Upscaling Of Permeability Research Articles

SVM-based fast 3D pore-scale rock-typing and permeability upscaling for complex rocks using Minkowski functionals

The rapid advancement of digital core analysis has greatly promoted the research progress of flow and transport in porous media. However, complex analytical process with exceeding computational load impedes the application on large data volume. Considering the strong heterogeneity of the underground porous media, the integration of pore-scale information into continuum scale is widely concerned for the future development of digital physical analysis. For hierarchical porous structures, pore-scale rock-typing and upscaling of petrophysical properties is a promising solution towards the issue, and morphological and topological descriptors associating data clustering methods are popularly utilized. However, the size of the regional support through which the parameter fields are generated heavily affects the descriptive capacities of the parameters and the following partitioning process. We propose in this work a robust integrated pore-scale rock-typing and upscaling technology for 3D porous structures which uses Minkowski functionals as the descriptive parameters. A fast-computational method utilising fast Fourier transform has been applied for efficient generation of the parameter fields. A comparative study between the two different classification methods of Support Vector Machine (SVM) and Gaussian Mixture Model (GMM) has been conducted on two complex artificial porous systems and a laminated sandstone through various regional support sizes. Throughout the test, SVM has illustrated obvious advantage of overcoming regional support size effect even with limited labelling information. The Upscaling of permeability on the natural sandstone sample based on the rock type distribution has demonstrated excellent accuracy comparing with full scale direct computation.

An efficient analytical approach for steady-state upscaling of relative permeability and capillary pressure

Upscaling in petroleum reservoir simulation captures the dynamic behavior of fine-scale models at the coarse-scale in a volume average sense. Traditional upscaling of immiscible two-phase flow can be implemented by solving the fluid flow equations at steady state in the capillary or viscous limit in fine scale, which requires modeling the single-phase flow numerically many times and is computationally demanding. In this study, an analytical approach is proposed, to replace the numerical simulation, for computing the relative permeability. The key idea is to utilize the perturbation expansion technique and Fourier analysis to derive an explicit expression of the equivalent permeability. The analytical expression accounts for spatial correlations and is more accurate than the simple averaging and renormalization methods. It matches well with the numerical method in all cases for the upscaling of the relative permeability and capillary pressure. The developed method is also validated by comparing the pressure and saturation results from the coarse-scale and fine-scale models. In the base case of SPE10 benchmark test, the numerical upscaling takes 436 s, whereas the analytical upscaling takes 13.6 s, which is about 30 times faster than the numerical method. Moreover, the analytical coefficients just need to be computed once for the whole space in a given geostatistical model, which naturally leads to improved efficiency and is clearly favorable for petroleum reservoir simulations.

The Hydro‐Mechanical Properties of Fracture Intersections: Pressure‐Dependant Permeability and Effective Stress Law

AbstractFluid flow through the brittle crust is primarily controlled by the capability of fracture networks to provide pathways for fluid transport. The dominant permeability orientation within fractured rock masses has been consistently correlated with the development of fracture intersections; an observation also made at the meso‐regional scale. Despite the importance attributed to fracture intersections in promoting fluid flow, the magnitude of their enhancement of fractured rock permeability has not yet been quantified. Here, we characterize the hydro‐mechanical properties of intersections in samples of Seljadalur Basalt by generating two orthogonal, tensile fractures produced by two separate loadings using a Brazilian test apparatus, and measuring their permeability as a function of hydrostatic pressure. We observe that intersecting fractures are significantly more permeable and less compliant than two independent macro‐fractures. We formulate a model for fracture intersection permeability as a function of pressure by adding the contributions of two independent fractures plus a tube‐like cavity with an effective elastic compressibility determined by its geometry. Permeability measurements during cyclic loading allowed determination of the effective stress coefficient (α in pe = pc − αpp) for fracture and intersection permeability. We observe a trend of lower αintersection values with respect to αfracture, which suggests that the channels controlling fluid flow have a higher aspect ratio (are more tubular) for the intersections relative to independent fractures. Our results suggest that fracture intersections play a critical role in maintaining permeability at depth, which has significant implications for the quantification and upscaling of fracture permeability toward reservoir‐scale simulations.

