Invasion Percolation Research Articles

Pore-scale binary diffusion behavior of Hydrogen-Cushion gas in saline aquifers for underground hydrogen Storage: Optimization of cushion gas type

Cushion gas is required to prevent hydrogen (H2) trapping and interactions between H2 and brine for underground hydrogen storage (UHS) in saline aquifers. However, selecting an appropriate type of cushion gas is not a straightforward task, as it affects the H2 diffusion characteristic in subsurface porous media, thereby impacting purity, recoverability, etc. In this paper, we developed a modified pore network model (PNM) for binary diffusion that incorporates multi-scale diffusion mechanisms to forecast the H2 effective diffusion coefficient (DH2e) and evaluate the impacts of the cushion gas on DH2e. Additionally, the model accounts for the water-lock effects of residual brine, focusing exclusively on the connected pore-throats occupied by the gas phase, which are identified using the invasion percolation algorithm with trapping. Our key findings are as follows: 1) CO2 and N2 demonstrate superior containment effects on H2 compared to CH4 under the specific conditions of the target aquifer, reducing the H2 contamination caused by binary diffusion; 2) The size and topology of porous media exert minimal impacts on the selection of cushion gas, yet they markedly affect the DH2e; 3) The pressure and temperature conditions of the saline aquifer are critical factors in cushion gas selection, with temperature being the more influential parameter. This study provides valuable insights for the implementation of industry-scale UHS in saline aquifers.

Machine Learning-Driven Quantification of CO2 Plume Dynamics at Illinois Basin Decatur Project Sites Using Microseismic Data

This study utilizes machine learning to quantify CO2 plume extents by analyzing microseismic data from the Illinois Basin Decatur Project (IBDP). Leveraging a unique dataset of well logs, microseismic records, and CO2 injection metrics, this work aims to predict the temporal evolution of subsurface CO2 saturation plumes. The findings illustrate that machine learning can predict plume dynamics, revealing vertical clustering of microseismic events over distinct time periods within certain proximities to the injection well, consistent with an invasion percolation model. The buoyant CO2 plume partially trapped within sandstone intervals periodically breaches localized barriers or baffles, which act as leaky seals and impede vertical migration until buoyancy overcomes gravity and capillary forces, leading to breakthroughs along vertical zones of weakness. Between different unsupervised clustering techniques, K-Means and DBSCAN were applied and analyzed in detail, where K-means outperformed DBSCAN in this specific study by indicating the combination of the highest Silhouette Score and the lowest Davies–Bouldin Index. The predictive capability of machine learning models in quantifying CO2 saturation plume extension is significant for real-time monitoring and management of CO2 sequestration sites. The models exhibit high accuracy, validated against physical models and injection data from the IBDP, reinforcing the viability of CO2 geological sequestration as a climate change mitigation strategy and enhancing advanced tools for safe management of these operations.

Non‐Linearity in Mean Annual Peak Flow Scaling With Upstream Basin Area: Insights From Percolation Theory

ABSTRACTUnderstanding how annual peak flow, , relates to upstream basin area, , and their scaling have been one of the challenges in surface hydrology. Although a power‐law scaling relationship (i.e., ) has been widely applied in the literature, it is purely empirical, and due to its empiricism, the interpretation of its exponent, , and its variations from one basin to another is not clear. In the literature, different values of have been reported for various datasets and drainage basins of different areas. Invoking concepts of percolation theory as well as self‐affinity, we derived universal and non‐universal scaling laws to theoretically link to . In the universal scaling, we related the exponent to the fractal dimensionality of percolation, (i.e., ). In the non‐universal scaling, in addition to , the exponent was related to the Hurst exponent, , characterizing the boundaries of the drainage basin (i.e., ). The depends on the dimensionality of the drainage system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation). We demonstrated that the theoretical universal and non‐universal bounds were in well agreement with experimental ranges of reported in the literature. More importantly, our theoretical framework revealed that greater values are theoretically expected when basins are more quasi two‐dimensional, while smaller values when basins are mainly quasi three‐dimensional. This is well consistent with the experimental data. We attributed it to the fact that small basins most probably display quasi‐two‐dimensional topography, while large basins quasi‐three‐dimensional topography.

