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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Prediction of Silicon Content in a Blast Furnace via Machine Learning: A Comprehensive Processing and Modeling Pipeline

Silicon content plays an important role in determining the operational efficiency of blast furnaces (BFs) and their downstream processes in integrated steelmaking; however, existing sampling methods and first-principles models are somewhat limited in their capability and flexibility. Current data-based prediction models primarily rely on a limited set of manually selected furnace parameters. Additionally, different BFs present a diverse set of operating parameters and state variables that are known to directly influence the hot metal’s silicon content, such as fuel injection, blast temperature, and raw material charge composition, among other process variables that have their own impacts. The expansiveness of the parameter set adds complexity to parameter selection and processing. This highlights the need for a comprehensive methodology to integrate and select from all relevant parameters for accurate silicon content prediction. Providing accurate silicon content predictions would enable operators to adjust furnace conditions dynamically, improving safety and reducing economic risk. To address these issues, a two-stage approach is proposed. First, a generalized data processing scheme is proposed to accommodate diverse furnace parameters. Second, a robust modeling pipeline is used to establish a machine learning (ML) model capable of predicting hot metal silicon content with reasonable accuracy. The method employed herein predicted the average Si content of the upcoming furnace cast with an accuracy of 91% among 200 target predictions for a specific furnace provisioned by the XGBoost model. This prediction is achieved using only the past shift’s operating conditions, which should be available in real time. This performance provides a strong baseline for the modeling approach with potential for further improvement through provision of real-time features.

Chemistry↗
DOE OSTI2022

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of neural networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stoichiometrically coupled carbon and nitrogen cycling in the MIcrobial-MIneral Carbon Stabilization model version 1.0 (MIMICS-CN v1.0)

Explicit consideration of microbial physiology in soil biogeochemical models that represent coupled carbon–nitrogen dynamics presents opportunities to deepen understanding of ecosystem responses to environmental change. The MIcrobial-MIneral Carbon Stabilization (MIMICS) model explicitly represents microbial physiology and physicochemical stabilization of soil carbon (C) on regional and global scales. Here we present a new version of MIMICS with coupled C and nitrogen (N) cycling through litter, microbial, and soil organic matter (SOM) pools. The model was parameterized and validated against C and N data from the Long-Term Inter-site Decomposition Experiment Team (LIDET; six litter types, 10 years of observations, and 13 sites across North America). The model simulates C and N losses from litterbags in the LIDET study with reasonable accuracy (C: R 2 =0.63; N: R 2 =0.29), which is comparable with simulations from the DAYCENT model that implicitly represents microbial activity (C: R 2 =0.67; N: R 2 =0.30). Subsequently, we evaluated equilibrium values of stocks (total soil C and N, microbial biomass C and N, inorganic N) and microbial process rates (soil heterotrophic respiration, N mineralization) simulated by MIMICS-CN across the 13 simulated LIDET sites against published observations from other continent-wide datasets. We found that MIMICS-CN produces equilibrium values in line with measured values, showing that the model generates plausible estimates of ecosystem soil biogeochemical dynamics across continental-scale gradients. MIMICS-CN provides a platform for coupling C and N projections in a microbially explicit model, but experiments still need to identify the physiological and stoichiometric characteristics of soil microbes, especially under environmental change scenarios.