Carbon Dioxide (CO2) Dissolution Efficiency During Geological Carbon Sequestration (GCS) in Randomly Stratified Formations

AbstractGeological carbon sequestration mitigates climate change by capturing and storing carbon dioxide (CO2) emissions in deep geologic formations. Dissolution trapping is one mechanism by which CO2 can be trapped in a deep formation. However, heterogeneity can significantly affect the dissolution efficiency. This work addresses the injection of CO2 in perfectly stratified saline formations under uncertainty. Monte Carlo two‐phase flow compositional simulations involving the dissolution of CO2 into brine and evaporation of water into the CO2‐rich phase are presented. We systematically analyzed the interplay between heterogeneity and gravity factor (G), which is shown to control the migration of the CO2 plume as well as the temporal evolution of dissolution efficiency. Results show that when G is important, vertical segregation controls the overall behavior of CO2, diminishing the influence of small‐scale heterogeneity on dissolution. However, when G is relatively small compared to , CO2 migrates preferentially through high permeability layers and dissolution efficiency increases with due to the stretching of the CO2 plume that enhances mixing. As a result, in this situation, the upscaling of permeability leads to an underestimation of the dissolution efficiency. A review of field sites shows that dissolution is heterogeneity‐controlled in most real systems. Knowing that most numerical models cannot afford to represent heterogeneity at an adequate scale, results indicate that dissolution efficiency can be typically underestimated by a factor close to 1.5.

Hybrid approach to predict the permeability in heterogeneous reservoirs

In this work, we present a new methodology to predict the permeability of heterogeneous reservoirs. This methodology is a hybrid approach based on the volume averaging method and the Kriging theory. The upscaling of permeability from core measurements begins with the application of Kriging to generate a permeabilities map. With this information, the solution of the associated closure problem is carried out in each element of the map leading to a unique effective permeability. Our results suggest that this methodology can help in the understanding and interpretation of measured permeability in cores and at reservoirs-scale.

Analytical Approach for Steady-State Upscaling of Relative Permeability and Capillary Pressure in Waterflooding

Analytical Approach for Steady-State Upscaling of Relative Permeability and Capillary Pressure in Waterflooding

Upscaling numérico baseado em uma metodologia multiescala para a simulação de escoamentos em reservatórios de petróleo heterogêneos e anisotrópicos / Numerical upscaling based on a multiscale methodology for simulating flows in heterogeneous and anisotropic oil reservoirs

This work aims to develop a scale transfer methodology in highly heterogeneous and anisotropic porous media, that makes it possible to solve elliptical problems with accuracy and low computational cost. A scale transfer method is developed that uses the Multiscale Finite Volume Method (MSFVM) to perform a flow based numerical upscaling of absolute permeability. The transmissibility matrix was built in the coarse mesh over the projection and restriction operators obtaining permeability in the coarse scale. This allows to solve only local problems in the coarse mesh volumes and to use pressure multiscale solution in the fine mesh. The permeability field can be obtained by different strategies, and enabling simulations directly on the coarse mesh, controlling the accuracy of the solutions and also with the possibility of updating the permeability field over the recalculated locally conservative multiscale solution.

Use of geostatistical modeling to improve the understanding of permeability upscaling in isotropic and anisotropic burrowed reservoirs

Coarse materials filling burrows in reservoirs can provide permeable pathways through an otherwise impermeable host rock matrix —thus enhancing fluid flow properties. However, understanding permeability anisotropy and permeability-upscaling under such conditions represents a challenge in the exploration and development of reservoirs. Herein, we examined 75 hypothetical models that represent diverse types and amounts of bioturbation. The aim is to understand the impacts of burrows on petrophysical characteristics, including upscaling of permeability where the matrix is isotropic. These models were simulated in a high-resolution 1-m3 grid (8 × 106 cells) using multipoint statistics (MPS) modeling techniques to systematically vary burrow morphology and bioturbation intensity in the same host rock matrix. The modeled burrow morphologies (vertical, horizontal, and boxwork morphologies) and bioturbation intensity―expressed as burrow percentage (BP, ranging from 2% to 50%)― show burrow connectivity trends increasing with increasing BP. In each trend, there is a burrow-morphology-dependent critical BP at which burrows develop connected permeability pathways. Accordingly, three unique patterns of burrow connectivity were identified among the 75 models. These include when burrows are: 1) just isolated volumes (isotropic system); 2) create unidirectional flow (anisotropic system); and 3) create omnidirectional flow (isotropic system). These connectivity patterns determine whether the permeability of the burrow-related reservoir is isotropic or anisotropic. Thus, identifying each of these connectivity patterns in burrowed reservoirs would help determine the appropriate averaging method to upscale permeability. The results of this study bridge an essential gap in reservoir modeling and simulation of hydrocarbon reservoirs and aquifers with burrowed strata.