A computationally efficient queue-based algorithm for simulating volume-controlled drainage under the influence of gravity on volumetric images of porous materials

Simulating non-wetting fluid invasion in volumetric images of porous materials is of broad interest in applications as diverse as electrochemical devices and CO2 sequestration. Among available methods, image-based algorithms offer much lower computational cost compared to direct numerical simulations. Recent work has extended image-based methods to incorporate more physics such as gravity and volume-controlled invasion. The present work combines these two developments to develop an image-based invasion percolation algorithm that incorporates the effect of gravity. Additionally, the presented algorithm was developed using a priority queue algorithm to drastically reduce the computational cost of the simulation. The priority queue-based method was validated against previous image-based methods both with and without the effect of gravity, showing identical results. It was also shown that the new method provides a speedup of 20X over the previous image-based methods. Finally, comparison with experimental results at three Bond numbers showed that the model can predict the real invasion process with a high accuracy with and without gravitational effects.

Petroleum system analysis of the komombo basin, southern Egypt: Insights from basin modeling and hydrocarbon geochemistry

Komombo Basin is the only hydrocarbon-producing basin in southern Egypt. However, its petroleum system is still poorly understood, leaving numerous geological questions unanswered. This study integrates seismic, borehole, and geochemical data, coupled with 1D and 2D basin models, to evaluate the hydrocarbon potential and analyze the petroleum system within the Komombo Basin. Geochemical data reveal four main source rocks: the B member of Six Hills, upper Maghrabi, Quseir, and Dakhla. The B member is interpreted as a very good source rock, characterized by Kerogen type II to II/III. The upper Maghrabi and Quseir are considered good to very good source rocks with organic matter type III and II/III, respectively. Conversely, the Dakhla Formation is recognized as a source rock of good to excellent quality with a mixed kerogen type of II/III. Temperature models highlight two heat anomalies during the Early and Late Cretaceous, aligning with the identified rift phases in the basin. The present-day thermal maturity model indicates that the B member is the only mature source rock that has entered the main oil window. However, in the deepest part of the basin, it reaches the gas window. Although the hydrocarbon generation from the B member began in the Early Turonian, most of the kerogen transformed into hydrocarbons during the middle Santonian-early Maastrichtian. Three migration scenarios were tested, however, the first scenario with the invasion percolation migration method aligns more with known hydrocarbon accumulations in the basin. The predicted accumulation zones are found within several sand units, including the A member, C member, sandy intervals within D-G members of Six Hills, and Sabaya-Maghrabi reservoirs. These zones are predominantly situated within structural traps. Comparative analysis using gas chromatograms between recovered oils from the reservoirs and an extracted bitumen sample from the B member source rock reveals a strong correlation among them.

MRI and PFG NMR studies of percolation effects in advanced melting during a cryoporometry characterisation of disordered mesoporous alumina

Cryoporometry (or thermoporometry) offers a way of pore structural characterisation for mesoporous materials that often needs little sample preparation, is relatively quick, and is statistically-representative for macroscopic samples. While it is well-known that freezing is controlled by pore-blocking, and is thus an invasion percolation process, the percolative nature of pore-to-pore co-operative advanced melting effects has been much less studied. In this work, PFG NMR studies, of diffusivity within the molten phase, have shown that the early melting process follows the scaling law, expected from percolation theory, below the percolation threshold. The percolation threshold thereby obtained was that for a 3D isotropic Poisson polyhedral lattice, consistent with the observation of patchwise macroscopic heterogeneities in the spatial distribution of local average pore size seen in MR relaxation time-weighted images. MRI has shown that once advanced melting effects kicked-in, around the percolation threshold, they occurred to different degrees in different slices along the length of the extrudate pellet. The macroscopic banding in pore-blocking, during freezing, and advanced melting effects, along the axis of the extrudate was consistent with anisotropic diffusional properties observed with MRI. Hence, it has been shown how the pore-pore co-operative effects can be utilised to improve structural characterisation of mesoporous solids.