58 GEOSCIENCES↗
DOE OSTI2022

Representative-cell-based Modeling of HTTF in SAM

Although the current nuclear power market is primarily occupied by the light water reactors (LWRs), the TRISO-fueled helium-cooled graphite-moderated high temperature gas reactors (HTGRs) are drawing growing attention as the nuclear power industry marches towards more advanced systems. Compared to that of conventional LWRs, the thermal hydraulics of HTGR cores show extra complexity from their multi-scale heat transfer mechanisms with varying importance during different operation modes or transient stages. The modeling of HTGR cores for the system analysis purpose therefore faces the challenge of reaching reasonable fidelity and accuracy while maintaining sufficient simplicity. Previous development and validation efforts have demonstrated that a “2-D ring model” with reasonable performance can be implemented in the System Analysis Module (SAM) for prismatic HTGR cores. In the current project, an alternative modeling methodology based on “representative cells” is proposed for the typical prismatic core of HTGRs. Different from the previous ring model approach, the proposed methodology first separately models and then combines the small- and large-scale thermal conductions, by connecting representative local heat transfer units (cells) with effective core- wise thermal resistance. A modeling practice for an integral high-temperature test facility (HTTF) elaborates the modeling details. Steady-state validation of the resultant candidate model is performed against a higher-resolution benchmark from a 3D-1D coupled simulation, which shows satisfactory prediction with reasonably captured global parameters and well-represented temperature fields. A postulated pressurized conduction cooldown (PCC) is also simulated and analyzed, demonstrating the model’s capability of transient prediction with physically captured phenomena resolved in both small and large temporal and spatial scales. In general, the current work achieves a preliminary success in proposing a methodology using representative cells to model prismatic HTGR cores in SAM. Future efforts are envisioned with more validation activities and with potential modeling improvements to eventually achieve the high confidence on a high-fidelity robust modeling methodology with reasonable accuracy.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Predicting the evolution of biomass bulk density through feedstock preprocessing: Discrete element modeling, regression analysis, and pilot-scale validation

Bulk density is an important material property of biomass feedstocks, influencing handling, storage, transport costs, and conversion efficiency. In this study, predictive regression models for loose and tapped bulk densities of Alamo and Cave-in-Rock switchgrass are developed using a comprehensive dataset generated via calibrated bonded-sphere discrete element method (DEM) simulations. Here, a key contribution of this study is the use of a DEM-based approach, which correlates density with moisture content and particle size distribution parameters and enables analysis across a continuous particle size range, overcoming limitations of purely experimental data. For comparison, regression models are also developed using only experimental data from pilot-scale runs at the Biomass Feedstock National User Facility at Idaho National Laboratory. Validation against pilot-scale data showed reasonable prediction accuracy for both model types, particularly for smaller particle sizes (post-secondary grinding). While the experimental model showed slightly better performance matching the validation data in some cases, the DEM-based model benefits from a much larger dataset, reduced predictor multicollinearity, and continuous parameter coverage, highlighting the utility of validated simulation models for developing robust predictive tools for biomass preprocessing applications.

09 - BIOMASS FUELS↗
DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗
DOE OSTI2021

Particle track classification using quantum associative memory

Pattern recognition algorithms are commonly employed to simplify the challenging and necessary step of track reconstruction in sub-atomic physics experiments. Aiding in the discrimination of relevant interactions, pattern recognition seeks to accelerate track reconstruction by isolating signals of interest. In high collision rate experiments, such algorithms can be particularly crucial for determining whether to retain or discard information from a given interaction even before the data is transferred to tape. As data rates, detector resolution, noise, and inefficiencies increase, pattern recognition becomes more computationally challenging, motivating the development of higher efficiency algorithms and techniques. Quantum associative memory is an approach that seeks to exploits quantum mechanical phenomena to gain advantage in learning capacity, or the number of patterns that can be stored and accurately recalled. Here, we study quantum associative memory based on quantum annealing and apply it to the particle track classification. We focus on discrimination models based on Ising formulations of quantum associative memory model (QAMM) recall and quantum content-addressable memory (QCAM) recall. We characterize classification performance of these approaches as a function detector resolution, pattern library size, and detector inefficiencies, using the D-Wave 2000Q processor as a testbed. Discrimination criteria is set using both solution-state energy and classification labels embedded in solution states. We find that energy-based QAMM classification performs well in regimes of small pattern density and low detector inefficiency. In contrast, state-based QCAM achieves reasonably high accuracy recall for large pattern density and the greatest recall accuracy robustness to a variety of detector noise sources.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Propagating synthetic populations with dynamic Bayesian networks: a framework for long-horizon demographic forecasting