Coupling image analysis and thermo-mechanical simulation results to produce a model of the fracture network in a nuclear glass canister

Understanding nuclear glass alteration in a fracture network of a block of nuclear glass is critical in predicting the release of the radionuclides in the subsurface and is relevant for the security of nuclear waste disposal. Here, we present an image processing-based fracture network characterization workflow that enables us to characterize a glass block fracture network, establish a link between a physical parameter representing an internal state of glass structural relaxation and an internal structure of the block fracture network, and generate multiple realizations of equivalent fracture networks by considering the variability of the fracture network parameters such as fracture distribution and apertures. The proposed workflow includes the following stages: (i) fracture network extraction, (ii) measurement of apertures of all distinct ramifications of the fracture network, (iii) image segmentation, (iv) anisotropy characterization, (v) passage to segment representation with the intention of modeling block equivalent fracture networks by using an algorithm of mesh growth, (vi) geostatistical modeling of average apertures and variables responsible for fracture spatial distribution, and (vii) simulation of equiprobable realizations of fracture network equivalent tessellations. Given this processing, the workflow is able to provide data for further steps including upscaling of diffusivity and permeability, and it facilitates reactive transport modeling at the glass block scale. As an illustrative example, we apply the proposed sequence of actions to a two-dimensional (2D) high-resolution image of two blocks of nuclear glass. This application brings into service both hard data obtained by direct measurement of the fracture network and soft physics-based explanatory data and considers the variability in the fracture network. The results show that implementation of the devised procedure presents an opportunity for better understanding of the impact of fracturing on aqueous alteration of glass.

Absolute Permeability Upscaling for Superelement Modeling of Petroleum Reservoir

A technique for local upscaling of absolute permeability is proposed intended for the superelement modeling of petroleum reservoir development. The upscaling is performed for every block of an unstructured superelement grid based on solving a series of stationary one-phase flow in reservoir problems on a refined grid with the initial permeability field under various boundary conditions reflecting the characteristic structural variants of the filtrational flow and taking into account the presence or absence of wells inside the block. The resulting components of the effective permeability tensor in each superelement are sought from the solution of the problem on minimizing the deviations of the normal flows through the faces of the superelement averaged on a refined computational grid from those approximated on a coarse superelement grid. The application of the method is demonstrated by examples of the reservoir of the periodic and nonperiodic structure. The method is compared with the traditional techniques for local upscaling.

Image‐Based Upscaling of Permeability in Opalinus Clay

AbstractThis paper presents an approach for upscaling permeability in Opalinus Clay from pore scale to a coarser scale, where pores cannot be resolved and where the transport properties are controlled by the geometry of the clay matrix considered as a distinct phase. Microstructures reconstructed from multiscale image data are cellular models with different sizes of basic building blocks, the so‐called voxels. Flow simulations were performed on the basis of the grid that is naturally inherent in the coarser‐scale image data that were acquired by synchrotron X‐ray computed tomography. Thereby, the spatial distribution of permeability at this coarser scale was determined from image data at the pore scale acquired by focused ion beam nanotomography. Then, coarse‐scale microstructures with different clay matrix contents were used as input for flow simulations, which allowed predicting the vertical and horizontal bulk permeability at the mesoscale. In agreement with results of other workers, it turned out that vertical (cross‐plane) permeability Kv decreases with increasing clay content, which can be explained in that the presence of coarse nonclayey grains increases permeability of the porous clay matrix when compared to a matrix consisting only of fine‐grained shales. Mesoscale permeability anisotropy Kh/Kv increases from about 1 to 2 if the clay content increases from 0.2 to 0.9. The predicted permeability behavior is discussed and compared to results from experiments and other predictive models.