Invasion percolation on power-law branching processes

Invasion percolation on power-law branching processes

Graph theory based estimation of probable CO2 plume spreading in siliciclastic reservoirs with lithological heterogeneity

Estimating plume spreading in geological CO2 storage reservoirs is critical for several reasons including the assessment of pore space utilization efficiency, preferential CO2 migration pathways and trapping. However, plume spreading critically depends on lithological heterogeneity of the reservoir and CO2 injection rate. It might require numerous high fidelity full physics numerical simulations to constrain the uncertainty in plume spreading for a given reservoir. This might not always be practical due to computational limitations. Hence, reduced physics approaches, such as invasion-percolation method and machine learning, could be useful to answer certain questions on plume spreading in the subsurface. This study presents a new reduced physics approach based on graph theory for estimating probable CO2 plume migration under very low and very high injection rates. The two end-member scenarios are assessed by performing random walk in the 3D reservoir space to constrain 20,000 possible paths of CO2 flow away from the injection well. The resistance to CO2 flow associated with each path is computed for viscous, capillary and gravity forces. The resistances are then transformed into the likelihood of CO2 migration along the path. The algorithm was applied to 45 reservoir models with varying degrees of lithological heterogeneity and the results were compared to those from full physics and invasion percolation simulations. The graph theory results showed a close match with the results from full physics approach for both flow regimes and with results from invasion-percolation approach for capillary-gravity dominated flow regime. The algorithm was further applied to answer key questions on reservoir screening such as pore space utilization potential. The graph theory approach was also integrated with machine learning to predict CO2 saturation. Testing suggested that the graph theory approach can be as much as 50 and 20 times faster than the full physics numerical simulations and invasion-percolation simulations, respectively.

An experimental investigation on the CO2 storage capacity of the composite confining system

Assuring secure containment of stored CO2 is of paramount importance—for climate change mitigation, for permitting, and for reassuring the public. Regional seals, such as those sealing petroleum accumulations, have proven to be effective for securing CO2. However, the goal of permanent sequestration can also be satisfied with “composite confining systems” consisting of multiple, possibly discontinuous flow barriers that, in aggregate, create a system with very high permeability anisotropy and effectively retard the vertical migration of CO2. This study focuses on investigating the barrier characteristics necessary for effective containment of CO2, using both physical flow experiments and modified invasion percolation simulations. The simulations are calibrated to the physical experiments and are used to further extend the analysis. Results show that for a composite confining system, a) even barriers with low capillary entry pressure contrast to the underlying flow unit can divert rising CO2; b) curved or anticlinal barrier topography can enhance CO2 trapping; c) fining-upward gradations make little difference to barrier effectiveness or CO2 retention; d) longer barriers retain more CO2 regardless of barrier topography. Finally, field-scale simulations have demonstrated the importance of barrier length for increasing CO2 storage capacity. The results presented can be used to inform the development of new screening criteria for characterization and effectiveness of composite confining systems.

The Interplay Between Pore‐Scale Heterogeneity, Surface Roughness, and Wettability Controls Trapping in Two‐Phase Fluid Displacement in Porous Media

AbstractPredicting the compactness of the invasion front and the amount of trapped fluid left behind is of crucial importance to applications ranging from microfluidics and fuel cells to subsurface storage of carbon and hydrogen. We examine the interplay of wettability, macro‐ and pore scale heterogeneity (pore angularity and pore wall roughness), and its influence on flow patterns formation and trapping efficiency in porous media by a combination of 3D micro‐CT imaging with 2D direct visualization of micromodels. We observe various phase transitions between the following capillary flow regimes (phases): (a) compact advance, (b) wetting and drainage Invasion percolation, (c) Ordinary percolation.

