Permeability Field Research Articles

Probabilistic assessment of scalar transport under hydrodynamically unstable flows in heterogeneous porous media

Quantitative predictions of scalar transport in natural porous media is a nontrivial task given the presence of multi-scale spatial heterogeneity in the permeability field. Due to data scarcity, the structural map of the permeability field is subject to uncertainty and therefore, model predictions are uncertain. For such reasons, probabilistic models of flow and transport in natural porous media are required in risk assessment and to provide reliable decision making under uncertainty. Further complexities arise when the viscosity of the injected solute differs from that of the ambient fluid. Under the presence of viscosity contrast, hydrodynamic instabilities give rise to viscous fingering, which induces additional disorder in both velocity and solute concentration fields. This work examines the combined role of viscous fingering and permeability heterogeneity in the probabilistic description of transport predictions. In particular, we focus on metrics that are important for risk analysis, such as the solute plume’s early arrival times and the maximum concentration observed at a given location. We propose to use the Projection Pursuit Adaptation (PPA) method in the Polynomial Chaos Expansion (PCE) framework to quantify uncertainty in transport model predictions. The PPA method is a data-driven approach that optimally represents a given quantity of interest in a low-dimensional manifold. Unlike other dimension reduction techniques in uncertainty quantification, the PPA method utilizes non-linear information of the quantity of interest to identify the low-dimensional manifold, thereby increasing the likelihood of finding a more accurate lower-dimensional space. Moreover, the PPA model converges to the physical solution in a mean squared sense with respect to the polynomial order, enabling the construction of a converged model even with limited available data. Then, the PPA results are compared to Monte Carlo simulations using the same amount of data. This comparison illustrates that while Monte Carlo simulations are able to capture low-order statistics, they struggle to represent more detailed probability density functions. Our results show how the combined effect of permeability heterogeneity and viscosity contrast can enhance the mobility of the solute plume.

Numerical simulation of multi-field coupling in geothermal reservoir heat extraction of enhanced geothermal systems

The coupled analysis of multi-field heat and mass transfer in geothermal reservoirs is a pivotal concern within the realm of geothermal rock exploitation. It holds significant implications for the assessment of thermal energy capacity and the formulation of reservoir optimization strategies in the context of geothermal rock resources. Parameters governing production, along with fracture network characteristics (such as injection well temperature, injection well pressure, fracture width, and fracture network density), exert an influence on enhanced geothermal systems (EGS) heat production. In this study, aiming to comprehend the dynamic heat generation of EGS during prolonged exploitation, a coupling of various fields including permeation within the rock formations of geothermal reservoirs and the deformation of these rocks was achieved. In this study, we formulated the governing equations for the temperature field, stress field, and permeability field within the geothermal reservoir rock. Subsequently, we conducted numerical simulations to investigate the heat transfer process in an enhanced geothermal system. We analyzed the effects of injection well temperature, injection well pressure, primary fracture width, and secondary fracture density on the temperature distribution within the reservoir and the thermal power output of the production well. The research findings underscore that ill-conceived exploitation schemes markedly accelerate the thermal breakthrough rate of production wells, resulting in a diminished rate of geothermal resource extraction from the geothermal reservoir rock. Variations in influent well temperature and secondary fracture density exhibit an approximately linear impact on the output from production wells. Crucially, injection well pressure and primary fracture width emerge as pivotal factors influencing reservoir output response, with excessive widening of primary fractures leading to premature thermal breakthrough in production wells.