A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale

Microstructure-based quantitative computation of the shale permeability is challenging due to the presence of organic matter with nanoporous features. In this study, a new three-dimensional (3D) coupled model is proposed to investigate the micro-scale permeability of organic-rich-shale matrix. The coupled model consists of two subdomains, organic matter and inorganic matrix. They are described by the pore network model (PNM) and continuum model to capture the non-Darcy and Darcy flow, respectively, and the gas flow in the two subdomains are coupled by finite element mortars (Mortar). The convergence error, grid discretization and parallel scheme are also investigated to get the optimal computing parameters for this model. Then, the effects of the total organic content (TOC), kerogen distribution and pore-size distribution on the apparent permeability (AP) of shale matrix are studied using the coupled model with computer-generated PNMs. And on the basis of FIB-SEM images, a Longmaxi shale sample from the Sichuan Basin, China is introduced to build a real shale model. Results show that AP is more sensitive to TOC and pore-size distribution than kerogen distribution. Additionally, in order to analyze the necessity of 3D model, a comparison of 3D and two-dimensional (2D) model is made and the error of 2D model is pointed out. The 3D couple model affords a foundation for further upscaling of shale permeability to REV scale and reservoir scale.

The structured gridding implications for upscaling model discrete fracture networks (DFN) using corrected Oda's method

Upscaling of fracture permeability in a field-size discrete fracture network (DFN) for a dual porosity model can be undertaken using Oda's method. It is known that Oda's method usually overestimates equivalent permeability and needs to be corrected by a flow-based numerical method. In this study we show that grid orientation can produce significant differences in single-phase (water) production volumes estimated through flow simulation in dual porosity models (Eclipse 300) when using corrected Oda's method. A five layer synthetic model in a water zone includes thirteen vertical wells. 10ft by 10ft structured gridding is performed in six directions: 0°, 15°, 30°, 45°, 60° and 75° counter-clockwise relative to the north. The model DFN used in this study consists of three sets: a dominant, high intensity N76°W set and two lower-intensity sets that strike N28°W and N75°E similar to the fracture sets observed in the Tensleep Formation at Teapot Dome, Wyoming, USA.The single-phase (water) flow simulation using Eclipse 300 flow simulator for the six synthetic models reveals that the production varies in proportion to the geometric mean of the permeability tensor with grid rotation. The production is at its maximum when the dominant fracture set orients 45° relative to the grid cell principal directions (i,j) and falls to a minimum when the dominant fracture set is parallel to either grid wall (i or j principal directions).This research reveals a shortcoming of systematic variability of simulated production with grid orientation even though Oda's results are corrected with a flow-based numerical method.

Upscaling of absolute permeability for a super element model of petroleum reservoir

This paper presents a new method of local upscaling of absolute permeability for super element simulation of an oil reservoir. Upscaling was performed for each block of a super element unstructured grid. For this purpose, a set of problems of a one-phase steady-state flow was solved on a fine computational grid with the initial scalar field of absolute permeability with various boundary conditions. These conditions reflect the specific variants of filtrational flow through the super element and take into account the presence or absence of boreholes in the coarse block. The resulting components of the effective permeability tensor in each super element were found from the solution of the problem of minimizing the deviations of the normal flows through the super element faces, averaged on a detailed computational grid, from those approximated on a coarse super element grid. The results of using the method are demonstrated for reservoirs with river-type absolute permeability. The method is compared with the traditional methods of local upscaling.

Perturbative Studies to Calculate the Permeability and Porosity of a CO2 Storage Formation in a Data Shortage Context