This study presents a dynamic demographic microsimulator using dynamic Bayesian networks to forecast long–term changes in household and individual life events. Leveraging longitudinal Panel Study of Income Dynamics (PSID) data, two networks for individuals and households were modeled to simulate transitions in employment, income, education, marriage, childbirth, leaving the parental home, home ownership, mortality, and household formation or dissolution. Across 1,000 simulation runs spanning 24 years, household–level outcomes remain highly accurate and individual–level predictions reasonable. Although accuracy naturally declines with projection horizon, performance remains promising at both levels. This study addresses a key limitation of existing population synthesis models, which typically generate only a single static snapshot of the population. In conclusion, by introducing a framework that propagates cross-sectional outputs into the future, the microsimulator enables the tracking of demographic evolution over time, enhances realism in population-based simulations, and supplies credible inputs to agent-based travel demand models.

Demographic modeling↗
DOE OSTI2021

pKPDB: a protein data bank extension database of p Ka and pI theoretical values

Abstract Summary pKa values of ionizable residues and isoelectric points of proteins provide valuable local and global insights about their structure and function. These properties can be estimated with reasonably good accuracy using Poisson–Boltzmann and Monte Carlo calculations at a considerable computational cost (from some minutes to several hours). pKPDB is a database of over 12 M theoretical pKa values calculated over 120k protein structures deposited in the Protein Data Bank. By providing precomputed pKa and pI values, users can retrieve results instantaneously for their protein(s) of interest while also saving countless hours and resources that would be spent on repeated calculations. Furthermore, there is an ever-growing imbalance between experimental pKa and pI values and the number of resolved structures. This database will complement the experimental and computational data already available and can also provide crucial information regarding buried residues that are under-represented in experimental measurements. Availability and implementation Gzipped csv files containing p Ka and isoelectric point values can be downloaded from https://pypka.org/pKPDB. To query a single PDB code please use the PypKa free server at https://pypka.org. The pKPDB source code can be found at https://github.com/mms-fcul/pKPDB. Supplementary information Supplementary data are available at Bioinformatics online.

Reis, Pedro B. P. S. (ORCID:0000000335636239)↗
DOE OSTI2022

Predicting the location of shear band initiation in a metallic glass

We report atomistic simulation results which indicate that the location of shear banding in a metallic glass (MG) can be ascertained with reasonably high accuracy solely from the undeformed static structure. Correlation is observed between the location of the initiation of shear bands in a simulated MG and the initial distribution of the density of fertile sites (DFS) for stress-driven shear transformations identified a priori based on a deep learning model devised in our recent work. In addition, we demonstrated that one can judge whether a glass is brittle or ductile solely based upon its initial DFS distribution. These validate that shear bands in MG arise from nonlinear instabilities and that the as-quenched glass structure contains inhomogeneities that influence these instabilities. In this study, we also reveal an important subtlety regarding the nondeterministic nature of athermal quasistatic shear simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A Modeling Toolkit for Comparing AC and DC Electrical Distribution Efficiency in Buildings

Recently, there has been considerable research interest in the potential for DC distribution systems in buildings instead of the traditional AC distribution systems. Due to the need for performing power conversions between DC and AC electricity, DC distribution may provide electrical efficiency advantages in some systems. To support comparative evaluations of AC-only, DC-only, and hybrid AC/DC distribution systems in buildings, a new modeling toolkit called the Building Electrical Efficiency Analysis Model (BEEAM) was developed and is described in this paper. To account for harmonics in currents or voltages arising from nonlinear devices, the toolkit implements harmonic power flow, along with nonlinear device behavioral descriptions derived from empirical measurements. This paper describes the framework, network equations, device representations, and an implementation of the toolkit in an open source software package, including a component library and graphical interface for creating circuits. Simulations of electrical behavior and device and system efficiencies using the toolkit are compared with experimental measurements of a small office environment in a variety of operating and load configurations. A detailed analysis of uncertainty estimation is also provided. Key findings were that a comparison of predicted versus measured efficiencies and power losses in the validation testbed using the initial toolkit implementation predicted device- and system-level efficiencies with reasonably good accuracy under both balanced and unbalanced AC scenarios. An uncertainty analysis also revealed that the maximum estimated error for system efficiency across all scenarios was 3%, and measured and modeled system efficiency agreed within the experimental uncertainty in approximately half of the scenarios. Based on the correspondence between simulation and measurement, the toolkit is proposed by the authors as a potentially useful tool for comparing efficiency in AC, DC, and hybrid AC/DC distribution systems in buildings.

