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- A DEIM driven reduced basis method for the diffuse Stokes/Darcy model
coupled at parametric phase-field interfaces-
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Abstract: Abstract In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal geometry. To accommodate possible changes in topology, we define the Stokes and Darcy domains implicitly via a phase-field indicator function. In our reduced order model, we approximate the parameter-dependent phase-field function with a discrete empirical interpolation method (DEIM) that enables affine decomposition of the associated linear and bilinear forms. In addition, we introduce a modification of DEIM that leads to non-negativity preserving approximations, thus guaranteeing positive-semidefiniteness of the system matrix. We also present a strategy for determining the required number of DEIM modes for a given number of reduced basis functions. We couple reduced basis functions on neighboring patches to enable the efficient simulation of large-scale problems that consist of repetitive subdomains. We apply our reduced basis framework to efficiently solve the inverse problem of characterizing the subsurface damage state of a complete in-situ leach mining site.
PubDate: 2022-12-01
- An adaptive discontinuous Galerkin method for the Darcy system in
fractured porous media-
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Abstract: Abstract Modeling flows in fractured porous media is important in applications. One main challenge in numerical simulation is that the flow is strongly influenced by the fractures, so that the solutions typically contain complex features, which require high computational grid resolutions. Instead of using uniformly fine mesh, a more computationally efficient adaptively refined mesh is desirable. In this paper we design and analyze a novel residual-type a posteriori error estimator for staggered DG methods on general polygonal meshes for Darcy flows in fractured porous media. The method can handle fairly general meshes and hanging nodes can be simply incorporated into the construction of the method, which is highly appreciated for adaptive mesh refinement. The reliability and efficiency of the error estmator are proved. The derivation of the reliability hinges on the stability of the continuous setting in the primal formulation. A conforming counterpart that is continuous within each bulk domain for the discrete bulk pressure is defined to facilitate the derivation of the reliability. Finally, several numerical experiments including multiple non-intersecting fractures are carried out to confirm the proposed theories.
PubDate: 2022-12-01
- Covariogram ranges for approximate global sensitivity analysis
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Abstract: Abstract Sensitivity analysis provides information to understand response models and helps make better decisions in many fields, including the petroleum and mining industries. A new approximate method for sensitivity analysis through extracting covariogram ranges is proposed in this paper. In this method, the covariogram range will be treated the same as the variogram range, and each factor in the response model will be looked as a separate coordinate in a pseudo-spatial space. The result indicates that the covariogram ranges calculated in this space for each variable have a strong relationship with the main effect sensitivity index in variance-based method, that is, a longer range has less sensitivity. Thus, the sensitivity of each factor is accessible through covariogram range calculation, which is a unique approach to sensitivity analysis compared to existing approaches. This approach provides a new perspective of understanding global sensitivity. Furthermore, a modified covariogram fitting algorithm is put forward to calculate the ranges through optimization. This iterative algorithm minimizes the squared error between the modified experimental covariogram and Gaussian covariogram model, which is useful in a high dimension with sparse sampling. The simulated data are also used to validate the automatic covariogram fitting, and the optimized ranges are very close to the true ranges even with a small sample size. Finally, this method is successfully applied in the parameter sensitivity analysis of reservoir simulation, and limitations or considerations for the practical application have been discussed.
