Parametrisation and Use of a Predictive DFN Model for a High-Energy NCA/Gr-SiOx Battery

We demonstrate the predictive power of a parametrised Doyle-Fuller-Newman (DFN) model of a commercial cylindrical (21700) lithium-ion cell with NCA/Gr-SiOx chemistry. Model parameters result from the deconstruction of a fresh commercial cell to determine/confirm chemistry and microstructure, and also from electrochemical experiments with half-cells built from electrode samples. The simulations predict voltage proles for (i) galvanostatic discharge and (ii) drive-cycles. Predicted voltage responses deviate from measured ones by <1% throughout at least 95% of a full galvanostatic discharge, whilst the drive cycle discharge is matched to a 1-3% error throughout. All simulations are performed using the online computational tool DandeLiion, which rapidly solves the DFN model using only modest computational resource. The DFN results are used to quantify the irreversible energy losses occurring in the cell and deduce their location. In addition to demonstrating the predictive power of a properly validated DFN model, this work provides a novel simplifed parametrisation work that can be used to accurately calibrate an electrochemical model of a cell.

On the Determination of Coordination Numbers of Coupled DEM-DFN Model for Modeling Fractured Rocks

Natural fractured rocks usually contain background granular media and multi-scale fractures. The coordination number is a crucial factor to characterize the connection of microstructural elements. The determination of coordination numbers for modeling fractured rocks is essential to interpret the distribution of cracks related to micromechanical properties. We have built a consistent workflow of discrete element models (DEMs) coupled with discrete fracture networks (DFNs). This DEM-DFN model could provide a simple formulation for high calculation efficiency to model a more realistic and detailed description of fracture system. A series of numerical experiments are set up, aiming to correlate window radius, particle size, and crack length, which will benefit the window selection for measuring coordination numbers based on the crack characteristics. The coordination number determined in the DEM-DFN modeling can be used to identify crack patterns in the spatial distribution.

Understanding rapid charge and discharge in nano-structured lithium iron phosphate cathodes

A Doyle–Fuller–Newman (DFN) model for the charge and discharge of nano-structured lithium iron phosphate (LFP) cathodes is formulated on the basis that lithium transport within the nanoscale LFP electrode particles is much faster than cell discharge, and is therefore not rate limiting. We present some numerical solutions to the model and show that for relevant parameter values, and a variety of C-rates, it is possible for sharp discharge fronts to form and intrude into the electrode from its outer edge(s). These discharge fronts separate regions of fully utilised LFP electrode particles from those that are not. Motivated by this observation an asymptotic solution to the model is sought. The results of the asymptotic analysis of the DFN model lead to a reduced order model, which we term the reaction front model (or RFM). Favourable agreement is shown between solutions to the RFM and the full DFN model in appropriate parameter regimes. The RFM is significantly cheaper to solve than the DFN model, and therefore has the potential to be used in scenarios where computational costs are prohibitive, e.g. in optimisation and parameter estimation problems or in engineering control systems.

Developing a new algorithm for numerical modeling of discrete fracture network (DFN) for anisotropic rock and percolation properties

The role of natural fractures in future reservoir performance is prominent. The fractured porous media is composed of an interconnected network of fractures and blocks of the porous medium where fractures occur in various scales and have a strong influence either when most of the flow is concentrated and them or when they act as barriers. A general numerical model for discrete fracture networks (DFN) is usually employed to handle the observed wide variety of fracture properties and the lack of direct fracture visualization. These models generally use fracture properties’ stochastic distribution based on sparse and seismic data without any physical model constraint. Alternatively, a DFN model includes usual numerical geomechanical approaches like boundary element and finite element. But here, a geostatistical methodology has been used to generate a DFN model. In this paper, an alternative modeling technique is employed to create the realization of an anisotropic fractured rock using simulated annealing (SA) optimization algorithm. There is a notable positive correlation between fracture length and position. There are three principal subjects in a study of fractured rocks. Firstly, the network’s connectivity, secondly, fluid flows through the system, and thirdly, dispersion. Here, connectivity of generated networks is considered. Continuum percolation is the mathematical model to study the geometry of connected components in a random subset of space. Different random realizations from the S.A. algorithm in four different sizes of L = 100, 150, 200, 250 at post-threshold condition are used as disordered media in percolation theory to compute percolation properties using Monte Carlo simulation. The percolation threshold (critical fracture density) and two crucial scaling exponents (β and υ) that dictate the model’s connectivity behavior are estimated to over 200 realizations.

Relationship between the representative element volume and discontinuity parameters

We introduce an application of the discrete fracture network (DFN) model and 3D persistence to study the relationship between the representative element volume (REV) size and discontinuity information. To avoid the influence of heterogeneity on the distribution of discontinuities, the dam abutment rock mass of the Songta hydropower station is divided into eight statistically homogeneous domains based on the discontinuity orientation and trace length. An optimum DFN model is established for each homogeneous domain. Cubes of different sizes are extracted from the centre of the corresponding DFN model. Based on the discontinuity projection method, the 3D persistence values within the DFN model and each cube are calculated separately. The relative error of persistence for each cube and the DFN model are used to evaluate the size effect and to identify the REV size. Subsequently, the relationship between the determined REV size and the corresponding discontinuity information is systematically researched. Our results show that the discontinuity diameter, the volume density and the Fisher constant have separate linear relationships with the REV size. We present the empirical formulas for estimating the REV size according to the discontinuity diameter, the volume density and the Fisher constant.