Injection of CO2 in geological formations is widely recognized as a promising technology within the set of strategies to be developed to reduce the concentration of atmospheric CO2. The management of long-term safety related with Geological Storage of CO2 (CGS) should be an iterative and interactive on-going improvement process throughout the life of the project. This process, through application of appropriate methodologies, should establish a robust and reliable framework for identifying, assessing and managing each project phase. It plays a key role in both the definition and planning of CO2 injection strategies at any scale and in its operational, closure and post-closure stages.A key element to calculate the probability of leakage risk includes the interaction of the CO2 plume with potential flow paths or with risk elements. This requires obtaining the temporal evolution of the injected CO2 plume (dynamic probability). Sufficient understanding of the CO2 plume migration within the reservoir is essential to assess the risks of leakage for different injection scenarios. The stochastic simulation can be a valuable tool to achieve a sufficient understanding of the underlying mechanisms that control the behaviour of a system. However, it is not uncommon that using probabilistic modelization to make predictions of future behaviour of a system (predictive modelization) turns out to be a complex process. The CO2 plume evolution and structural and hydrodynamic trapping mechanisms are key elements in the safety of a site. These are determined by the number of gravity, Γ, a dimensionless parameter that measures the ratio between buoyancy and viscous forces, and which is defined from both operating and reservoir parameters and, among others, is a function of the injection rate.The models used in this work are based on published studies on CO2 injection from a single well into a deep permeable aquifer saturated with saline fluid (saline aquifer). The type of solution obtained is a function of the relationship between buoyancy and viscous forces. According to the injection rate, in viscous forces domain cases it is possible to decouple the petrophysical variables of the system that determine the advance of the plume (porosity and permeability) depending on the shape ratio of the plume (rmin/rmax or ratio between the radii at the bottom and top of the CO2 plume).This is a methodology that makes sense for applying it to the initial stages of characterization of potential CO2 geological storage sites in situations of shortages of data, which it is a common feature of deep saline aquifers. Hontomín site intends to be a demo site for CO2 injection in carbonate formations, these being the probable most promising CO2 geologic storage formation type in Spain. A basic characteristic of these sites is the lack of deep carbonate formations porosity and permeability data, critical variables especially in risk studies. This methodology has its scope in the injection phase for a preliminary characterization, before the start of a possible systematic characterization of the site prior to a potential industrial use. So, a study has been conducted to explore the possibility of using the perturbation of the system by the CO2 injection to get an upscaling of both porosity and permeability en grand of the storage formation from the in situ or laboratory characterization phases through stochastic modelling of the CO2 plume and the appropriate injection strategies within the range of viscous forces domain cases. This provides a reduction of the uncertainties in the calculation and adjustment of dynamic probabilities of both the plume advance and the pressure increase due to the injection of CO2. As a whole it will result in an improvement in the storage safety assessment

Rate Dependency in Steady-State Upscaling

Steady-state upscaling of relative permeability is studied for a range of reservoir models. Both rate-dependent upscaling and upscaling in the capillary and viscous limits are considered. In particular, we study fluvial depositional systems, which represent a large and important class of reservoirs. Numerical examples show that steady-state upscaling is rate dependent, in accordance with previous work. In this respect we introduce a scale-dependent capillary number to estimate the balance between viscous and capillary forces. The difference between the limit solutions can be large, and we show that the intermediate flow rates can span several orders of magnitude. This substantiate the need for rate-dependent steady-state upscaling in a range of flow scenarios. We demonstrate that steady-state upscaling converges from the capillary to the viscous limit solution as the flow rate increases, and we identify a simple synthetic model where the convergence fails to be monotone. Two different sets of boundary conditions were tested, but had only minor effects on the presented reservoir models. Finally, we demonstrate the applicability of steady-state upscaling by performing dynamic flow simulation at the reservoir scale, both on fine-scaled and on upscaled models. The considered model is viscous dominated for realistic flow rates, and the simulation results indicate that viscous limit upscaling is appropriate.

Upscaling of Relative Permeability Using Pseudo Functions

Approximately all of the petroleum reservoirs are heterogeneous, and this heterogeneity exists on all levels from pores to simulation models. Since reservoir data are available on different scales and each property does not measure at the individual level, scale-up must be used for acquiring properties of coarse grid models. One of the most important reservoir properties in multiphase upscaling is relative permeability. Pseudo functions are the main methods for upscaling of relative permeability. Kyte and Berry and transmissibility weighted pseudos are two kinds of dynamic pseudo functions. The Kyte and Berry method is based on Darcy's law and the transmissibility weighted pseudos concentrate on saturation effects rather than pressure effects and uses a transmissibility weighted average for calculation of pseudo relative permeabilities. In this work, the effects of directional inter-block pseudos and well pseudos were first investigated. Then the results of coarse grid simulation with directional transmissibility weighted pseudos and Kyte and Berry pseudos were compared with the reference fine grid results.