Scaling of the cumulative weights of the invasion percolation cluster on a branching process tree

Scaling of the cumulative weights of the invasion percolation cluster on a branching process tree

A new method of the hydrocarbon secondary migration research: Numerical simulation

A three-dimensional invasion percolation simulation model is introduced and integrated into a novel three-dimensional geological modeling framework based on the “unit element” theory to study secondary hydrocarbon migration. Leveraging the computational efficiency inherent in the invasion percolation theory, the simulation method is effectively applied to basin-scale hydrocarbon migration using finely discretized grids. Sensitivity analysis demonstrates the substantial influence of geological parameters including structural configuration, sedimentary facies, and pressure, on simulation results. Noteworthy observations from this study encompass: (1) The intricate influence of sedimentary facies and petrophysical properties characteristics on hydrocarbon migration and accumulation patterns within structural and lithological traps. Favorable petrophysical attributes in the carrier beds enhance the likelihood of accumulation in the structural traps, while lithological traps are prevalent in less conducive carrier beds. (2) The significant impact of sand bodies exhibiting favorable petrophysical attributes, such as channels, on migration and accumulation profiles. This underscores the necessity of incorporating sedimentary facies and rock attributes into oil and gas resource exploration. (3) The pronounced effects of overpressure magnitude and direction on hydrocarbon migration and accumulation dynamics. (4) Optimal strategies for oil and gas resource exploration necessitate a comprehensive assessment of rock attributes, overpressure considerations, and sedimentary facies. The practical implementation of this methodology is demonstrated in an actual exploration project within China's Junggar Basin. The simulation results closely align with established oil recovery data and facilitate predictive identification of promising exploration areas. This indicates the methodology is applicable to all petroleum systems similar to Junggar Basin. Through practical applications, the development of a scientifically rigorous three-dimensional geological model for the study area, coupled with numerical simulations of oil and gas migration, facilitates the elucidation of accumulation patterns. This approach aids in identifying pivotal factors such as sand body distribution, internal structural composition, permeability attributes, and fracture behavior, which collectively influence oil and gas migration. Furthermore, by correlating insights obtained from oil and gas discoveries in wells, a deeper understanding of carrier bed properties and their geological evolution is attained.

On the Potential Role of Viscoelasticity in Fluid‐Induced Seismicity

AbstractFluid‐induced earthquakes adversely affect industrial operations like hydraulic fracturing (e.g., 4.6 Mw in Alberta, Canada) and enhanced geothermal systems (e.g., 5.5 Mw in Pohang, South Korea). Identifying all underlying physical processes contributing to fluid‐induced seismicity presents an open challenge. Recent work reports signatures of event‐event triggering or aftershocks—common for tectonic settings—within the context of fluid‐induced seismicity. Here, we investigate the underlying potential cause of these field observations from a modeling perspective. We extend a novel conceptual model to simulate the characteristics of crustal rheology and stress interactions in a porous medium by combining viscoelastic effects with fluid diffusion and invasion percolation associated with a point source. Our model successfully reproduces realistic aftershock behavior and statistical properties similar to those resulting from tectonic loading indicating that the statistical properties of aftershocks are unaffected by the fluid injection rate. At the same time, the Gutenberg‐Richter relation, the spatial footprint of fluid‐induced events and their dependence on the permeability field are largely unaltered by the viscoelasticity of the medium and the aftershocks it causes. Furthermore, we investigate the impact of varying fluid injection rates on detecting aftershocks and event‐event triggering sequences during viscoelastic stress redistribution. We find that when the injection rate is sufficiently high, aftershock detection and recovery of their statistical properties are only feasible when the underlying internal stress redistribution is directly accessible. This could explain why aftershocks have not been reported in some field studies of fluid‐induced seismicity.

New insights into reservoir on chip: Numerical investigation and experimental validation