INVESTIGATIONS ON REPRESENTATIVE ELEMENTARY VOLUME AND DIRECTIONAL PERMEABILITY OF FRACTAL-BASED FRACTURE NETWORKS USING POLYGON SUB-MODELS

Since the directional permeability of fractured rock masses is significantly dependent on the geometric properties of fractures, in this work, a numerical study was performed to analyze the relationships between them, in which fracture length follows a fractal distribution. A method to estimate the representative elementary volume (REV) size and directional permeability ([Formula: see text] by extracting regular polygon sub-models with different orientation angles ([Formula: see text] and side lengths ([Formula: see text] from an original discrete fracture network (DFN) model was developed. The results show that the fracture number has a power law relationship with the fracture length and the evolution of the exponent agrees well with that reported in previous studies, which confirms the reliability of the proposed fractal length distribution and stochastically generated DFN models. The [Formula: see text] varies significantly due to the influence of random numbers utilized to generate fracture location, orientation and length when [Formula: see text] is small. When [Formula: see text] exceeds some certain values, [Formula: see text] holds a constant value despite of [Formula: see text], in which the model scale is regarded as the REV size and the corresponding area of DFN model is represented by [Formula: see text] (in 2D). The directional permeability contours for DFN models plotted in the polar coordinate system approximate to circles when the model size is greater than the REV size. The [Formula: see text] decreases with the increment of fractal dimension of fracture length distribution ([Formula: see text]. However, the decreasing rate of [Formula: see text] (79.5%) when [Formula: see text] increases from 1.4 to 1.5 changes more significantly than that (34.8%) when [Formula: see text] increases from 1.5 to 1.6 for regular hexagon sub-models. This indicates that the small non-persistent fractures dominate the preferential flow paths; thereafter, the flow rate distribution becomes more homogeneous when [Formula: see text] exceeds a certain value (i.e. 1.5). A larger [Formula: see text] results in a denser fracture network and a stronger conductivity.

Construction of 3D Discrete Fracture Network Model using Structural and Hydrogeological Data

&lt;p&gt;The presence of fractures and discontinuities in the intact rock affects the hydraulic, thermal, chemical and mechanical behavior of the underground structures. Various techniques have been developed to provide information on the spatial distribution of these complex features. LIDAR, for instance, could provide a 2D fracture network model of the outcrop, Geophysical borehole logs such as OPTV and ATV can be used to investigate 1D geometrical data (i.e. dip and dip direction, aperture) of the intersected fractures, and seismic survey can mainly offer a large structure distribution of the deep structures. The ability to combine all the existing data collected from various resources and different scales to construct a 3D discrete fracture network (DFN) model of the rock mass allows to adequately represent the physical behavior of the interested subsurface structure.&lt;/p&gt;&lt;p&gt;In this study, an effort on the construction of such a 3D DFN model is carried out via combination of various structural and hydrogeological data collected in fractured crystalline rock. During the pre-characterization phase of the In-situ Stimulation and Circulation (ISC) experiment [Amann et al., 2018] at the Grimsel Test Site (GTS) in central Switzerland, a comprehensive characterization campaign was carried out to better understand the hydromechanical characteristics of the existing structures. The collected multiscale and multidisciplinary data such as OPTV, ATV, hydraulic packer testing and solute tracer tests [Jalali et al., 2018; Krietsch et al., 2018] are combined, analyzed and interpreted to form a combined stochastic and deterministic DFN model using the FracMan software [Golder Associates, 2017]. For further validation of the model, the results from in-situ hydraulic tests are used to compare the simulated and measured hydraulic responses, allowing to evaluate whether the simulated model could reasonably represent the characteristics of the fracture network in the ISC experiment.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;ul&gt;&lt;li&gt;Amann, F., Gischig, V., Evans, K., Doetsch, J., Jalali, M., Valley, B., Krietsch, H., Dutler, N., Villiger, L., Brixel, B., Klepikova, M., Kittil&amp;#228;, A., Madonna, C., Wiemer, S., Saar, M.O., Loew, S., Driesner, T., Maurer, H., Giardini, D., 2018. The seismo-hydromechanical behavior during deep geothermal reservoir stimulations: open questions tackled in a decameter-scale in situ stimulation experiment. Solid Earth 9, 115&amp;#8211;137.&lt;/li&gt; &lt;li&gt;Golder Associates, 2017. FracMan User Documentation.&amp;#160; Golder Associates Inc, Redmond WA.&lt;/li&gt; &lt;li&gt;Krietsch, H., Doetsch, J., Dutler, N., Jalali, M., Gischig, V., Loew, S., Amann, F., 2018. Comprehensive geological dataset describing a crystalline rock mass for hydraulic stimulation experiments. Scientific Data 5, 180269.&lt;/li&gt; &lt;li&gt;Jalali, M., Klepikova, M., Doetsch, J., Krietsch, H., Brixel, B., Dutler, N., Gischig, V., Amann, F., 2018. A Multi-Scale Approach to Identify and Characterize the Preferential Flow Paths of a Fractured Crystalline Rock. Presented at the 2&lt;sup&gt;nd&lt;/sup&gt; International Discrete Fracture Network Engineering Conference, American Rock Mechanics Association.&lt;/li&gt; &lt;/ul&gt;