An encoder-decoder ConvLSTM surrogate model for simulating geological CO2 sequestration with dynamic well controls

In Geological Carbon Sequestration (GCS), effectively managing the project requires predicting state variables such as pressure and saturation. However, numerical simulation of multiphase flow in subsurface porous media involves solving large linear algebra systems, resulting in a substantial computational burden. This can make it impractical for real-time history matching or optimization. Meanwhile, deep learning-based surrogate models are emerging as fast and accurate approximators. This study delves into the application of the Encoder-Decoder Convolutional Long Short-Term Memory (ED-ConvLSTM) neural network for predicting the complex evolution of state variables under dynamic CO2 injection schemes. Inception blocks enhanced with light-weighted attention modules are introduced in the encoder to extract high-dimensional input features. ConvLSTM is employed to propagate spatial temporal information in the low-dimensional latent space. Further, progressive upsampling blocks are used to reconstruct the latent features for the desired output. Instead of taking discrete time steps as an input feature, the proposed network captures the dynamic dependencies with the inherent ConvLSTM cell. The network has access to data at only portion of the initial time steps during training stage, while it is used to predict the state variables at unseen time steps during testing stage. Results show that the network can produce excellent predictions for both pressure and saturation, even at unseen future time steps. The remarkable generalizability to different geological permeability fields is also evaluated. ED-ConvLSTM outperforms the standard U-Net by far, especially when predicting beyond the training time period. These numerical experiments demonstrate the advantages of ED-ConvLSTM in terms of prediction accuracy, extrapolability and generalizability. This study highlights the importance of incorporating recurrent connections into the deep neural networks for simulating time-dependent multiphase flow problems. The proposed methodology has great potential in GCS surrogate modeling and offers a possible approach for real-time optimization of CO2 injection.

Reciprocal cross‐correlation analysis of two‐phase seepage processes and reservoir heterogeneities in CO2 saline aquifer sequestration

AbstractWhen CO2 saline aquifer storage is carried out, the heterogeneity of reservoir rock is an important factor affecting CO2 transport, and the reservoir heterogeneity in numerical simulations is mainly manifested as the heterogeneity of the parameter field. Since the parameter distributions across the reservoir are not available with the existing probes, the stochastic finite element method is combined with a two‐phase flow model to establish an unconditional random field of permeability, and computations are performed using the Monte Carlo method. The permeability, CO2 maximum migration distance (Md) and CO2 sweep area (Sa) were analyzed for mutual correlation. The permeability correlation area affecting Md and Sa was obtained, and the changes in the correlation area under the coefficient of variation (Cv) and correlation length (λx) of the permeability field in the different reservoirs were analyzed. The kriging superposition approach (KSA) was subsequently used to estimate both the Md and Sa of the target reservoir by establishing conditional random fields based on the sampling parameters in regions with different correlations, resulting in errors of 0.66% for Md and 0.96% for Sa in the high correlation region and 4.86% and 3.12% for Md and Sa in the low correlation region, which suggested that the sampling results from the high correlation region were less biased in the estimation. Under limited sampling conditions, it is recommended that samples be collected in regions with high correlations to reduce the uncertainty of CO2 transport analysis due to unknown heterogeneity. © 2024 Society of Chemical Industry and John Wiley & Sons, Ltd.

Flow prediction of heterogeneous nanoporous media based on physical information neural network

The simulation and prediction of fluid flow in porous media play a profoundly significant role in today's scientific and engineering domains, particularly in gaining a deeper understanding of phenomena such as the migration and fluid flow in underground rock formations and the enhancement of oil recovery rates. The flow of fluids in nanoscale porous media requires consideration of the effects of microscale phenomena, which are challenging to accurately describe using traditional physical models. Currently, research in deep learning for porous media predominantly focuses on conventional porous media, and there is an urgent need for investigations into heterogeneous nanoporous media. Simultaneously, there is a necessity to overcome the limitations of traditional data-driven models lacking physical prior knowledge. Therefore, the integration of physics-informed neural networks, which combine deep learning with physical principles, becomes essential for inferring relatively accurate results from sparse data. In this work, based on the heterogeneity of porous media in shale, we have introduced a deep learning model that couples physical information to predict the flow in heterogeneous nanoscale porous media. In the Physical Information Neural Network model, we utilize point clouds and couple them with deep residual networks. Discrete sampling points are used as inputs, and a multi-level residual connection, along with dimension concatenation, is employed to fuse feature information. The network, through backpropagation, takes into account the Navier-Stokes equations and wall conditions in heterogeneous nanoscale porous media. The results indicate that the apparent permeability and pressure field accuracy are over 90% and 95%, respectively. The Physical Information Neural Network demonstrates promising prospects for predicting flow in nanoscale porous media. Future work will extend to the multiphase complex flow in three-dimensional porous media.

