scholarly journals Multi-Scale Microfluidics for Transport in Shale Fabric

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Bowen Ling ◽  
Hasan J. Khan ◽  
Jennifer L. Druhan ◽  
Ilenia Battiato
Keyword(s):  
Spatial Scales ◽  
Fracture Network ◽  
Breakthrough Curves ◽  
Fracture Aperture ◽  
Imaging Data ◽  
Fracture Networks ◽  
Multi Scale ◽  
Microfluidic Flow ◽  
Scaling Relationship ◽  
Fracture Apertures

We develop a microfluidic experimental platform to study solute transport in multi-scale fracture networks with a disparity of spatial scales ranging between two and five orders of magnitude. Using the experimental scaling relationship observed in Marcellus shales between fracture aperture and frequency, the microfluidic design of the fracture network spans all length scales from the micron (1 μ) to the dm (10 dm). This intentional `tyranny of scales’ in the design, a determining feature of shale fabric, introduces unique complexities during microchip fabrication, microfluidic flow-through experiments, imaging, data acquisition and interpretation. Here, we establish best practices to achieve a reliable experimental protocol, critical for reproducible studies involving multi-scale physical micromodels spanning from the Darcy- to the pore-scale (dm to μm). With this protocol, two fracture networks are created: a macrofracture network with fracture apertures between 5 and 500 μm and a microfracture network with fracture apertures between 1 and 500 μm. The latter includes the addition of 1 μm ‘microfractures’, at a bearing of 55°, to the backbone of the former. Comparative analysis of the breakthrough curves measured at corresponding locations along primary, secondary and tertiary fractures in both models allows one to assess the scale and the conditions at which microfractures may impact passive transport.

scholarly journals Evaluating Flow in Fractal-Fracture Networks: Effect of Variable Aperture

2021 ◽  
Vol 56 ◽  
pp. 117-128
Author(s):  
Ajay K. Sahu ◽  
Ankur Roy
Keyword(s):  
Practical Interest ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Aperture ◽  
High Porosity ◽  
Fracture Networks ◽  
Building Models ◽  
Variable Aperture ◽  
Almost All ◽  
Fractal Fracture

Abstract. While fractal models are often employed for describing the geometry of fracture networks, a constant aperture is mostly assigned to all the fractures when such models are flow simulated. In nature however, almost all fracture networks exhibit variable aperture values and it is this fracture aperture that controls the conductivity of individual fractures as described by the well-known cubic-law. It would therefore be of practical interest to investigate flow patterns in a fractal-fracture network where the apertures scale in accordance to their position in the hierarchy of the fractal. A set of synthetic fractal-fracture networks and two well-connected natural fracture maps that belong to the same fractal system are used for this purpose. A set of dominant sub-networks are generated from a given fractal-fracture map by systematically removing the smaller fracture segments with narrow apertures. The connectivity values of the fractal-fracture networks and their respective dominant sub-networks are then computed. Although a large number of fractures with smaller aperture are eliminated, no significant decrease is seen in the connectivity of the dominant sub-networks. A streamline simulator based on Darcy's law is used for flow simulating the fracture networks, which are conceptualized as two-dimensional fracture continuum models. A single high porosity value is assigned to all the fractures. The permeability assigned to fractures within the continuum model is based on their aperture values and there is nearly no matrix porosity and permeability. The recovery profiles and time-of-flight plots for each network and its dominant sub-networks at different time steps are compared. The results from both the synthetic networks and the natural data show that there is no significant decrease in fluid recovery in the dominant sub-networks compared to their respective parent fractal-fracture networks. It may therefore be concluded that in the case of such hierarchical fractal-fracture systems with scaled aperture, the smaller fractures do not significantly contribute to connectivity or fluid flow. In terms of decision making, this result will aid geoscientists and engineers in identifying only those fractures that ultimately matter in evaluating the flow recovery, thus building models that are computationally less expensive while being geologically realistic.