PubDate: 2022-12-01
- Rock thin sections identification under harsh conditions across regions
based on online transfer method-
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Abstract: Abstract Automatic identification of rock thin sections provides valuable geological information for oil and gas exploration. However, the application of rock thin sections identification in new blocks works poorly. The reason is that the geological data of target blocks are extremely scarce in the early stage of exploration and development. Therefore, using an improved MaSE-ResNetXt network, data enhancement, feature extractors, online transfer learning and other strategies, a stable, efficient and continuously growing end-to-end identification system based on online transfer learning was built. In case one, the use of the basic MaSE-ResNetXt network on regional rock properties and model categories was compared with previous studies and experiments, and performance improvements of 5% and 14.3% were achieved respectively, which verified the high efficiency of the basic MaSE-ResNetXt network for feature extraction in a large-scale dataset. In case two, sensitivity analysis was conducted for similar categories that are easily confused, during which parameters of the network and optimizer were compared. The sensitivity problems of oolitic structure feature maps were discussed and optimized. After that, a weighted F1-score of 0.95 was reached, proving the prediction stability of cross-regional transfer. In case three, real-time online transfer learning for the cold boot was conducted with scarce geological data. Compared with the previous studies, the training speed was improved by 15 times, and the accuracy was improved by 20%. An improved method based on MaSE-ResNeXt with transfer learning using a neural network feature map for rock characteristics analysis was proposed. By proposing inheritance and real-time online transfer learning solutions, the problems of automatic rock thin sections identification in a new area were solved, and the geological data of multiple blocks were fully used. By doing so, this study bridged the gap that experiences from the former regions could not be inherited effectively for cross-regional rock thin sections identification, so that empowered the development of new blocks.
PubDate: 2022-12-01
- Well testing of radial jet drilling wells in geothermal reservoirs
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Abstract: Abstract Radial Jet Drilling (RJD) is a stimulation technique to increase a well’s performance through creation of multiple laterals of up to 100 m long. The technique has been used in the petroleum industry for several years and recently also for geothermal reservoirs. Interpretation of well tests of a well with multiple laterals may become problematic if the effect of the laterals is not correctly modelled. In this work it is investigated what the impact of RJD laterals is on the pressure transients for both single and dual porosity reservoirs. A semi-analytic model for the calculation of the transient well pressure that accounts explicitly for the RJD well geometry is developed and validated with a detailed numerical simulation. The results show that changes in the lateral configuration affect the pressure transients significantly. In particular for single porosity media, the laterals affect the pressure transients in ways that cannot be captured by representing the stimulation by a skin factor. Since the RJD process is unsteered and the exact configuration of the laterals uncertain, the model may potentially assist in estimating the effectiveness of the stimulation such as the achieved reach of the laterals. Although the work was carried out in the context of RJD application in geothermal reservoirs, the presented model approach can be extended to multi-lateral wells in oil or gas reservoirs.
PubDate: 2022-12-01
- Benchmark study for the simulation of Underground Hydrogen Storage
operations-
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Abstract: Abstract While the share of renewable energy sources increased within the last years with an ongoing upward trend, the energy sector is facing the problem of storing large amounts of electrical energy properly. To compensate daily and seasonal fluctuations, a sufficient storage system has to be developed. The storage of hydrogen in the subsurface, referred to as Underground Hydrogen Storage (UHS), shows potential to be a solution for this problem. Hydrogen, produced from excess energy via electrolysis, is injected into a subsurface reservoir and withdrawn when required. As hydrogen possesses unique thermodynamic properties, many commonly used correlations can not be simply transferred to a system with a high hydrogen content. Mixing processes with the present fluids are essential to be understood to achieve high storage efficiencies. Additionally, in the past, microbial activity, e.g. by methanogenic archaea, was observed, leading to a changing fluid composition over time. To evaluate the capability of reservoir simulators to cover these processes, the present study establishes a benchmark scenario of an exemplary underground hydrogen storage scenario. The benchmark comprises of a generic sandstone gas reservoir and a typical gas storage schedule is defined. Based on this benchmark, the present study assesses the capabilities of the commercial simulator Schlumberger ECLIPSE and the open-source simulator DuMux to mimic UHS related processes such as hydrodynamics but also microbial activity. While ECLIPSE offers a reasonable mix of user-friendliness and computation time, DuMux allows for a better adjustment of correlations and the implementation of biochemical reactions. The corresponding input data (ECLIPSE format) and relevant results are provided in a repository to allow this simulation study’s reproduction and extension.