Impact of entropy generation and temperature gradient heat source on Couette flow in a permeable magnetic field

AbstractThis research paper focused on investigating the influence of various factors on steady Couette flow beneath a permeable bed. Factors studied included aligned magnetic field, thermal radiation, temperature gradient heat source, viscous dissipation, and Joules dissipation. The momentum and energy equations governing flow and heat transmission were analytically solved to predict the generation of entropy. The findings were visually presented through graphical representations, which effectively demonstrated the effect of these factors on the fluid's velocity, temperature, entropy production, and Bejan number. In addition, the shear stress and rate of heat transfer coefficient at the channel walls were computed and their behavior was documented in tables to provide further insights.

On the logarithmic nature of axial dispersion in Darcy flow through heterogeneous porous media

The present study provides novel insights in how spatial velocity variations in a heterogeneous porous medium cause the dispersion of a passive tracer. The study consists of two parts. The first part describes a series of numerical computations of the axial dispersion in the flow through heterogeneous porous media, idealized as Darcy flow through two-dimensional and three-dimensional patchwork geometries of zones with randomized permeability fields. Data on the axial dispersion were obtained using the mean age theory, which transforms the transient advection–diffusion equation into the steady-state mean age field equation, thus reducing the required computational effort by multiple orders of magnitude. This allowed to consider a sufficiently large number of randomizations to obtain a statistically representative ensemble average, as well as to consider sufficiently large systems to reduce the influence of boundary conditions. In the second part, it is shown that the relation between the axial dispersion coefficient and the velocity can be represented as a series, summing up the effect of velocity differences on all length scales, assuming the velocity differences are analogous to white noise. The sum can be closely fitted by a logarithmic law containing only two parameters with a well-defined physical meaning. A similar logarithmic dependency was also obtained by Saffman, Koch, and Brady. However, the logarithmic dependency obtained in the present work emerges from the heterogeneity of the porous medium, whereas the logarithmic dependency in the aforementioned works emerged from the no-slip boundary conditions at solid surfaces.

Impacts of Permeability Uncertainty in a Coupled Surface‐Subsurface Flow Model Under Perturbed Recharge Scenarios

AbstractCoupled simulations of surface and variably saturated subsurface flow, termed integrated hydrologic models (IHMs), can provide powerful insights into the complex dynamics of watersheds. The system of governing equations solved by an IHM is non‐linear, making them a significant computational burden and challenging to accurately parameterize. Consequently, a large fraction of the IHM studies to date have been “numerical hypothesis testing” studies, but, as parallel computing continues to improve, IHMs are approaching the point where they might also be useful as predictive tools. For this to become reality, the predictive uncertainty of such highly parameterized simulations must be considered. However, uncertainty is seldom considered in the IHM literature, likely due to the long runtimes of the complex simulations. The questions considered herein are how much uncertainty is there in an IHM for a common watershed simulation scenario, and how likely is it that any one realization of a system will give the same relative change as any other due to a perturbation in recharge? A stochastic ensemble of 250 permeability field realizations was used to show that uncertainty in a high‐mountain headwaters systems is dominated by the subsurface. Recharge perturbation scenarios echo these results, but the uncertainty of changes in streamflow or groundwater pressure heads were significantly smaller than the uncertainty in their base‐case values. The main finding is that IHMs do provide confident, predictive estimates of relative changes in watersheds, even when uncertainty in specific simulation outputs may be high.