The Impact of Reservoir Properties on Pseudo Functions: Upscaling of Relative Permeability

Relative permeability is the most challenging parameter during the scale-up process. Dynamic pseudoization approaches are the best methods for upscaling of relative permeability. However, dynamic pseudo functions are dependent to some reservoir properties. In this study, the effects of absolute permeability, PVT properties, vertical to horizontal permeability ratio, and reservoir dip angle on three dynamic pseudo functions of Kyte and Berry, Stone, and transmissibility weight were investigated. Different reservoir properties on a 2-D cross-sectional heterogeneous model were studied. Between the properties were studied, the ratio of vertical to horizontal permeability had the most pronounced impact on all dynamic pseudo functions. Dip angle also had an intensive effect on Stone pseudos.

From characterisation of pore-structures to simulations of pore-scale fluid flow and the upscaling of permeability using microtomography: A case study of heterogeneous carbonates

We propose a workflow to provide detailed characterisation of microstructures, simulations of permeability at micro-scale, and to analyse the upscaling of permeability. The workflow is fully tested using two very different microtomographic datasets of carbonate samples with strong heterogeneity. The characterisation of microstructures includes not only routine parameters but also anisotropy of the pore-structure. The critical pore diameter is also obtained through morphological implementations. The method of stochastic analysis of extended local porosity theory is used to determine the sizes of representative volume elements (RVE). We demonstrate criteria for determining the size of the RVE and show a sample that satisfies the criterion. We also discuss a sample that does not suffice the RVE criterion, because of the strong anisotropy. Permeabilities are computed using Lattice-Boltzmann (LB) simulations on the RVE and compared with laboratory measurements. Techniques and procedures are used to extract scaling parameters for both of the samples including: 1) percolation threshold — by using a shrinking/expanding algorithm; 2) crossover length — by analysing the mass density; 3) the critical exponent of correlation length — by using the finite-size scaling scheme; and 4) the critical exponent of permeability — by running LB simulations on a series of derivative models close to the percolation threshold. Our results of critical exponents are different from the previous studies and the mass density distributions are irregular. This pilot study provides new information on the relationships between microstructures and permeability of natural rocks with complex microstructures. The study also reveals the scaling parameters. Our results clearly put into question whether natural rocks can be idealised by classical theoretical solutions. A robust workflow for embracing a computational approach of microstructures may provide a solution.

Novel permeability upscaling method using Fast Marching Method

Despite computational advances, geo-cellular models are routinely upscaled for reservoir simulation purposes. Geo-cellular models typically incorporate small scale variations obtained from static data; whereas, simulation models capture dynamic data obtained from production of the field. The process of reducing the number of grid blocks in the geological model so that the simulation model can be run efficiently is called the process of upscaling. Upscaling requires combining the small grid blocks from geological model to make a larger grid block, as well as assigning reservoir properties on the coarse scale. Among the physical properties that need to be assigned, the assignment of permeability is the most challenging. Unlike porosity (or saturation), permeability is a dynamic property and capturing the fine scale dynamic displacement requires a non-linear upscaling of fine scale permeability values.The two types of methods used for permeability upscaling can be broadly categorized as static upscaling and dynamic upscaling. Static upscaling methods average fine scale values to calculate an upscaled value. These methods are efficient but may not capture the dynamic behavior. The dynamic upscaling methods are computationally expensive and may be dependent on boundary conditions. In this paper, we propose a new dynamic method for areal upscaling based on the fast marching algorithm. The Fast Marching Method (FMM) accurately captures the propagating pressure front as a function of time. We define the objective function as the difference in the propagation time between fine scale and coarse scale models. By minimizing the objective function, we calculate the permeability of the upscaled model.The Fast Marching Method is an extremely efficient method for calculating the pressure front propagation time based on reservoir properties. This method is based on solving the Eikonal equation using an upwind finite difference approximation. The advantage of this method is that, without running any flow simulation, we can calculate the pressure front location (radius of investigation) as a function of time. In this paper, using 2D and 3D models, we demonstrate that the calculated effective permeability using the new method can reproduce the dynamic behavior of the fine scale model.