DC distribution↗
DOE OSTI2022

Optical Imaging for Understanding of Thermal Barrier Coated Piston Engine Performance

Thermal barrier coatings (TBC) applied to pistons have been a recently renewed research topic in the field of internal combustion engines. Single cylinder testing of a conventional C15™ Tier 4 final pro-duction steel piston and a TBC coated piston showed that the Yttrium stabilized Zirconia (YSZ) TBC did not significantly alter engine performance, with the TBC piston having slower combustion rates and higher criteria emissions. For deeper understanding, research continued by studying 3D-piston sections optically in a constant pressure vessel using photodiodes, four high-speed cameras (natural luminosity, CH*, and OH*), and visualization of the flame from two orthogonal directions. Particle Im-aging Velocimetry (PIV) algorithms were adapted to perform Combustion Imaging Velocimetry (CIV) to aid in quantification of the observed visual combustion flow field differences. The optical work showed that the TBC piston flame development is slower, spatially different, with lower mixing energy for the TBC variant. Geometric profiles of engine pistons and optical vessel 3D-piston sections were measured using a Coordinate Measurement Machine (CMM), and surface roughness was measured with a stylus surface profilometer. CMM results showed that the TBC piston bowl had reasonable macroscopic accuracy, but the rim had a larger radius with less reentrancy. A discussion of the results and analyses in relation to future TBC effort and direction concludes the work.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Advanced Energy Scale Correction Techniques for the X-ray Transition Edge Sensors of the Athena mission

The X-ray Integral Field Unit (X-IFU) onboard the future European X-ray telescope Athena will be the first space instrument carrying an array of more than a thousand transition edge sensors. One of the key challenges of the X-IFU is the measurement of narrow X-ray atomic lines to determine velocity shifts at an unprecedented level of accuracy. For this reason, the energy scale of the instrument needs to be known with extreme accuracy, of 0.4 eV (1σ) up to 7 keV. The energy scale will be measured on the ground through a dedicated calibration campaign using fiducial X-ray sources. Though calibrated, the energy scale is extremely sensitive to the environmental conditions around the TES array, and drifts in the readout chain electronics. Uncorrected, the energy scale can naturally drift up to hundreds of eVs. Changes of the TES gain will be monitored via onboard X-ray calibration sources, and the energy scale will be corrected either per pixel, or within a small groups of pixels. Although simulations show that a 0.4 eV level can be achieved, the very high accuracy required by the X-IFU calls for experimental validation. A dedicated measurement campaign has been performed by NASA Goddard Space Flight Center to characterize the energy scale of a prototype kilo-pixel array of X-IFU-representative TESs. The analysis of the data demonstrated the ability to correct for various drifts using two fiducial lines to track the temporal gain variation. In this paper, we propose to extend this study on the same data set by investigating multi-parameter correction techniques based on both the pulse-height of the fiducial line and the prepulse baseline level, using the knowledge of the TES energy scale at reference temperature/magnetic field set points acquired on the ground. Investigations on the co-adding of pixels to perform a joint correction over pools of pixels is also explored.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Predicting Intensive Care Unit Length of Stay and Mortality Using Patient Vital Signs: Machine Learning Model Development and Validation