Modeling the influence of climate on groundwater flow and heat regime in Brandenburg (Germany)

This study investigates the decades-long evolution of groundwater dynamics and thermal field in the North German Basin beneath Brandenburg (NE Germany) by coupling a distributed hydrologic model with a 3D groundwater model. We found that hydraulic gradients, acting as the main driver of the groundwater flow in the studied basin, are not exclusively influenced by present-day topographic gradients. Instead, structural dip and stratification of rock units and the presence of permeability contrasts and anisotropy are important co-players affecting the flow in deep seated saline aquifers at depths >500 m. In contrast, recharge variability and anthropogenic activities contribute to groundwater dynamics in the shallow (<500 m) freshwater Quaternary aquifers. Recharge fluxes, as derived from the hydrologic model and assigned to the parametrized regional groundwater model, reproduce magnitudes of recorded seasonal groundwater level changes. Nonetheless, observed instances of inter-annual fluctuations and a gradual decline of groundwater levels highlight the need to consider damping of the recharge signal and additional sinks, like pumping, in the model, in order to reconcile long-term groundwater level trends. Seasonal changes in near-surface groundwater temperature and the continuous warming due to conductive heat exchange with the atmosphere are locally enhanced by forced advection, especially in areas of high hydraulic gradients. The main factors controlling the depth of temperature disturbance include the magnitude of surface temperature variations, the subsurface permeability field, and the rate of recharge. Our results demonstrate the maximum depth extent and the response times of the groundwater system subjected to non-linear interactions between local geological variability and climate conditions.

Exploring substitution random functions composed of stationary multi-Gaussian processes

Simulation of random fields is widely used in Earth sciences for modeling and uncertainty quantification. The spatial features of these fields may have a strong impact on the forecasts made using these fields. For instance, in flow and transport problems the connectivity of the permeability fields is a crucial aspect. Multi-Gaussian random fields are the most common tools to analyze and model continuous fields. Their spatial correlation structure is described by a covariance or variogram model. However, these types of spatial models are unable to represent highly or poorly connected structures even if a broad range of covariance models can be employed. With this type of model, the regions with values close to the mean are always well connected whereas the regions of low or high values are isolated. Substitution random functions (SRFs) belong to another broad class of random functions that are more flexible. SRFs are constructed by composing (Z=Y∘T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z=Y\\circ T$$\\end{document}) two stochastic processes: the directing function T (latent field) and the coding process Y (modifying the latent field in a stochastic manner). In this paper, we study the properties of SRFs obtained by combining stationary multi-Gaussian random fields for both T and Y with bounded variograms. The resulting SRFs Z are stationary, but as T has a finite variance Z is not ergodic for the mean and the covariance. This means that single realizations behave differently from each other. We propose a simple technique to control which values (low, intermediate, or high) are connected. It consists of adding a control point on the process Y to guide every single realization. The conditioning to local values is obtained using a Gibbs sampler.

Physics-informed machine learning for reservoir management of enhanced geothermal systems