Influence of Aperture Distribution on Flow in Fractal-Fracture Networks

2021 ◽  
Author(s):  
Ajay Kumar Sahu ◽  
Ankur Roy
Keyword(s):  
Practical Interest ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Fracture Systems ◽  
Fractal System ◽  
Porosity And Permeability ◽  
Aperture Distribution ◽  
Fractal Fracture

<p>While fractal models are often employed for describing the geometry of fracture networks, a constant aperture is mostly assigned to all the fractures when such models are flow simulated. While network geometry controls connectivity, it is fracture aperture that controls the conductivity of individual fractures as described by the well-known cubic-law. It would therefore be of practical interest to investigate flow patterns in a fractal-fracture network where the apertures also scale as a power-law in accordance to their position in the hierarchy of the fractal. A set of synthetic fractal-fracture networks and two well-connected natural fracture maps that belong to the same fractal system are used for this purpose. The former, with connectivity above the percolation threshold, are generated by spatially locating the fractured and un-fractured blocks in a deterministic and random manner. A set of sub-networks are generated from a given fractal-fracture map by systematically removing the smaller fracture segments. A streamline simulator based on Darcy's law is used for flow simulating the fracture networks, which are conceptualized as two-dimensional fracture continuum models. Porosity and permeability are assigned to a fracture within the continuum model based on its aperture value and there is nearly no matrix porosity or permeability. The recovery profiles and time-of-flight values for each network and its dominant sub-networks at different time steps are compared.</p><p>The results from both the synthetic networks and the natural maps show that there is no significant decrease in recovery in the dominant sub-networks of a given fractal-fracture network. It may therefore be concluded that in the case of such hierarchical fractal-fracture systems with scaled aperture, the smaller fractures do not significantly contribute to the fluid flow.</p><p><strong>Key-words: </strong>Fractal-fracture; Connectivity; Aperture; Dominant Sub-networks; Streamline Simulator; Recovery</p>

U-Th Dating of Syntectonic Calcite Veins Reveals the Dynamic Nature of Fracture Cementation and Healing in Faults

2020 ◽  
Author(s):  
Randolph Williams ◽  
Peter Mozley ◽  
Warren Sharp ◽  
Laurel Goodwin
Keyword(s):  
Direct Analysis ◽  
Fracture Network ◽  
Reservoir Rock ◽  
Fracture Networks ◽  
Heterogeneous Distribution ◽  
Strength Recovery ◽  
Calcite Veins ◽  
Length Width ◽  
Function Correlation ◽  
Fracture Apertures

<p>Fracture cementation is an important control on the recovery of prefailure levels of permeability and strength in faults and reservoir rock. The timescales of this process, however, are almost entirely unknown from direct analysis of the rock record. We report U‐Th dating results that quantify rates of fracture cementation in syntectonic calcite veins from the Loma Blanca fault, New Mexico, USA. Measured cementation rates vary from ~0.05 to 0.80 mm/ka and exhibit a power function correlation with minimum fracture apertures. We argue that this correlation is the result of crystal growth in a transport‐limited system, where cementation rates were proportional to rates of fluid flow in individual fractures. We argue that such transport‐limited growth necessarily leads to a heterogeneous distribution of cementation rates as fluids migrate through fracture networks of variable and changing aperture. For this reason, individual fractures are not expected to seal at monotonic rates through time but could instead experience order‐of‐magnitude increases or decreases in sealing rate depending on their geometric properties (e.g., aperture, length/width, and orientation) and position within a continually evolving fracture network. We further argue that such transport‐limited, flux‐dependent cementation necessarily leads to a heterogeneous distribution of permeability and strength recovery as fluids migrate through fault‐zone fracture networks. These heterogeneities may influence rupture propagations pathways and the continual development of fault‐zone architecture/complexity.</p>

Fracture stratigraphy, fault architecture and DFN modeling of both diffuse and localized fracture networks

2020 ◽  
Author(s):  
Fabrizio Agosta
Keyword(s):  
Oil And Gas ◽  
Damage Zone ◽  
Fracture Network ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Present Contribution ◽  
Fracture Porosity ◽  
Fractured Limestone ◽  
And Migration ◽  
Fault Architecture