The present study reports a numerical investigation of oil extraction from a pore-scale perspective using water as the injection fluid. The pore network is constructed from the statistical realization of the pore space of the reservoir rock. Conceptually, the pore network model used in the study miniaturizes the porous reservoir containing oil/gas onto a microfluidic platform, capturing the actual pore-level length scale and it complex features. The validity of the numerical model is established through an experimental investigation of single-phase flow. The experimentally calculated absolute permeability based on the Darcy law shows an excellent agreement with the numerically attained value. The two-phase numerical model uses the phase field technique to track the development of the interface between the two immiscible phases, i.e., oil and water. The numerical model shows a piston-like displacement and captures interesting pore-level phenomena like snap-off and trapping. Implementing the complete network for simulation reveals the unstable nature of the flooding, which is persistent with invasion percolation. The complete network simulation reveals the discontinuous flood front with a segregated flow configuration. Two-phase experiments conducted on a polydimethylsiloxane test chip with an equivalent pore level network also showed similar flow features, thereby establishing the credibility of our two-phase simulations. The recovery factor obtained from the simulation was found to be 0.78, which is in close agreement with experimental data reported in the literature. The modified Darcy law applied to the numerical model generates relative permeability plots similar to the experimental core flooding plots reported in the literature. The numerical model presented here provides valuable insight into the oil recovery process and its implications at field scale. To the best of our knowledge, this is the first instance involving numerical analysis of the full-scale system of Reservoir on a Chip system detailing the pore-level flow dynamics.

Multisource invasion percolation on the complete graph

Multisource invasion percolation on the complete graph

Dynamic In Vivo Computation for Learning-Based Nanobiosensing in Time-Varying Biological Landscapes

We have recently proposed a framework of in vivo computation which transforms the early tumor sensing problem into a computational problem. In the framework, a tumor-triggered biological gradient field (BGF) guides swarm-intelligence-assisted targeting process, where externally manipulable and trackable magnetic nanorobots act as computational agents for the optimization procedure. As BGF can be viewed as an objective function which is utilized to define the fitness landscape for the agents, the inherent attributes of BGF are critical to the in vivo computational process. All our previous investigations are based on the hypothesis that the BGF landscape remains time-invariant during the tumor targeting process, which results in a static function optimization problem. However, the properties of internal environment, such as the flow state of body fluid, will naturally lead to time-dependent variation of BGF, which means that the targeting process should be modeled as a dynamic function optimization problem. Based on this consideration, we focus on dynamic in vivo computation by considering different variation patterns of BGF in this paper. Two computational intelligence strategies named “swarm-based learning” and “individual-based learning” are proposed for dealing with the turbulence of the fitness estimation caused by the BGF variation. The in silico experiments and statistical results demonstrate the effectiveness of the proposed strategies. In addition, the above process is conducted in a three-dimensional search space, where the tumor vascular network is generated by an invasion percolation algorithm, which is more realistic compared to the two-dimensional search space in our previous works.

The capillary pressure vs. saturation curve for a fractured rock mass: fracture and matrix contributions

The fractal topography of fracture surfaces challenges the upscaling of laboratory test results to the field scale, therefore the study of rock masses often requires numerical experimentation. We generate digital fracture analogues and model invasion percolation to investigate the capillarity-saturation Pc-Sw fracture response to changes in boundary conditions. Results show that aperture is Gaussian-distributed and the coefficient of variation is scale-independent. The aperture contraction during normal stress increments causes higher capillary pressures and steeper Pc-Sw curves, while shear displacement results in invasion anisotropy. The three-parameter van Genutchen model adequately fits the fracture capillary response in all cases; the capillary entry value decreases with fracture size, yet the fracture Pc-Sw curve normalized by the entry value is size-independent. Finally, we combine the fracture and matrix response to infer the rock mass response. Fracture spacing, aperture statistics and matrix porosity determine the rock mass capillarity-saturation Pc-Sw curve. Fractures without gouge control the entry pressure whereas the matrix regulates the residual saturation at high capillary pressure Pc.

Simulating field-scale thermal conductive heating with the potential for the migration and condensation of vapors

Thermal conductive heating (TCH) is an in-situ thermal treatment (ISTT) technology for treating non-aqueous phase liquid (NAPL) source zones. Numerical models can be useful tools for improving remedial performance, but traditional multiphase flow models are rarely used to simulate mass recovery during ISTT applications at the field scale due to their computational expense. This study developed a 3D model based on macroscopic invasion percolation to simulate the vaporization of NAPL, and the subsequent vapor migration and potential condensation at the field scale. The model was used to simulate the mass recovery of trichloroethene (TCE) from a NAPL source zone under seven scenarios of different heater placements, including three scenarios with an undersized target treatment zone (TTZ). Simulation results showed that TCH was effective in removing NAPL within the TTZ, but the treatment zone did not extend far from the perimeter heaters. In addition, during heating, NAPL condensation outside the TTZ due to the escaping vapor was observed in all scenarios. Overall, the resulting mass recovery was lower in the three scenarios with an undersized TTZ (91–95%) than in the other four scenarios (≈ 99%). Moreover, the locations of unrecovered/condensed NAPL could be inferred by monitoring mass recovery tailing at individual extraction wells.