With the energy demand arising globally, geothermal recovery by Enhanced Geothermal Systems (EGS) becomes a promising option to bring sustainable energy supply along with mitigating CO2 emission. However, reservoir management of EGS primarily relies on reservoir simulation, which is quite expensive due to the reservoir heterogeneity, the interaction of matrix and fractures, and the intrinsic multi-physics coupled nature. Therefore, a robust optimization framework is critical for the management of EGS. We develop a general Physics-Informed Machine Learning (PIML) framework for reservoir management with multiple optimization options. A robust forward surrogate model fl is developed based on a convolutional neural network, and it successfully learns the nonlinear relationship between input reservoir model parameters (e.g., fracture permeability field) and interested state variables (e.g., temperature field and produced fluid temperature). fl is trained using simulation data from the EGS coupled thermal-hydro simulation model by sampling reservoir model parameters. As fl is accurate, efficient and fully differentiable, EGS thermal efficiency can be optimized following two schemes: (1) training a control network fc to map reservoir geological parameters to reservoir decision parameters by coupling it with fl; (2) directly optimizing the reservoir decision parameters based on coupling the existing optimizers with fl. We evaluate the impact of reservoir model parameters on the thermal recovery based on simulation datasets through sensitivity analyses, and demonstrated that injection mass rate dominates thermal recovery. Further, the forward model fl performs accurate and stable predictions of evolving temperature fields (relative error 1.27 ± 0.89%) in EGS and the time series of produced fluid temperature (relative error 0.26 ± 0.46%), and its speedup to the counterpart high-fidelity simulator is 4564 times. When optimizing with fc, we achieve thermal recovery with a reasonable accuracy but significantly low CPU time during inference, 0.11 seconds/task. When optimizing with Adam optimizer, we achieve the objective perfectly with relatively high CPU time, 4.58 seconds/task. This is because the former optimization scheme requires a training stage for fc but its inference is non-iterative, while the latter scheme requires an iterative inference without training. We also investigate the option to use fc inference as an initial guess for Adam optimizer, which decreases Adam’s CPU time but achieves excellent convergence in the objective function. This is the highest recommended option among the three evaluated. The efficiency, scalability and accuracy observed in our reservoir management framework makes it highly applicable to near real-time reservoir management in EGS as well as other similar system management processes.

Automatic History Matching for Adjusting Permeability Field of Fractured Basement Reservoir Simulation Model Using Seismic, Well Log, and Production Data

Developing automatic history matching (AHM) methods to replace the traditional manual history matching (MHM) approach in adjusting the permeability distribution of the reservoir simulation model has been studied by many authors. Because permeability values need to be evaluated at hundreds of thousands of grid cells in a typical reservoir simulation model, it is necessary to apply a reparameterization technique to allow the optimization algorithms to be implemented with fewer variables. In basic reparameterization techniques including zonation and pilot point methods, the calibrations are usually based solely on the production data with no systematic link to the geological and geophysical data, and therefore, the obtained permeability distribution may be not geologically consistent. Several other reparameterization techniques have attempted to preserve geological consistency by incorporating 4D seismic data; however, these techniques cannot be applied to our fractured basement reservoirs (FBRs) as they do not have 4D seismic data. Taking into account these challenges, in this study, an AHM methodology and workflow have been developed using a new reparameterization technique. This approach attempts to minimize the potential for geological nonconsistency of the calibrated results by linking the permeability to geophysical data. The proposed methodology can be applied to fields with only traditional geophysical data (3D seismic and conventional well logs). In the proposed workflow, the spatial distributions of seismic attributes and geomechanical properties were calculated and estimated from 3D seismic data and well logs, respectively. After that, a feed-forward artificial neural network (ANN) model trained by the back-propagation algorithm of the relationship between initial permeability with seismic attributes and geomechanical properties of their grid cell values is developed. Then, the calibration of the permeability distribution is performed by adjustment of the ANN model. Modification of the ANN model is performed using the simultaneous perturbation stochastic approximation (SPSA) algorithm to calibrate transmission coefficients in the ANN model to minimize the discrepancy between the simulated results and observed data. The developed methodology is applied to calibrate the permeability distribution of a simulation model of Bach Ho FBR in Vietnam. The effectiveness of the methodology is evident by comparing the historical matches with an available manually history-matched simulation model. The application shows that the proposed methodology could be considered as a suitable practical approach for adjusting the permeability distribution for FBR reservoir simulation models.