PubDate: 2022-12-01
- An approximate cut-cell discretization technique for flow in fractured
porous media-
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Abstract: Abstract A new discretization technique for fractured porous media is presented. The most accurate representation for such system is the discrete fracture and matrix (DFM) model where the fractures, their intersections, and the surrounding rock are explicitly represented using a conforming mesh. However, the construction of such meshes becomes challenging for complex systems. The objective of the proposed method is to construct an equivalent DFM model without explicitly constructing a conforming mesh. The method is based on an approximate cut-cell framework where all geometrical quantities needed for discretization are estimated numerically using a local subgrid. The method has built in simplification capabilities and is not very sensitive to the complexity of the model. It is able to generate an equivalent DFM model as well as an embedded discrete fracture model (EDFM). The methodology will be described in detail and illustrated with examples of varying degrees of complexity.
PubDate: 2022-12-01
- TOUGH3-FLAC3D: a modeling approach for parallel computing of fluid flow
and geomechanics-
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Abstract: Abstract The recent development of the TOUGH3 code allows for a faster and more reliable fluid flow simulator. At the same time, new versions of FLAC3D are released periodically, allowing for new features and faster execution. In this paper, we present the first implementation of the coupling between TOUGH3 and FLAC3Dv6/7, maintaining parallel computing capabilities for the coupled fluid flow and geomechanical codes. We compare the newly developed version with analytical solutions and with the previous approach, and provide some performance analysis on different meshes and varying the number of running processors. Finally, we present two case studies related to fault reactivation during CO2 sequestration and nuclear waste disposal. The use of parallel computing allows for meshes with a larger number of elements, and hence more detailed understanding of thermo-hydro-mechanical processes occurring at depth.
PubDate: 2022-12-01
- The method of forced probabilities: a computation trick for Bayesian model
evidence-
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Abstract: Abstract Bayesian model selection objectively ranks competing models by computing Bayesian Model Evidence (BME) against test data. BME is the likelihood of data to occur under each model, averaged over uncertain parameters. Computing BME can be problematic: exact analytical solutions require strong assumptions; mathematical approximations (information criteria) are often strongly biased; assumption-free numerical methods (like Monte Carlo) are computationally impossible if the data set is large, for example like high-resolution snapshots from experimental movies. To use BME as ranking criterion in such cases, we develop the “Method of Forced Probabilities (MFP)”. MFP swaps the direction of evaluation: instead of comparing thousands of model runs on random model realizations with the observed movie snapshots, we force models to reproduce the data in each time step and record the individual probabilities of the model following these exact transitions. MFP is fast and accurate for models that fulfil the Markov property in time, paired with high-quality data sets that resolve all individual events. We demonstrate our approach on stochastic macro-invasion percolation models that simulate gas migration in porous media, and list additional examples of probable applications. The corresponding experimental movie was obtained from slow gas injection into water-saturated, homogeneous sand in a 25 x 25 x 1 cm acrylic glass tank. Despite the movie not always satisfying the high demands (resolving all individual events), we can apply MFP by suggesting a few workarounds. Results confirm that the proposed method can compute BME in previously unfeasible scenarios, facilitating a ranking among competing model versions for future model improvement.
PubDate: 2022-11-23
- Impact of geostatistical nonstationarity on convolutional neural network
predictions-
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Abstract: Abstract Convolutional neural networks (CNNs) are gaining tremendous attention in subsurface studies due to their ability to learn from spatial image data. However, most deep learning studies in spatial context do not consider the impact of geostatistical nonstationarity, which is commonly encountered within the subsurface phenomenon. We demonstrate the impact of geostatistical nonstationarity on CNN prediction performance. We propose a CNN model to predict the variogram range of sequential Gaussian simulation (SGS) realizations. Model performance is evaluated for stationarity and three common forms of geostatistical nonstationarity: (1) large relative variogram range-related nonstationarity, (2) additive trend and residual model-related nonstationarity, and (3) mixture population model-related nonstationarity. Our CNN model prediction accuracy decreases in the presence of large relative variogram range-related nonstationarity, for the additive trend and residual model-related nonstationarity, the relative prediction errors increase for high trend variance proportions with a decrease in variogram range; regarding the mixture population model-related nonstationarity, the predictions are closer to the smaller variogram range. Common forms of geostatistical nonstationarity may impact CNN predictions, as with geostatistical estimation methods, trend removal and workflows with stationary residuals are recommended.