<p>Quantification of the geometry, distribution, and dimension of fracture networks is key to fully understand the petrophysical properties of outcrop-to-reservoir scales rock volumes. On these regards, Discrete Fracture Network (DFN) modeling is a very useful tool to compute the values of fracture porosity and equivalent permeability of geo-cellular volumes populated with stochastic or deterministic fracture networks. Independently of their size and cell dimensions, the single geocelullar volumes are populated by inputting the following parameters for each fracture set: (i) length; (ii) aspect ratio; (iii) mechanical and hydraulic apertures; (iv) fracture intensity, and (v) attitude. A sensitivity analysis is always carried out in order to test the seeding procedure of the employed software, and to check the validity of the fracture aperture values employed as input data. The latter values, in fact, are the most critical to assess from outcrop and laboratory analyses. The present contribution focuses on the results of recent works performed on the fractured limestone rocks of the Apulian Platform, which are widely exposed along the Italian peninsula. Outcrops are first introduced in order to define the fracture stratigraphy and fault architecture of the Meso-Cenozoic limestone rocks. Then, the criteria behind the construction of DFN models are illustrated. Methods employed for the build of individual fracture units and single fault damage zone domains are illustrated. Finally, the computed values of fracture porosity and equivalent horizontal permeability obtained for multiple DFN models are presented. Discussion of the data focuses on the fluid accumulation and migration properties of the fractured limestone rocks by considering their amount of exhumation experienced during Plio-Quaternary times. Results of DFN modeling could be helpful to optimize the appraisal and development operations of hydrocarbon reservoirs, and minimize the pollution of freshwater aquifer. In fact, the Apulian carbonates host in the underground significant amounts of freshwater of the Mediterranean Region, and the largest oil and gas reserves of continental Europe. Furthermore, the results could shed new lights into the role exerted by faults and fractures on subsurface CO<sub>2</sub> storage in depleted carbonate reservoirs, a practice that envisioned to decrease the greenhouse gas concentration in the atmosphere in the next future.</p>

Modeling Coupled Fracture-Matrix Fluid Flow in Geomechanically Simulated Fracture Networks

2005 ◽  
Vol 8 (04) ◽  
pp. 300-309 ◽  
Author(s):  
Zeno G. Philip ◽  
James W. Jennings ◽  
Jon E. Olson ◽  
Stephen E. Laubach ◽  
Jon Holder
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Flow Simulation ◽  
Fracture Network ◽  
Fracture Aperture ◽  
Grid Cells ◽  
Fracture Networks ◽  
Fracture Permeability ◽  
Fracture Length ◽  
Fracture Patterns

Summary In conventional reservoir simulations, gridblock permeabilities are frequently assigned values larger than those observed in core measurements to obtain reasonable history matches. Even then, accuracy with regard to some aspects of the performance such as water or gas cuts, breakthrough times, and sweep efficiencies may be inadequate. In some cases, this could be caused by the presence of substantial flow through natural fractures unaccounted for in the simulation. In this paper, we present a numerical investigation into the effects of coupled fracture-matrix fluid flow on equivalent permeability. A fracture-mechanics-based crack-growth simulator, rather than a purely stochastic method, was used to generate fracture networks with realistic clustering, spacing, and fracture lengths dependent on Young's modulus, the subcritical crack index, the bed thickness, and the tectonic strain. Coupled fracture-matrix fluid-flow simulations of the resulting fracture patterns were performed with a finite-difference simulator to obtain equivalent permeabilities that can be used in a coarse-scale flow simulation. The effects of diagenetic cements completely filling smaller aperture fractures and partially filling larger aperture fractures were also studied. Fractures were represented in finite-difference simulations both explicitly as grid cells and implicitly using nonneighbor connections (NNCs) between grid cells. The results indicate that even though fracture permeability is highly sensitive to fracture aperture, the computed equivalent permeabilities are more sensitive to fracture patterns and connectivity. Introduction High-permeability fracture networks in a matrix system can create high-conductivity channels for the flow of fluids through a reservoir, producing larger flow rates and, therefore, larger apparent permeabilities. The presence of fractures can also cause early breakthrough of the displacing fluid and lead to poorer sweep efficiencies in displacement processes. A better understanding of reservoir performance in such cases may be obtained by including the details of the fluid flow in fractures in a coupled fracture-matrix reservoir flow model. It is very difficult to directly measure interwell fracture-network geometry in sufficient detail to model its effect on reservoir behavior. Thus, most modeling approaches have been statistical, using data from outcrop and wellbore observations to determine distributions of fracture attributes such as fracture length, spacing, and aperture to randomly populate a field. In this paper, we use a mechanistic approach to generate the fracture patterns. Attributes of the fracture network depend on the applied boundary conditions and material properties.