Background: Patient monitoring is vital in all stages of care. In particular, intensive care unit (ICU) patient monitoring has the potential to reduce complications and morbidity, and to increase the quality of care by enabling hospitals to deliver higher-quality, cost-effective patient care, and improve the quality of medical services in the ICU. Objective: We here report the development and validation of ICU length of stay and mortality prediction models. The models will be used in an intelligent ICU patient monitoring module of an Intelligent Remote Patient Monitoring (IRPM) framework that monitors the health status of patients, and generates timely alerts, maneuver guidance, or reports when adverse medical conditions are predicted. Methods: We utilized the publicly available Medical Information Mart for Intensive Care (MIMIC) database to extract ICU stay data for adult patients to build two prediction models: one for mortality prediction and another for ICU length of stay. For the mortality model, we applied six commonly used machine learning (ML) binary classification algorithms for predicting the discharge status (survived or not). For the length of stay model, we applied the same six ML algorithms for binary classification using the median patient population ICU stay of 2.64 days. For the regression-based classification, we used two ML algorithms for predicting the number of days. We built two variations of each prediction model: one using 12 baseline demographic and vital sign features, and the other based on our proposed quantiles approach, in which we use 21 extra features engineered from the baseline vital sign features, including their modified means, standard deviations, and quantile percentages. Results: We could perform predictive modeling with minimal features while maintaining reasonable performance using the quantiles approach. The best accuracy achieved in the mortality model was approximately 89% using the random forest algorithm. The highest accuracy achieved in the length of stay model, based on the population median ICU stay (2.64 days), was approximately 65% using the random forest algorithm. Conclusions: The novelty in our approach is that we built models to predict ICU length of stay and mortality with reasonable accuracy based on a combination of ML and the quantiles approach that utilizes only vital signs available from the patient’s profile without the need to use any external features. This approach is based on feature engineering of the vital signs by including their modified means, standard deviations, and quantile percentages of the original features, which provided a richer dataset to achieve better predictive power in our models.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Why is My Zero Energy Home Not a Zero Carbon Home?

For years, carbon calculations were done very simply. The method of calculation was to take annual totals of energy consumption and multiply by an average emission factor, either for the grid serving a project or for a larger region (e.g. an EPA eGRID sub region). The level of accuracy of this approximation was reasonably good, although the issue of accuracy was not, to our knowledge, tested. And the data required were minimal – just a year’s worth of bills for each fuel and one lookup factor. But this method assures that a net zero energy home is automatically a net zero carbon home because zero times any possible emission factor is still zero. Starting in the early 2010s, things changed – grids were starting to rely more and more heavily on renewables, and the difference was showing up on aggregate load curves. This was perhaps noticed first in California, where aggressive renewable policies led to significant renewable power generation large enough to affect the overall shape of the diurnal load curve for the Independent Systems Operator.

14 SOLAR ENERGY↗
DOE OSTI2022

Preconditioned least‐squares Petrov–Galerkin reduced order models

Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.

Lindsay, Payton↗
DOE OSTI2021

Verification of Coupled Hydraulic Fracturing Simulators Using Laboratory-Scale Experiments

In this work, we aim to verify the predictions of the numerical simulators, which are used for designing field-scale hydraulic stimulation experiments. Although a strong theoretical understanding of this process has been gained over the past few decades, numerical predictions of fracture propagation in low-permeability rocks still remains a challenge. Against this background, we performed controlled laboratory-scale hydraulic fracturing experiments in granite samples, which not only provides high-quality experimental data but also a well-characterized experimental set-up. Using the experimental pressure responses and the final fracture sizes as benchmark, we compared the numerical predictions of two coupled hydraulic fracturing simulators—CSMP and GEOS. Both the simulators reproduced the experimental pressure behavior by implementing the physics of Linear Elastic Fracture Mechanics (LEFM) and lubrication theory within a reasonable degree of accuracy. The simulation results indicate that even in the very low-porosity (1–2 %) and low-permeability (10 -18 m 2 - 10 -19 m 2 ) crystalline rocks, which are usually the target of EGS, fluid-loss into the matrix and unsaturated flow impacts the formation breakdown pressure and the post-breakdown pressure trends. Therefore, underestimation of such parameters in numerical modeling can lead to significant underestimation of breakdown pressure. The simulation results also indicate the importance of implementing wellbore solvers for considering the effect of system compressibility and pressure drop due to friction in the injection line. The varying injection rate as a result of decompression at the instant of fracture initiation affects the fracture size, while the entry friction at the connection between the well and the initial notch may cause an increase in the measured breakdown pressure.

15 GEOTHERMAL ENERGY↗