PubDate: 2022-11-17
- Prediction of permeability of porous media using optimized convolutional
neural networks-
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Abstract: Abstract Permeability is an important parameter to describe the behavior of a fluid flow in porous media. To perform realistic flow simulations, it is essential that the fine scale models include permeability variability. However, these models cannot be used directly in simulations because require high computational cost, which motivates the application of upscaling approaches. In this context, machine learning techniques can be used as an alternative to perform the upscaling of porous media properties with lower computational cost than traditional upscaling methods. Hence, in this work, an upscaling methodology is proposed to compute the equivalent permeability on the large grid through convolutional neural networks (CNN). This method achieves suitable precision, with less computational demand, when evaluated on 2D and 3D models, if compared with the local upscaling approach. We also present a genetic algorithm (GA) to automatically determine the optimal configuration of CNNs for the target problems. The GA procedure is applied to yield the optimal CNN architecture for upscaling of the permeability fields with outstanding results when compared with counterpart techniques.
PubDate: 2022-11-05
- Lithology identification in carbonate thin section images of the Brazilian
pre-salt reservoirs by the computational vision and deep learning-
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Abstract: Abstract Currently, the computer vision area, which represents one of the subfields of artificial intelligence and machine learning, has been widely used to process data in the oil and gas industry. In this context, the detection of specific properties inside carbonate rocks in different datasets from petroleum reservoirs represents a considerable challenge, that consumes enormous resources and time. Therefore, the automatic separation of the lithologies within rocks of reservoirs has attracted the increasing attention of many research groups. The consistent classification of these lithologies is the main factor for the construction of reliable depositional, diagenetic, and reservoir models. This work deals with this last issue by presenting the development of a technique for the automatic classification of carbonate thin sections obtained from plane-polarized and cross-polarized microscopy images corresponding to natural rocks belonging to the Brazilian pre-salt reservoir. Our proposed model transforms the analyzed images into structured data by defining texture parameters (Haralick parameters), and Wavelets transforms. Later, a stacked autoencoder neural network is used to eliminate images with anomalies and/or distortions in order to define relevant characteristics of the data. This stage is followed by supervised classifier called multilayer feed-forward neural network. The definition of the model’s hyperparameters is tuned by Bayesian optimization and the Gaussian process. For training and testing of the network, images of 570 thin sections were used (each image obtained with plane-polarized and cross-polarized light) totaling 1140 images. Our model reported an accuracy of 83% for the test samples, confirming the validity of the proposed model in the automatic classification of carbonate rocks.
PubDate: 2022-10-05
- Automatic reconstruction method of 3D geological models based on deep
convolutional generative adversarial networks-
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Abstract: Abstract How to reconstruct a credible three-dimensional (3D) geological model from very limited survey data, e.g. boreholes, outcrop, and two-dimensional (2D) images, is challenging in the field of 3D geological modeling. Against the limitations of the huge computational consumption and complex parameterization of geostatistics-based stochastic simulation methods, we propose an automatic reconstruction method of 3D geological models based on deep convolutional generative adversarial network (DCGAN). In this work, 2D geological sections are used as conditioning data to generate 3D geological models automatically. Various realizations can be reproduced under a same DCGAN model established through deep network training. A U-Net structure is used to enhance the fitting effect of the DCGAN model. In addition, joint loss functions are exploited to increase the similarity between 3D realizations and reference models. Three synthetic datasets were used to verify the capability of the method presented in this paper. Experimental results show that the proposed 3D automatic reconstruction method based on DCGAN can capture the features, trends and spatial patterns of geological structures well. The output models obey the used conditioning data. The complex heterogeneous structures are reconstructed more accurately and quickly by using the proposed method.