CREEPING FLOW OF COUPLE STRESS FLUID OVER A SPHERICAL FIELD ON A SATURATED BIPOROUS MEDIUM

This problem emphasizes the dynamic interaction between a biporous medium and a couple stress fluid of laminar flow. The flow around a permeable field engulfed in a couple stress fluid is examined. When examining the motion of an oil droplet in a porous collector that is surrounded by an aqueous medium (oil-in-water emulsion) and is subject to an external pressure drop, this formulation of the problem is typical. A similar issue arises when lymph enters the tissues of humans or animals: the inside permeable spherical field saturated with viscous fluid and outside region saturated with couple stress fluid. The Brinkman equations are utilized to characterize the couple stress fluid flow in a saturated biporous medium. The couple stress tensor and velocity fields are expressed using Gegenbauer polynomials and Macdonald functions. For the axially symmetric motion, both pressure distribution and the stream function solution are explicitly solved. The method of variable separation is used to investigate an analytical resoluteness for the flow field. The drag force on a saturated biporous medium and the drag coefficient <i>D<sub>N</sub></i> are calculated, and the impacts of the permeability κ, the ratio of viscosity (γ<sup>2</sup> = μ<sub>1</sub> /μ<sub>2</sub>), the couple stress viscosity ratio (τ = η'/η), and the parameter of couple stress (λ = √μ/η). The appropriate dependencies are graphically delineated and reviewed, including the permeability κ, couple stress parameter λ, viscosity ratio γ<sup>2</sup>, and couple stress viscosities (η, η'). According to the findings, increasing permeability gradually raises the drag coefficient, which is used to describe a spherical field’s surface with a high level resistance of flow. Limits statements are used to illustrate specific cases that are well-known. The current study is significant primarily in the course through a layer formed by penetrable particles and has very important and compelling applications in both nature and innovation, with a variety of potential outcomes.

Horizontal borehole azimuth optimization for enhanced stability and coal seam gas production

Horizontal boreholes have been widely used to extract natural gas from coal seams. However, these boreholes can encounter severe instability issues leading to production interruption. Optimizing drilling azimuth is a potential solution for enhancing borehole stability while considering gas production. In this work, we improved and implemented a dual-porosity, fully coupled geomechanical-hydraulic numerical model into COMSOL Multiphysics to investigate into this factor. The sophisticated numerical model incorporates various critical factors, including desorption-induced matrix shrinkage, stress-dependent anisotropic fracture permeability, and the interactions of gas flow and reservoir deformation in matrices and fractures.A suite of simulation scenarios (e.g., varying coal strength) was carried out to quantify the impact of drilling azimuth on coal permeability evolution, cumulative gas production, and the borehole break-out width for Goonyella Middle Seam of Bowen Basin, Australia. The model was calibrated against both theoretical permeability values and field gas production data. Due to the lack of directly measured matrix permeability data, the actual gas production was used to back calculate the best-matched matrix permeability, which is 0.65 μD for this particular work. Moreover, based on the breakout shape and induced volumetric strains around the borehole, drilling along the maximum horizontal stress does not necessarily lead to the best stability of the borehole, as generally believed. A drilling azimuth between 0° and 60° results in similar breakout width, whereas a drilling azimuth between 60° and 90° achieves the most efficient gas production. By considering both gas production efficiency and borehole stability, for this particular reservoir condition, the optimum drilling azimuth is determined to be between 45° and 60°.This study presents a practical approach for determining the optimum drilling azimuth in coal seam gas extraction through in seam boreholes.

A DIMENSION-ADAPTIVE COMBINATION TECHNIQUE FOR UNCERTAINTY QUANTIFICATION

We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic partial differential equation, where the diffusion coefficient is parametrized by means of a Karhunen-Loève expansion. The approximation of the equivalent parametric problem requires a restriction of the countably infinite-dimensional parameter space to a finite-dimensional parameter set, a spatial discretization, and an approximation in the parametric variables. We consider a sparse grid approach between these approximation directions in order to reduce the computational effort and propose a dimension-adaptive combination technique. In addition, a sparse grid quadrature for the high-dimensional parametric approximation is employed and simultaneously balanced with the spatial and stochastic approximation. Our adaptive algorithm constructs a sparse grid approximation based on the benefit-cost ratio such that the regularity and thus the decay of the Karhunen-Loève coefficients is not required beforehand. The decay is detected and exploited as the algorithm adjusts to the anisotropy in the parametric variables. We include numerical examples for the Darcy problem with a lognormal permeability field, which illustrate a good performance of the algorithm. For sufficiently smooth random fields, we essentially recover the spatial order of convergence as asymptotic convergence rate with respect to the computational cost.