Estimation of Fracture Porosity of Naturally Fractured Reservoirs With No Matrix Porosity Using Fractal Discrete Fracture Networks

2009 ◽  
Vol 12 (02) ◽  
pp. 232-242 ◽  
Author(s):  
Tae H. Kim ◽  
David S. Schechter
Keyword(s):  
Fractured Reservoirs ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Fracture Porosity ◽  
Fracture Systems ◽  
Discrete Fracture ◽  
Naturally Fractured ◽  
Matrix Porosity

Summary Matrix porosity is relatively easy to measure and estimate compared to fracture porosity. On the other hand, fracture porosity is highly heterogeneous and very difficult to measure and estimate. When matrix porosity of naturally fractured reservoirs (NFRs) is negligible, it is very important to know fracture porosity to evaluate reservoir performance. Because fracture porosity is highly uncertain, fractal discrete fracture network (FDFN) generation codes were developed to estimate fracture porosity. To reflect scale-dependent characteristics of fracture networks, fractal theories are adopted. FDFN modeling technique enables the systematic use of data obtained from image log and core analysis for estimating fracture porosity. As a result, each fracture has its own fracture aperture distribution, so that generated FDFN are similar to actual fracture systems. The results of this research will contribute to properly evaluating the fracture porosity of NFR where matrix porosity is negligible.

scholarly journals Fracture Reconstruction and Analysis of Low Permeability Carbonates using x-ray Tomography for Comparison with Outcrop Data

2018 ◽  
Author(s):  
Stephanie G. Zihms ◽  
Helen Lewis ◽  
Tiago Siqueira de Miranda ◽  
Stephen A. Hall ◽  
James M. Somerville
Keyword(s):  
Fracture Network ◽  
Carbonate Reservoir ◽  
Low Permeability ◽  
Fracture Networks ◽  
Thin Sections ◽  
X Ray ◽  
Subsurface Structures ◽  
Key Characteristics ◽  
Induced Fractures ◽  
Fracture Apertures

Abstract: Comparing outcrop data to laboratory results is important to verify and validate experiments of analogue and reservoir materials especially regarding conditions for deformation experiments. This is important better understand highly complex carbonate reservoir strata and their response to changes in subsurface conditions, reducing subsurface uncertainty. This study develops methods to allow for a more straightforward comparison of outcrop data (m-scale) with experimentally created fracture arrays developed in cylindrical samples (cm-scale). The main objective is to assess usefulness of experimentally-produced fracture networks as analogues for subsurface structures, typically at the meter and above scale by developing new techniques to use the lab deformation. It analyses key characteristics of laboratory-induced fracture networks by adapting scanline methods to use with x-ray tomography (XRT) images to allow for comparison with outcrop and field data. To test and verify these new methods two low permeability carbonate samples were used for deformation testing and analysis. Applying the different scanline methods we show that they can be used to analyse lab induced fractures (mm to cm-scale) identified in XRT images for comparison with outcrop data (m-scale). In addition, these methods also allow for quantification of fracture network attributes e.g. fracture spacing, fracture apertures, orientation. This new data bridges the gap between micro-scanlines using thin sections and outcrop scanlines.