PubDate: 2022-10-01
DOI: 10.1007/s10596-022-10152-8
- Model-based characterization of permeability damage control through
inhibitor injection under parametric uncertainty-
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Abstract: Abstract Damage in subsurface formations caused by mineral precipitation decreases the porosity and permeability, eventually reducing the production rate of wells in plants producing oil, gas or geothermal fluids. A possible solution to this problem consists in stopping the production followed by the injection of inhibiting species that slow down the precipitation process. In this work we model inhibitor injection and quantify the impact of a set of model parameters on the outputs of the system. The parameters investigated concern three key factors contributing to the success of the treatment: i) the inhibitor affinity, described by an adsorption Langmuir isotherm, ii) the concentration and time related to the injection and iii) the efficiency of the inhibitor in preventing mineral precipitation. Our simulations are set in a stochastic framework where these inputs are characterized in probabilistic terms. Forward simulations rely on a purpose-built code based on finite differences approximation of the reactive transport setup in radial coordinates. We explore the sensitivity diverse outputs, encompassing the well bottom pressure and space-time scales characterizing the transport of the inhibitor. We find that practically relevant output variables, such as inhibitor lifetime and well bottom pressure, display a diverse response to input uncertainties and display poor mutual dependence. Our results quantify the probability of treatment failure for diverse scenarios of inhibitor-rock affinity. We find that treatment optimization based on single outputs may lead to high failure probability when evaluated in a multi-objective framework. For instance, employing an inhibitor displaying an appropriate lifetime may fail in satisfying criteria set in terms of well-bottom pressure history or injected inhibitor mass.
PubDate: 2022-10-01
DOI: 10.1007/s10596-022-10148-4
- On several numerical strategies to solve Richards’ equation in
heterogeneous media with finite volumes-
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Abstract: Abstract We propose several numerical approaches building on upstream mobility two-point flux approximation finite volumes to solve Richards’ equation in domains made of several rock-types. Our study encompasses four different schemes corresponding to different ways to approximate the nonlinear transmission condition systems arising at the interface between different rocks consisting in the continuity of the pressure and the fluxes, as well as different resolution strategies based on Newton’s method with variable switch. We benchmark the robustness and accuracy of the different methods on filling and drainage test cases with standard nonlinearities of Brooks-Corey and van Genuchten-Mualem type, as well as with challenging steep nonlinearities.
PubDate: 2022-10-01
DOI: 10.1007/s10596-022-10150-w
- Investigation of thermal-hydro-mechanical coupled fracture propagation
considering rock damage-
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Abstract: Abstract Thermal-hydro-mechanical (THM) coupled fracture propagation is common in underground engineering. Rock damage, as an inherent property of rock, significantly affects fracture propagation, but how it influences the THM coupled fracturing remains stubbornly unclear. A pore-scale THM coupling model is developed to study this problem, which combines the lattice Boltzmann method (LBM), the discrete element method (DEM), and rock damage development theory together for the first time. This model can more accurately calculate the exchanged THM information at the fluid-solid boundary and fluid conductivity dependent on fracture and rock damage. Based on the developed model, the synergistic effect of injected temperature difference (fluid temperature below rock temperature) and rock damage (characterized by the parameter “critical fracture energy”, abbreviated as “CFE”) on fracture propagation of shale are investigated particularly. It is found that: (1) the generation of branched cracks is closely related to the temperature response frontier, and the fracture process zone of single bond failure increases in higher CFE. (2) through the analysis of micro failure events, hydraulic fracturing is more pronounced in the low CFE, while thermal fracturing displays the opposite trend. The fluid conductivity of fractured rock increases with a higher injected temperature difference due to the more penetrated cracks and wider fracture aperture. However, this enhancement weakens when rock damage is significant. (3) in the multiple-layered rock with various CFEs, branched cracks propagating to adjacent layers are more difficult to form when the injection hole stays in the layer with significant rock damage than without rock damage.
PubDate: 2022-10-01
DOI: 10.1007/s10596-022-10155-5
- Coastline matching via a graph-based approach
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Abstract: Abstract This paper studies the problem of unsupervised detection of geometrically similar fragments (segments) in curves, in the context of boundary matching. The goal is to determine all pairs of sub-curves that are geometrically similar, under local scale invariance. In particular, we aim to locate the existence of a similar section (independent of length and/or orientation) in the second curve, to a section of the first curve, as indicated by the user. The proposed approach is based on a suitable distance matrix of the two given curves. Additionally, a suitable objective function is proposed to capture the trade-off between the similarity of the common sub-sequences and their lengths. The goal of the algorithm is to minimize this objective function via an efficient graph-based approach that capitalizes on Dynamic Time Warping to compare the two subcurves. We apply the proposed technique in the context of geometric matching of coastline pairs. This application is crucial for investigating the forcing factors related to the coastline evolution. The proposed method was successfully applied to global coastline data, yielding a bipartite graph with analytical point-to-point correspondences.