Fabrication of breathable superhydrophobic composite fabric with moisture permeability and weak-electric-field bactericidal ability designed for protective clothing applications

Most protective clothing on the market today cannot provide both comfort properties and protectability, which would not match the requirement for preventing or killing the rapidly growing and changing virus. Hence, a novel breathable and waterproof composite fabric used in protective clothing was designed through the hot-press process with three functional layers. The waterproof ability, moisture permeability, mechanical property, electricity and bactericidal ability of three layers and composite fabric were studied. Results showed that the moisture permeability of coated thermoplastic polyurethane (TPU) membrane reached 19854 g m2 d−1. The composite fabric had still excellent moisture permeability of up to 13956 g m2 d−1 and water contact angle of 151.7°. The coated TPU membrane had good tensile strength and acid resistance. The voltage and current of composite fabric after 7 days were approximately 0.336 V and 1.4 μA. The composite fabric had a 97.5 % filtering effect for NaCl aerosols, a 99 % bacteriostatic rate, and the ability to withstand the Phy-X174 phage with a diameter of 0.027 μm. This composite fabric based on the principle of moisture permeability and weak electric field could be used in protective clothing, which would be of theoretical significance and guiding practical production.

Multiscale simulation of highly heterogeneous subsurface flow with physically adaptive 3D unstructured grids

The multiscale finite volume framework is extended with physical-based grid adaptation (MSFV-GA) for three-dimensional fully unstructured grids. The MSFV method produces large errors for highly heterogeneous and anisotropic problems on standard coarse grids generated based on geometrical features. Adding constraints based on the fine-scale physical properties to construct coarse grids can increase the accuracy and robustness of the MSFV solutions. A novel and automated coarse grid generation strategy adaptable to the reservoir heterogeneity for 3D unstructured grids is presented. Adaptive coarse grids are generated based on local variations of fine scale permeability field. The proposed procedure is very flexible respect to the local physical and geometrical limitations in coarse blocks. Multiscale coarse grid adaptation notably improves the basis functions calculations. The performance of the MSFV-GA in handling challenging problems involving high media contrasts or impermeable shale layers is assessed. The results are very promising and show that the MSFV-GA can accurately approximate complex physics problems. The presented 3D unstructured procedure can notably improve the applicability of the multiscale finite volume method and provide a promising framework for the next generation of reservoir flow simulators.

Simulation of thermo-hydro-mechanical coupled heat extraction process of geothermal reservoir under varied geological conditions with CO2 as working fluid

The use of supercritical CO2 as a working fluid instead of H2O in an enhanced geothermal system (EGS) for extracting heat from hot dry rock geothermal resources has garnered significant attention. The objective of this study is to investigate how different geological conditions affect the heat extraction behavior of supercritical CO2 and to reveal the efficiency differences between supercritical CO2 and H2O as working fluids in each geological scenario, providing deeper insight into reservoir management. A series of 3D coupled thermo-hydro-mechanical models were established. Besides, the impact of initial temperature, pressure, porosity, permeability, and stress field on the heat extraction of EGS with different working fluids are also analyzed and compared. Results indicate that, at the same circulating volumetric flow rate, CO2-EGS generally exhibits an earlier thermal breakthrough time, lower net energy production, and reduced heat extraction rate compared to H2O-EGS. Taking into account the extended reservoir lifespan and the relatively small pressure difference between injector and producer in CO2-EGS, CO2 is a more suitable working fluid than H2O. Furthermore, the performance of CO2-EGS is primarily affected by the initial temperature, porosity, and permeability distribution pattern, rather than the initial pressure. On the one hand, a reservoir with low initial temperature, porosity and homogeneous permeability were found to be more conducive to enhancing the average net energy production. On the other hand, reservoir vertical permeability anisotropy can have a more profound impact on CO2-EGS efficiency compared to horizontal y permeability anisotropy. Additionally, this study also examined the impact of in situ stress field. It was found that, compared to H2O-EGS, both isotropic and anisotropic in situ stress fields have a weak effect on the performance of CO2-EGS, which can be attributed to the similarity of the channelization degree of the flow field under different stress conditions.