scholarly journals Complex community responses underpin biodiversity change following invasion

2021 ◽  
Author(s):  
Alessandra R. Kortz ◽  
Anne E. Magurran
Keyword(s):  
Invasive Species ◽  
Species Richness ◽  
Spatial Scales ◽  
Species Abundance ◽  
Ecological Systems ◽  
Multi Scale ◽  
Mechanistic Approach ◽  
Α Diversity ◽  
Biodiversity Change ◽  
Insight Into

AbstractHow do invasive species change native biodiversity? One reason why this long-standing question remains challenging to answer could be because the main focus of the invasion literature has been on shifts in species richness (a measure of α-diversity). As the underlying components of community structure—intraspecific aggregation, interspecific density and the species abundance distribution (SAD)—are potentially impacted in different ways during invasion, trends in species richness provide only limited insight into the mechanisms leading to biodiversity change. In addition, these impacts can be manifested in distinct ways at different spatial scales. Here we take advantage of the new Measurement of Biodiversity (MoB) framework to reanalyse data collected in an invasion front in the Brazilian Cerrado biodiversity hotspot. We show that, by using the MoB multi-scale approach, we are able to link reductions in species richness in invaded sites to restructuring in the SAD. This restructuring takes the form of lower evenness in sites invaded by pines relative to sites without pines. Shifts in aggregation also occur. There is a clear signature of spatial scale in biodiversity change linked to the presence of an invasive species. These results demonstrate how the MoB approach can play an important role in helping invasion ecologists, field biologists and conservation managers move towards a more mechanistic approach to detecting and interpreting changes in ecological systems following invasion.

scholarly journals Scale-dependent intrinsic entropies of complex time series

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150204 ◽  
Author(s):  
Jia-Rong Yeh ◽  
Chung-Kang Peng ◽  
Norden E. Huang
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Spatial Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Complex Time ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations

2013 ◽  
Author(s):  
Hannes Hofmann ◽  
Tayfun Babadagli ◽  
Günter Zimmermann
Keyword(s):  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Network Development ◽  
Complex Fracture ◽  
Fracture Patterns ◽  
Fracture Systems ◽  
Fracture Development ◽  
Complex Fracture Network ◽  
Treatment Designs

The creation of large complex fracture networks by hydraulic fracturing is imperative for enhanced oil recovery from tight sand or shale reservoirs, tight gas extraction, and Hot-Dry-Rock (HDR) geothermal systems to improve the contact area to the rock matrix. Although conventional fracturing treatments may result in bi-wing fractures, there is evidence by microseismic mapping that fracture networks can develop in many unconventional reservoirs, especially when natural fracture systems are present and the differences between the principle stresses are low. However, not much insight is gained about fracture development as well as fluid and proppant transport in naturally fractured tight formations. In order to clarify the relationship between rock and treatment parameters, and resulting fracture properties, numerical simulations were performed using a commercial Discrete Fracture Network (DFN) simulator. A comprehensive sensitivity analysis is presented to identify typical fracture network patterns resulting from massive water fracturing treatments in different geological conditions. It is shown how the treatment parameters influence the fracture development and what type of fracture patterns may result from different treatment designs. The focus of this study is on complex fracture network development in different natural fracture systems. Additionally, the applicability of the DFN simulator for modeling shale gas stimulation and HDR stimulation is critically discussed. The approach stated above gives an insight into the relationships between rock properties (specifically matrix properties and characteristics of natural fracture systems) and the properties of developed fracture networks. Various simulated scenarios show typical conditions under which different complex fracture patterns can develop and prescribe efficient treatment designs to generate these fracture systems. Hydraulic stimulation is essential for the production of oil, gas, or heat from ultratight formations like shales and basement rocks (mainly granite). If natural fracture systems are present, the fracturing process becomes more complex to simulate. Our simulation results reveal valuable information about main parameters influencing fracture network properties, major factors leading to complex fracture network development, and differences between HDR and shale gas/oil shale stimulations.

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