PubDate: 2022-09-30
- Design of optimal operational parameters for steam-alternating-solvent
processes in heterogeneous reservoirs – A multi-objective optimization
approach-
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Abstract: Abstract Steam injection is a widely-used process for heavy oil and bitumen recovery. However, a significant drawback is the excessive energy requirement, water consumption, and CO2 generation. The Steam Alternating Solvent (SAS) process has been proposed as an eco-friendlier alternative to the existing steam-based methods. It involves injecting steam and solvent (i.e. propane) in separate cycles. The interplay between reservoir heterogeneity and the complex physical mechanisms of heat and mass transfer has made optimizing its design parameters quite challenging. This work aims to develop a hybrid Multi-Objective Optimization (MOO) scheme for determining the optimal operational parameters using the Pareto dominance concept while considering several conflicting objectives (i.e. RF, steam, and solvent injection) under several heterogeneous scenarios. A 2-D base homogenous reservoir model is built according to the Fort McMurray formation in the Athabasca region in Alberta, Canada. Next, shale barriers with varying proportions, lengths, and locations are superimposed onto the base model. Then, a sensitivity analysis is performed to assess the controllable operational parameters’ impact and formulate several objective functions; proxy models are introduced to speed up the objective function evaluations. Finally, different Multi-Objective Evolutionary Algorithms (MOEAs) are applied to establish the optimal ranges to operate the selected decision variables. Different optimal operating strategies are needed depending on the shale barrier distribution. Injector bottom-hole pressure, steam trap, and producer gas rate significantly impact the model response. Injecting high propane concentration over short durations is recommended. The length of the steam injection phase seems to be more sensitive to the reservoir heterogeneities; extended steam injection is needed for the more heterogeneous models. This paper is the first work comparing different MOEAs to optimize the SAS process using multiple heterogeneous models.
PubDate: 2022-09-29
- Numerical simulation of crack propagation and coalescence in rock
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Abstract: Abstract The strain energy density softening criterion is introduced to the peridynamic theory to reflect the failure characteristics of rock-like materials. At the same time, the critical damage condition, obeying Weibull distribution, is utilized to describe the heterogeneity of rock—making up for the deficiency that the peridynamic method cannot embody the strain-softening features and heterogeneity of rock when simulating crack propagation of rock materials. The crack extension process of rock, with a single crack under uniaxial compression, was simulated using the improved method, the results of which were then compared to the results of previous laboratory tests to verify the effectiveness of the proposed theory. Furthermore, the crack propagation patterns and failure mechanism of rock materials which contain single crack and double cracks with different prefabrication angles under uniaxial compression condition were explored in this study. The results showed that the propagation of a prefabricated single crack specimen was divided into wing crack, shear crack, and anti-wing crack, and the order of appearance was influenced by the inclination angle. The penetration modes of prefabricated double cracks were divided into wing mode (W-mode), shear mode (S-mode), and mixed mode (M-mode), which were primarily affected by the inclination angle and relative angle.
PubDate: 2022-09-26
- The traveling wavefront for foam flow in two-layer porous media
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Abstract: Abstract The injection of foams into porous media has gained importance as a method of controlling gas mobility. The multilayer structure of the porous medium raises a question on its efficiency in dealing with layers of different permeabilities. The present work shows the existence of a single traveling wavefront in a two-layer porous medium for a simplified model, which was derived from a realistic two-dimensional one. Besides the necessary conditions for the solution’s existence, we prove that the traveling wave velocity is a weighted average of the velocities as if both layers were isolated. All theoretical estimates were validated through one- and two-dimensional simulations. Finally, we estimated the order of magnitude of the characteristic time the traveling wavefront needs to stabilize.
PubDate: 2022-09-24
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