribution coefficient ( K d ). Sediment heterogeneity significantly enhances hyporheic exchange and skews solute breakthrough behavior, while in homogeneous sediments, interfacial flux and solute transport are instead controlled by geomorphology and local-scale riverbed topographies. The hyporheic zone is compressed in sediments with high sorptive capacity, which limits solute interactions to only a small portion of the sedimentary architecture and thus increases retention. Our results have practical implications for groundwater quality, including remediation strategies for contaminants of emerging concern.
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