Significance of a permeable semi-circular body and magnetic field on thermo-solutal natural convection and irreversibilities

This study explores the intriguing phenomenon of thermo-solutal buoyancy-driven traits in the presence of a magnetic force within a square cold enclosure housing a soluted and heated permeable semi-circular cylinder. The amalgamation of flat and curved edges, alongside the permeable characteristics, serves as the driving motivation behind this investigation. The primary objective is to scrutinize the impact of magnetic force and its orientation, buoyant force, permeability on the thermo-solutal convection occurring within and around the permeable body. To achieve this, a thorough parametric investigation is carried out, focusing on the significance of Hartmann number (Ha), magnetic field angle (γM), buoyancy ratio (BR), and Darcy number (Da), concerning flow, heat, concentration transfer, and the variation in irreversibilities. The Darcy-Brinkmann-Forchheimer equation as a source term in lattice Boltzmann technique is utilized to accurately solve the intricate porous medium flow. The investigation reveals that escalating the buoyant force, and permeability, and magnetic field angle yields favourable heat and concentration traits. Additionally, aligning the magnetic force opposite to gravity diminishes the inhibitory effects on the thermal and solutal transfers exerted by the magnetic force. Notably, unsteady behaviour is predominantly observed when the BR assumes a negative value, with the amplitude and frequency of these phenomena amplified by the Da and γM. Also, a few anomalous spikes in the NuM and ShM are witnessed, attributed to the development of a robust uni-vortex in the top region of the cavity. Interestingly, the irreversibilities induced by the magnetic field diminish as the BR increases. Among these irreversibilities, entropy generation due to concentration emerges as the dominant contributor, with the exception of cases exhibiting atypical rises, where fluid entropy resulting from friction takes precedence.

Numerical simulation study of enhanced geothermal system modification and heat mining performance under cyclic injection

Enhanced geothermal systems (EGS) involve complex thermal–hydraulic-mechanical (THM) coupling. The reservoir's permeability evolution and heat extraction characteristics under cyclic variable pressure injection conditions are unknown. In this paper, a THM model that considered the dynamic changes of rock matrix and fluid properties was developed based on the theory of local heat balance. The THM coupling model investigated the effects of the number of fractures, initial permeability of fractures (kf), maximum injection pressure (P), frequency (td), and working fluid on the heat recovery performance of the EGS under cyclic injection for 20 years. Finally, the sensitivity of each parameter was discussed. When the number of fractures increased from 100 to 200, the temperature of the reservoir decreased by 68.5 K, and the cumulative heat energy extracted increased by 6.6 × 1014 J. With the increase of the initial permeability of the fractures, the irregularities in the temperature and permeability fields of the reservoir were significantly enhanced. When the maximum injection pressure increased from 34 MPa to 40 MPa, the permeability ratio of the reservoir increased by about 13.45 %, and the cumulative extracted thermal energy increased by 3.5 × 1014 J. The frequency of cyclic injection increased from 5 d to 45 d, the production temperature decreased by 26.78 K, and the permeability ratio of the reservoir and the cumulative extracted thermal energy increased. The low-temperature range of CO2-EGS is significantly larger than that of H2O-EGS, and the reservoir temperature decreases faster. The permeability of CO2-EGS increases by 29.32 %, and the cumulative thermal energy extraction increases by 17.5 × 1014 J compared with H2O-EGS. Parameter sensitivities were found for cyclic injection. Factors affecting production temperature and reservoir permeability in that order: P > td > kf. Injection frequency had a slightly greater impression on cumulative extracted thermal energy than injection pressure.