Modeling evaluation of physiochemical processes controlling gas migration in shallow groundwater systems

Gases may be released into shallow groundwater systems during energy development and geological carbon storage (commonly referred to as gas migration, GM) and can result in greenhouse gas emissions, safety concerns, and the reduction of groundwater quality. The physiochemical processes occurring during GM, including gas release, movement, partitioning, and dissolved-phase transport in the saturated groundwater zone, are difficult to characterize and model; however, modeling is important to develop strategies for detecting and monitoring GM and formulate conceptual models to describe GM at impacted sites. In this study, a previously developed numerical model, which coupled macroscopic invasion percolation (macro-IP) and multicomponent mass transfer, was enhanced to simulate gas releases in the shallow subsurface. Evaluation of the effects of the coupled physiochemical processes was performed by comparing model simulations to previously conducted bench-scale gas injection experiments. Results show that gas flow is highly sensitive to the entry pressures assigned within the model domain and the critical gas saturation (Sg,crit) used to model gas-water flow based on macro-IP; however, mass transfer and the resulting domain-scale dissolved-gas transport were relatively insensitive to these parameters. Multicomponent mass transfer, considering not only the partitioning of the released gas, but also the dissolved background gases ubiquitous in shallow groundwater, was vitally important to simulate dissolution and the resulting free-phase gas distribution within the experimental systems. The use of the local equilibrium assumption for gas-water mass transfer could not consistently describe the experimental observations. Overall, the modeling evaluation performed in this study provides improved understanding of the key processes controlling GM in the shallow subsurface and will advance efforts including up-scaling and scenario testing to accurately quantify the environmental impacts of GM.

Constraining hydrocarbon migration and accumulation by two-dimensional numerical simulation: Ordovician carbonate reservoirs of the Daniudi Area, Ordos Basin

The various types of reservoir space in carbonate reservoirs make the process of hydrocarbon migration and accumulation very complex. How to quantitatively characterize the characteristics of hydrocarbon migration and accumulation in carbonate reservoirs is one of the key problems for carbonate hydrocarbons exploration and exploitation. Taking the Ordovician in the Daniudi area of Ordos Basin as an example, three types of source rock-reservoir-cap assemblages, namely upper-generation assemblage, lateral variable assemblage, and self-generation-reservoir-cap assemblage, were determined by characterizing the forming elements of carbonate reservoirs. Petromod software is used to build a two-dimensional profile model, and vitrinite reflectance of source rock and porosity of the reservoir were used as correction parameters, and the hydrocarbon migration and accumulation process was simulated by the invasion percolation algorithm. It is confirmed that the Ordovician Majiagou formation in the study area has three periods of hydrocarbon charging and three periods of hydrocarbon adjustment. The hydrocarbon migration pathways in carbonate rocks include lateral contact in the pinch-out area, source rock-reservoir contact in the trough area, fault-connected, and source rock-reservoir superposition. The source rock-reservoir-cap assemblages of upper-generation assemblage and lateral variable assemblage correspond to the lateral contact in the pinch-out area, source rock-reservoir contact in the trough area, fault-connected, while self-generation-reservoir-cap assemblage corresponds to the fault-connected, and source rock-reservoir superposition. The high part of the structure and fault zone are the strongest structural deformation parts, whose fractures are relatively developed, controlling the location of hydrocarbon accumulation, meanwhile, the reservoir quality directly controls the degree of hydrocarbons saturation. The research results are beneficial to establish a more accurate quantitative evaluation method of hydrocarbon migration and accumulation in carbonate rocks and to understanding the controlling factors of hydrocarbon migration and accumulation in carbonate rocks.